The paper presents inverse modelling results using atmospheric transport models at varying spatial resolution. It is certainly of interest to the scientific community. In general the paper is well written, and I recommend publication after the following minor concerns have been addressed.

General Comments:

Regarding the sensitivity of inversion results to the assumed a priori emission distribution, it should be discussed a bit more why the inversion is not able to adjust and correct the spatial pattern. Which part is related to station density (coverage of the combined sensitivity) and which part is related to the lack of flexibility via the a priori uncertainty? It is a good suggestion to use different prior estimates with different spatial patterns, but then it needs to be ensured that those different estimates actually cover the range of possible distributions.

Specific comments

Lines 51-54: It was actually Lin et al (2003) who showed this for the first time.

Lines 58-66: Errors in inversions and in transport have been discussed in the literature prior to 2018, please cite earlier studies.

Line 89: reference Bergamaschi et al., change year from 2017 to 2022

Line 331: change “a-posterior” to “a posteriori”.

Line 345: ad a comma between the indices in the subscript (as in Eq. 12)

Line 349: a temporal correlation length of 0.01 days would only have an impact if the observations would be at a higher rate that about 1/hour. Is this the case? May be this should be mentioned clearly. It is not so clear that representation and model errors are uncorrelated between e.g. subsequent days or even hours, so this might need additional explanation or discussion.

Table 2: SEAS1 and SEAS2 have identical entries in the table, may be mention in a footnote to table 2 what the difference is.

Line 458: please briefly explain the iterative approach here, what is iterated? Are simply posterior residuals used to inform on model-data mismatch error?

Lines 484-486: What are typical scales for near- vs. far-field? This needs to be elaborated a bit more. To me it is unclear why in the far-field the diffusion should be depending on the size of the eddies, certainly at some distance the main cause of “diffusion” is the loss of correlation (or coherence) in the mean wind fields.

Line 494: remove comma after “overfitting”

Line 519: add “.” at the end of the line sentence

Line 524: When I calculate the relative uncertainties, I get 12.5% and 18.8% for Base1 and Base7 respectively. Please correct

Figure 6 caption: e) and f) are missing

Line 542: Is it not expected that the reduced chi-square values are always close to 1 given that uncertainty covariance parameters are estimated using maximum likelihood?

Line 553: “rational state” not clear why that would not be rational, given the (wrong) prior, that is the solution one retrieves using a completely rational approach.

Line 569: why is the uncertainty for the SEAS2 inversion results for JJA not given? It would also be interesting to discuss if the seasonality in retrieved fluxes is significant.

Line 577: It would be interesting to see if taking into account seasonality improves the performance (e.g. using statistics as shown in Table 3). Not allowing for seasonal variations in combination with seasonal changes in transport patterns can be expected to result in larger model-data mismatch error.

Line 597 / Table 3: it would be helpful to also have the posterior estimates and uncertainties included.

Lines 681-685: It needs to be mentioned that the case of Switzerland is special given the orography. The manuscript has not shown similar impacts of resolution increase in domains with more benign orography.

Lines 694-695 “While … uncertainty,” the sensitivity is the other way around (emission estimates being sensitive to parameters), please correct.

Lines 736-737: May be reformulate “… which is not true for the low-resolution inversions, in which when the uniform distribution is employed the low-resolution inversion fails and produces unrealistic results.” e.g. to “… which is not true for the low-resolution inversions, which fails and produces unrealistic results when using the uniform distribution.”

Katharopoulos et al presented a study that estimates posterior emissions of f-gases over Switzerland. In this study, the meteorological fields were driven using COSMO model with 7 (C7) and 1 km (C1), with an improved turbulent scheme for C1. Source-receptor relationships were obtained using FLEXPART model. Prior emissions were spatially and temporally distributed considering different assumptions, which resulted in a set of scenarios. In general, the results are consistent and in agreement with the literature. Authors claim that the uncertainty on baseline concentrations and spatial distribution of prior emissions have more impact on posterior estimates.  However, the authors must explain and clarify some issues first. Also, there are some minor issues to be solved.

Line 55: explain why is harder with Eulerian models

Line 65: It is general knowledge of the complex terrain of Switzerland, however, it would be appreciated if the authors can provide some numbers.

Line 71: "Thus, a potential decline of fossil fuels will possibly see increased emissions from refrigerants" Can you explain the logic?

Line 190: How did you aggregate the observations?

Line 197: Regarding REBS, can you mention other methods? Is it possible to use Thin Spline for instance? 



  Wood, S.N. (2003) Thin-plate regression splines. Journal of the Royal Statistical Society (B) 65(1):95-114.

Line 221: Is Flexpart capable of read and run with meteorological fields from ICON?

Line 244: A mention to Hysplit seems appropiate.

Stein AF, Draxler RR, Rolph GD, Stunder BJ, Cohen MD, Ngan F. NOAA’s HYSPLIT atmospheric transport and dispersion modeling system. Bulletin of the American Meteorological Society. 2015 Dec 1;96(12):2059-77.

Line 309: It is not very clear, but it seems that to reduce computation cost, cells with lower sensitivities are aggregated. However, higher prior fluxes in the same cells can produce convolved emissions which may be not neglected. Comment, please.

Line 410: A recent publication states that SF6 seems appropriate (Hu et aL., 2023)