This paper presents a comprehensive understanding of SF₆ emissions worldwide using inverse modeling, which improves our knowledge on global SF6 emissions and their regional (spatial) distributions. It could be the first study that I am aware of presenting SF6 emissions worldwide from an extensive combination of measurements. The manuscript is well-written and well-structured. The analyses are reasonable and conclusions are generally solid. The description of the methods is generally clear. The authors have also acknowledged the uncertainties of the derived emissions and the limitations of the current observation in constraining emissions in several regions including South America etc., and call for attention for enhancing measurement network in these regions, which is important for not only SF6 but others important gases.

The authors have done a very nice piece of work, that will be of interest to the community! I would recommend the publication of this manuscript on ACP. The following are some specific/minor comments, corrections or questions:

Line 15: I suggest making the potentially increasing emissions in countries other than China (e.g. India) a separate point in the abstract, together with the accompanied uncertainties (arising from the limited measurement sites) which you already stated in point(5). The emissions in these countries are very important for understanding the global SF6 emissions and their variations.

Line 30: I suggest changing concentrations to mole fractions. Concentration is more for something per volume.

Line 48: Typo “shwn” to “shown”

Line 49: It should be top-down, not bottom-up

Line 100: how do you chose the “3h interval”? Auto-correlated errors could still exist within this period (biased systematic errors). Have you tested different intervals?

Line 111: I would like to know more about this 50-day back-trajectory duration. Why do you choose 50 days? Will the uncertainties from the Lagrangian dispersion model increase rapidly when running time grows? I believe it is not a primary task of this study but I suggest adding a brief explanation of the period chosen here in the Method section. You give some details in Lines 261-265 but I do not think the Figure 5b is enough to illustrate your statement in the text.

Line 119: I suggest adding the observation error term to eq (1).

Line 133: I suggest changing “cannot be determined well” to “may not be determined well”. You need to combine with your error reductions to decide whether these emissions can be constrained well, which I suggest adding in the results and discussion section.

Line 157: Here you are using the “UP” a priori emissions to drive the baselines. What is the reason for choosing this? You stated later that you cannot determine which prior is better (Line 239-240), but eventually find in line 448 that EDGAR is actually the most reliable estimate for SF6 emissions. Why not using EDGAR in generating the mole fraction field?

Line 219: It is good to show the available number of observations each year.

Line 226: Eq (3), I would like to know whether you apply the same inequality constraints for a posteriori baselines? Give more details of how the baselines, posterior error matrix for emission and baseline, prior and posterior uncertainty for y (observation error matrix) etc. are determined or calculated.

Line 230ff: Do you show the results of the sensitivity tests somewhere? I would suggest doing so in Supplement.

Line 243: suggest revising it to “observed and modeled mole fractions (before and after the inversion) at the Gosan observation station….., using the E7P emissions field as the a priori in the inversion”, to make it clear.

Line 259: define “detrended” here when it first appears.

Line 268: add how you calculate the uncertainty reductions in the Methods section. It will be easier for readers without inversion expertise. Do you use the Averaging Kernal? Will the posterior uncertainties the same with analytical solution when no inequality constraints are used?

Figure 6: I am curious about the increments in the very northeast region of China. In the prior distribution, emission is already very high in this region. Is there any explanation for this? In addition, you are using the average of different variations of a priori as the inversion results, but here you are showing the increments and uncertainty reductions for only one of the variation. Suggest showing the average here, or show plots for all the variations in a separate supplement file.

Figure 7: I would like to see the separate posteriori emission spatial distributions from 6 different prior distributions. Also, in Line 235-236, you claim that inversion results using different variations are similar, I suggest showing them in SI Figure.

Line 304: I hope you can discuss a bit about the interannual variations in the posterior emissions, e.g., the increase in 2019-2020 then drop. I am curious if the authors have any insight into this.

Line 351: the citation here is the conference abstract version and I do not think they provide insight into whether there is any underestimation from Simmonds et al., neither in An et al. 2024. Perhaps just remove the citation here. As you claim that your emissions in China are more influenced by Gosan site, you can look further in to the reason for the difference between Simmonds and other emissions, rather than refer to a previous publication.

Line 359ff: I suggest that the discussion of emissions in these potentially less-constrained regions is accompanied by the discussion of error reductions. For GAINS prior, have you tried to increase the prior uncertainty and test it?  You stated in the methods part that you did the relevant sensitivity tests with different prior emission uncertainties. I am afraid the inversion cannot constrain this region at all when using GAINS prior (no error reduction in Fig. 6).

Line382: “see Sec. 3” in the bracket. please specify the specific section here for the prior uncertainty assignment.

Line 402ff: for AGAGE 12-box global SF6 emissions, you can refer to the latest ozone assessment report (providing emissions up to 2020) or An et al. 2024 (providing emissions up to 2021).

[Laube, J. C. & Tegtmeier, S. Chapter 1: Update on Ozone-depleting Substances (ODSs) and Other Gases of Interest to the Montreal Protocol. in Scientific Assessment of Ozone Depletion: 2022 vol. 278 (World Meteorological Organization, Geneva, Switzerland, 2022).

An, M. et al. Sustained growth of sulfur hexafluoride emissions in China inferred from atmospheric observations. Nat Commun 15, 1997 (2024).]

Line 418-419: I do not believe this could be the case. The ocean is very heterogeneous and the ocean flux is highly dependent on the locations (see Gruber et al. 2001). I suggest you discuss the potential uncertainties from that previous study you cite (Ni et al. (2023)) arising from scaling measured flux from a region (with potential strong sink) to global (with strong sources at other regions). Your explanation in lines 425ff seems plausible. Also, in this paragraph, always clarify that the overestimation is specific to the UNFCCC-ELE inversion, not all the inversion in the study, to avoid confusion.

[Gruber, N., Gloor, M., Fan, S.M. and Sarmiento, J.L., 2001. Air‐sea flux of oxygen estimated from bulk data: Implications for the marine and atmospheric oxygen cycles. Global Biogeochemical Cycles, 15(4), pp.783-803.]

L440: “underestimation of the emission residuals between the global and the Chinese emissions”, clarify that it is in GAINS prior emissions.

L454-456: consider the uncertainties for the trend for both global and China.

L457-458: state here that your bias may be especially in the poorly-observed regions.

Line 488-490: is there any result to support your statement here that your results are mainly driven by the high-frequency data in the U.S.? In addition, you can also have a look at the mole fraction enhancements, either in the observations or the posterior simulated ones, to check the seasonality in mole fraction enhancements. Do you have any data with reference (e.g., the high power transmission in summer in Line 490-491) to help justify your seasonal cycle?

Line 520ff: Again, you need to consider the uncertainties. If the two trends are not significantly different, then I suggest you remove this bit in the conclusion. In addition, I suggest also mentioning that the China’s official voluntary reports are improved in the latest reports compared to the top-down results (Figure 10), and also discussing this in the main text.

Regional and global atmospheric observation-based estimates of SF6 emissions are presented using a Lagrangian inverse modelling system. Emissions trends are derived for the major emitting regions, China, the USA and EU, which are generally consistent with other available regional studies, but mostly higher than reported emissions. Global emissions are also broadly consistent with previous studies.

The article is detailed and meticulous and very well written. The methods are interesting and novel, and the application is important and timely. I think the paper is suitable for publication in Atmospheric Chemistry and Physics, subject to some minor corrections.

Main text:

L15: Point 5 in this list is somewhat confusingly worded. Perhaps something like: “Global total SF6 emissions are comparable to previous studies but are sensitive to a priori estimates, because of the poor network sensitivity to some regions (e.g., Africa, South America)””

L22 and L27-29: I suggest deleting the lines beginning “However, this GWP 100 value…” and “Thus, GWPs, which are typically…”. I don’t think it’s accurate to say that the GWP 100 value “underplays the climate impact of this gas”. If you wanted to examine the climate impact over longer timescales, you could define a longer-term GWP. It’s well known that GWP has several flaws, but I don’t think you need to go into them here.

L43: I’d separate out the part of this sentence on SF6 measurements being used to determine stratospheric OH into its own sentence. The other parts of this list are sources, whereas this is a measurement of atmospheric SF6. You could also add that it has been used as an ocean tracer though.

L44 and 54: I suggest removing “developed” and “developing”. These terms are not needed here.

L70: This statement isn’t true, as Rigby et al., 2011 was a global inverse modelling study that used a 3D (Eulerian) model.

L113: Measurement location and time?

L115 – 118 and throughout the following sections: I think you need to be careful with the notation here. In this section, where you define He, e, etc. it implies that these sensitivities are to the grid-scale emissions or mole fraction fields. However, you’ve used a basis function decomposition of the emissions field in your inversion (but I’m not sure how you’re scaling your initial conditions field, see below). Therefore, the matrices and vectors in Equations 2 and 3 are different to those defined here. I think you could make this consistent by stating that e, He, etc are for aggregated groups of grid cells when you define them?

Figure 2: How have you dealt with the different frequency between the flask and high-frequency data here? Is this the average over all time points, with zeros during times where there are no flask data?

Section 2.5: Please clarify:

• if emissions and boundary conditions are being scaled in the inversion, or if absolute values are being derived. Furthermore, how are grid cells aggregated within the spatial basis functions? Is the spatial pattern of the underlying grid cells preserved, or are emissions spread out uniformly within the aggregated cells?
• how the initial conditions are being adjusted. Is the whole field adjusted each month (or, equivalently, are the baseline mole fractions at the stations being adjusted uniformly? Or perhaps adjusted on a per-station basis?), or is there some spatial decomposition?
• Does R contain only “observational errors”, as stated? If so, how is this defined (i.e., is it just measurement repeatability)? And if this is the case, what about model (or mismatch) uncertainty? How have you accounted for this critical (but highly uncertain) term? It seems that this term should also be the subject of a sensitivity test.
• Have the observational data been filtered at all? For example, excluding points under low boundary layer heights, or at night, as is often done due to poorer model performance under these conditions? Furthermore, note that SF6 mole fractions in populated regions show occasional very large events, perhaps linked to equipment failure (see, for example, the note that very large emissions are derived during some months, here: https://assets.publishing.service.gov.uk/media/62d7b9bee90e071e7e59c97e/verification-uk-greenhouse-gas-emissions-using-atmospheric-observations-annual-report-2021.pdf). Do these need to be excluded, since your emissions model assumes constant fluxes (at least during each month)?
• How was the baseline uncertainty of 0.15 ppt, and correlation length scales, arrived at? Why 70% for the prior uncertainty?
• I don’t understand why a 70% level of prior uncertainty on a per-grid cell basis doesn’t lead to a vanishingly small prior global uncertainty. Can you clarify? If you have ~5000 grid cells, wouldn’t the global uncertainty be ~70% / sqrt(5000), which is ~1% (notwithstanding spatial correlations and minimum values).
• Surely the temporal correlation of 90 days plays very little role, given that you are solving for annual emissions in the main results? Is this term needed?

L253 – L256: I would remove these statements (or at least the sentence on L256), as it suggests the inversion has more capacity to focus on “incorrect” parts of the model than it really has. It is of course better if the prior model baseline is better, but the optimization is of the whole system. Even if the prior model simulated a perfect baseline, errors in sensitivities to boundary conditions or footprints could still lead to an adjustment away from that perfect baseline.

L261 – 265: I think these lines should be removed. I don’t doubt that a 50-day simulation period is more “accurate” than a 10-day period. But it’s not shown here.

L289 and throughout this section. Please provide an uncertainty to these quantities.

L298 – 299: Remove the sentence about it being “reassuring”. This is subjective and not needed.

Section 3.3.4: My reading of all of these subsections is basically that there is, not surprisingly, very sensitivity to these regions. I suggest moving this content to the Supplement and summarizing this message in a paragraph or two in the main paper.

L434: Should this be “is larger than, and inconsistent with, the global atmospheric SF6 growth…”. Furthermore, I wouldn’t use “postulated” in this sentence (use “derived” or similar).

L461: “could be brought relatively close to these previous estimates”, rather than “known values” (there are no “known values”).

L462: Suggest deleting “which has rarely been achieved before”, as it’s too broad here. There are many studies using global Eulerian models that do this (although only one for SF6 that I’m aware of; i.e., Rigby et al., 2011).

L462 – 468: I don’t agree with the framing of these sentences. The novelty of this work is that it attempts to create a global picture using a backward running Lagrangian model. This is very nice in itself. But we shouldn’t get carried away that 50-day back trajectories can really give us a full global picture, given the sparse measurement network. As this work shows, there is negligible sensitivity to large parts of the world, irrespective of the integration time. Without additional measurements, emissions derived from these regions will always be subject to biases from the prior and the accumulation of transport errors. Furthermore, the last part of these sentences is conjecture, that there is a “clear direction” in the adjustments to these unsampled regions. This seems to be subjective to me. I suggest cutting these sentences. The work is impressive in itself. You don’t need to over-sell it.

Section 3.3.6: Note that seasonal emissions were also briefly noted for north-east Europe in Reddington et al. (2019). Similarly to Hu et al, these maximized in the winter.

L499: I suggest “boundary conditions”, rather than “initial conditions”

L502 – 503: I suggest deleting the final sentence for the reasons outlined above (comment to L253)

L504 – 505: I also suggest deleting the final sentence of this bullet for the reasons outlined above (comment on L462)

L509 and throughout this section: provide uncertainties

L517: Delete the final sentence, as this is conjecture.

L527: Delete the two final sentences, as I don’t see how you could know this. It’s not supported by your investigation.

L529 – 530: I think this bullet should be deleted, as there’s so little sensitivity to this region.

L542: Delete the final bullet, as it’s well outside the scope of your work.

Supplement:

L14: full stop needed.

L44: Please confirm that the following is correct and has been checked in your analysis: The cited paper (Guillevic et al., 2018) quotes the ratio NOAA-2014 / SIO-05 = 1.002 ± 0.002. However, the wording on this line suggests that conversion from NOAA-14 to SIO-05 is by multiplication by 1.002. The cited reference suggests that division by 1.002 would be required.

References

Redington, A. L., Manning, A. J., O’Doherty, S. J., Say, D., Rigby, M., Hoare, D., Wisher, A., Rennick, C., Arnold, T., Young, D., and Simmonds, P. G.: Long-Term Atmospheric Measurement and Interpretation of Radiatively Active Trace Gases, Annual Report, Sept 2018 – Sept 2019, Department for Business, Energy and Industrial Strategy, London, UK, https://assets.publishing.service.gov.uk/media/5eddf868d3bf7f4601e57730/verification-uk-greenhouse-gas-emissions-atmospheric-observations-annual-report-2018.pdf, 2019.