This paper offers a detailed accounting of error estimates for retrievals from the MIPAS instrument.  The analysis is rigorous and is as complete as can be expected.  There will always be error sources that cannot be estimated because there is insufficient information in the measurement system, such as the impact of measuring from a moving platform.  Retrievals always implicitly assume a vertical column, but measurements are smeared geographically, which could cause problems if measuring something with high variability or moving across the polar vortex boundary partway through an altitude scan.  Note that a changing scene over the course of a single FTS measurement (e.g., when moving through a region of high variability in H2O) would give rise to a contribution to the imaginary component in the Fourier transform, which is the source of the noise information in the analysis, but perhaps the effect would be negligible compared to the noise level for an instrument measuring in emission.

                There will be systematic errors from using Voigt profiles in the calculated spectrum rather than more accurate line shapes, but one would hope the available uncertainties on the Voigt parameters would encompass this effect.

                Some of the labels are a bit whimsical (e.g., headache errors), but their meanings are clear.  I had to look up some of the Latin phrases, not being familiar with the language.

                I have no suggestions for changes, other than a few typos and minor changes, listed below:

>Line 51: variable definitions

        Every variable is defined except for y (unless you count it as being defined by the phrase “the signal y” on line 94, well after the fact).

>Line 67: …denotes the errors source

        errors -> error

>Line 325:  witht

         with

>Line 358: …between to independent measurement systems

        to -> two

>Line 378: The component of the instrument line shape error related to the phase does not need to be considered explicitly, because it affects the frequency shift only and thus is implicitly included in ∆shiftx

         A non-zero phase in the modulation function would imply a physical asymmetry in the ILS (unless it is just a straight line as a function of optical path difference), the effect of which is not just a frequency shift; it affects the shape of the calculated line.

>Table B1: CFC-22

       CFC-12

The authors present linear error estimation methodology for the multi-step MIPAS temperature and trace gas retrieval from limb spectra. The approach considers multiple error sources at multiple steps of the retrieval process and provides their mathematical definitions using conventions recently proposed in the collaborative TUNER activity in the remote sensing retrieval community.

The technical development of the error estimation methodology is comprehensive and appropriate for MIPAS retrieval system. Multiple elements of this work, which aims to align with the TUNER enterprise, provide welcome exposition and appropriate mathematical detail for the error analysis of atmospheric remote sensing retrievals. In particular, the authors emphasize the dual role of certain unknowns, such as temperature, as fixed parameters or retrieved quantity of interest, depending on the retrieval step in question. The TUNER conventions for error source notation provide additional clarity in the development. Finally, the detailed specification of perturbation-based calculations versus Gaussian propagation is appreciated.

My first major comment is on the balance of methodology versus results in the paper. As currently presented, the paper is very heavy on the methodology development and light on results. After presentation of the only figure in the paper, the last few sections rapidly discuss multiple additional analyses and summaries that have been or could be undertaken without any illustration of their impact or interpretation. It reads very much like an algorithm theoretical basis document (ATBD) as opposed to a presentation of research results or a data user’s guide. This current format is potentially appropriate for this journal and certain segments of its audience, but broader appeal might be achieved with additional focus on results.

I recommend the authors assess this balance of the presentation in terms of their intended audience. I can imagine the MIPAS data user community would benefit from further presentation of the error estimates and the availability of them as supplementary data. If this is not within the intended scope of the paper, at least it would be useful to discuss how these materials would be made available. The abstract mentions estimated uncertainties available for multiple atmospheric conditions. While the conditions are discussed in different sections, the error estimates are not provided. There is not an explicit presentation of the systematic versus random error estimates.

A second major comment is that the early sections of the paper could be aided by some sort of stage-setting schematic or table on the MIPAS retrieval steps and the potential error sources considered at the various steps. While the specific details of the retrieval system are documented elsewhere, a high-level summary of the steps of this complex retrieval system would aid understanding.

Some specific comments by section are provided below.

2. Definition and notation

• The specification of the notation is useful at this early stage of the paper. It might be worth mentioning that the regularization matrix R translates to the inverse of the a priori covariance matrix in the optimal estimation nomenclature of Rodgers (2000).

3. Error propagation

• Is there any practical difference between the meas and noise error sources in this work or more generally?
• The final sentence of the section attempts to convey multiple ideas and information and comes across as a bit confusing. It might be better to have two separate sentences that first identify the constituents retrieved in the logarithmic domain including any special cases. The second can simply mention that the error estimates are similarly computed in the logarithmic domain.

4. Terminology

• Regarding the synonymous use of uncertainties and estimated errors, I would agree that this tends to be the case in the remote sensing literature, particularly in the realm of linear analysis of the type in this paper. However, in other disciplines (statistics, uncertainty quantification) with a probabilistic focus on estimation, error is often considered a random variable, a realization of the difference between an estimated quantity of interest and its true value. Uncertainty is a description/summary of a distribution (e.g. standard deviation), which may be a distribution of errors.
• In the final remarks on headache errors, the authors mention that these will be catalogued appropriately as systematic or random errors. Would it be expected that part of the “headache” induced is that the resulting systematic and random errors from these sources would vary in magnitude across soundings and geophysical conditions?

5. Selected reference scenarios

• This section seems to suggest that error estimates are available for all of the reference classes. Subsequent sections discuss how the estimates are computed, but any mention of archiving the estimates themselves (e.g. in a collection of data files) is absent. The paper and potential user community would benefit from making this connection between the methodology and availability of products/results.

6. Temperature and pointing retrieval

• In the first line of section 6.1, is the retrieval really for a “target gas” in this step?
• In Eq. 8, an inverse is needed with the S_y;noise. The same is true for Eq. 16 in section 7
• What spectroscopic database(s) is/are used in the MIPAS retrievals?
• In this section and others, the text sometimes reads “1sigma” and uses the Greek letter in other places (e.g. 6.3.3. versus 6.3.4). This should be checked for consistency.

7. Trace constituents retrieval

• The remarks on separate versus joint propagation of temperature and pointing errors in 7.2 (line 426) and 7.2.1 (line 438) seem to contradict each other. I suspect there is a subtle distinction between the error sources in these two paragraphs, but that should be clarified.
• Line 602: does the bold 1 symbol represent the identity matrix? Also note that S_a is the a priori covariance if not previously defined.

9. Case study

• Are there further details available on the Kiefer paper in preparation?

10. Representative error estimates

• This section describes a number of post-processing steps that could provide additional insight to the error estimation procedure, but no further results are presented. Some illustration or example of these procedures would be useful here.

11. Aggregation

• More information on the decomposition of random and systematic errors would be welcome here. Without them, this section does not seem to add much to the paper.

13. Conclusion

• The conclusion could use further discussion about what information/resources are available to data users resulting from this work (e.g. software, supplemental data products, if any).
• Further context would also be useful in the conclusion. Validation studies are mentioned, but do any of these currently exist? Has there been previous error assessment work presented for previous retrieval product versions?