This manuscript presents a novel approach to assess NOx emissions by utilizing nitrate wet deposition (NWD) as a potential predictor. The authors used NWD flux data from the United States National Atmospheric Deposition Program (NADP) and the European Monitoring and Evaluation Programme (EMEP). To evaluate the effectiveness of the proposed approach, the authors employed the GEOS-Chem chemical transport model spanning the years 1980 to 2020, comparing simulated and observed NWD fluxes with anthropogenic NOx emissions data derived from the Community Emissions Data System (CEDS) for both the United States and Europe. They further investigated the impact of NOx emissions changes on tropospheric ozone concentrations, using data collected by ozonesondes and by the Tropospheric Ozone Assessment Report (TOAR) Surface Ozone Database.

The analysis reveals that NWD might be used as a predictor for NOx emissions fairly well, and its usage further enabled to reinforce trends such as a decline in anthropogenic NOx emission, and the subsequent reduced sensitivity of NWD to these emissions. Notably, the study also identifies overestimations in anthropogenic NOx emissions, which appear to contribute to an overestimation of surface ozone levels over Europe.

While the methodologies employed are generally suitable for addressing the research objectives, several limitations warrant discussion. Firstly, the methodology does not account for the dry deposition of nitrogen, a process that can significantly contribute to NOx and its chemical products deposition, especially involving chemical products like HNO, and through the dry deposition of aerosols. Additionally, the study does not consider the potential increase in soil NO emissions under elevated temperatures, which becomes particularly relevant in warmer seasons. These limitations should be thoroughly discussed to provide context for the study's findings. Moreover, it should be emphasized that the utility of NWD as a predictor for NOx emissions is expected to be limited in relatively small spatial and temporal scales, such as urban areas. Discussing these limitations is vital in the context of the applicability of the proposed method. Specific comments are included below.

Specific comments

 Line 19 – “These results suggest that NWD fluxes constrain total NOx emissions well.” However, this statement does not fully consider the insights about anthropogenic effect as specified in section 3.2: “Our work underscores the value of measurements of NWD extending into the future for constraining total NOx trends in areas with strict NOx emissions regulations.”

Lines 21 – 27 Here, you present the evaluation results of the comparison between observed and modeled NWD and NOx emissions using CEDS data for both the US and Europe. It is essential to specify, both here and elsewhere, the spatial and temporal resolution at which this comparison was conducted. These details are of significant importance as they can influence the interpretation of your findings concerning the utility of NWD as a predictor for NOx emissions.

Line 28 – “EMEP” is defined twice

Line 44- “those processes” is not clear in the context of the sentence

Lines 120, 150 – multiple definition for “EMEP”

Line 160 – only “point sources”?

Line 164 – I understand that you don’t consider dry deposition in your analysis due to observational limits. Nevertheless, I believe it is important to discuss the potential effects of dry deposition on both your analysis and the resulting conclusions, particularly with regard to seasonal variations, meteorological conditions, and geographical locations.but I think that the potential effect of dry deposition on both your analysis and conclusions, possibly with respect to season/meteorological conditions and location, should be discussed.

Line 217 – what is the justification for constraining lightning NOx emissions at ~6 Tg N per year ?

Line 277 – “NO2 measurements are commonly used to infer NOx concentrations due to the short lifetime of NO2, which results in robust correlations between NOx emissions and NO2 column amounts (Goldberg et al., 2021).” This argument, which is based on the lifetime of NO2, may be applicable at sufficiently large spatial and temporal scales but may not hold for relatively smaller scales. Therefore, in reference to the preceding statement, it would be valuable to understand whether a strong correlation exists between NO₂ measurements from surface stations or satellites and NWD in urban areas or in proximity to air pollution sources. This aspect warrants further investigation and discussion.

Line 290- Specify what kind of observations

Line 308 – “solely” – “dominantly” or similar should be more appropriate.

Line 372 – it is not clear to me what do you mean by – “total NOx emissions calculated using GEOS-Chem …”

Figure 5 – In the text you refer to NOx emissions while in the figure you refer to NO emissions. It should be estimated what bias this can impose on your results and conclusions.

Line 492 – “However, we find that summertime and autumnal NOx is still overestimated by ~36% in the sensitivity simulation, suggesting that further reductions of NOx may be appropriate in certain areas during summer and fall” - Do you estimate that the change in NWD due to reduction in a factor of 2 of the NOx emissions is in line with your earlier statement on line 397? (:"Our work underscores the value of measurements of NWD extending into the future for constraining total NOx trends in areas with strict NOx emissions regulations").   

Can you develop an empirical/mathematical expression to better characterize the correlation between NO_X emission (or mixing ratios) and NWD? this can be highly valuable.

Line 503 – “with overestimates of 145% in summer and 140%” – the observed overestimation of 145% in summer and 140% raises questions about its underlying causes. Do you have any further insights or speculations regarding the factors that might be contributing to such a significant level of overestimation?

Line 519: “The surface ozone overestimate over Europe is reduced from 14% (6 ppb) to 2% (0.7 ppb) on average, bringing it within agreement of observations.” - Does it mean that tropospheric ozone is NOx-limited over Europe? While your analysis is pertinent to larger scales, it's important to note that the relevance of ozone analysis is more substantial on a mesoscale or in urban areas.

Figure 8 – 1. the reader is referred to panel “a”, but “a” is not specified on the figure; 2. Which schemes are used to capture the turbulence in the boundary/surface layer in the model? It seems to not capture the trend in ozone with height, close to the ground; 3. The averaging period, for both modeling and observation, should be specified for the right-hand side panel.

Line 547 – multiple definition for “NWD”

Line 548 – “total NOx emission trends” should be better defined.

Line 563 - which “trends”?

Line 563 – “Our work shows that NWD fluxes can be a useful constraint on total NOx emissions and their trends…” – not clear to me what do you mean by “trends” here.

Line 564 – “…emissions and their trends…” – At what scale is the relevance of these findings?

General comments

This manuscript is well written and focuses on a topic that should be of broad appeal to the ACP readership. It pushes forward the use of a robust, publicly available dataset for a novel application—inferring NO_x emissions and trends—with strong utility for atmospheric chemists. Although I agree with the authors’ premise that NWD should prove to be a useful dataset for constraining NO_x emissions, I disagree that the magnitude of biases and trends in NWD are directly equivalent to NO_x emissions and trends as implied for results over the USA. I suggest some analyses that I hope may serve as a constructive supplement for addressing this concern. With these additions, I believe that this paper would serve as a wonderful reference for many pressing questions in air quality science.

Excellent attention to detail—I have no suggestions for editing the paper in terms of typography or semantics.

Minor revisions

In general, the figures in this manuscript are thoughtful, attractive and clear.

General comment related to NEI discussions (for example, bottom of page 2 through Figure 1): I found the comparison among different versions of the NEI confusing. From my understanding, new iterations of the NEI are meant to supersede previous versions, so that they’re expected to diverge from one another with availability of improved methods. It was not clear to me what readers are meant to conclude from this comparison across versions and the inclusion of multiple NEI iterations in Figure 1. It would be helpful to either clarify this point, or it could be more constructive to discuss how the NEI has been updated in the most recent version included (2017) and the relationship of those updates to the references cited. If the overall point is that there is uncertainty among NO_x emission estimates, I think that is effectively communicated through the comparison across different inventories without needing to invoke multiple versions of the NEI.

L210: Based on a later reference to sector-level emissions, I believe that McDuffie et al. 2020 should also be cited here. McDuffie, E. E., Smith, S. J., O'Rourke, P., Tibrewal, K., Venkataraman, C., Marais, E. A., Zheng, B., Crippa, M., Brauer, M., and Martin, R. V.: A global anthropogenic emission inventory of atmospheric pollutants from sector- and fuel-specific sources (1970–2017): an application of the Community Emissions Data System (CEDS), Earth Syst. Sci. Data, 12, 3413–3442, https://doi.org/10.5194/essd-12-3413-2020, 2020.

In general (e.g., L248, Figure 2), I didn’t understand the motivation for including the v10-01 GEOS-Chem simulation. I think that could be better clarified, or this simulation could be taken out of the analysis. The only point of interpretation that I found was in L345-346, but I believe that this point could be made more simply with other existing comparisons of the two inventories.

Quantitative results starting on L276: What is the +/- indicating?

Paragraph starting L315: This paragraph may benefit from a discussion of the differences in spatial distribution between the satellite and ground-based measurements referenced. A greater urban influence in the satellite data could belie differences in the dataset trends.

L367 (caption of Figure 4): Colors for met and anthropogenic emission simulations seem to differ from figure, please check.

Figure 4: My confusion may stem from the legend/caption inconsistency, but based on the figure legend (emissions: green, met: blue)--Some of the conclusions from this figure are not intuitive to me. The trend line changes most when meteorology is held constant: doesn’t that imply a larger role for meteorology than anthropogenic emissions? The sentence L356 (“As long as…”) doesn’t seem correct to me because the anthro-constant simulation largely matches the trendline of the base case. If the legend colors are incorrect/swapped, please ignore this point.

L371 starting with “total NO_x…”: consider specifying that CEDS is used for anthro and the others described are the ones calculated? consider: "total NO_x emissions, with the natural component calculated using GEOS-Chem..."

Table 2: The European soil NO_x reduction case doesn’t seem to show a larger influence of soil NO_x in later timeframes. Suggest that it’s specified in L395-396 that these results relate to the USA. It’s also a little unclear to me the role that meteorology has in this analysis. While I understand the NWD results to be precipitation-corrected, isn’t there also a role for other met variables (e.g. temperature in soil NO_x, or the loss of NO_x between urban areas and NTN sites)? I realize and respect that this result already required quite a lot of work, so I don’t mean to suggest this as a necessary addition, but it may be worth considering bookend cases with incremental reductions within a year (for example, 5% and 10% scenarios in 1985 and 2017) to control for the role of meteorology.

L405-406: It would be helpful to present model bias results. Figure 3 seems to imply that the model aligns well with the observations and, if anything, the model underestimates NWD. It’s not clear to me how the model can “agree” over the CONUS domain but that NOx emissions are “overestimated in certain regions and seasons.” Wouldn’t that imply that there are also underestimates in some regions and seasons also (in order to agree on a spatial average basis)? Should those be explored?

L540: I found the phrase “Such underestimates are not present in other models” to be overly broad—could you please clarify which models?

Major comments

Lines 21-23: For the sentence beginning, “Over the United States…” is this overestimate intended to reference NWD, rather than NO_x emissions? I believe that this sentence should specify that the overestimate pertains to NWD specifically and not NO_x emissions.

Lines 43-44: This assumption underpins this analysis and merits expansion.

Paragraph lines 164-168: 

• I agree that there are greater limitations in the availability of dry deposition (vs wet deposition) measurements, however, the phrase “Dry deposition measurements are available only after 2000 over the CONUS” seems to imply that there is a long-term dry deposition network as part of NADP, which is not true (unless the authors are referencing short-term field studies, which may be clarified). To the extent that dry deposition estimates are made available, to my knowledge they are based on simulations which draw from CASTNet measured concentrations with the Multilayer Model. Overall, the authors’ important assertion that dry deposition observational constraints are limited is well supported, but the evidence provided for this should be corrected or clarified.
• The phrase “Trends between dry deposition and wet deposition are similar” should include a citation or be removed. Related to my comments on Section 3.3. below, which suggest expanded consideration of NO_x product composition, the phase of NO_x products also relates to their rate of dry or wet deposition. This could merit discussion depending on the extent to which this phase composition has shifted over the timeframe considered.
• Lines 167-168: I don’t believe that this is correct. For one, the Jaeglé reference is not on an annual basis. More influential is that neither study compares against dry deposition measurements but rather infers a role for dry deposition based on comparisons against measured concentrations. It is important to clarify this point for readers to understand what would be needed for a better understanding of this process (specifically, dry deposition measurements).

Section 3.3. As mentioned in the “General comments,” I disagree that the magnitude of biases and trends in NWD are directly equivalent to NO_x emissions and trends as implied here, at least over the USA. The relationship between NWD and NO_x emissions has likely changed over the timeframe of study, which is in some way indicated by the authors’ demonstration that the sensitivity of nitrate to NO_x has changed over time. However, this finding is not applied for interpretation of the relationship between NWD and NO_x emissions.

I believe that more thought should be given to the change in NO_x lifetime and phase composition over the data record. If anything, the decreased sensitivity of NWD to NOx emissions seems to imply a shorter lifetime over time, differing from the references included in the introduction. Could it be that the lifetime has decreased in less polluted areas? Also, the lifetime of aerosol nitrate is much longer than NO_x, so that a change in NO_x chemical fate to gas v. aerosol over time could affect the distance that NO_x ultimately travels. In other words, I am wondering to what extent NO_x contributes to wet nitrate deposition in the gas (e.g. HNO₃) or aerosol phase, and how has this changed over the timeframe considered? What is the role for a growing influence of organic nitrate? How do the lifetimes of the principal end products differ, and how has that changed over time? If the authors prefer not to add these aspects to the analysis, I feel that the quantitative conclusions should be significantly softened.

The analysis over Europe differs by bringing in a sensitivity simulation that specifically quantifies how the bias changes when NO_x emissions are halved, which is a more appropriate approach. A similar simulation could be developed for the US toward addressing my concern here, but I believe that the analyses suggested above related to lifetime and phase composition could help to inform the process basis for underlying changes in the NWD-NO_x relationship (otherwise, the authors may consider suggesting this as a path for future work).