First of all we thank the reviewer for the suggestions. Below in italic the reviewer comments and in bold our answers

line 74—sp.  (Fisher → Fischer)

Already corrected in the on-line version of the manuscript

line 213—What is the nominal covered altitude range?

From 0 to about 65 km (pressure level 0.1 hPa). We will correct the text accordingly.

Section 6—The figures in this section are good and represent appropriate summaries of the dataset.

Thanks for this comment

Lines 505-507—It would be helpful to know (can you provide a reference or two?) whether or how scientific studies with MIPAS L2-v8 may differ or be improved from those already reported in the literature.

This is a difficult question, since we cannot predict how the scientific studies using the new MIPAS data could differ from the previous ones. However, the introduction of new species will surely trigger new investigations, like the one reported in the paper of Pettinari et al. (2021) about phosgene trends evaluated with MIPAS level2-v8. The new database has been obtained using MIPAS level 1 data where in the calibration process the time dependent detector non linearities have been correctly taken into account, therefore we expect that trends estimated with this dataset will better represent the real atmospheric trends. We will add few sentences in the revised version of the paper

First of all we thank the reviewer for the corrections and the suggestions on how to improve the paper. Below the reviewer comments in italic and our answers in bold.

GENERAL COMMENTS

================

The paper describes a new level 2 data set for the MIPAS instrument. All parts

of the instrument, level 2 processing, and associated data products are well

described in sufficient detail for the purpose of this paper.

The topic fits the journal, but the paper might be even better suited for ESSD

(https://www.earth-system-science-data.net/).

In principle we agree with the reviewer, but at this stage of the publishing procedure we prefer to stay with AMT

I do not have any major criticism on this very nice paper, only a couple of

minor issues mostly related to proper terminology and precise description.

I suggest that a language service should be used to review grammar and

expressions; maybe the "normal" copy-editing by the journal is already

sufficient for this purpose. I collected some suggestions for improvements as

Minor Remarks.

We have implemented the suggestions, for the grammar we will wait for the copy-editing suggestions

The paper can be published after addressing the specific comments (a very minor

revision).

MAJOR COMMENTS

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None

SPECIFIC COMMENTS

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line 194

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This and the preceding sentences sounds as if optimal estimation would be an alternative technique to Levenberg-Marquardt. According to mathematical literature, Levenberg-Marquardt is an algorithm for minimizing non-linear least

squares problems (it's a special case of the trust region methods), whereas optimal estimation is a regularization scheme that can be seen as a special (or extended, depending on perspective) case of Tikhonov regularisation. That is,

one can use the Levenberg-Marquardt algorithm to solve the non-linear minimisation required by an optimal estimation formulation of the problem.

Please clarify the text such that Levenberg-Marquardt is used in both cases for both problem formulations or clarify.

We agree, the reviewer is correct, we have reworded the text to avoid the confusion

Regarding the “regularizing Levenberg-Marquardt” method used, please see also later, the answer to the comment about line 269.

line 219

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You use a constant a priori to capture the variability contained from the MIPAS

information and not introduce any bias. Why did you deviate in the case of HDO

from this principle?

This strategy has been adopted because the altitude of the hygropause can change significantly according to latitude and season, and a profile with a fixed shape, even if in pressure, was too far from reality to be a good a-priori estimate. A sentence to explain this has been added to the text.

line 269

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The Levenberg-Marquardt method is not a regularisation method, but an algorithm for identifying a (local) solution to (reasonably behaved) non-linear least-square problems. In contrast, regularisation approximates the original not well-behaved problem by a well-behaved one and thus typically leads to a different (but stable!) solution compared to the original problem (which is why one probably tries to have as "weak" as possible regularisation). When the Levenberg-Marquardt algorithm converges, it identifies a minimum to the original problem, not an approximate one and thus it is not a regularization by definition (see e.g. Engl, Hanke&Neubauer or Nocedal&Wright).

Please adopt the text to use mathematical standard terminology.

The method used is actually the “regularising Levenberg-Marquardt” (LM) described in Sect. 7.2.2 of the book of Doicu et al. 2010. In this method the iterations are stopped when a pre-defined convergence criterion is met. Iterations may stop also if the current value of the LM damping coefficient is not negligibly small. This implies that the method behaves like an iterative Tikhonov regularization using the zero-order derivative operator, and a-priori given by the state vector at the previous iteration. Generally, the regularisation obtained is very soft (small bias of retrieved profiles) and its actual strength is properly quantified by the averaging kernels, when they are evaluated with the correct iterative formula presented in Ceccherini and Ridolfi 2010. The online discussion of this paper (https://acp.copernicus.org/articles/10/3131/2010/acp-10-3131-2010-discussion.html ) contains further information on the characteristics of the approach.

In the revised paper we have introduced a reference to Doicu et al. 2010.

line 385

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I am sure how to interpret this. When applying the AVK, e.g. to model data, one

always needs to employ all columns of the AK matrix on the model data, whereas

one may skip rows if the AKM associated with "not useful" elements of the

profile. Is this what you are trying to express?

We wanted to say that the user should use all the terms of each averaging kernel and not only the ones relative to the vertical range that the user has selected. We have rephrased the sentence.

Further, you are using also non-zero a priori profiles (at least for OE). It would be useful to remind users here to not forget the (I-A) x_a term.

We have introduced the suggested recommendation in the revised text

lines 363, 366, 478, Figure 5, Figure 6

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CFC-22 -> HCFC-22

 Done, changed also in figure 16

MINOR REMARKS

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All the following suggestions have been accepted and implemented

line 67

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time lapse -> period?

line 75

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connections with -> connections to

line 83

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a part from -> apart from

line 92

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to the -> to

line 102

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the "." should be on the end of the preceding line

line 176

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Section -> section

line 184

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HDO -> and HDO

line 232

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Table numbers are missing (??)

line 262

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netcdf -> NetCDF; also in the following

line 273

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AKs; abbreviation not introduced

line 542

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"are thought for" -> "are for" ?