Dear authors,

Congratulations on this comprehensive analysis and well-written paper. It was a pleasure to review this work. Error/uncertainty characterisation of satellite retrievals is more and more gaining the attention it deserves, and this paper clearly demonstrates the way to go about this. It is (almost, see below) complete in terms of identified sources of errors, and the propagation using numerical  techniques ensures sensitivity to those tricky situations where random errors turn into systematic contributions. 

The only source of errors I did not see addressed is that related to horizontal smoothing: if the actual sensitivity is not centered on the tangent point (and the atmosphere is inhomogeneous) this will lead to additional errors/uncertainty. Addressing this is not trivial (you'd need horizontal AKs and a 3-D model of the atmosphere, e.g. from a reanalysis), but it has been done before, e.g. for MIPAS on ENVISAT(von Clarmann et al., AMT, 2009, and application in Cortesi et al., ACP, 2007). I think this deserves to be at least mentioned.   

That said, my other comments are all minor. See below for the list.  

Again, congratulations for this work!

A Referee

-------------------------------------------------

Abstract:

- Maybe add a few words on the impact of the cross section source? 

Intro: 

- I'd reorder the arguments for the importance of the error characterization: foremost, correct uncertainty estimates are needed to ensure correct geophysical interpretation. Only in 2nd order are they important in the validation. Actually, the validation should validate also these ex-ante/prognostic uncertainty estimates (as you do). 

- Can you not create a short reference, e.g. Rault and Loughman (2012), hereafter RL12. And then change "The authors" into "RL12". To be checked against the AMTD style guidelines.

Sect 2: 

-I guess there is also an official NASA retrieval that deserves to be mentioned before presenting the Bremen retrieval? Or is the Bremen retrieval the official product? 

-The SNR is in principle something to characterize random noise. But perhaps you see systematic features in the residuals? How are these accounted for?

- out of curiosity: how does your vertical resolution estimate compare to actually measuring the FWHM of the AK row? No need to invest much time in this, as you wish. 

Sect 3: 

- if I understand correctly, you first derive a SNR from the residuals and then use this as starting point for the Gaussian generator, forcing the input errors to have a normal distribution. Could you not take the actual residuals (of many retrievals) as a distribution to draw (randomly) from? That way, you'd also propagate potential systematic effects, no? 

Sect 4:

- errors on these parameters can all be assumed to be random?

- pointing errors: out of curiosity: is there any drift in the platform that would lead to a systematic but slowly changing pointing error that could cause a long-term drift in the retrieved profiles?

Sect. 5:

- line 278: by "changing the used cross section", I guess you mean the source of the cross sections? For clarity, I'd rephrase to "cross section source" or "cross section database". This also needs to be changedin line 280.  

Sect. 7:

- Eq. 11: you're entirely confident that they are all independent? Intuitively, I would agree. But maybe this assumption needs to be made explicit. EDIT: I guess Fig 13 demonstrates that they are not independent. What does that mean for Eq. 11?

Typos:

- abstract, line 3: complaint -> compliant

- line 36 (Sheese et al. ref): \cite -> \citep

- line 70: increases -> decreases; up to -> down to

- line 92: parameters -> parameter

Review of:

Assessment of the error budget for stratospheric ozone profiles

retrieved from OMPS limb-scatter measurements

by Arosio and colleagues.

----- General comments

This is a nice solid paper that does a thorough and robust job of

quantifying the uncertainties associated with the Bremen group's

retrievals of ozone profiles from the OMPS-LP instrument.  My comments

are only minor.  The discussion is generally very clear and well

motivated.  The language and graphics are both of very good quality.

I'm very happy to recommend this paper for publication pending the

minor corrections that I detail below.  I do not feel a need to review

an updated version (but clicked on the "willing" button if the editor feels

another read through is needed).

----- Specific comments

Line 2: I think the mission is now called the "Suomi National

Polar-orbiting ..., Suomi NPP", right?

Line 3: I suggest rewording as: "The error characteristics are

presented in a form that is compliant with ...".  Note the spelling

error on compliant (you have "complaint").

Line 8: Suggest rewording start of sentence to: "We have classified

the various different error..."

Line 11: You have a short hyphen (single "-" character in LaTeX) for

the first (3-50%) range, but longer ones ("--" in LaTeX, which are more correct) for

the other two.   Modify the first to be consistent/correct.  There

were some other examples of this issue elsewhere in the paper.

Line 12: "related" -> "due"

Line 13: saying both "absolute value" and quoting a percent (which

many would see as a "relative value" is confusing).  Please clarify, do

you mean abs(error) - to use programming terminology? - expressed as a

percent?

Line 13: What above between 20 and 50 km, would be good to quantify

that in abstract too.

Line 18: Insert "Suomi"before "National"

Line 26: "was in the meantime" -> "has since been"

Line 41: Put commas before and after "as in von Clarmann et

al. (2020)"

Line 43: Would it be better to insert "mainly" before "contribute"

here?  I leave it to you.

Line 55: Suggest inserting "in Sect. 2.1" after "instrument" for

better flow/consistency.  Then insert "of" before "the retrieval

algorithm" and delete "given"

Line 70: Suggest "increases" -> "coarsens".  "Increased" resolution

sounds good from an English perspective, but is worse from a numerical

perpective if quantified in terms of a length.  (Similarly

precision/accuracy.  I generally advocate saying coarser/finer and/or better/worse

rather than more/less for all such terms to avoid ambiguity).

Line 81: Delete "what concerns"

Line 86: "... and are preconvolved with the OMPS-LP instrument line

shape" ("are beforehand" is awkward wording).

Line 90 (and 95): Not being familiar with UV/Vis instruments, I hadn't

understood/remembered that the Chappuis bands are not in the UV.  Thus

this paragraph was very confusing to me (is the shift and squeeze

included or not?).  I suggest you make that clearer by pointing out

that the Chappuis bands are in the visible spectrum).

Line 91: "tells" -> "suggests" or "implies"

Line 94: Not sure what is meant by "differential absorption" here, I

presume you mean fine-scale spectral structure, but it's not 100%

obvious.  Saying "differential" could mean from TH to TH. Please

clarify.

Line 109: Suggest you delete "percentage" and then add ", expressed as a

percentage of the true profile," after "reported" on the next line.

Line 118: Not clear what "actual" means in this context.  Does it

refer to the spacing of the levels in the state vector?  (I forget if

that was discussed anywhere in the paper).  If so, then I'm not quite

sure how the UV vs. Chappuis comes into it, so perhaps that's a bad

guess on my part.  Please clarify.

Line 131: Some inconsistency here, this discussion of the Gaussian

generator and the multiplication by the SNR discussed in line 133

suggest that these "noise sequences" are Normal(mu=0, sigma=1).

However, the caption for figure 3 states that the lower panel is

showing the "noise sequences" too, and these clearly have sigma

smaller than 1.0.  Not a big deal, I'm sure everything's been done

correctly, but make the terminology consistent between the text and

the figure caption.

Line 132:  "Simulated spectrum" may be unclear here, as we're still

dealing with real OMPS data, right, not the radiances corresponding to

a modeled truth.  Perhaps "fitted" might be better for this particular

sentence, rather than "simulated"?

Line 134: Suggest you say 50 rather than N here, for consistency with

earlier in the sentence (some may forget that N==50).

Line 136: "profile" -> "profiles" or "a first guess profile"?

Line 137: Clarify "unperturbed" here.  It's clear to me that you mean

you have yet to do any perturbations associated with parameters,

calibration, spectroscopy etc., but readers less familiar may be

confused as your 50 noise sequences are themselves perturbations.

Line 143: insert "is" between "what" and "ideally"

Line 143/144: "This feature" is vague - is it the point discussed in

the preceding sentence or the whole of this paragraph.  Please

clarify.

Line 156: Suggest you change "shift-squeeze" in the math symbol to

"shift&squeeze" to avoid confusion with a minus sign (\& in LaTeX).

Also, the kerning for this and other things (e.g., "param", "fix",

etc.) is wrong because you're in math mode.  Suggest you use, e.g.,

$\sigma_{x, \text{shift\&squeeze}}$ (needs amsmath.sty) or,

$\sigma_{x, \text{\textit{shift\&squeeze}}}$ if you prefer.  And

similar for others.

Line 166 / Table 2: For completeness/clarify you should state what

these numbers convey.  Are they ranges? 95% confidence intervals?

1-sigma (which is what I assume the are, from the contex), 2-sigma?

This then impacts the interpretation of the resulting O3

uncertainties.

Line 168.  The sentence here feels like it belongs at (or near) the

end of the paragraph rather than at the start.  Where it is now, it

interrupts the flow of discussing the input parameter uncertainties.

Line 186: Suggest adding "radiance" before "noise" to remind people

what you mean here.

Line 187:  I wonder if the superscript "n" might not be better as an

"i"?  In any case, it should be defined.

Equation 7: I can sort of see why you call this a sigma rather than a

delta, but it looks like it should be the latter from the definition,

so take some time to explain to the reader why you're not labeling it

as a delta.  Indeed, it might be easier to explain if you talk about

the Monte Carlo approach first rather than second.  Then this

delta-like parameter becomes an estimate of the associated sigma from

the MC approach.

Line 214: "are going to be" -> "will be".  Also, end of line change "fix" to

"fixed".

Line 215: "... and conveys information on the relationship between the

sign of the parameter perturbation and the sign of the consequent

ozone perturbation."

Line 224: Would be good (here or somewhere else) to point out that

you're changing Temperature at all heights by 2K, not just one height

(or each height in turn, right?).  Indeed there are multiple

temperature, pressure, TH, and aerosol perturbations that could be

made, but only one albedo one, correct? (Though hydrostatic balance,

if you're imposing that, reduces the degrees of freedom for

Temperature/pressure/TH perturbations) Perhaps discuss this more, and

explain why you didn't consider more complex (i.e., height-dependent

perturbations).

Figure 5 caption, line 2, insert "in the top and bottom rows, " before

"respectively".  Also, delete "- like" after "Monte Carlo"

Line 282: "It has to be taken into consideration that" -> "It should

be borne in mind that"

Line 284: "On the contrary" -> "In contrast"

Line 285: "less" -> "fewer", or "a narrower range of" if that's a

better description.

Line 437: "exemplification" -> "example"