From the journal Environmental Science: Atmospheres Peer review history

02-Jul-2022

Dear Dr Mims:

Manuscript ID: EA-ART-02-2022-000009
TITLE: A conceptual model of northern midlatitude tropospheric ozone

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Reviewer 1

Review of Mims et al. A conceptual model of northern midlatitude tropospheric ozone
Kelvin H. Bates and Viral Shah

This manuscript reports a simple multi-box model designed to simulate mid-latitude Northern Hemispheric ozone on broad spatial (regional and boundary layer vs. free troposphere) and temporal (annual and monthly) averages. By constructing a model that is much more straightforward and less complex than the standard chemical transport models, with easily adjustable terms for the most salient processes controlling ozone, the authors hope to provide a instructional framework for diagnosing the factors that influence overall (averaged) features of ozone patterns in their target region. After describing the various parameterizations and quantitative inputs used for each of the terms in the boxes' differential equations for ozone concentrations with respect to time, the authors discuss the sensitivity of simulated ozone to various changes in model parameters (e.g. ozone removal rates in the marine BL and production rates in the continental BL), the effects of adding a simplified seasonal cycle, and some comparisons between the model and measurements.

Our main concerns with this manuscript are: (a) missing processes and insufficient justification for some parameters included in the model, (b) sparse comparisons with observational data, and (c) lack of citations in the introduction, as detailed below.

General comments:
1. It is not clear why it is important to focus on the northern midlatitudes. There are significant precursor emissions in the tropics and photochemistry is more active there. Besides, how valid is the assumption that the midlatitude is relatively isolated from the tropics and the polar regions and can be treated as such?

2. It is stated that "regionally representative data are difficult to obtain", but there is a wealth of additional ozone data available from TOAR (https://toar-data.org/) that could be regionally averaged as the authors please or that could be individually used in the same way the Mace Head and European Alpine data are applied already. Most notably, it could be argued that aircraft or sonde data would be more representative of the background free troposphere than terrestrial European Alpine sites.

One of the results emphasized in the paper is that the free troposphere over the northern midlatitudes can be thought of as a well-mixed reservoir based on the model simulations, which the authors present as consistent with observations. However aircraft and satellite observations find differences of ~20 ppb in the free tropospheric ozone in the northern midlatitudes (e.g., Hu et al. 2017 (doi: 10.1016/j.atmosenv.2017.08.036); Gaudel et al. 2020 (doi: 10.1126/sciadv.aba8272)).

It would also be helpful to give readers some sense of the range of variability of ozone measurements within and between the regions defined by the boxes in this model, which could in turn provide a sense of the range of reasonable values for the somewhat arbitrary production and loss parameters assigned to the boxes.

3. The introduction is markedly devoid of citations and, while compellingly written, contains a number of strong statements that are not properly supported. Most notably, it is not clear that complex models necessarily obscure "the connection of the average response of the atmosphere to these large-scale features". Such models can simply be averaged themselves, or run with averaged meteorology and emissions, and with more accurate treatment of ozone photochemistry and surface-dependent deposition, complex models are likely more useful "to separately investigate the effects of specific ozone sources and sinks" that one than combines all production and loss processes within each box. The unique benefits of a simple model are further undermined by later references to complex models that have previously reached similar conclusions (e.g. the references to Lelieveld & Dentener later on). The introduction would benefit from a more detailed and specific description of what is lacking in complex models, what simple treatments of the ozone system can provide, and what is the current state of the literature on the range of complexity in said models.

Specific concerns about the model parameters:
1. Eq 2: The outflow term from compartment i to i+1 is missing.

2. How justifiable is the treatment of all losses as first-order? Some important photochemical loss processes of ozone (or, rather, odd oxygen; e.g. HO2 + O3, OH + O3, XO + HO2 where X = I, Br, Cl) depend on HOx, which in turn depends on ozone, providing the potential for second-order dependence.

3. The decision to exclude photochemical production and loss terms in the FT, and photochemical production in the MBL, seems to be justified by (a) the Northern-midlatitude-averaged net production and loss terms being roughly in balance in the FT, and (b) net production being negative in the MBL, both according to the ATom dataset. However, this neglects the potential spatial and temporal variability within the FT average, or within the MBL average. How much of an effect could that variability have?

In addition, the *gross* terms are in balance only on annual and zonal mean basis. The ozone chemical lifetime in the free troposphere is on the order of months, so production and loss do not necessarily cancel out within each compartment and in each month.

Further, the *gross* terms may matter more than the *net* terms, especially if they also have spatial and temporal differences. Because the loss processes are (presumably) first-order while the source terms are presumably (though maybe not entirely?) independent of ozone concentrations, the net balance will be dependent on ozone concentrations, which could have interesting effects not captured by this model.

Finally, the inclusion of the gross terms in the FT might substantially dampen the effects of STE-derived ozone, which would alter the conclusions drawn about the importance of stratospheric ozone on Page 5.

4. The specific choices for numbers applied to photochemical ozone production in the continental BL are not well justified. Why is 50% of total tropospheric production chosen, and why is it (almost) evenly distributed across the continental BL boxes? This is not representative of precursor emissions distributions, which are much higher in eastern US, Europe and East Asia than elsewhere. Why is the reduction for central Asia specifically 10%, and if this box is scaled, why not scale others? Page 3 (2nd paragraph on right) states that the “model results are insensitive to these choices.” We would expect the simulated continental boundary layer concentrations to be sensitive to this parameter.

5. Is there good evidence that the STE of ozone is evenly distributed zonally across the study area, or does it matter to the conclusions here?

6. It is not clear how the first-order loss rate of ozone in the continental boundary layer is set. It is stated (page 3) that the loss rate is “determined by that needed to balance the total ozone production in the continental boundary layer.” Why is it necessary to satisfy this condition?

7. The first order ozone loss rate in the continental boundary layer is ~20 times greater than that in the marine boundary layer. Is this a reasonable assumption? The multi-model results of Stevenson et al. (2006; doi: 10.1029/2005JD006338) show much smaller differences in chemical loss between marine and continental regions.

8. The model assumes a seasonally uniform ventilation rate for continental boundary layers. Is this realistic? I expect ventilation to be faster in summer because of convection.

9. The sensitivity of the model results of some of the other omitted processes is discussed in detail in the supplement (Section S8), but it would be useful to add a summary in the main text.

Specific comments on figures and tables:
1. Figure 1: Why are there arrows starting below the boundary layer boxes and pointing into them? (Or perhaps the low resolution on this part of the figure is making it difficult to interpret). These appear to represent emissions, which wouldn't make sense for ozone, but even if they represent production, shouldn't they only apply to the continental boxes and not the marine ones?

2. Figures 3 and 4: Missing labels on the x-axis.

3. What are the lines on Fig. 5 derived from?

Reviewer 2

The manuscript of Mims et al., 2023 presents the development and application of a conceptual model to analyse the northern midlatitude Ozone. The model is practically a continuous stirred tank reactor with different compartment to differentiate between free troposphere (FT) and boundary layer components (PBL) as well as different geographical areas. The mass balance equation (i.e. accounting for the production and losses of Ozone) is used to retrieve the Ozone dynamic balance in each of the compartment. Production, losses and influx of Ozone in the various compartment are parametrized with available literature data, and in case not available, omitted.
On top of several sensitivity tests with respect to the chosen parameters, the authors show that the model could reproduce very well the seasonal variation of Ozone concentrations at several free troposphere sites (located in the Alps), as well as in the Marine boundary layer.
I found the manuscript very interesting, well written and with both the results and discussion section sound. I do not have specific comments on the model set-up and the parameters used for the budget calculation, which are all taken from previous literature study, and I would be in favour of publication after my comments below are taken into account:

<b>Major comments:</b>

My only concern is about the possible applications of such a tool. CTM simulations are now used at very high levels of details (in terms of physical, chemical and meteorological parameters) and often used to corroborate measurements data and to perform sensitivity tests. The authors rightly acknowledge that CTM applications are very demanding (both in terms of the correct preparation of the input data, as well as of the proper execution of massive parallel programs) and therefore such “reduced tool” are indeed helpful to conduct similar analysis. However, it is not still clear how. I would recommend the author to elaborate more on this point throughout the manuscript, maybe by giving a few specific example about future applications.

<b>Minor comments:</b>

Page 2: Introduction: “Over time, as atmospheric modelling effort…” I am not sure I have properly understood the meaning of this paragraph. Do the authors implies that, as high resolution CTMs are becoming more and more available (i.e. often down to 1km) this is shifting the focus of the research from Ozone dynamics at large-scale to local-scale? If so, I feel that the sentence would need some rewording: high-resolution CTM applications are always set-up in nested configurations in order to pass chemical species, and meteorological parameters, from the parent grid (at large-scale) to the high-resolution grid. For these applications, the large-scale features of Ozone are modelled on the coarser domain (eventually several domains depending on the specific application), and are often also used to further corroborate the Ozone dynamics at local scale.

Figure 3: Please consider improving the cosmetics of the plot (i.e. the colour legend and size of the data points). It is not straightforward to read the graph in its current state.

This text has been copied from the PDF response to reviewers and does not include any figures, images or special characters.

RESPONSE TO REVIEW OF MANUSCRIPT ART-02-2022-000009 - A conceptual model of northern midlatitude tropospheric ozone by Mims, Parrish, Derwent, Astaneh, Faloona
The text of the reviews is reproduced in italics and our responses are contained in text boxes. Resulting modifications to the document are noted in each box, and summarized at the conclusion of this response.
I. RESPONSE TO THE REVIEWERS' REPORTS
Overview of our response:
We thank the referees for their careful reviews of our manuscript. Many of their valuable suggestions have been implemented as detailed below and have improved our paper.
To give context to our responses, we first quote our aim in this paper as stated in the last paragraph of our Introduction: “develop a simple model that can reproduce reported large-scale average ozone gradients and seasonal variations at northern hemisphere midlatitudes with sufficient fidelity to be broadly instructive.”
Regarding the model construction, both referees agree that our simple model has successfully described the ozone seasonal cycle in the northern hemisphere midlatitude troposphere. Referees #1 do not believe we have sufficiently justified many aspects of the model construct and the parameters, while Referee #2 has no such concerns, and does not question "the set-up and parameters used in the budget calculation, which are all taken from previous literature study". Referee #2 also states that the "results and discussion section (is) sound". We have added detailed responses to Referee #1's concerns, since they test the rigor of this basic picture, potentially identifying flaws in our approach. We believe that these responses show that the model construct is valid for our stated purpose and believe these valuable clarifications requested by the referees should increase the community's acceptance of our aims and methods.
Regarding the model's potential impact, both referees ask how such a model can be used - in fact this is referee #2's sole major concern. We are grateful for such questions since they are precisely the sort we hoped our paper would provoke in the community. Many of the questions arise from confusion about the purpose of this and other simple models. We and others see the simple models as reflecting a basic understanding of the system - understanding not easily identified in the complex models or measurements. These simple models are meant to be used in conjunction with the complex models and are not competitive interpretations. We have strengthened our statement of this philosophy and refer more intensively to significant references in this regard.
The specific questions about the model parameters, although addressed in our responses to them, identify aspects of the more complex measurements and models that are worthy of further research. The current stream of beautifully detailed GCM simulations and extremely detailed measurements, such as provided by the ATom project can be averaged to produce a lower resolution picture similar to ours. Such an exercise could extract similarly averaged parameters and answer some of the referees’ questions. The full answers to some of those questions (e.g., how do the ozone losses differ from overall first order kinetics) will await such research. We also describe a second type of utility. Simpler pictures such as ours, with robust overall (climatic) physical constraints, can serve as "reality checks" for the interpretation of more complex data, and can identify erroneous interpretations and/or erroneous data. We include two important such examples of such use of our model in our response below and include a new Supplement S9 which addresses the uses of the model more generally.
In the following, the referees' individual comments are reproduced, given an identifying label (e.g., 1A) and each is followed by a text box giving our response. Each also describes our additions/revisions to the manuscript relevant to that comment. In the manuscript the identifying label is attached by comment to the changes in the Track Changes manuscript, which also documents the details of the changes. Additions to the Supplement are similarly identified.
RESPONSE TO INDIVIDUAL REVIEWER COMMENTS:
Referees 1 (Kelvin H. Bates and Viral Shah)
This manuscript reports a simple multi-box model designed to simulate mid-latitude Northern Hemispheric ozone on broad spatial (regional and boundary layer vs. free troposphere) and temporal (annual and monthly) averages. By constructing a model that is much more straightforward and less complex than the standard chemical transport models, with easily adjustable terms for the most salient processes controlling ozone, the authors hope to provide a instructional framework for diagnosing the factors that influence overall (averaged) features of ozone patterns in their target region. After describing the various parameterizations and quantitative inputs used for each of the terms in the boxes' differential equations for ozone concentrations with respect to time, the authors discuss the sensitivity of simulated ozone to various changes in model parameters (e.g. ozone removal rates in the marine BL and production rates in the continental BL), the effects of adding a simplified seasonal cycle, and some comparisons between the model and measurements.

Our main concerns with this manuscript are: (a) missing processes and insufficient justification for some parameters included in the model, (b) sparse comparisons with observational data, and (c) lack of citations in the introduction, as detailed below.
We thank Bates and Shah for their very thorough and thoughtful review of our manuscript. They raise many interesting points, which we address sequentially in the text boxes herein. The relevant changes to the manuscript and supplement are described. Each comment is given an identifier in square brackets in order to associate manuscript changes with the related comment.

General comments:
1. It is not clear why it is important to focus on the northern midlatitudes.[1A] There are significant precursor emissions in the tropics and photochemistry is more active there. Besides, how valid is the assumption that the midlatitude is relatively isolated from the tropics and the polar regions and can be treated as such [1B] ?
[1A] The northern midlatitudes have received the most attention in tropospheric ozone research, having been the dominant region of human industrial activities leading to the pronounced increase in background ozone throughout the late 20th century (e.g., Cooper et al., 2014). In terms of NOx, likely the most consequential ozone precursor, late 20th Century inventories of the 30-60N latitudinal belt comprised about 60% of the global NOx emissions (Kanakidou & Crutzen, 1993; Zhang et al., 2016). The more recent emission increase in East Asian subtropical regions, and other developing megacities, is shifting the distribution equatorward, but still suggests ~50% of the global emissions are generated in the 30-60N band, and still maintains the peak emissions to be near 35 N (Zhang et al., 2016).
Manuscript change: This material is added as the first paragraph of Section 2 - Model Description.
[1B] The motivating principle behind our simplified model is based on the simplistic 3-cell model of the general circulation with weak easterlies in the tropics giving way to strong prevailing westerlies in the middle latitudes, where the mean zonal winds are an order of magnitude larger than mean meridional components, with a less well-defined picture at high latitudes. The illustrated ERA 40 reanalysis cross section in the figure below shows how the dominant current of fast moving air that circumnavigates the globe is readily contained in our selected 30 – 60 N latitude band.
This rapid longitudinal transport creates a unique environment where the horizontal advection timescale is less than or comparable to the net photochemical production/loss (Parrish et al., 2021) providing the necessary conditions for the validity of our simplified model.
Despite very modest average meridional flows in this latitude band, there is the possibility that significant mean and eddy (transient and spatial) transport of air (and ozone) into and out of the 30-60 N atmospheric channel may occur. Miyazaki et al. (2005) calculate the meridional ozone fluxes in both the stratosphere and troposphere using five years of the Meteorological Research Institute – Japan Meteorological Agency (MRI- JMA) ozone reanalysis system on the basis of mass-weighted isentropic zonal means (similar to the more common Transformed Eulerian Mean.) Their Figure 3 (e-h) shows how the poleward mean fluxes in the midlatitude middle to upper troposphere are largely compensated by the equatorward eddy fluxes at the same levels and similar equatorward ozone fluxes in the lower troposphere. Nevertheless, even at times of the greatest fluxes in the northern midlatitudes (winter/spring), the largest net fluxes reported by Miyazaki et al. (2005) of ~200 kg/s only amount to rate of change in 20 – 60 N latitude band of less than 0.01 ppb d-1.

Manuscript change: Much of this discussion and the above figure has been incorporated into the introductory paragraphs of Section 2 (Model Description).
References:
Cooper, O.R., et al., Global distribution and trends of tropospheric ozone: An observation-based review, Elem. Sci. Anth., 2014, 2, 000029 doi: 10.12952/journal.elementa.000029.
Kanakidou, M., and P. J. Crutzen, Scale problems in global tropospheric chemistry modeling: comparison of results obtained with a three-dimensional model, adopting longitudinally uniform and varying emissions of NOx and NMHC, Chemosphere, 1993, 26, no. 1-4: 787-801.
Miyazaki, K., T. Iwasaki, K. Shibata, and M. Deushi, Roles of transport in the seasonal variation of the total ozone amount, Journal of Geophysical Research: Atmospheres, 2005, 110, no. D18.
Zhang, Y., O.R. Cooper, A. Gaudel, A. M. Thompson, P. Nédélec, S.-Y. Ogino, and J.J. West, Tropospheric ozone change from 1980 to 2010 dominated by equatorward redistribution of emissions, Nature Geoscience, 2016, 9, no. 12: 875-879.
2. It is stated that "regionally representative data are difficult to obtain", but there is a wealth of additional ozone data available from TOAR (https://toar-data.org/) that could be regionally averaged as the authors please or that could be individually used in the same way the Mace Head and European Alpine data are applied already. Most notably, it could be argued that aircraft or sonde data would be more representative of the background free troposphere than terrestrial European Alpine sites. [1C]
[1C] Our quoted comment appears just before figure 8 and addresses continental BL data only. It is true that the TOAR data base contains “a wealth of additional ozone data”. These data are quite useful for evaluating human health impacts (e.g., Fleming et al., 2018; DOI: 10.1525/elementa.73) and impacts on vegetation (e.g., Mills et al., 2018; DOI: 10.1525/elementa.302) through the required wide scale spatial averaging over the large ozone variability that occurs within the continental boundary layer. However, it is very difficult to determine how these data can be averaged to obtain mean continental BL ozone concentrations that are representative of the relatively remote continental regions we are modeling. Care must be taken to select data that are unbiased by local human activity and accurately represent regional averages. We chose to utilize the Clean Air Status and Trends Network (CASTNET) data included in Figure 8, because US EPA designed that network precisely for the purpose of determining regional ozone concentrations.
With regard to the background free troposphere, Parrish et al. (2020) demonstrate that ozone at the high elevation European Alpine sites is consistent with aircraft and sonde data collected within the Western European region, both with respect to annual average and seasonal cycle. Thus, either these alpine data or the aircraft or sonde data could be used. We chose the surface site data because they cover a much longer time period at greater temporal resolution, providing more precisely determined representative ozone concentrations.

Manuscript changes: We have explicitly acknowledged the "wealth of data" and state that "care must be taken in order to obtain regionally representative average ozone concentrations".
One of the results emphasized in the paper is that the free troposphere over the northern midlatitudes can be thought of as a well-mixed reservoir based on the model simulations, which the authors present as consistent with observations. However aircraft and satellite observations find differences of ~20 ppb in the free tropospheric ozone in the northern midlatitudes (e.g., Hu et al. 2017 (doi: 10.1016/j.atmosenv.2017.08.036); Gaudel et al. 2020 (doi: 10.1126/sciadv.aba8272)). [1D]
[1D] When considering differences in FT ozone we do acknowledge in our paper that a vertical gradient exists in accord with a natural source from the stratosphere aloft and a sink at the surface. This gradient is on average ~1.5 ppb/km in the bulk of the FT, and therefore ozone routinely increases by 15 ppb across the depth of the troposphere. Therefore, when evaluating differences in observed free-tropospheric ozone, it is important to compare averages of profiles throughout the FT and, not include the vertical variation in an estimated "range" of observed FT ozone.
The idea that the free troposphere over the northern midlatitudes can be thought of as a well-mixed reservoir came to us originally from the simple consideration that the ozone lifetime in the free troposphere is long with respect to circum-global transport times – hence the well-mixed picture must be valid, as discussed in more detail by Parrish et al. (2021) and in our response to these referees’ Comment 1 above. Indeed, this idea led us to develop the model we describe in our manuscript, rather than being revealed by the model results. We have since learned that we were not the first to reach this realization; Junge (1962) had this idea ~40 years earlier. As discussed above, we expanded the Introduction to the model description to clarify this issue.
Parrish et al. (2020) tested the well-mixed reservoir idea through examination of vertical profiles of baseline ozone from the surface up through the mid-free troposphere at the west coasts of North America and Europe. They found no statistically significant differences between the data sets in either the annual mean vertical profile (see their Fig. 5) or the seasonal cycle (see their discussion of Figs. 6 and 7; note that, as discussed by Parrish et al. (2020), the somewhat larger annual mean ozone from the European sonde data at high altitudes in Fig. 5 is believed to be a measurement issue with the sonde data). Our goal in that paper was to quantify the degree of zonal similarity; a high degree of similarity was indeed found.
Gaudel et al. (2020) (doi: 10.1126/sciadv.aba8272) focus primarily on ozone trends; however, their Figure 3C illustrates vertical profiles of median ozone concentrations from many regions of the globe that show differences of ~20 ppb. However, their 5 northern midlatitude data sets (Europe, Eastern and Western North America, Northeast China/Korea, and Southeast US) all agree within  ~2 ppb in the FT above 700 mb – certainly well within reasonable estimates of their confidence limits. The one exception is the western US, which is the sparsest data set that has significant seasonal and spatial biases (see expanded discussion below in our response to Referee #2’s major comment). In our judgment the Gaudel et al. (2020) analysis is consistent with our “well-mixed reservoir" picture for the northern midlatitudes.
Hu et al. (2017) (doi: 10.1016/j.atmosenv.2017.08.036) illustrate mean vertical ozone profiles from nine regions of the globe (their Fig. 8) that show differences of ~20 ppb. It is difficult to quantitatively compare the two northern midlatitude data sets (Western Europe and Southeastern US), which are given in different panels in the figures; however an attempt to read the 500 mPha averages from the graphs indicates that these two data sets also agree within  2 ppb. Again, in our judgment the Hu et al. (2017) analysis is consistent with our midlatitude “well-mixed reservoir" picture.
Another important conclusion from Hu et al. (2017) is that computer models of FT ozone in the northern midlatitudes are quite regularly 10-20 ppb too low, and therefore consideration of the natural variability of the background ozone field may be unduly biased by these types of variations in the modeled ozone fields.
One other paper should be considered in this regard. Bourgeois et al. (2020 - doi.org/10.5194/acp-20-10611-2020) analyze the Atom and HIPPO data sets. They present multiple comparisons between those data, sonde data and IAGOS data. They conclude “… that the ozone distribution below 8 km was similar in the extra-tropics of the Atlantic and Pacific basins, likely due to zonal circulation patterns.”
In summary, to the best of our knowledge, all recent examinations of northern midlatitude ozone measurements agree with our concept that ozone in the free troposphere at northern midlatitudes is accurately described as a “well-mixed reservoir” (with the acknowledged averaging over the vertical gradient).
Manuscript modifications: Our revised Section 2 now provides the reader with a firmer foundation for our “well-mixed reservoir” description. The detailed justification above for treating the FT boxes as well-mixed is included in the revised Supplement S8 (Section entitled “Assumption of a well-mixed free troposphere”) and mentioned in Section 2.
[1E] It would also be helpful to give readers some sense of the range of variability of ozone measurements within and between the regions defined by the boxes in this model, which could in turn provide a sense of the range of reasonable values for the somewhat arbitrary production and loss parameters assigned to the boxes.
[1E] As just discussed, no significant spatial differences exist in the mean ozone concentrations in the free troposphere at northern midlatitudes, beyond the vertical gradient that is apparent in the Hu et al. (2017) and Gaudel et al. (2020) figures discussed above. There is, of course, large variability in the continental boundary layers, both spatial (between and within regions) and temporal (on time scales of minutes to decades), but we do not attempt to treat this variability in our model; we are interested solely in the (climatic) average values. To our knowledge the largest deviation from a unform mean baseline ozone distribution at northern midlatitudes is a relatively small (~18%) difference in the mean ozone concentrations within the MBL between the Pacific Coast of North America and the Atlantic Coast of Europe, as discussed in Parrish et al. (2020) (doi.org/10.5194/acp-21-9669-2021) and more MBL comparisons of that order in Parrish et al. (2016) (doi:10.1002/2015JD024101). The spatial distribution of the continental production and loss parameters, though arbitrary, is beyond the scope of the model. The average net values, to which the free troposphere responds, are constrained by the overall mass balance.

Manuscript changes: We have added a discussion of the variability of mean ozone concentrations to the penultimate paragraph of Section 2.2 to more clearly inform the readers.
3. The introduction is markedly devoid of citations and, while compellingly written, contains a number of strong statements that are not properly supported. [1F]
[1F] We have added 3 general references to the Introduction to support some of our strong statements, and to provide a view of the current state of the literature on the range of complexity in more complex models.
Most notably, it is not clear that complex models necessarily obscure "the connection of the average response of the atmosphere to these large-scale features". Such models can simply be averaged themselves, or run with averaged meteorology and emissions, and with more accurate treatment of ozone photochemistry and surface-dependent deposition, complex models are likely more useful "to separately investigate the effects of specific ozone sources and sinks" that one than combines all production and loss processes within each box. The unique benefits of a simple model are further undermined by later references to complex models that have previously reached similar conclusions (e.g. the references to Lelieveld & Dentener later on). The introduction would benefit from a more detailed and specific description of what is lacking in complex models, what simple treatments of the ozone system can provide, and what is the current state of the literature on the range of complexity in said models. [1G]
[1G] This touches the central aspect of the paper and is also the subject of the only significant concern of Referee 2 - how such simple models can be used in the understanding of complex systems. We agree with the referees that complex models with more accurate treatment of ozone photochemistry and surface-dependent deposition, are likely more useful "to separately investigate the effects of specific ozone sources and sinks than one that combines all production and loss processes within each box”. To assess complexity, a complex model is required. There seems to be misconception that the simple models are a substitute for complex models. The simple models provide understanding and work in parallel with the evolving complex models. This aspect is covered in our references 4 and 5. Our model uses simple understanding of the system to provide overarching constraints into which the complex behavior, modeled or measured, must fit. As such, it is a useful tool for more complex and complete investigations as illustrated in the following example.
The ambitious, even heroic, ATom measurements of detailed atmospheric compositions and chemistry were summarized in the analysis by Guo et al. (2021). We included Fig. S16 based on this analysis in our Supplement to support our assumption of a long effective lifetime of ozone in the FT due to very small mean net ozone production. However, that figure also includes results from the MBL, which are also near zero (mean = -0.27 ppb d-1). Our simple model, in a calculation that can readily be done in a spreadsheet, shows that a mean ozone loss rate of ~2.2 ppb d-1 is necessary to maintain the mean MBL ozone concentration of 39 ppb with any reasonable estimate of the rate the MBL mixes with a free troposphere with 52 ppb. This is almost an order of magnitude higher than the MBL results in Figure S16.

A significant disagreement of these measurements with more complex models is acknowledged in their abstract.

Comparing the ATom reactivities over the tropical oceans with
climatological statistics from six global chemistry models, we find
excellent agreement with the loss of O3 and CH4 but sharp disagreement
with production of O3. The models sharply underestimate O3
production below 4 km in both Pacific and Atlantic basins,
and this can be traced to lower NOx levels than observed.

There is a clear inconsistency between the conclusion above and the strong constraints of our simple model. One could argue, as above, that the ATom reactivities over the oceans are correct, and our simple model - and the six global chemistry models - are wrong. However, if that were the case, the firmly established diurnal cycle of ozone in the MBL, driven by relatively rapid daytime ozone loss, the strong vertical ozone gradient widely observed between the MBL and the FT, and the differing MBL and FT seasonal cycles could not be explained.
We offer an alternative explanation - that the models are correct and the difference can be traced to a bias in the observed MBL NOx levels. Notably, there is good reason to suspect that the instrumentation utilized in the ATom mission suffered an artifact when descending from the relatively dry, cool FT into the moist, warm MBL, resulting in an overestimate of the MBL NO concentrations.
It is not within the scope of our paper, however, to resolve this particular discrepancy, but it is relevant to the referees comment. Awareness of the overarching constraints provides a "reality check" and in this case clearly illuminates an inconsistency, which is harder to see in more complex model results. Such a "reality check" might have altered the published conclusions.
So, although we do agree with the referees that “it is not clear that complex models necessarily (emphasis ours) obscure the connection of the average response of the atmosphere to these large-scale features", we do stand by our (slightly revised) wording in the final paragraph of the introduction:
Over time, as atmospheric modelling efforts have become more complex and model output more detailed, the connection of the average response of the atmosphere to the large-scale driving processes has become obscured by the high variability of the fine-scale temporal and spatial observations and simulations. Consequently, a realization has dawned of the utility in developing a 'hierarchy' of models of varying complexity in order to assist in the understanding of extremely complex systems like the Earth's climate. Here we aim to do just that; viz., develop a simple model that can reproduce reported large-scale average ozone gradients and seasonal variations at northern hemisphere midlatitudes with sufficient fidelity to be broadly instructive.
We believe that the atmospheric chemistry literature contains many papers in which complex model results or detailed measurements either contain unrecognized errors or in which model results and/or measurement data, while correct, are erroneously interpreted. A key value of simple models like ours is to provide researchers with the basis for critically evaluating the results of detailed observations and potentially more accurate model results, and for diagnosing errors when they inevitably creep into the more complex models. Consideration of these complex results from the perspective of our conceptual model could perhaps have flagged this issue during the analysis of those data. As we discuss further regarding Referee 2's comments, we believe such "reality checks" are a primary value of simple models such as ours.

**(Note: Since we composed this response - and since one of the authors discussed this issue in a presentation to the Tropospheric Chemistry Group of NOAA’s Chemical Sciences Laboratory, where two of the coauthors of the Guo et al. paper are members – we have learned that the Guo et al. authors are preparing a corrigendum regarding this issue for submission to ACP.)

We respectfully disagree with the referee's statement that "the unique benefits of a simple model are further undermined by later references to complex models ...". We believe that this statement arises from a misunderstanding of the simplified model's purpose that we intended to convey. We believe that combined deployment of complex models and the simple renditions are tools that mutually inform one another. In no way do we claim that the simple models make the complex ones redundant. The simple models provide the most basic reasoning for an observed behavior that contains the kernel of the science behind it. Such reasoning, once validated, is in a form most accessible. It is easily described, maybe even to politicians, and provides a scientific base from which more complex behavior can be addressed. In the case above it provides a "reality check" on the ATom results.

Manuscript changes: In Section 4: Conclusions, we include text describing how these models are useful both as forward looking research guidance and also as a tool for "reality checks". We emphasize the mutual role of simple models as discussed in our reference 4. Prompted by this cognitive role and by Referee comment 2A regarding uses of simple models, we have also added a new Supplemental Section S9 elaborating such uses of the model.

Specific concerns about the model parameters:
1. Eq 2: The outflow term from compartment i to i+1 is missing. [1H]
[1H] Given unidirectional (west to east) zonal flow, with no back mixing between compartments, the equation is complete as written. Compartment i gains material by advective flow from i-1 and, in outflow, loses material from itself.
2. How justifiable is the treatment of all losses as first-order? Some important photochemical loss processes of ozone (or, rather, odd oxygen; e.g. HO2 + O3, OH + O3, XO + HO2 where X = I, Br, Cl) depend on HOx, which in turn depends on ozone, providing the potential for second-order dependence.[1I]
[1I] We do acknowledge the non-linear kinetics that result from the complex mechanisms of ozone formation and destruction. According to global budgets of tropospheric ozone estimated by more complex models (e.g. Hu et al., 2017) the largest sinks are in fact first-order; namely, photolysis (responsible for about half of the photochemical terms) and dry deposition. Furthermore, outside of net production regions, because their losses are quadratic by nature, the abundance of HOx is primarily proportional to the square root of ozone (the main source.) Therefore, the odd oxygen mediated losses will tend not to deviate strongly from a linear dependence.
More germane to the issue of the fidelity of our model, any 2nd order character of the loss processes would not cause a problem within the model. The loss processes serve to balance the production terms at specified mean ozone concentrations in the MBL and FT. It is convenient, and approximately correct, to represent those loss terms as first order in ozone; however, including a more complex description of the loss processes would not change the production vs. loss balance. A more complex treatment of the loss processes could possibly affect the ozone concentration in the CBL, but the comparison of our model results with observations (Fig. 8, now Fig. 9) suggests that this simplification does not add large uncertainty to our model results.
Manuscript changes: A reference in the text is included that refers to an added item in the Supplement Section S8 (Section entitled “Assumption of first order ozone destruction kinetics”, which contains this full discussion.
3. The decision to exclude photochemical production and loss terms in the FT, and photochemical production in the MBL, seems to be justified by (a) the Northern-midlatitude-averaged net production and loss terms being roughly in balance in the FT, and (b) net production being negative in the MBL, both according to the ATom dataset. However, this neglects the potential spatial and temporal variability within the FT average, or within the MBL average. How much of an effect could that variability have? [1J]
[1J] This comment is not entirely clear to us. As shown in Fig. S16 the Northern-midlatitude-averaged net production and loss terms derived from the ATom data set are very nearly in balance in the FT as the referees note. The averages shown in the figure are from the work of Guo et al. (2021), which treated the ATom data at a spatial resolution of 2 km, which corresponds to 10 s temporal resolution. Those authors specifically note that there is little concern regarding unrecognized spatial or temporal variability in the ATom data. We addressed this in the original text in Section 2.1 of our paper “Any imbalance (in production and loss of ozone in the FT) would be compensated by a small difference in the production or loss terms in the BL compartments.”
We approximate photochemical production in the MBL by setting it to zero. This is consistent with its minor contribution compared to ozone entrainment from the free troposphere. Any contribution from this source, whether or not affected by spatial or temporal variability would be expected to be smaller than the uncertainty in the photochemical loss, so no significant effect is expected.
Manuscript changes: These considerations are summarized in the revised Supplement Section S8.
In addition, the *gross* terms are in balance only on annual and zonal mean basis. The ozone chemical lifetime in the free troposphere is on the order of months, so production and loss do not necessarily cancel out within each compartment and in each month. [1K]
[1K] We agree with this statement. In particular, no ozone seasonal cycle could be generated within our model if production and loss did cancel out within each compartment and in each month. However, our model does not assume that such cancelation exists. In treating the seasonal cycle in Section 3.2, we impose seasonal cycles on STE, photochemical ozone loss in the MBL, and photochemical ozone production in the continental boundary layer. Time dependent model results are derived by integration of equations 1 and 2; there is no requirement within our model for the existence of the balance the referees mention.
Further, the *gross* terms may matter more than the *net* terms, especially if they also have spatial and temporal differences. Because the loss processes are (presumably) first-order while the source terms are presumably (though maybe not entirely?) independent of ozone concentrations, the net balance will be dependent on ozone concentrations, which could have interesting effects not captured by this model [1L] .
[1L] Within our model, all terms are first order; we are thus dealing with a linear system. In that case the behavior of averages = average of behaviors. This is not the exact situation existing in the real world; there may indeed be interesting effects in the real world that our model cannot capture. Again, our aim is to “develop a simple model that can reproduce reported large-scale average ozone gradients and seasonal variations at northern hemisphere midlatitudes with sufficient fidelity to be broadly instructive.” We believe that we have accomplished that goal, and extension to more sophisticated models would be required to capture other interesting effects in the atmosphere in keeping the model hierarchy idea mentioned in the introduction.
We have included such ideas in the revised Conclusions section 4 and in the new Supplement Section S9.

Finally, the inclusion of the gross terms in the FT might substantially dampen the effects of STE-derived ozone, which would alter the conclusions drawn about the importance of stratospheric ozone on Page 5.[1M]
[1M] Since our model describes all processes as first order in ozone, inclusion of gross terms in the FT would not alter the conclusions we draw about the importance of stratospheric ozone. In the real world, the gross terms may not be exactly first order in ozone; however (as we note) the conclusions from our model do agree well with the conclusions from Lelieveld and Dentener (2000), a modeling study that presumably takes such complexities into account; this suggests that our linear model results are not greatly in error.
4. The specific choices for numbers applied to photochemical ozone production in the continental BL are not well justified. Why is 50% of total tropospheric production chosen, and why is it (almost) evenly distributed across the continental BL boxes? This is not representative of precursor emissions distributions, which are much higher in eastern US, Europe and East Asia than elsewhere. Why is the reduction for central Asia specifically 10%, and if this box is scaled, why not scale others? Page 3 (2nd paragraph on right) states that the “model results are insensitive to these choices.” We would expect the simulated continental boundary layer concentrations to be sensitive to this parameter [1N] .
[1N] The 50% of total tropospheric production assigned to northern midlatitudes was initially a guess. The discussion of emission inventories included in the response to Comment 1 suggests that this was a reasonably accurate guess. As we mention, it does not matter for the MBL and the FT how the total ozone production is distributed between the five continental BL segments. We included a reduction for central Asia to show the influence of non-uniform distribution; this reduction is restricted to the central Asia to avoid further complicating the curves illustrating the continental BL seasonal cycles (Figs. 7 and 8). Our model is not intended to reproduce spatial differences in the continental BL, so the distribution of the tropospheric ozone production across the continental BL compartments does not affect our results.
Manuscript change: We have clarified the discussion of this issue in the 2nd paragraph on page 3 (now on page 4).
5. Is there good evidence that the STE of ozone is evenly distributed zonally across the study area, or does it matter to the conclusions here?[1O]
[1O] There is excellent evidence that STE is not evenly distributed zonally across northern midlatitudes (e.g., Škerlak, Sprenger, and Wernli, A global climatology of stratosphere–troposphere exchange using the ERA-Interim data set from 1979 to 2011, Atmos. Chem. Phys., 14, 913–937, 2014, doi:10.5194/acp-14-913-2014). The referees are correct in their question - it does not matter to the conclusions here since zonal transport in the FT is much faster than ozone loss, either by transport to the BL or chemistry, so the STE contribution becomes zonally well-mixed in the FT. Also note that the distribution of STE ozone is weighted to the upper troposphere where the strongest winds exist to promote mixing. Therefore, while we are considering a well-mixed FT in our model, the ozone originating from STE is especially well-mixed in a zonal sense.
6. It is not clear how the first-order loss rate of ozone in the continental boundary layer is set. It is stated (page 3) that the loss rate is “determined by that needed to balance the total ozone production in the continental boundary layer.” Why is it necessary to satisfy this condition?[1P]
[1P] The value is set by the requirement of an overall mass balance for ozone in the northern midlatitude troposphere. Most simply: Input - output = accumulation: the first law of Chemical Engineering. The relatively well known terms (STE, MBL losses, and average continental BL production) constrain the values of the other parameters. The value of kc,B is fixed by the constraint that the net contribution of the CBL achieves a mass balance.
Manuscript change: We have clarified the discussion of this issue in the penultimate paragraph of Section 2.2.
7. The first order ozone loss rate in the continental boundary layer is ~20 times greater than that in the marine boundary layer. Is this a reasonable assumption? The multi-model results of Stevenson et al. (2006; doi: 10.1029/2005JD006338) show much smaller differences in chemical loss between marine and continental regions. [1Q]
[1Q] Thank you for pointing out this related aspect. As in the previous response, we do not assume these boundary layer loss rates; these loss rates are derived from the requirement of balance between total ozone input (STE plus total PB) and total ozone loss (photochemical loss in the MBL, photochemical loss in the continental BL, and dry deposition to continental and ocean surfaces). We do show that the first order loss quantified for the MBL is physically realistic. Moreover, typical dry deposition rates over the ocean are 15-20 times smaller than over continental land surfaces. While the global loss due to dry deposition is estimated to be only about 17% of total gross losses (Hu et al., 2017; Stevenson et al., 2006) that is in a global sense where only ~30% of the surface is continental. Scaled to the northern midlatitudes where the land/ocean coverages is close to 50/50, this would imply that dry deposition is over 25% of the gross ozone loss rate. So the fact that dry deposition is built into our model's loss rates, means that much larger values are expected over the continents. Furthermore, because we have forced all gross ozone photochemical production and loss to occur in the continental BL and none in the FT, the first order ozone loss rate in the continental boundary layer is unrealistically large, since it must accommodate the total tropospheric ozone loss (beyond the photochemical loss in the MBL) without any contribution from photochemical loss in the FT. As a consequence the magnitudes of both the ozone production and loss in the continental BL are too large to realistically describe the actual photochemistry. However, it is the difference in these two quantities that determine ozone concentrations, so these model results are unaffected by this lack of physical realism.
Manuscript change: We have added a brief discussion of this issue to the paper in the penultimate paragraph of Section 2.2. We have also added a section in Supplement S8 entitled “Assumption of no ozone all photochemistry in the FT”, which addresses the issue of ozone production and loss in the free troposphere and its impact on the derived value of the first order loss rate in the continental boundary layer, as well as the implications for the sources of ozone in the continental boundary layer.
8. The model assumes a seasonally uniform ventilation rate for continental boundary layers. Is this realistic? I expect ventilation to be faster in summer because of convection.[1R]
[1R]This is a good question. A related issue is the acknowledged seasonal dependence of boundary layer depth. These are issues that could be addressed if further refinements of the model are undertaken. The model as it stands does reproduce seasonal ozone variations at northern hemisphere midlatitudes with quite respectable fidelity.
We note that these related seasonal variations may largely cancel each other, and we describe further investigation of this issue as a possible future use of the model in the final paragraph of Supplement Section S9.
9. The sensitivity of the model results of some of the other omitted processes is discussed in detail in the supplement (Section S8), but it would be useful to add a summary in the main text. [1S]
[1S] An excellent suggestion.
Manuscript change: A reference to Supplement Section S8 and its content is noted in two places at the end of section 2 and in the conclusions before the uses of the model are described. The revised Supplement Section S8 covers additional issues raised by this reviewer.

Specific comments on figures and tables:
1. Figure 1: Why are there arrows starting below the boundary layer boxes and pointing into them? (Or perhaps the low resolution on this part of the figure is making it difficult to interpret). These appear to represent emissions, which wouldn't make sense for ozone, but even if they represent production, shouldn't they only apply to the continental boxes and not the marine ones? [1T]
[1T] Thank you for this comment. We have improved the resolution of this figure and corrected the arrows so that they make better sense and removed arrows indicating a source in the marine BL.
2. Figures 3 and 4: Missing labels on the x-axis.[1U]
[1U] The original x-axis labels were obscured by the figure captions (in text boxes) in the submitted document and are visible now. We have improved both the figures and captions of Figs. 3 and 4 (now Figs. 4 and 5).
3. What are the lines on Fig. 5 derived from? [1V]
[1V] Figure 5 is now Figure 6. As in Figures 4 and 5 (previously 3 and 4) the solid lines are the results obtained from the 3 box model. The data points from the 18-box model simulations show bars which indicate the range of values (hi-lo) observed in each group of compartments. This information has been added to the caption for Fig. 6.

 
Referee 2: (anon.)

Comments to the Author
The manuscript of Mims et al., 2023 presents the development and application of a conceptual model to analyse the northern midlatitude Ozone. The model is practically a continuous stirred tank reactor with different compartment to differentiate between free troposphere (FT) and boundary layer components (PBL) as well as different geographical areas. The mass balance equation (i.e. accounting for the production and losses of Ozone) is used to retrieve the Ozone dynamic balance in each of the compartment. Production, losses and influx of Ozone in the various compartment are parametrized with available literature data, and in case not available, omitted.
On top of several sensitivity tests with respect to the chosen parameters, the authors show that the model could reproduce very well the seasonal variation of Ozone concentrations at several free troposphere sites (located in the Alps), as well as in the Marine boundary layer.
I found the manuscript very interesting, well written and with both the results and discussion section sound. I do not have specific comments on the model set-up and the parameters used for the budget calculation, which are all taken from previous literature study, and I would be in favour of publication after my comments below are taken into account:
We thank this referee for thoughtful and supportive comments.
Major comments:
My only concern is about the possible applications of such a tool. CTM simulations are now used at very high levels of details (in terms of physical, chemical and meteorological parameters) and often used to corroborate measurements data and to perform sensitivity tests. The authors rightly acknowledge that CTM applications are very demanding (both in terms of the correct preparation of the input data, as well as of the proper execution of massive parallel programs) and therefore such “reduced tool” are indeed helpful to conduct similar analysis. However, it is not still clear how. I would recommend the author to elaborate more on this point throughout the manuscript, maybe by giving a few specific example about future applications. [2A]
[2A] We thank the referee for this central question. In our view, the primary utility of this model is providing the reader/researcher with a mental picture on which to base evaluation of published literature and the reader’s own measurement or modeling results. Further, we believe that incorporation of the schematic model that we present into a scientist’s basic understanding of the tropospheric ozone budget could be beneficial. As we discuss in our response to Referee comment 1G, the simple models are meant to be used in parallel with complex measurements and simulations. We hope that this paper will trigger such uses by the community. The "use" of the model developed in this paper is to provide a concise explanation for, and to facilitate the understanding of, the average (climatic) seasonal behavior of northern midlatitude ozone and illustrate the governing influence of the marine boundary layer on this averaged (climatic) behavior.
Specific uses of this "tool" can be forward looking, prompting questions to be gleaned from the measurements and models. For example, how closely does a first order destruction rate coefficient in the continental boundary layer fit the detailed data?, and how does it diverge due to a departure from our assumed first order loss? What is the influence of the seasonal cycle of ventilation of the boundary layers? Do the related and competing effects of boundary layer height and convective mixing intensity produce a BL mixing "ventilation" time that varies significantly with season or do they largely cancel? We expect some revealing results to emerge when such analyses are performed, prompted by such questions.
The knowledge can also guide the analysis of measurements or complex modeling results, serving in a critical manner as a "reality check". In our response above to comment #3 of referees #1 (identified by us as 1G), we discuss one example, where a published interpretation of the implication of ATom measurements for ozone production in the MBL (Guo et al., 2021) is at odds with simple atmospheric constraints contained in simple models like ours and may need revision.
In this regard, it is possible for us to point out many other examples of inconsistencies in published papers that mis-interpret measurement or modeling results; consideration of those results from the perspective on our model could possibly improve that situation. Here is another example: Referees 1 mention the Gaudel et al. (2020) paper. That paper discusses 5 northern mid-latitude data sets; four are consistent with our model. For example, their Fig. 2A shows that the FT trends derived from four data sets - eastern North America (green), Europe (blue), Northeast China/Korea (red), southeast United States (brown) - are very similar as expected from the zonal symmetry that is a fundamental result of our model. However, the 5th data set - (western North America (gray) – is an outlier. Similarly, the vertical profiles of annual median ozone above 700 mb (their Fig. 3C) agree within about  2ppb for four of the data sets, but again the western North America profile (gray) is an outlier giving smaller concentrations at high altitudes. Consideration of this analysis from the perspective of our conceptual picture, would suggest a more critical review of that western North America data set is required; such a review might well notice some concerning issues:
1. That data set comprises fewer profiles (1569 flights in the 1994 to 2016 period) compared to 2,580-28,905 profiles in the other 4 data sets.
2. A majority of the western North America flights occurred early in the data period, and the temporal coverage was not uniform (see graph on left below); in fact about one-third of all 1569 flights were conducted in only two consecutive years – 2004 and 2005.
3. There is a large seasonal bias (at least over these early years plotted) with the winter flights in the north and summer flights in the south (see graph on right below).
These considerations suggest that the western North America data set could well give misleading results.
This is not meant to refute any existing published results, nor do we want to accent the negative. It would be inappropriate to highlight these examples in the current manuscript or in the published Supplement. We have included them here to illustrate, in hindsight, the value of such knowledge and oversight during analysis in order to glean the best information from the extensive and valuable measurements and modeling efforts that are available.

Manuscript changes: We have strengthened the discussion in the text, particularly the final paragraph of the Conclusions. A new Supplement S9 has been added to provide a more complete discussion of the of current and future uses of this simple model.

(Note: These graphs were prepared by one of our coauthors during a 2007 ozone trends analysis; this data set was rejected from consideration due to the biases discussed above.)
Minor comments
Page 2: Introduction: “Over time, as atmospheric modelling effort…” I am not sure I have properly understood the meaning of this paragraph. Do the authors implies that, as high resolution CTMs are becoming more and more available (i.e. often down to 1km) this is shifting the focus of the research from Ozone dynamics at large-scale to local-scale? If so, I feel that the sentence would need some rewording: high-resolution CTM applications are always set-up in nested configurations in order to pass chemical species, and meteorological parameters, from the parent grid (at large-scale) to the high-resolution grid. For these applications, the large-scale features of Ozone are modelled on the coarser domain (eventually several domains depending on the specific application), and are often also used to further corroborate the Ozone dynamics at local scale.[2B]
[2B] The message that we intend to convey is that as modelling becomes more complex, and the model output become more voluminous and detailed, the large-scale features of the ozone distribution and its driving processes have become obscured; in effect it has become difficult to discern the forest from the detailed descriptions of the trees. This is connected to our discussion in [2A] of the use of simple models. In our response to the 3rd major comment of Referees #1, [1G,1L,1R] we discuss this issue in more detail, and we have clarified this introductory statement in the manuscript.

Figure 3: Please consider improving the cosmetics of the plot (i.e. the colour legend and size of the data points). It is not straightforward to read the graph in its current state.[2C]
[2C] Thank you. Figure 3 (now Figure 4) has been improved.

04-Sep-2022

Dear Dr Mims:

Manuscript ID: EA-ART-02-2022-000009.R1
TITLE: A conceptual model of northern midlatitude tropospheric ozone

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Reviewer 1

Thank you for addressing our comments thoroughly.

Reviewer 2

The authors have replied my comments, and I recommend publications.