Dear authors,
thank you for careful consideration of the reviewers' comments. The paper is almost ready for publication. I have only a couple of minor comments. I do not insist on their implementation, please judge yourself if you find them useful.
1. Abstract l 20. I know that I am quite pedantic in such issues, but the term "a priori" I think is used in context with "information", "knowledge", "assumption" or similar, and "emission" seems to me to be a word of another category. What about "a priori estimates of emissions"?
2. Abstract l 22. The term "background" is an equivocation. On the one hand it is used as a technical term in a data assimilation context, almost synonymously with "a priori" (This explains the index "b" in Eq. 3, but here you call it "a priori, which I find much clearer). On the other hand, "background" is used in a rather common language sense, denoting a value for, say, quiescent or unperturbed conditions. I think your statement would be clearer if you could clarify the connotation of this term.
3. p2 l 30 It is not true that SF6 is distributed rather uniformly in the atmosphere (see "Reassessment of MIPAS age of air trends and variability" by F. J. Haenel, G. P. Stiller, T. von Clarmann, B. Funke, E. Eckert, N. Glatthor, U. Grabowski, S. Kellmann, M. Kiefer, A. Linden, and T. Reddmann Atmos. Chem. Phys., 15, 13161-13176, 2015. and references there is. I suspect the same might hold for the other gases mentioned. The easiest solution to this problem might be to replace the term "atmosphere" by "troposphere". Then the statement should be ok. (Reference to the paper mentioned is of course NOT necessary here. I mention it only to make clear what I am talking about)
4. p5 l34 shouldn't it read "least squareS solver"?
5. In Table 1 you still use the term "state vector length". Wouldn't "dimension of the state vector" be a more adequate term? The length of a vector could be understood as the norm of the vector, like e.g. length = sqrt(x_1**2 + x_2**2 ...).

I have another comment. This refers to Section 3.3 where you discuss the uncertainty reductions. I do not expect you to include this comment in this paper but it might be interesting for future work: Have you considered to assess the Shannon information content? This includes not only the uncertainty reduction in terms of variances but also the information gain implied by the change of the correlations in the covariance matrix.

Regards,
Thomas von Clarmann