Please attend to the referee comments and revise the m/s accordingly.

Thank you for the detailed attention to the referee comments and corresponding text revisions. I have read the responses and find the paper suitable for publication.

Although you answered the referee regarding the question of the cost function (see below), it was not clear to me if the RfullExp and RdiagExp options actually converge on the same retrieval solution (to within the expected formal retrieval errors, although you do indicate that the RfullExp solutions display “generally larger errors”). However, I assume you tested this and therefore please clarify in the final m/s e.g. in Fig 6 “ALL” around 200 hPa are the blue and green lines separated by more than the RMS of their combined retrieval errors?

Referee comment...
…. I worry that the IASI observations could be strongly down-weighted, and I wonder how the cost function in RfullExp compares to that in RdiagExp. Is it possible to include a plot of the cost function versus iterations for a cycle of RfullExp and RdiagExp, either in the response or in the revised article?

Author reply…
…. For the RfullExp, the convergence is achieved due to the stationarity of the cost function (1stcriterion). The fact that the observations are downweighed in RfullExp is likely the reason for the faster convergence.

Revised text submitted ….
…. The widespread correlations (high condition number) and larger variance of the estimated R matrix conduct to a downweight

Referee comment ...
In the above revised text I suggest replacing “conduct” with “lead”.