The manuscript presents an in-depth description how three scattering models perform for the retrieval of non-spherical mineral dust particles from remote sensing measurements. It is of great interest to find a good representation of the irregular shape of dust aerosol particles in optical models. The figures are well prepared and the text is written in a clear, but rather descriptive manner. However, I have major concerns whether the content fits to a publication in Atmospheric Chemistry and Physics. In the following, I will describe my concerns.

1. The title states “Retrieval of microphysical properties …” And you retrieve microphysical properties, but we don’t know if they are correct. The manuscript merely describes the differences between two scattering models, namely the spheroid model and the irregular hexahedra (IH), and the calculations using spheres. The models are applied to synthetic data and to real world lidar measurements. However, the authors just report the retrieved microphysical properties without any validation. It remains unclear which of the non-spherical models retrieves more realistic values. The only validation briefly discussed is provided by an AERONET photometer retrieval which is as well based on the spheroidal model (stated very late in the text). Without a validation by independent observations, ideally with in situ measurements, I don’t see that the paper fills in the scope of ACP and might be better submitted to another journal.
2. From an atmospheric science point of view, it is even more problematic, that you move in a circle while calculating the optical properties with the IH model and then invert these optical data to microphysical properties using the same model (Section 4). It is no surprise that the 3+2+3 inversion with the IH model leads to the best agreement if the optical data were calculated with this model before. Looking at an irregular hexahedron and describe it with a spheroid will of course lead to some differences when it comes to shape-dependent properties. But the driving question is how do we best describe the real dust particles.
   
   The same circle appears in Section 5 where you retrieve the microphysical properties with the IH model and then calculate with the same model (and the other models) back the optical properties like lidar ratio and depolarization ratio. This is not a real comparison.
3. The settings used for the calculations appear arbitrary (although to a certain degree reasonable) and are not based on literature or sensitivity studies. The three size distributions used 4.1 are arbitrary and I don’t see why they should fit to the observations. There are numerous measurements of dust particle size distributions in literature. Why don’t you base your assumptions on them? Or at least explain why you choose certain settings. The same holds for the 3+2+3 data set. What about 3+2+1 or 3+2+2? Have you tested your results with only one depolarization ratio as input as well? It seems arbitrary or at least not explained why you have taken 3 depolarization ratios.
4. The work is not properly set into the context of previous literature. The discussion section which is commonly used to place the new findings in the scientific context does not contain any citation. Over wide parts in Section 3, 4, 5 & 6 the manuscript just describes the findings and does not discuss them. Why do we see a certain behavior? – Sometimes it is shortly mentioned. What is new? What was not known before? And many findings were known before, e.g., the comparison between spheres and spheroids. This prior knowledge was not used or is not properly acknowledged by the authors.

With the reasoning listed above, I come to the conclusion that major revisions are necessary. Alternatively, you may prepare the comparison of the irregular hexahedra model to the spheroidal model in a dedicated publication in a more technically/modelling journal. There you could really focus on the model comparison and point out the differences in the model and their implications on the retrieval as you nicely did in Section 3 & 6.

Specific comments on the sections

1. General
   1. Please explain abbreviations at first instance, e.g., AERONET, SAMUM, VIS, NIR.
   2. I still have troubles with the naming of the models: Sphere model or spherical model, Spheroid model or spheroidal model?
   3. While reading, I sometimes got lost in the results and lost the track why you are doing it. Or in other words, the storyline behind is sometimes not clear. It would be recommended to have a short introduction at the beginning of each section.
2. Sections 2.1 & 2.2
   1. BOREAL was described in Chang et al., 2022 and it is good to give a short recap of it. By why do you not mention that it is a Maximum Likelihood Estimation. I find this fact rather central. What are the advantages and disadvantages of this method?
   2. L137: Which studies? You certainly need to consider several previous studies.
   3. What are the limitations of the spheroids and the IH?
   4. Here and also in the introduction, you completely omit the approaches which use the discrete dipole approximation (DDA). Why? They provide some realistic particle shapes.
   5. L173-175 Please provide a formula how you converted the diameter.
   6. How comparable are the results of the two particle shape models? How do you ensure to use the same shape distribution? The results probably depend (strongly or not) on the assumption of the shape distribution. Do you choose a sphericity for the IH which matches the shape distribution assumed for the spheroid model?
3. Section 2.4
   1. Section 2.4.1 needs to be updated. There are several studies conducted in the last 15 years concerning the size distribution of mineral dust and the contribution of fine and coarse mode dust and its changes during transport process. Furthermore, it remains unclear if the morphology is expected to change with source region or not. Overall this section is more a lose collection of facts and needs to be straighten. What do you want to tell me? And how are these findings linked to your own research? With this general literature section, you do not explicitly motivate the choice of your size distributions in Sect. 4.1.
   2. L233 What are the a priori constraints for m_R?
4. Section 3
   1. Please add subsections to make it easier for the reader.
   2. You rarely set your results into context of previous findings. Especially in this basic section, many findings were known before or observed in similar studies. Reading your manuscript evokes the impression you are the first ones to observe this behavior of the optical properties. You may reduce some of text and put a stronger focus on the comparison between spheroids and IH.
   3. Furthermore, the findings are not compared against observations from laboratory and field measurements. It remains unclear whether the reported results are found in reality or if they are “just” an output of different models.
   4. It would be good to show three typical size distributions for three ranges of r_eff which you are discussing. You may add it as an additional subplot in Fig. 3. The constraint of V_t =1 (L315-316) will then become more visible.
   5. L317-319 Why do we see this behavior?
   6. L325-328 Why do we see this behavior?
   7. Fig 4f: It seems that the blue line goes to negative depolarization ratios for large particles. Can it really be the case?
   8. Fig 4: You may add a dashed line at r_eff = 1.25µm to enhance the link to Fig. 5+6.
5. Section 4.1 & Fig. 10
   1. The comparison of the IH to the results of Hu et al., ACP 2020, was already shown by Saito and Yang, GRL 2021. Where are the differences and similarities to that comparison?
   2. There are certainly more multiwavelength observations of mineral dust. Why have you chosen these ones and no other ones? Recently, I found some new results in Gebauer et al., ACP 2024.
   3. TD, FD and BD should be written in each figure because the abbreviations are not self-explaining (here and in the following figures).
   4. Which dust size distribution would you expect to be present in the field observations? The reasons for the fitting or not are not properly discussed.
   5. The text from line 430 onwards already belongs to Section 4.2 or to an own subsection, but it is not really linked to the content of Section 4.1.
6. Sections 4.2 & 4.3
   1. Now, you introduce some quantities with a *, probably to distinguish true and retrieved parameters. However, the ^ for retrieved parameters as introduced before is not used. Please be more consistent and if necessary add a short description at first instance.
   2. Overall, I don’t really see the significance of these two sections (4.2 & 4.3). You use one model (here IH) to generate particles and this model of course retrieves the results with less uncertainties. What is the benefit? What do we learn from it?
   3. Fig 11, 13, 14: Please find a better representation of the x-axis. The CRI pairs in the current version are not very intuitive. One idea would be to add a two dashed lines to separate the 3 m_R blocks. In that way the correlation with m_I would be easier to grasp.
   4. L475 Why do you see this behavior?
   5. L504 The formulation is not clear.
7. Sections 4.4 & 4.5
   1. Much of the information presented in Tab. 3+4 is not used in the manuscript.
   2. And again, I don’t really see the value in it. It tells us, how far from the truth we get, when using a certain model or model configuration. If we create our data with IH, we get the best results with 3+2+3 IH. You show, how far we get from the simulated truth, if we describe it differently. But who knows how the mineral dust particles look like? 
      
      All these comments underline the need of a clear motivation for your model comparison study. Because I think it is important to compare these scattering models and to point out the strengths and weaknesses. The focus of your study appears to me rather the comparison of these models than the retrieval of microphysical properties (as stated in the title). Because to do this retrieval you would need some more validation which retrieval fits best.
   3. L531: “the corresponding standard deviation of the noise distribution is a third of the maximum error” – Does it mean that you use a standard deviation of 3.3% for extinction and backscatter at 355 and 532?
   4. I am a bit puzzled why you omitted the spheroids in this section. Please show the results for the spheroids as well or instead of the spheres.
   5. L559-560 From the presented results of EAE and BAE you can not conclude on the limitations of the scattering models, because EAE and BAE seem to vary a lot with the assumed aerosol size distribution, which you state at the end of the sentence.
   6. L561: What about only one depolarization ratio? Would you expect the same improvement or do you really need 3 depolarization ratios?
   7. Section 4.5: Again, you don’t link your findings to previous literature. What is new? What was studied already before? And I believe, if you do a careful literature search you’ll find many conclusions going in the same or a similar direction. I am interested in your new conclusions on top of previous knowledge. Or at least to set your conclusions in the context of previous findings.
8. Section 5.1
   1. L573: Do you really use the fluorescence measurements in the shown case studies to detect the dust layers?
   2. Fig 16: The data are not shown until 16 April 2019, 05:00 UTC as indicated in the figure caption.
   3. L594: What do these values tell me? Without an independent measurement or retrieval, I don’t know which model fits best. m_R ranging between 1.45 and 1.68 it is a very wide range for mineral dust, the same holds for r_eff. You state, it was freshly emitted dust. However, a r_eff of 0.4-1.3 µm is much lower than your assumptions for fresh dust in Table 1.
   4. Please compare the retrieved CRI to the measurements of Di Biagio et al., 2019. What are their values for the Taklamakan and the Sahara? Are the retrieved CRI values reasonable?
   5. L605-610: The discussion is related to Fig 18 (whole layer) or Fig 19 (200 m layer)? Fig. 19 shows the size distribution and it so not so easy to get V_t and r_eff from it.
   6. Fig 19f: Please increase the scale for the depolarization ratio. The 3+2 spheroid results do not fit the measurements.
   7. L607-608: “Compared to the measurement error bars, all the scattering models are able to well fit the measurements.” It is a very dangerous statement, because it evokes the impression that everything fits. But this conclusion can not be drawn from your results. You use the optical data and invert them with a scattering model (IH) and then you apply the different scattering models to get to the optical data. And of course, this should fit somehow. But you are moving in a circle.
9. Section 5.2
   1. Looking at Fig. 20, the dust layer seems quite homogeneous. Why do you limit your intensive optical properties to the tiny layer between 5.4 and 5.6 km height? What are the intensive optical properties for the whole layer (not shown)?
   2. The AERONET retrieval at 15:58 UTC, might it be affected by the feature at 9 km height (possibly an ice cloud) which is visible in Fig. 20?
   3. Why do you provide only the coarse mode r_eff from AERONET in Tab. 6? Especially, in case 2, the overall r_eff would be interesting to compare to your monomodal results. Then, it is not surprising that r_eff is higher for AERONET (L659). Please provide additionally r_eff for the whole AERONET size distribution.
   4. Table 5, case 1: Here report a layer height of 1 – 2.2 km, in Sect. 5.1 and Fig. 19, you use 2.0 - 2.2 km. Which layer do you use for the comparison in Tab. 6?
   5. To which layer height does the layer-averaged AERONET volume concentration correspond? Please add in L652 the layer height used for each case.
   6. I am bit puzzled what epsilon_fit represents in this section. Previously, you state that it quantifies how well the measurements are represented by the retrievals (L447). But here you have only the lidar measurements and then you do the retrieval. You don’t have another independent quantity to compare your retrieval. Probably, you use the retrieved microphysical quantities and apply the same model to get the optical properties to report an epsilon_fit. However, it does not tell us, how well it fits in reality. Again, you’re moving in a circle.
10. Sections 6 & 7
    1. At the beginning of discussion, you state it correctly, that BOREAL is able to reproduce the input measurements. But as long as we don’t know the “microphysical truth”, it is just a circle. You put some measurements in and get them out at the end. What do we learn from this? We know that the model works in the forward and backward direction.
    2. L695: “the 𝑟eff decreases to 11–12 μm due to the loss of sensitivity.” What do you mean?
    3. L726-727: “All the retrievals fit the measurements well with a fitting error comparable with the measurement uncertainty.” Again, I find dangerous to state it like this, because you do the retrieval on the retrieved quantities and then it is no surprise that it fits the original measurement. See also my previous comments.
    4. L728: If you consider the coarse mode r_eff from AERONET only. But to have a fair comparison, you should take r_eff from the whole AERONET size distribution.
    5. The data availability is not sufficient. Request to whom? Even better would be to publish the retrieval results separately as data set.
    6. It is unusual to explicitly thank one of the co-authors in the acknowledgment section.

Technical corrections

• L185 reference appears twice.
• In Latex it is \AA ngstr\”o m exponent -> please use correct spelling
• L391 How does …
• Tab 3 caption: in parentheses ? The standard deviation is not given in parentheses. TD, FD, BD – please repeat the words in the table and not just the abbreviations.
• L579 Figure 16 shows the …
• L620 date is formatted differently here.

Please see the attached file with my detailed comments.