I support this paper for publication subject to the major comments in my attached report.

The changes are mainly to do with a restructuring of the paper to make it easier to read.

I have made a lot of comments, but each should be reasonably quick for the authors to deal with as I do not think any additional experiments are needed to make the work publishable.

The authors of "German methane fluxes in 2021 estimated with an ensemble-enhanced scaling inversion based on the ICON–ART model" document and validate a very interesting approach to methane inversions. The manuscript is interesting and understandable, and is definitely worthy of publication. It fits the goals of ACP, and I recommend publication with minor revisions. I only have one small request to the authors, and some smaller comments.

My main point is that I would like to see better visualised how the R matrix as made in this paper improves the inversion. The calculation is quite complex, and covers a large part of the paper. Nevertheless, some arbitrary choices remain (like the 10 ppb standard, and the inflation factor). I now wonder if 'standard' R values (like in Steiner et al., 2024b (reference as in manuscript):" we use a model-data mismatch of 2 ppb + 40% of the anthropogenic signal") would give similar results. For this, the χ²-innovation can be used. χ² is used to assess the uncertainty, relative to the model-observation mismatch (i.e. ((y-Hx)² ) / HPHT, where y are observations, Hx are transported (prior mean) fluxes and P is the prior covariance matrix of the fluxes). One would like the χ²-innovation to be as close as possible to 1.0 (which means uncertainty and model error are balanced). It would help the paper to include a figure of the χ²-innovation to show that the 'new' R is an improvement over e.g. Steiner et al., 2024b. A run with a fixed (diagonal) R can also be included in Figure 7.

Some other, smaller comments are listed below

- Almost all IDs tested are within 15% in their flux-solution. To me, this seems like the posterior uncertainty is under-estimated. Can the authors comment on this?

- Can the authors explain to me the strange boundaries in Fig. 4b and d? With this, I mean the darker lines that run through e.g. France.

- in Section 5.5.1, a gaussian noise of 2ppb random error is added to the pseudo-observations. However, the σ_const is already 10 ppb, which means the added white noise is quite small compared to the uncertainty associated to these observations. Can the authors explain this choice?