Review of the manuscript

"A multimodal approach to derive cloud microphysics in deep convective clouds from polarized measurements of the cloudbow"

by L. Volkmer, L. Dorfer, and B. Mayer

General comments

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The paper describes a new fitting algorithm for analysis of airborne polarimetric measurements in cloudbow angular range. It assumes up to 3 modes in cloud droplet size distribution (DSD), which is an advantage compared to traditional monomodal retrieval techniques. Another advantage of this method is the extended droplet size range, which allows to characterize drizzle and rain droplets. The algorithm was applied to real airborne observations of clouds, and detailed comparison of its results with those of the existing Rainbow Fourier Transform (RFT) method is provided. The comparison shows good agreement in the RFT's droplet size range (which is shorter, so no rain droplets detected by RFT).

The paper is very detailed and well-written, however, some of its important parts require clarification. I suggest to accept the paper after some minor while mandatory revisions described below in line comments.

Line comments

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l.143

In Eq.10 what does the subscript A in f^_A,i stand for?

l.135

Eq.9 was first introduced by Breon and Goloub (1998), so it would be appropriate to cite that paper here.

l.155

Eq.12 assumes that N = 3 without explicitly stating this, while in all previous equations N can be any number. Please, clarify.

ll.157-159

I don't understand Eq.13 at all. If all A_i are the same, then according to Eq.12 A_tot = N*A_i, and f_A,i = A_i/A_tot = 1/N and does not depend on i (while f^_A,i obviously does). Or what is "general scaling factor" _within_ A_i? Please, explain.

ll.169-173

Denoting droplet number concentration by the same letter N that was already used for the number of DSD's modes is confusing. Please, chose different notation.

1.185

Again yet another parameter is denoted by N. I suggest to use subscripts to avoid confusion.

l.195

Lambda should be 1/(2 r_eff v_eff) to be consistant with Eq.6, since variable in Eq.21 is D = 2 r.

ll.256-262

It is not clear what "adding" another mode means. What information from the previous step is retained? If an actual bimodal distribution has, say, 5 um mode and 15 um modes the monomodal fit would return ~10 um mode, that should be split into two on the next step. But if results of the monomodal fit are not used, the bimodal unconstrained fit would be in the space of 6 parameters (3 for each mode) and is likely to be a very ill-posed problem requiring regularization (that is not included in the presented algorithm). Please, clarify.

Fig.9

Panel (a) is not mentioned in the caption.

ll.448-450 and Figs.12-15

While initial RFT distribution may be noisy and include negative values, these artifacts are removed by mode decomposition. The satellite dataset from PACE HARP-2 instrument does not include the initial RFT curve but only mode decomposition parameters (currently for 2 modes). This also significantly reduces the data volume. 

Thus, for "apple to apple" comparison I strongly recommend changing the RFT representation in Figs.12-15 with solid dark-blue curves representing mode decomposition results, while the initial curve may be depicted by light color possibly dashed (or entirely removed). 

Actually, comparisons of multimodal-fit distributions with RFT mode decomposition results look quite good, so emphasizing them would only benefit the paper. Of coarse, due to the limited radius range RFT cannot see rain droplets. 

Also, RFT mode decomposition algorithm rejects any mode with fraction less then 5% (0.05), while the rain modes retrieved by the fitting technique have fractions around 0.01 and DSD maxima so small that they are visible only on the plot with logarithmic y-axis. However, the rainbow curves in (b) panels are consistent with presence of rain droplets. Are there in situ measurements demonstrating that such weak rain modes are real?

Monomodal curves in Figs.12-15 are plotted in yellow and are barely seen on the white background. I suggest using green instead. 

General Comments:

“A multimodal approach to derive cloud microphysics in deep convective clouds from polarized measurements of the cloudbow” presents a new algorithm capable of retrieving up to three cloud droplet size distribution modes over a large droplet size range. The algorithm was demonstrated using data from specMACS during the 2024 PERCUSSION air campaign. The multimodal retrievals were compared to results from the Rainbow Fourier Transfer (RFT) algorithm and generally show good agreement in the shorter radius range that RFT provides.

This paper is generally well-written and represents a substantial contribution to the field. I recommend it be accepted after clarifying questions are addressed and minor changes to improve the clarity of figures and mathematical formulae/notation are implemented.

Specific comments (by line)

1-20: The abstract doesn’t address the cloud droplet effective variance which is also being retrieved in this algorithm. This is particularly valuable given the application to precipitating clouds.

24-26: Citation needed for “The cooling effect…and the size and shape of the cloud particles”.

111: Equation 1 is the form in Bohren and Huffman. Although this book is cited, this should be made clear.

143: It is unclear what A{A,i} is in equation 10. Please ensure that variables used in all equations are clearly defined upon the first instance of their use.

152: Do you have any insight on how the algorithm handles the change in slope of the polarized phase function due to, for example, ice contamination?

155: Equation 3 limits the sum to 3 but this isn’t really discussed in this section. It was mentioned in the abstract but should be stated clearly here.

158: It’s not clear to me where equation 13 comes from.

169-170: The variable N is already used for the droplet size distribution modes.

185: Here is another different use of N. The authors should take care with clarity of notation and avoid using the same variables in different ways.

193: Strange to switch to diameter when the rest of the paper consistently uses radius.

245-262: Presumably the best first fit would give the same result as the typical monomodal parametric retrieval. If subsequent modes are added to compensate and improve the fit, can’t you get multiple solutions? Please clarify this section.

Figure 4: Figure 4 is not referenced in the text.  

Figure 5b: There is artificial looking dark line at retrieved v_eff~0.025. Can you address what aspects of the algorithm might be causing that?

Figure 7b: The RGB of DOLP is very dark and it’s hard to see the cloudbow. The authors might consider additional image processing to make it more apparent.

Figure 9a: Panel a in figure 9 is not mentioned in the caption.

Figures 12-15: The yellow dashed line for single mode in panels c and d is very hard to see.

569-570, 598,647: References that cite an entire textbook should be updated so they only cite the relevant sections/chapters.

Technical corrections:

Please address the following grammar issues/ typos:

75: “…Atlantic before transferred to…”

227: “It exemplary shows the effect…”

294:” …might be caused because of hitting…”

337:” … but the sideward viewing geometry allows to observe rain…”

573: Missing accent in "Bréon"

This study provides a new algorithm for polarimetric cloud retrievals, though it is based on the same physical basis as Bréon et al.'s parametric retrieval and Alexandrov et al.'s RFT retrieval. The authors describe the similarities and differences and emphasize the advantages of their approach over the others. The paper is well written and shows substantial potential for contributing to and improving the existing body of work. In short, great work. I think that, after addressing the questions and points raised, this work would be a excellent addition to the field.

That said, following are my general comments, followed by some line by line comments,

1. I'd rather see this algorithm described as an extension to parametric fitting. This is because, even in the "recipe" (Fig. 4), the extended, multi-mode retrieval is only performed when the single-mode parametric retrieval suggests a "suspicious quality assessment." This is not a criticism. In fact, I believe it's a smart way to improve existing methods. However, I'd suggest mentioning this appropriately in the abstract, i.e., noting that the multi-mode extension is applied when single-mode retrievals are unreasonable, and the method itself is extension of parametric retrievals, rather than a new technique between parametric and RFT.

2. Another important missing part, for me, is how important angular resolution is for performing such retrievals up to very large CER values. When the CER is large, cloudbow features become very narrow. It would be a natural, practical question to ask what the minimal angular resolution would need to be to perform such 3-mode retrievals. I couldn't find any information about the angular resolution of specMACS used here. In addition, a sensitivity study on the importance of viewing-angle resolution would greatly strengthen the work.

3. Another point I'd argue is that polarimeters only see the top of the clouds. So, is it possible to see big droplets at such high levels? I agree with the point made (around line 356) that it is possible to see raindrops from the side with sufficient angular resolution, or that this kind of method would generally be useful for satellite retrievals. However, in this particular case study shown in Fig. 8, I can't shake the feeling that it's unclear whether we can really see those large droplets in the regions where Fig. 10 shows multi-mode retrievals. Perhaps you could check how the stereographic cloud-top retrievals shown in Fig. 9 (b) can be overlaid on Fig. 8(b), along the track where radar observations are available, and then show the multi-mode retrievals from Fig. 10 on the same figure. In this way, if the multi-mode retrievals coincide with regions where larger droplets are closer to the identified cloud top, it would strengthen the argument that the algorithm is correctly identifying and performing multi-mode retrievals where large droplets exist near the cloud top.

line 5: "Since current look-up tables ..." At this point readers would have no clue what meant by "current" here. I'd suggest avoid doing that.

line 40: "phase tables" or "phase function table" ??

line 106: "Theoretical basics" or "Theoretical basis"?

line 324: ".., while there is hardly any *overestimation* for ..."

line 397: Why do the cloud top height uncertainties matter here? Is it because all observations are mapped to cloud top before performing retrievals? If so, I think this would be a major pint worth mentioning explicitly.

line 443: "... RFT is its current implementation only retrieves radii up to 100 um .." Wouldn't it be possible to extend RFT to those larger CER values, so that we could see whether RFT can also handle them?