Review of “A thousand inversions to determine European SF6 emissions from 2005 to 2021” by Vojta et al. for publication in Atmospheric Chemistry and Physics

Vojta et al. present a comprehensive atmospheric inversion study estimating European SF6 emissions from 2005 to 2021. This study utilised a large number of measurement stations and an extensive combination of inversions to report a robust estimate of the country-level SF₆ emissions and their uncertainties. The study reports a declining trend in the SF6 emissions for major European countries attributed to the various EU regulations that came into effect during the study period. The manuscript is very well-written and structured.

Studies on European SF6 are scarce, making this manuscript a valuable contribution to a topic of significant scientific interest. The authors have done impressive work, and I strongly recommend its publication.

I have a few minor comments and questions listed below:

The authors employ a Gaussian prior error distribution within an analytical inversion framework. Even though the posterior emissions are reported to be consistently higher than the prior, were there any instances where the inversion produced negative posterior emissions at the grid-cell level? If so, how was this issue dealt with?

Could the authors clarify how the averaged posterior uncertainty shown in Fig. 4d was computed? Specifically, was temporal correlation across different years taken into account in this calculation? Since the posterior uncertainties in Fig. 4d appear visually comparable in magnitude to the emissions themselves, despite Fig. 4b indicating substantial uncertainty reduction and the prior uncertainty being set at 50%.

The authors can consider making the y-axis range the same for Figs. 7b and 7c to highlight the different trends in the German emission time series across the two regions.

The manuscript by Martin Vojta and co-authors does a thorough analysis of European SF6 emissions derived by inverse modelling. The study builds on a previous publication by the same authors but focuses on national scale emissions in Europe. The authors carefully re-explore sources of uncertainty in their inversion estimate and provide an updated uncertainty estimate through the application of a large (59 members) ensemble of inversions. Parameters that should be varied for these inversions were selected by first identifying those with largest impact on posterior results and finally ensemble members were selected by randomly scanning the parameter space through an ensemble of inversions. The general idea of the publication of improving uncertainty estimates of inverse modelling through sets of sensitivity inversions is not new. However, the systematic exploration of the parameter space and the large number of inversions to derive final posteriori emission and their uncertainties is novel and a way forward in the field. The applied methods are appropriate and state of the art. The paper is clearly structured and well written. The length of the manuscript with various appendices is somewhat discouraging and the publication would benefit from a certain degree of shortening. Furthermore, I have several general and specific comments that should be addressed before publication.

General comments

Title: Unfortunately, the title is misleading and needs to be amended. Just because an ensemble of inversions with 59 members was run over 17 years in yearly batches, we should not call this "a thousand inversions". The publication would lose none of its importance if the title would state correctly what was evaluated: a large ensemble of inversions.

Selection of parameters and their ranges for ensemble construction: There are several questions connected to the construction of the inversion ensemble. First of all, there is very little quantitative information why certain parameters were selected while others were omitted from the ensemble. For example, L269/270 states that the inversions were 'most sensitive' to the 'baseline uncertainty'. Nevertheless, in L240 it is stated that baseline uncertainty was fixed for all ensemble members. Sec. 2.6 also states that parameter ranges were narrowed as compared to the sensitivity tests but why remains unclear. Second, the choice of uniform distributions for the parameters may also introduce more 'extreme' events than may be representative of the true uncertainty of the parameter space. The uniform distribution also makes the selection of the parameter range much more critical as compared to using a normal distribution. Some additional explanation of the choices needs to be given to clarify if these are reasonable choices to represent real uncertainty. My concern is that by using (or by over-representing) parameter values that are unlikely or even unreasonable the posterior ensemble uncertainty gets blown up. Third, what tests were done to assure that the ensemble is representative? How different would the results look if another 59-member ensemble would have been selected or the number of ensemble members halved/doubled? How was the Monte Carlo sampling of the parameter space performed? Independent for each parameter and sample?

Validation: Although, the results presented in this study are exhaustive, I am missing a basic evaluation of model performance as expressed through comparison with observed concentration time series. This could be presented in a very condensed form through a Taylor plot with prior and posterior results or through a table giving statistics for the individual sites. It would help to better understand which observations are well represented by the model and which are less well captured and, hence, do not constrain emissions as much. Furthermore, and because the network was not stable over the study period, it would be good to get an overview which and how many observations were available each year (again this could be given as a plot or as a table).

Specific comments:

Abstract: Usually, an abstract should start with a problem statement and then outline what the current work adds to understanding/solving the problem. Hence, I suggest adding one sentence discussing the importance of SF6 (potentially very similar to the one in introduction).

Introduction 1^st and 3^rd paragraph: To me it would make sense to move the 3^rd paragraph up and continue the 1^st paragraph with it (atmospheric importance of SF6) and then come to the usage/sources.

L89ff: It would be good to understand how different these observational datasets are in the end. Maybe add a table giving number of observations for each of the eight groups. Also, the distinction between 1 and 2 is not so clear, since Fig 1 only shows European sites. Which global sites were used that would provide any reasonable constraint on European emissions. The description implies that all your inversion domains are always global. Is this correct? Should be highlighted somewhere besides mentioning the previous method paper.

L131ff: The GAINS inventory is mentioned without a reference, only link to previous study by Vojta et al. 2024. Please clarify if the inventory is available at two different resolutions, as it seems, and why you chose two different re-gridding strategies. I suppose the second is simply a smoothing of the inventory, but the rational behind that should be explained.

Sec. 2.3: What is the reason for using the population and the night-light proxies that seem to have an extremely similar distribution (judging from Fig.3). Instead, a proxy with very different distribution could have been interesting (e.g., uniform within each country or reflecting the electric grid). In addition: what is the reference year for the population and night-light data?

Sec. 2.3, UNFCCC-based prior: How are non-reporting countries treated? Several Eastern European Countries seem to have extremely low emissions compared to GAiNS and EDGAR. On the other hand, north African countries seem to have large emissions

L179: Does this take the posterior covariance between different grid cells into account?

Sec. 2.5: Although, there is information in Tab. 1, I am missing a short description of the reference inversion in the text. A short explanation how parameter values were chosen for the reference inversion would also be helpful.

L204: Please comment on the question of how much omitting off-diagonal covariance may impact the inversion results. In addition, to simply scaling the diagonal elements of the covariance matrix, changing its structure is usually another important sensitivity test.

Observation and prior uncertainty: Others have tested more objective ways of setting observation and prior uncertainties; for example, by evaluating Chi-square statistics of the cost function. Here, values for the observational uncertainty within a range of a factor of 5 were tested, the smallest of which almost certainly are too small given the analytical uncertainty alone. Too small values of the observational uncertainty are known to lead to over-fitting of results and can mostly be avoided from the beginning. Including ensemble inversions with unrealistic settings will artificially increase posterior uncertainties as explored here through the ensemble spread. How did the two 'variable' estimates of observational uncertainty compare to the fixed values.

L218: 'global field at once' Do you mean global field as a whole? Or in other words: one scaling factor for the whole global field? Please rephrase.

L254f: An alternative way to look at the information content in a Bayesian inversion, would be the exploration of the averaging kernel, which should be closer to one in areas where the posteriori result is mostly informed by the observations and closer to zero where information comes mainly from the prior. Most likely, the averaging kernel will be similar to the uncertainty reduction, but I wonder if areas like Israel and Russia would show up in it as well.

L287: One advantage of the presented ensemble approach could be to give non-Gaussian uncertainties of the posterior. However, it seems that uncertainty is given here as the standard deviation of the ensemble instead of 2.5 % and 97.5% percentile range. How do these two estimates compare?

Fig. 6 and others: It is somewhat difficult to distinguish the vertical lines for network extension from the grid lines. Could the grey lines for network extension be given as dashed lines instead?

L312: Consider starting new paragraph after 'inventory.' New point and figure.

L316: Comment on the fact that the reduction on Northern Germany is quite similar to the reduction in the UK (about a factor of 3).

L351f: I find this conclusion too far fetched. Seeing the range of possible inversion results from one system by changing some of the critical parameters and not knowing any of these, or similar, parameters used by Manning et al. (2022), the good agreement may just be by chance. What would be needed for the suggested conclusion would be a direct switch of transport models between the two inversion systems and an alignment of input parameters to cross-check the results. Hence, I suggest to somewhat weaken the conclusion at this point.

L515f: Is it worth discussing these uncertain results with a dedicated Figure?

L525ff: This is connected to my general comment on observational data availability and model performance. If I am not mistaken, Monte Cimone only provided reliable SF6 data until the end of 2017 (WDCGG). Then in 2023 a new Medusa-GCMS was installed. For the period between there is very little constraint on Italian emissions. Hence, the results, as discussed in this section, need to acknowledge the observational data availability.

L578: I suppose this statement refers to larger a priori uncertainty for individual grid cells? Or does the domain total uncertainty change with correlation length?

L598: I would rather be skeptical about this statement. I would think that very distant observations may introduce large biases in posterior estimates for two reasons: 1) long transport is usually connected to large uncertainties, 2) infrequent observation of the same source area when source and receptor are very distant.

L603: Should MCN be CMN?

L620f: If posterior emissions change little with applied observation uncertainties, how does posterior uncertainty change? Smaller posterior uncertainty should be seen for smaller observation uncertainty unless observation uncertainty is generally underestimated.

Fig A2 and I1: The colours for individual inversions only distract. Unless there is another grouping that should be indicated by the colours, I suggest dropping the colours and represent individual runs by gray lines.