The manuscript presents a method to "interpolate" the aerosol extinction coefficient between measurement wavelengths based on data from SAGE III.  The manuscript is well-written, and concerns an important topic of how aerosol extinction datasets that are natively on different wavelengths can be harmonized.  The method isn't perfect, but it is a marked improvement over simply using the angstrom exponent or assuming a specific particle size distribution.  I recommend the manuscript for publication after a few issues are considered. Comments follow below.

General Comments

The manuscript deals with an important problem and provides a lot of useful analysis on the SAGE III data, but in my opinion motivation for the project and how these corrections are intended to be used needs to be expanded upon.  I believe the main motivation for this work is so that SAGE II can be brought to ~750 nm for CREST/GLoSSAC, but this is never explicitly stated.  I understand the authors wish to present a general technique, but many choices made by the authors are directly motivated by this specific application (e.g. the AE wavelengths, correction factors only given at the SAGE III wavelengths) chosen, and unless the reader knows this beforehand it can be hard to follow.  As a reader I cannot think of another application beyond this at least for the current instruments we have, if the authors have other applications in mind they need to be explicitly stated.  To be clear, I believe the conversion of SAGE II is a very important application, but the authors should provide concrete (rather than vague) examples of how this work is going to be used early in the manuscript to help the reader understand the authors choices.

Specific Comments

p. 2 l 40 "The only assumption used in the retrieval is that the “aerosol spectrum” (i.e., extinction as a function of wavelength) should be slowly varying in almost all stratospheric conditions"

- The authors probably mean the only assumption on aerosol microphysical parameters or something similar since there are many assumptions made in the SAGE III retrieval. 

p. 3 l. 55 "For this study AE is evaluated using the 520 and 1021 nm channels as this is one of the most common pairs for evaluating the AE using SAGE data"

- Going back to my general comments, on the first read through I did not pick up that here SAGE is meant more generally, i.e. for SAGE II. And as far as I can tell this is the only hint so far as to what this correction is actually going to be used for at this point.

p.3 l.63 "since at lower altitudes the signal in this channel drops significantly from molecular scattering..."

- The same dip is also visible in the highest altitude in the picture (23 km) during the Hunga-Tonga eruption, so it can be caused by molecular scattering or large aerosol optical depth. For the Hunga-Tonga time period in particular, is it possible that the signal due to direct forward scattering is no longer insignificant as assumed by SAGE III?  

p.4 l 85 "The 1 km buffer is meant to avoid any field-of-view or smoothing effects."

- Has the SAGE III data been post-processed with one of the standard altitude smoothing filters?

p.6 l 135 "extinction of the sun"

- Does this mean the solar only spectra that is used for normalization?

p.8 l 179 "it seems that theoretical Mie-based corrections for the AE 180 interpolation bias are smaller than, though still fairly consistent with, those derived here from SAGE III/ISS measurements."

- This should be expanded upon. Mie scattering is the fundamental physics behind these errors, are you saying that these previous corrections did not include some factor (large enough particles, correct composition) or are you saying that there is a potential bias in the SAGE III extinction spectrum? I'm sure as the authors know, there are a few recent studies on deriving aerosol microphysical parameters from SAGE III extinction spectra, this could have implications for that.

p.9 l 188 "Repeating this analysis for multiple channels provides slopes and intercepts of this behavior that can be used when converting aerosol from other instruments when measurements of the desired wavelength are not available. ..."

- Here and the rest of the paragraph is when the motivation for this work is given, some of this information similar needs to be in the introduction/abstract.

p. 9 l 196 "In theory, this work could be repeated using other possible wavelength pairs to compute the AE such as the combination of 756 and 1544 nm."

- I understand the author's desire to present a general technique, but do the authors have another application in mind besides converting SAGE II using the 520/1021 AE? 

Technical Corrections

Entire manuscript-> In many cases the units for extinction are missing

The paper "An Empirical Characterization of the Aerosol Ångström Exponent Interpolation Bias using SAGE III/ISS Data" by Damadeo et al. covers an important topic of uncertainties which arise through recalculation of aerosol extinction coefficient using an Ångström exponent (AE). Using SAGE III occultation data, authors show an extent of those uncertainties for a wide array of aerosol loading conditions. They also derive a relationship to correct for these uncertainties using the 520 nm and 1020 nm channels to obtain the 756 nm aerosol extinction values and compare to the measured by SAGE III 756 nm extinction as the true value. Overall, the paper presents a very important problem in aerosol community offering a solution and would be an important publication for a wide array of stratospheric aerosol applications, not only limited to long-term records like GloSSAC and CREST, but also to everyone who tried to compare products from different satellite instruments provided on different wavelengths. However, the manuscript in the current form has a few points of major and minor concern. I will be happy to recommend the paper to publication once these points are addressed. Please see below for details and suggestions. 

Major comments

1. A lot of information and motivations seems to be omitted in the text and it is implied that reader knows that information or assumes from the context. As a result, it makes the paper very hard to comprehend, in particular on the first read. A few examples:
   
   a)  In discussion of Fig. 3 and Fig. 4, neither of which are not temporally resolved, authors mention Ambae (p.6, l. 117) and Tonga (p. 8, l. 172) eruptions, which is implied that the reader knows of the magnitude of the aerosol extinction and AE and can easily identify them at the extinction/AE plot. While Tonga eruption was extraordinary, I doubt that even stratospheric aerosol specialists will be able to point that eruption on those plots. On the other hand, Ambae eruption was large, but there were other events which were of comparable magnitude during SAGE III operation time (e.g., 2019 Raikoke eruption), so again, on the 2D extinction/AE histograms these eruptions are extremely hard to identify. As a solution I suggest to either specifically circle those regions on the plots or provide the extinction and AE value ranges for these eruptions.
   
   b)  Another example, relates to the knowledge of occultation technique. In the first sentence of Sec. 2 it is mentioned that occultation technique "intrinsically provides vertical profiles of extinction data", which is absolutely true; however, a little more information on the technique should be given. If authors are concerned about the length, then at least some references should be provided.  
   
   c)  I couldn't find explicit information on the the extent of altitudes used for Figs. 2-5 (and as a result for Eq. (2)). Based on the text of the whole paper, I assume it is some range between surface and 17 km as the lowest border and 45 km as the top since clouds and small particles above Junge layer are discussed. Please, provide this information since it is extremely important for interpretation of the results.   

2. Maybe this comment will arise from the previous, but I did not quite understand the purpose of the discussion of the regions A-C in Sec. 2. While it is nice to see why people did what they did in the conference talks, here this part makes the paper unnecessarily long and harder to read. As far as I could tell the outcome of almost two page of the description of regions A-C is: the clouds, tropospheric aerosols and data with large uncertainties were filtered out (actually through region D, not through region C). Clouds are a known problem in the stratospheric aerosol retrieval community (cited in the paper Rieger et al. (2019), Kovilakam et al. (2023) or any other paper on stratospheric aerosol retrieval). Similarly, justification for not including tropospheric data could be summarized more briefly. While I might be wrong in my interpretation of the importance of this part, in the current form in my opinion these two pages could be summarized in a couple of sentences without lengthy descriptions. If authors agree with this comment, but would like to keep the descriptions, they could move them into supplement, otherwise context needs to be provided.

3. While the derived Eq. (2) is highly important, and I anticipate it to be used by many, I think the discussion of its transferability and limitations needs to be included. Few things come in mind:  
   
   a) Related to the last bullet in the first major comment is the formula independent of altitude, or is there a specific altitude range where it can be used? Or only low threshold on the extinction coefficient mentioned at p.9 l.195-196 matters? Is there an upper threshold?
   
   b) This formula was derived for 756 nm from 520/1021 AE. Is this formula transferable to the other instruments (e.g., SAGE II, SCIAMACHY) which operated at the same wavelengths but under different stratospheric conditions? Can it be used for occultation or it is applicable to limb scattering instruments too? 
   
   c) While the formula was derived for the SAGE III data, would it be the same if calculated with Mie theory using a plausible range of particle sizes (e.g., using the cited in the text Wrana et al. (2021) product)? There is a discussion about the other authors getting much lower uncertainties with Mie theory (p.8 l.168 - p.9 l.185) using SAGE II, but I was wondering why is that so?  Is it because the assumption on the unimodal log-normal distribution made by Rieger et al. (2015) and Malinina et al. (2019) is incorrect (possible, and that would be an important statement)? Or is it some sort of SAGE III instrument-specific feature (which is also possible)? Maybe it does not make sense to compare directly with the other authors' results, but it is quite feasible to do this simulation for SAGE III.
   
   
   
   While I understand that covering all those point in details might be enough for another paper, at least acknowledging those issues would be crucial for the formula's future application. 

Minor and technical comments

1. Throughout the text the term "aerosol(s)" is used as a substitute term for "stratospheric aerosols" and while for certain contexts it is fine (p.4 l.81), in some it leads to misleading statements (e.g., p2. l. 30-32). Please, correct throughout the text. 
2. P.1 l.23. "aerosol spectrum" is a jargonism, it is defined at p.2 l.41. Either define here, or change to "extinction as a function of wavelength" or similar.
3. P.2 l.30. Please, add "space-borne" before instrument and "stratospheric" before aerosol. Otherwise, you summarize even over such measurements like AERONET (Holben et al., 1998) for the total column.
4. P.2 l.41. It is not obvious what you mean under "should be slowly varying in almost all stratospheric conditions".
5. P.2 l.53. Malinina et al. (2019) cited in this paper a few times showed that the AE on one wavelength pair is not an indicator of particle size. Please rephrase this statement.
6. Fig. 1, please add years of the eruptions and wildfires.
7. P.3 l.61-62 vs Fig. 1. From what I can tell from the Fig. 1, the "dip" is not always an artifact with bias being present just in half of the shown spectra, which indicates that there is some information in there. Can you please elaborate? 
8. P.3 l.69. I would list the instruments with the retrieved products at 750 nm. 
9. P.4 l.86. Technically, in Fig. 3 you show log(k_{756_meas}).
10. Color bars labelling in Figs. 2-5 is needed (I assume it is probability density). 
11. P. 8 l. 172: "Tonga aerosol" is a jargonism. Also, please, use consistent naming for the volcano (in Fig. 1 it is "Hunga-Tonga").  Maybe, "aerosols after the 2021 Hunga-Tonga eruption"? 
12. Section 5. Please, update based on the major comments on limitations.

References

HOLBEN, Brent N., et al. AERONET—A federated instrument network and data archive for aerosol characterization. Remote sensing of environment, 1998, 66. Jg., Nr. 1, S. 1-16.