General Comments

The manuscript entitled „Troposphere – stratosphere integrated BrO profile retrieval over the central Pacific Ocean” by Koenig et al. presents a novel retrieval algorithm for the simultaneous determination of tropospheric and stratospheric trace gases and aerosols from MAX-DOAS measurements performed on mountain tops.

Knowledge on the composition of the atmosphere, in particular in the upper troposphere and stratosphere, is crucial for the understanding of the atmospheric chemistry and its impact on climate. MAX-DOAS measurements provide a simple and cost-effective way to retrieve information on the vertical distribution of atmospheric trace gases. The mountain-top based MAX-DOAS system presented here allows for gaining enhanced information on the UT/LS region. The authors describe novel and improved retrieval methods, and the subject of the manuscript fits well into the scope of AMT.

The level of agreement of modelled and measured diurnal variability of dSCDs is impressive, indicating that the retrieval is modelling the atmospheric radiative transfer realistically. However, I find it difficult to understand the principal approach of the so-called “Time-dependent retrieval”, and I feel that the respective section 2.5.3. requires substantial revision as detailed in the specific comments.

The abstract is too long and should, as an AMT contribution, focus more on the retrieval algorithm itself than on the chemistry of the UT/LS region, for which far too many details are provided.

Specific Comments

L13: The term “trace element” is not appropriate for bromine since it has an impact on atmospheric chemistry not only in its elemental form.

L76: It would be good if you would be more specific regarding the exploitation of the “sun motion” (i.e., increase in light path with increasing SZA).

L149: It is possible to fit certain parameters or state/measurement vector elements, but it not possible to fit “degrees of freedom”. Please specify what is fitted here.

L161 and thereafter: What do you mean with the term “principal program”? Are the RTMs not just programs?

L177: Can you give an estimate how large the errors are if the atmosphere below the instrument is not considered in the DISORT model? Can this simplification be justified?

Section 2.3.: Please explain why you use two different RTMs in a single retrieval algorithm. This is a quite unusual approach. McArtim is capable of modelling both tropospheric and stratospheric radiative transfer also during twilight, so it is not clear what the advantage of using DISORT is.

L195: It is not clear what you mean with “layering approach”.

Sections 2.5.1 and 3.3.3: Is there a specific reason why SCD_ref is not simply retrieved as part of the state vector in the optimal estimation algorithm, instead of using Langley plots as an extra step?

Section 2.5.3 requires substantial revision as it is not possible to understand what the actual approach is. What is the basic idea behind your approach? What is the difference between time-dependent and time-independent retrievals? The term “time-independent formulation” occurs in L291, but it is not explained anywhere what this means. What is the exact meaning of the mathematical objects in Equation 3, which of these are scalars, vectors or matrices, and what are their shapes/dimensions? Does the vector x contain profiles at a single time or are BrO profiles over a period of time which are retrieved simultaneously? What exactly is x_0 and how is it determined? Please specify in detail the individual components of the measurement vector and the state vector.

Eq. 4: It is stated that H represents a Jacobian, but H = K_0*x is not a Jacobian Matrix but a vector in measurement space.

L317: I suppose the “high concentrations” of BrO are expected in the FT. Please specify.

L354: Cross-sections do not have an optical density. Please rephrase.

L357: To what is the Aliwell fit window insensitive?

L363: Is a wavelength shift of 3 pm leading to any noticeable difference in the fit if the instrument has a spectral resolution of about 0.5 nm?

L376: Please explain why the O4 scaling factor should scale with lambda^4 like Rayleigh extinction. I do not see an immediate physical reason for this.

L382: Please explain what you mean with “intensity effects”. Could this be instrumental non-linearity? If you suspect that NO2 is affected by such effects, then why not other trace gases, in particular if they have lower optical density?

L395ff: Here it is not clear what you mean with the terms “component” and “signal”. Do they refer to the retrieved dSCDs or to the fit residuals? What exactly are replicate measurements? Do you mean subsequent measurements along the same line of sight?

L564: A “change” has no DoF.

L635: Here it would be good to cite Rodgers and Connor [2003].

L640: In what respect is the analysis limited by the RTM calculations? In terms of accuracy? Computational time?

L643: To my knowledge, McArtim already fulfils the required capabilities listed here – see Deutschmann et al. [2011].

Please add a “Code Availability” section stating the availability of the retrieval algorithm presented here.

Technical Corrections

L30: near -> nearly

L56: “BrOx adds radical species to oxidative capacity” does not make much sense. Suggestion: “BrOx increases the oxidative capacity”

L106: I guess you mean the azimuth angle when you talk about “primary viewing direction”?

L123: What do you mean with the dagger symbol as prefix for the elevation angles?

L175: Stratospheric aerosol WAS modelled…

L189: Tropospheric aerosol WAS assumed…

L190: Approximated by an approximation?

L194: Add “The retrieval of” to the beginning of the sentence

L393: The term “method-based anticorrelation” is not clear to me.

L404: The part of the sentence after the semicolon is without any context.

L409: I suggest to add that the additional HCHO absorption feature is at 330 nm.

L497: comparison -> difference

L506: “While it is clear the retrieval … can be further improved” is grammatically incorrect. Is a “that” missing?

L585: Explain abbreviation “KOA”.

References

1. Deutschmann et al., “The Monte Carlo atmospheric radiative transfer model McArtim: Introduction and validation of Jacobians and 3D features,” J. Quant. Spec. Rad. Trans., vol. 112, pp. 1119–1137, 2011, doi: 10.1016/j.jqsrt.2010.12.009.
2. D. Rodgers and B. J. Connor, “Intercomparison of remote sounding instruments,” J. Geophys. Res, vol. 108, no. D3, pp. 4116–4229, 2003, doi: 10.1029/2002JD002299.

“Troposphere – stratosphere integrated BrO profile retrieval over the central Pacific Ocean” by Koenig et al. utilizes a mountaintop DOAS to retrieve vertical profiles of BrO throughout the troposphere and stratosphere in the Central Pacific. This method utilizes an elevated MAX-DOAS instrument to increase sensitivity to large portions of the atmosphere and builds on previous BrO observations in the Western and Eastern Pacific. This manuscript also develops a novel approach to BrO differential slant column density retrievals to increase the stability of their observations. The paper also discusses the development of a time-sensitive vertical profile retrieval. These methods help to better understand the amount of BrO in the background free tropophsere and other often unobserved areas of the atmosphere with utility for anthropogenic pollution monitoring in large cities.

Ultimately, this is an important work that would be beneficial to extend to other areas. However, some specific information on the retrieval methods is under-described or omitted. Similarly, the mathematics of the time-dependent retrieval are not well defined. The method described here would be difficult to reproduce based on the current state of this paper. The “Results and Discussion” section also skews too much toward discussion and omits some important results, which should be more of the focus in this work.

Major Comments:

The BrO fit routine seems somewhat arbitrary. I understand using a fit that results in less negative BrO values, however it is also important to discuss how the fit uncertainty is affected by these decisions. Similarly, it is not mentioned if the negative values retrieved for some specific elevations are outside of the retrieval uncertainty. If not, then the BrO fit constraints seem like they may not be necessary. I am also somewhat concerned that two of the fit constraints depend on radiative transfer modelling as this is a source of uncertainty. Similarly, I am wary of constraining three parameters in the BrO fit while also using a quite high polynomial order. Ideally, a sensitivity study would be conducted on how the three constrained fit parameters impact the retrieved BrO dSCD. I understand that this is likely not feasible on your timeline, so I would at least ask for detection limits/uncertainties for the different trace gases (BrO, O₄, HCHO, NO₂). This also leads to another issue. Utilizing just the BrO fit uncertainty for your measurement error covariance matrix likely underestimates the true uncertainty of these retrievals. As I have discussed, there is likely more uncertainty from these sources that is unaccounted for, but the uncertainty of the BrO cross-section should also be considered. Again, I understand it is not possible to update your profile inversions on this time scale, but a more detailed discussion of error propagation would be appreciated.

It is unclear how the aerosol profiles are retrieved for the MT-DOAS observations. It is stated that the difference between measured and modelled O₄ was calculated for each scan. However, it is not clear how this is used to retrieve a particle extinction profile? Is an inversion done for each scan?

I am still unsure how the time-dependent retrieval works. You explain how the Jacobians are determined, but outside of that I am not sure how the retrieval works. I also do not know what the inversion retrieves. It seems that the inversion retrieves x₀ and C^L, but I’m not sure how the inversion retrieves both values. Are two inversions performed, or is only one performed to retrieve both parameters? If so, it seems that the inversion could settle on a local minimum rather than the “true” solution. How is this accounted for? I also do not quite understand what this retrieval tells you, and how you combine the parameters to retrieve a profile. You also state that the retrieval of C^L is particularly sensitive to the apriori profile. Just how sensitive is it, and how confident are you in the apriori value used? I also do not understand the physical representation of C^L, and the choice of apriori described in the supplement seems somewhat arbitrary. It seems that this sensitivity could impact the retrieval uncertainty in a way not accounted for in the output covariance matrices. I also do not fully understand the ramp function. You state that the domain is from -1 to 1, though it seems in practice that it is actually from 0 to 1. I also do not understand how this is tied to the O₃ VCD, particularly since this retrieval is not described. Line 80 also says that this method accounts for non-photochemical diurnal variability. That was not the impression that I got from this method. Lastly, it seems that the utility of this method is that it utilizes the change in zenith retrievals as a function of time, whereas fitting each scan with a local zenith would remove sensitivity to the stratosphere. If this is the case, I feel this method could be motivated a little better.

Minor Comments:

Line 43: The C-shaped Western Pacific BrO profile is only mentioned here and in the conclusion. Considering you compare and contrast with Eastern and Western Pacific profiles later, this needs to be introduced in the introduction and cited here.

Line 74: Define MT-DOAS here.

Line 123-124: I do not understand this sentence.

Line 126: Local time would be preferable. This is later in the morning than what data?

Line 127-128: What are the moving reference analysis and fixed reference analysis?

Line 141: What is the naming convention of the flight segments? Later you use RF01-06 for example. It would be nice to introduce this here.

Line 142: Local time would be preferable.

Line 156: Regarding “full non-linear treatment,” are there limits applied to the shift and squeeze?

Line 168: Why do you specify these SZAs and altitudes?

Line 261-264: It seems like you set the apriori to 50% of the Theys et al., 2009 climatology with a 50% uncertainty above 17.4 km. This would indicate that the climatology value at these altitudes is not within the apriori uncertainty. What was the reason for this choice?

Line 487: Reference the figure at the end of this line.

Line 510: Is this technically 3.2 DOF? I think I may prefer seeing the total DOF of the entire profile here before you break it down into different altitude layers.

Line 561: is 7e13 molecules/cm² correct? I am not sure what this value is, but it is much larger than any other value here.

Technical Comments:

I often think of MAX-DOAS and ZS-DOAS as the instrument itself. I would suggest changing references to the different observations to zenith and off-axis or something similar for clarity (e.g. lines 161 and 187).

RW-DT and RWB seem to be used interchangeably. If this is the case, the text should commit to one name. If this is not the case, the difference needs to be clarified.

Discussion of results is often confusing as a range of values is often given (e.g., line 31, 554, 555, 556, etc.). Are these the ranges from the different scans? If so, why are they not always lowest-largest? These values need a little more context.

Line 305: I am curious how you reduce the apriori uncertainty by a factor of 10 and result in a higher retrieval DOF. Can you explain this?

Section 3.1 does not really contain any results. It may be more appropriate in Section 2.

Was the impact of O₃ reference temperature considered in Section 3.2?

I am still unclear on why AMFs and SCDs were used to constrain HCHO in the BrO fit.

Section 3.3.1 – Low on results. I would prefer discussion of the retrieved profiles including the DOF.

Section 3.3.3 – Is the SCD_ref used to add to the dSCDs to retrieve the BrO profiles with SCDs? If so, this is not entirely clear. Also, the fit routine described here is not entirely clear. It seems like the SCD_ref is used to calculate the AMFs, where the resulting Langley plot is used to determine a SCD_ref. However, the AMF calculation is more dependent on profile shape and the distribution of BrO in the troposphere compared to the stratosphere. Based on the plot, the choice of 2e13 molecules/cm² seems to be the best choice, but the fact that the SCD_ref input results in the same SCD_ref output is not as significant without knowing how the other parameters are constrained.

Line 554-571: These results are difficult to interpret. It is difficult to tell what the ranges mean, and I believe you alter between giving values and changes in values. The section needs to be streamlined to be clearer. For example, I am not sure what line 561-564 is meant to indicate?

Line 592: The plot seems to indicate that there is low measurement sensitivity for the retrieval in the lowest layer of the atmosphere. That would explain the large uncertainty.

Line 628: I’m unclear why you would apply the MT-DOAS AVKs to the aircraft profile. Are you indicating this is how the MT-DOAS would view this profile?

Line 632: Which model predicted a more intense RWB?