Dear Dr. Ceccherini et al.,

thank you very much for answering the reviewer comments carefully. The paper is certainly ready for publication. There is no need to defer more of the derivations into an appendix.

Though, I would have one request related to the remark on using "sigma" (p.2,l.21) as a term for the "errors". If I am not mistaken, by "errors", you refer to the departures of the observations/retrievals from the truth. I think "departures between truth and observation/retrieval" would be a less ambiguous term. Please consider rewording the following sentence accordingly:
"where the vector sigma_i contains the actual errors on the vertical profile obtained propagating the errors of the observations through the retrieval process"
->
"where the vector sigma_i contains the departures between retrieved and true vertical profiles." (Does it actually need the part with "propagating the errors of the observations"?)

Best regards,
André Butz.