This article introduces a systematic approach for constructing a Look-Up Table (LUT) aimed at estimating stratospheric aerosol particle size parameters. The summary below simplifies the main points of the paper and includes some suggestions.

Theoretical Study:

 A theoretical investigation was carried out to assess the methodology's efficacy and correctness. Simulations and analyses were conducted to evaluate the algorithm's capability to infer particle size distribution parameters under various scenarios and degrees of uncertainty.

Application to SAGE Data and Case Study:

The designed solution algorithm was tested with real data from the SAGE II and SAGE III/ISS instruments, subjected to real-world circumstances. A brief case study analysis of the 2022 Hunga Tonga eruption utilized the algorithm to examine the associated data. Similarly, the algorithm was applied to various volcanic and wildfire events during SAGE II and SAGE III/ISS, and the results are also presented.

Through statistics, comparisons are presented to support the findings. To put it briefly, the work primarily makes use of assumption-driven mathematics and comparative statistics. There are no questions regarding the results because the conclusions are predicated on assumptions established during computation.

I just have a few suggestions:

Structural Suggestion:

“Characterization of Particle Size Distribution Uncertainties Using SAGEII and SAGEIII/ISS Extinction Spectra"

1. I believe the title should be revised, adding “Characterization of Stratospheric...".
2. The affiliation list for the third author, 2,1, seems odd. Switching it to 1,2, if it is associated with both institutes, appears more appropriate.
3. Is this approach not a revisiting or improvement of Wrana et al.'s Stratospheric Aerosol Size Distribution Retrieval from SAGEIII/ISS?
4. Some of the figures below Figure 7 could potentially be suitable for the supplementary section.
5. Section 2.1 seems like a less significant subsection.

Yes, the computational strategy remains a fundamental aspect of data loading, processing, and modeling. In open science research, limitations in computational resources should not serve as excuses for achieving suboptimal results. Nevertheless, it is ultimately up to the authors to decide what they choose to present.

Line 44: The challenge of performing “traditional” ????

Some comments or questions about the assumption made:

As I've pointed out, the results with various adjustments are presented effectively. The method's usefulness is another aspect to consider.

In this context, I am highlighting the assumptions made:

Line 85:

"65%, 70%, 75%, and 80% sulfuric acid by weight.”

At what conditions are all these propositions of sulfuric acids present in the stratospheric aerosols?

75% is conventional acceptance for background aerosols. May be going up to 90% just after significantly impactful volcanic eruptions makes more sense, especially when SGAE signals are not penetrating below tropopause or so.

Do the black carbon and brown carbon are uniformly present in the stratospheric aerosols? If so, is the Mie theory still suitable for this situation? Yes, the possibility of the existence of absorbing aerosols may be considered, but it is not guaranteed solely based on sporadic occultation extinction.

Also, "65%, 70%, 75%, and 80% sulfuric acid by weight.” So, what constitutes the remaining fraction of water vapor, black or brown carbon, or unknowns?

Also in line 250: “H2SO4 is typically assumed to be 75%.”

It seems appealing to use black or brown carbon, but it cannot ignore the complex chemistry in the stratosphere at higher temperatures and shorter wavelengths of radiation, as well as the ozone at its maximum. So, we need to be mindful while making such arguments with limited resources.

Line 148: (0.3±15%,1.2±10%)

It should be explained: the basis of 0.3 and 1.2 to be selected as representative and any reasoning for selecting these two ratios. Is there any information provided by these ratios (just an arbitrary random number or something else)?

Shorter wavelengths (448 nm) are susceptible to the other molecules. So, the ratio obtained by using them is reliable and consistent?

In Figure 5 (a),

The ratios on the x-axis place the larger wavelength's extinction in the numerator, while on the y-axis, the smaller wavelength occupies the numerator position. If there's no specific reason for this arrangement, it might be more consistent to use the same approach for both ratios and incorporate their respective values unless there is an otherwise to do otherwise.

Same also in line 240 (#5, #6, and #15) from table 3 applied further.

Lines 459 and 499: The cloud is filtered.

The aerosol product is already cloud (opaque) filtered. Is it not? (SAGE III/ISS documents suggest that.) Don’t we miss out on the fresh, larger particles after the eruption during cloud filtering? Did your results show a significant difference between cloud-filtered and non-cloud-filtered?

Typo:

Figure 15 caption: last line: “(i.e.,k1020/k1020≤1.4)”

The paper describes a new algorithm to retrieve particle size distribution (PSD) parameters from SAGE II and SAGE III/ISS extinction ratios using a look-up table approach. An advantage of this algorithm is the provision of a statistical representation of the solution space for uncertainty estimation. The authors evaluate the retrieval accuracy in terms of the PSD parameter range, channels to be used, the uncertainty of extinction ratios, the sulfuric acid content, and the presence of smoke and a second PSD mode. A general overview of PSD values retrieved from the entire SAGE II and SAGE III/ISS record is given with a brief case study of the Hunga-Tonga eruption. The paper is written clearly and comprehensibly. I recommend it for publication after a minor revision.

Page 1, line 6-8: although a short abstract is appreciated, some results/conclusions to both general headings would be worthwhile.

Page 2, line 44: What does “traditional” mean?

Page 2, line 46: “through hundreds, sometimes thousands, of kilometers”? How do these figures come about?

Page 2, line 50: typo: “that 35%” → than 35%

Page 4, line 91: “by multiplying Qext with … P” → cross sectional area is missing (pi r²)

Page 4, line 93: “rm is the mode radius” → It is not the mode radius, it is the median. Although the authors make this clear, it would be desirable to stick to the correct convention rather than the “common” naming. This would help the readers, provide 100% clarity, and prevent misunderstandings in e.g., interpreting the figures – especially when the additional information in brackets(!) is inadvertently overlooked.

Page 4, line 97: typing error: “... mode radius,and ...”

Page 4, Equation 2: Maybe also include the term required for the bimodal distribution?

Page 5, line 107: Probability of what?

Page 5, line 111: “one” can infer...

Page 5, caption Figure 2: typing error “selected SAGE”

Page 5, line 116: Please provide the definition of distribution width for clarification.

Page 5, line 119-120: “if the desired accuracy for k is 1% for all channels then rmax must be > 525 nm when rm=70 nm, >1um for rm=150nm, and >2.4 um when rm=500 nm.” 1) typo at the end of the sentence: “)”. 2) I cannot see this statement in the Figure. Do you mean an accuracy of 0.1%? An accuracy of 1 % is already achieved with lower rm values than specified.

Page 7, Figure caption 4: “typical background particle size (75 nm).” → This value is rather low for a typical background value.

Page 7, line 138: “The necessity of using extinction ratios, as opposed to extinction coefficients, for eliminating the influence of number density (N) and inferring aerosol physical parameters has been discussed previously.” → This information should be given earlier, maybe already in the introduction?

Page 7, line 148: +/- 15%, +/- 10% → Where do these uncertainties come from?

Page 9, line 186: typo: “can be can be”

Page 13, line 233: insert “#” before conditions #5 and 6.

Figure 8: Why does the fraction decrease when errors > 20 % are removed? I would assume the opposite case: The more accurate data in a data set, the more valid results. What exactly is the denominator of the presented fractions?

Figure 8: I can clearly see a distribution of the fraction. However, I can hardly distinguish between fractions smaller than 0.7 (line 226) and larger than this limit. Maybe the authors could use a stronger color gradient?

Figure 9: Maybe the authors could show this Figure before Fig. 8?

Page 14, line 245: What are “challenging aspects of real-world aerosol compositions and PSD parameters”? Please specify.

Page 16, line 264: Please give definition of SAD and VD.

Page 19, line 296: Please specify used UWY OPC data set (e.g. time frame, location, number of profiles, influence of volcanic aerosols, …)

Sec. 4.4.2 – 5.3: I am not convinced that one can compare the PSD parameters of the first mode of a bimodal distribution with the parameters of a monomodal PSD and draw conclusions about the quality of the retrieval. E.g., page 24, line 389: “though r2 was underestimated by ~ 90%.” How can something be underestimated if the reference does not even exist? PSD parameters of a bimodal curve and PSD parameters of a monomodal curve are completely different things. In this case, comparisons can only be made on the basis of integrated parameters (SAD, VD, re).

Figure 12: How is N retrieved?

Page 21, line 328: “was not unexpected” → was expected

Page 21, line 335: typo: r1=, sigma1=, r2=, sigma1= → sigma2

Figure caption 13: Please specify OPC record.

Page 30, line 478: “1. … ,2. ….” → First, …., second, …

Page 30, line 484: “PSD estimates are reasonable” → What is this statement based on?

Page 31, line 495-499: Do the authors see a “jump” in the retrieved data when they change the conditions within the retrieval?