The study uses 14 realistic Asian dust particles with sizes from r = 0.46 to 0.93 µm and describe their scattering properties by using the discrete dipole approximation (DDA). They calculate lidar ratios and depolarization ratios at 3 commonly used lidar wavelengths based on their realistic particles with the limited size range. They reveal an asymptotic behavior of the lidar ratio and depolarization ratio with increasing size parameters and develop a parameterization for the later one. The study is interesting and contributes to the challenging task of modelling the scattering properties of irregularly shaped mineral dust particles. The DDA technique allows to create any particle shape which has advantages above predefined particles shapes. However, it is difficult to extend it to large size parameters, where the asymptotic behavior might be helpful. The manuscript can still be improved and therefore, I recommend to consider my major revisions listed below.

Major comments:

1. Size

Your studied particles range roughly between 1 – 2 µm in diameter. Is this sufficient to realistically describe atmospheric mineral dust? The fine mode or sub-micrometer mode is missing but contributes to the optical properties observed with lidar. And on the other end, the large particles are missing as well. It is a major limitation of the study and hampers a good comparison to real world observations with lidar. Please discuss how representative your particle size range is for atmospheric observations.

Because you don’t vary CRI nor shape, there is no additional information in using different wavelengths. If you would stick to one wavelength (e.g., 532 nm), you would just cover the size parameters from 5.5 to 11, this is much less than in Järvinen et al., 2016. And from this, you cannot draw the conclusions presented in Sect. 4. Now, you just add calculations at other wavelengths, in principle you could take any wavelength to cover the size parameter space from 0.1 to 20. And in fact, you’re just covering the size parameter space from 2.7 to 16.5. So, the smallest size parameters, i.e., the fine mode, is not included. Please start your figures at 0 and not at 2 (Fig. 6-8).  If you take for example Fig. 12a and mark the covered size range of your particles, you will see that just a small part of the size distribution is covered.

2. CRI

If you cannot include the spectral dependence of the CRI, i.e., the increase towards the UV, I would omit the results at 355 nm. In case you want to keep the results at 355 nm, please find a way to mimic a realistic increase in the imaginary part of the CRI. Otherwise, your discussions might be misleading.

The complex refractive index (CRI) is an important quantity. However, you missed completely to set your results in the context of previous observations. The first study which comes into my mind is the one by Di Biagio et al., 2019.

3. Asian Dust

The term “Asian dust” is widely used in literature, especially to separate it from Saharan dust. However, Asia is a huge continent and at some point, you should be more specific about the source region, which is probably in the Gobi Desert. Dust from Central or West Asian (Middle Eastern, Persian or Arabian) deserts might exhibit different optical properties.

And there are differences in the optical properties, especially in the lidar ratio, between Asian and Saharan dust, which was summarized by Floutsi et al., AMT 2023 based on observations of Hofer et al., ACP 2020. A lidar ratio of 35 sr might be not that bad for Asian dust, but not for (West) Saharan dust.

4. Asymptotic Behavior

The measurements of Järvinen et al., 2016, show an asymptotic behavior for the depolarization ratio as you mentioned correctly. But you are hiding that this plateau was found at around 0.30 and not 0.41. This is a significant difference. Does your model overestimate the depolarization ratio of mineral dust? And why? What could be the reason? Asian dust was included in the study of Järvinen et al., 2016. Kahnert et al., 2020, used the laboratory results of Järvinen et al., to test various modelling parameters. Please take these two studies seriously and discuss the differences to your results.

L511-518: The asymptotic value of the depolarization ratio (0.41) is quite high compared to approximately 0.3 in Järvinen et al., 2016. How do you explain the differences? If I as a user would like to apply a parameterization like your eq 10, I would apply it rather to the measured data from Järvinen than to the purely modelled data. It is too far from the observations and maybe linked to some limitations in the model. Even if you use realistic shapes, it is still a model.

Furthermore, in Fig. 11: Why don’t we see an asymptotic behavior for the irregular hexahedra? It seems to decrease for 355 nm after reaching a maximum. This finding questions your derived plateau.

And to further add, you did the calculations up to a size parameter of 16.5 (Fig. 6). And by purely looking at Fig 6b, I would not be sure if the plateau continues to exist above x =12. Who knows what will happen for larger size parameters?

I know that you are still far from lidar observations in the atmosphere. However, the spectral slope of the depolarization ratio was measured for Saharan dust (see literature, which comes close to the shape in Fig. 12) and for dust from the Taklamakan dessert by Hu et al., 2020.

5. Data availability

A statement about the data and code availability is missing although it should be included in the ACP style file. Please ensure the availability and traceability of the used data.

Minor comments

• The overall impression is that the manuscript would have benefited if the authors would have spent another month to carefully check the manuscript. There are several minor, but annoying issues which could have been eliminated, e.g., figure captions which mention different quantities than shown in the figure (e.g., Fig. 3), changing symbols for lidar ratio and depolarization ratio (Fig. 10) or color coding with the same quantity as shown on the x-axis (Fig. 8). Furthermore, a more careful literature study would have been great.
• The introduction is not really an introduction but already describes the theoretical background. I would move all equations to a separate section and keep a more clear and straight forward structure of the introduction.
• Furthermore, the first paragraph of the introduction discusses extensively the radiative forcing of mineral dust, but this is of minor importance for the presented study. Please reshape the introduction and reduce it to the parts relevant for the present study. To my opinion, the first paragraph can be reduced to 2 sentences.
• All figures missing the unit of the lidar ratio and probably some other units as well.
• The unit of the lidar ratio is sr and not sr-1 as used throughout your manuscript.
• The size parameter is defined quite late (L411) and later on defined differently (L514). Please define it earlier and keep one convention (2 pi or just pi).
• You are discussing Asian dust, but through an US American perspective (e.g., lines 51-53) omitting a long tradition of Asian dust research in Japan, but also in China and Korea, which are countries much stronger affected by Asian dust. Please add the respective literature.
• This American perspective continues when solely name MPL Net and CALIPSO omitting European and Asian lidar networks which already use much more advanced lidar systems. The new EarthCARE satellite measures not only the elastic backscatter like CALIPSO but is equipped with an HSRL channel to measure directly the extinction coefficient and so the lidar ratio. The products are described by Donovan et al., AMT 2024.
• L73-78 You’re talking about the optical properties of a single particle and at the same time introduce the bulk properties. Please keep it well separated.
• L138-141 Kemppinen et al., 2015a,b used realistic dust shapes as well for their DDA calculations. The 2 papers are cited later (L504), but should be already mentioned here.
• Fig 1: Please be sure what you want to show. 4 CALIPSO cross sections are a lot and less would be sufficient as well. The captions are not readable at all and the plots are only understandable for people familiar with CALIPSO. Which color represents dust? The dashed lines in 1a are not vertical.
• The date format is changing throughout the manuscript. MDY – Month Day Year – is not a well-defined date format, even if it is commonly used in the United States. Please choose to go from specific to general (DMY) or from general to specific (YMD).
• L365-367: Quantitatively, the same behavior for the spectral depolarization ratio and lidar ratio was measured by Haarig et al., 2022. However, the values are different.
• Eq 4,5 & 7 are not a real equation, but only a matrix. Please write them as equations.
• L393: Which dust transport region you are referring to? I would guess you are referring to Asian dust over the Pacific when you speak about dust transport region.
• L454-457: Please compare to Saito & Yang, GRL 2021 and Gasteiger et al., TellusB 2011.
• L699 ASL does not appear in the list of coauthors, probably it refers to the first author.
• L700: “ASL contributed to the methodology, data collection, interpretation and analysis and data visualization” – But who has done the data collection and analysis? If ASL just contributed to it, someone else had to do it. But who?
• It seems that the manuscript was made in word – it is recommended to use a latex environment instead. This will prevent that figure captions are given on the next page and not below the figure, and that formulas have different sizes. Furthermore, with latex the references are given in a consistent manner. In your manuscript some references are cited with the initials of the first author, e.g., L 58, but most not.

Technical corrections

• L65 gases
• L531: r_vg is not used in eq 13.
• L692: fine and coarse mode dust
• Burton et al., 2012 – the reference appears twice in your list.

References (which are not already in the paper):

Di Biagio, C.; Formenti, P.; Balkanski, Y.; Caponi, L.; Cazaunau, M.; Pangui, E.; Journet, E.; Nowak, S.; Andreae, M. O.; Kandler, K.; Saeed, T.; Piketh, S.; Seibert, D.; Williams, E. & Doussin, J.-F.: Complex refractive indices and single-scattering albedo of global dust aerosols in the shortwave spectrum and relationship to size and iron content, Atmospheric Chemistry and Physics, 2019, 19, 15503-15531

Donovan, D. P.; van Zadelhoff, G.-J. & Wang, P.: The EarthCARE lidar cloud and aerosol profile processor (A-PRO): the A-AER, A-EBD, A-TC, and A-ICE products, Atmospheric Measurement Techniques, 2024, 17, 5301-5340

Floutsi, A. A.; Baars, H.; Engelmann, R.; Althausen, D.; Ansmann, A.; Bohlmann, S.; Heese, B.; Hofer, J.; Kanitz, T.; Haarig, M.; Ohneiser, K.; Radenz, M.; Seifert, P.; Skupin, A.; Yin, Z.; Abdullaev, S. F.; Komppula, M.; Filioglou, M.; Giannakaki, E.; Stachlewska, I. S.; Janicka, L.; Bortoli, D.; Marinou, E.; Amiridis, V.; Gialitaki, A.; Mamouri, R.-E.; Barja, B. & Wandinger, U.: DeLiAn -- a growing collection of depolarization ratio, lidar ratio and Ångström exponent for different aerosol types and mixtures from ground-based lidar observations, Atmospheric Measurement Techniques, 2023, 16, 2353-2379.

Hofer, J.; Ansmann, A.; Althausen, D.; Engelmann, R.; Baars, H.; Fomba, K. W.; Wandinger, U.; Abdullaev, S. F. & Makhmudov, A. N.: Optical properties of Central Asian aerosol relevant for spaceborne lidar applications and aerosol typing at 355 and 532nm, Atmospheric Chemistry and Physics, 2020, 20, 9265-9280.

Hu, Q.; Wang, H.; Goloub, P.; Li, Z.; Veselovskii, I.; Podvin, T.; Li, K. & Korenskiy, M.: The characterization of Taklamakan dust properties using a multiwavelength Raman polarization lidar in Kashi, China, Atmospheric Chemistry and Physics, 2020, 20, 13817-13834

The manuscript by Anthony La Luna et al. presents optical modeling results for the linear depolarization ratio and the lidar ratio of Asian desert dust aerosol at three lidar wavelengths. The study is based on 14 particle morphologies derived with FIB tomography. The topic is very relevant and the manuscript can be a useful contribution to the literature. The proposed parameterization is potentially very useful as well. Some assumptions and simplifications are done in order to make such simulation studies feasible. But a bit more discussion of the limitations is highly recommended. Furthermore, there are some unclarities and a larger number of minor issues that need to be corrected. Overall, I recommend publication after the authors have carefully checked the manuscript for language and other minor issues and after they have considered the suggestions detailed below.

Major comments:

1. Unclear description of refractive indices used

There are 14 particles and 3 wavelengths. If I understood correctly, in the main part of the study two different refractive indices were used for each of these 42 combinations (of particle/wavelength). However, the description around line 238-248 is a bit vague in my view. Which refractive indices did you actually use? In line 242 and 245, what does 'possible' mean? Please improve the description.

2. Data availability

Since the number of cases is not too large, I recommend to make the input and output data available in tables. For example, a list of radii, aspect ratios, used refractive indices for the 14 particles (in the main text), as well as a list of the obtained depolarization ratios and lidar ratios (in an appendix).

3. Size

A volume-equivalent radius range from 0.46 to 0.93 µm is covered by the 14 particles, which is quite a narrow range. Since the authors assumed a wavelength-independent refractive index, the size range is a bit extended if viewed in size-parameter space as done in this study. However, the size range and also the size sampling remains limited. You might scale the size of the existing particles to get a better sampling and range but I understand that it takes considerable effort to do the additional simulations. Nonetheless, I would recommend to reconsider this possibility. In any case, adding some more discussion of this limitation is recommended.

4. Fine-mode non-dust particles

In the discussion of your results I didn't find mentioning of the fact that in most cases desert dust aerosol contains a fine mode of non-dust aerosol particles which affects in particular lidar measurements at short wavelength. For example, these kind of particles are considered as WASO particles in the mineral dust mixture of OPAC [1]. Another example is the SAMUM campaign, where they were observed and considered in the optical modeling study of Gasteiger et al. (2011) (already referenced in the manuscript). I think it is necessary to take into account the effect of fine mode non-dust in the discussion of your results.

5. Settings of ADDA

Nowhere is mentioned which version of ADDA and which settings of ADDA you are using. Did you just use the default settings? Did you try other settings? Please provide more details to make the study as reproduceable as possible.

6. Definitions in introduction

Lidar-related parameters are defined in the introduction. I find this unusual and would recommend to move this part into section 2. (If Copernicus guidelines allow it to be in the Introduction, I am also OK with it)

Minor and technical suggestions / comments:

Line 51: 'this dust' should be replaced by 'dust aerosol'.

Line 55: 'facilitate the working of' should be 'being part of'.

Line 74-79: There is an inconsistency: You start with 'For a single dust...' but the equation 1 is for bulk aerosol.

Line 81: There is an inconsistency: Beta is a bulk property, while C_sca is a single particle property.

Line 88: It unclear why 'it is fundamentally important'. Please improve the argumentation.

Line 98 and 101+102: The fact that delta is used for aerosol and cloud classification is repeated here within a few lines.

Line 176: 'The fourteen FIB dust particles' should be reformulated to something including 'particles measured by FIB' or 'sampled by FIB'.

Figure 1: Labels are hardly readable. 

Figure 1: Plots c) and e) are not compatible (different lat/lon).

Figure 1 / l195-201: Please explain better the content of the figure.

Figure 2: The coordinate system axes are hardly visible.

Line 231-232: Could be simplified to 'In this study we follow the ... convention of Conny et al. (2019)'.

Line 237-238: Use plural 'which have ... indices'.

Line 260: The Extinction cross section is usually labelled as C_ext.

Line 261-262: The scattering properties also depend on wavelength which is missing here.

Line 291: 'for' is missing .

Line 293: Insert 'the' before 'random'.

Line 294: 'that' is repeated.

Line 303-304: Insert 'by' before the three angles.

Line 310 / 315: For n=6 the equation results in (2^6+1)^3=274625 orientations while 262144 orientations are reported; it is not consistent.

Line 318: What was exactly the convergence criterion? A threshold? 

Figure 3c: The y-axis has label 'Variance Index' which is not defined. Do you mean the CI? 

Figure 3: I would try to add the n values somewhere in the plots to make the approach clearer. E.g. as labels at the top? If this is not possible, improve the legend such that it becomes clear immediately that n=2 to n=6 is covered.

Line 325: Insert 'number of' before 'orientations'.

Line 326: Is (a) and (b) also for particle 3D?

Line 326: The label should mainly explain the content of the Figure and not the interpretation. Therefore I suggest to write 'S and linear depolarization ratio as function of the number of orientations'.

Line 335: The meaning '~20 nm3' is unclear. Do you really mean a volume? 

Line 341: 'For each wavelength, more than 60 ADDA simulations are carried out': I thought it would be 14 particles and 2 refractive indices at each wavelength. Please clarify which simulations were performed.

Line 349/350: The scattering angle is missing here.

Figure 4: Is there one line for each of the 14 particles? Are there more lines? Please explain better what is shown here.

Line 361: Size should be singular.

Figure 6a: There is quite some spread at size parameter 16-17. Why is there an outlier? What is special is that case?

Line 393: The wavelength of the depolarization (i.e. 532nm) could be added.

Line 432: 'session' -> 'section'

Line 484: It is unclear to me what the range 11.4% to 7.9% represents. Uncertainty of the iron mass in one particle? Please explain better.

Line 489-490: This sentence is unclear to me. Please improve.

Equation 11: Scattering angle missing.

Line 531: r_vg is not used in the equation. What does 'median' refer to here?

Line 540: 'elected' doesn't sound right to me. Maybe 'selected'?

Line 551-553: The sentence should be made clearer.

Line 571: Eq. (13) does not contain a parameterization. Please check the equation number.

Line 587: 'Diameter' is not consistent with the label in plot b.

Line 588: 'through parameterized approximations': Please be more explicit, e.g. mention equation XX

Line 616: There is no vertical line in Fig 12a.

Line 618: 'as described previously' should be rewritten to 'as described in the text'

Line 619: I suggest not to start the paragraph like this. 'promising' might be better suited as a conclusion that you may get after a discussion of the results.

Line 638: You write that the decrease of the depolarization ratio from 532nm to 355nm is a result of absorption. But how can it be an absorption effect if the decrease is observed only for the full PSD and not for fine mode and not for the coarse mode (like in Fig. 12b)? To me it looks more like a size effect. 

Line 656-657: What do you mean with 'theoretical libraries for some amount of calculation'?

Line 619-670: In particular this part should be reworked to make it clearer. 

Line 673: 'FIB particles' should be reformulated, see comment on Line 176.

Line 685: Absorption also greatly increases S.

Line 688: 'CI' should be replaced by 'convergence index'

Line 690: Add 'size distribution'.

Line 692: This section lacks a summary of the limitations of the study / of the proposed parameterization.

[1] Koepke, P., Gasteiger, J., and Hess, M.: Technical Note: Optical properties of desert aerosol with non-spherical mineral particles: data incorporated to OPAC, Atmos. Chem. Phys., 15, 5947–5956, https://doi.org/10.5194/acp-15-5947-2015, 2015.