Authors suggest an approach to inversion of multiwavelength lidar measurements to the particle microphysical parameters based on iteration scheme with prior assumption about particle properties. In this manuscript authors make an important step considering parameters both the fine and the coarse mode. Simulation performed with synthetic data provides estimation of retrieval uncertainties for different lidar configurations. The manuscript is well and clearly written and matches AMT scientific criteria.

I have just several short comments.

Authors consider 12 independent parameters of aerosol, when even for “super-lidar” only 9 observations are available. The problem is underdermined and unique solution does not exist. I think this principal question should be discussed in the beginning of the manuscript.

This becomes especially critical when configuration corresponding CPL or ATLID lidar are considered.

Choose of model refractive indices for different types of aerosol is somehow convenient, but question is how sensitive are results to the choice of model. For example, in Table 1 the imaginary part of dust at 355 nm is 1.66*E-2. The same time, in recent study the Im for dust at 370 nm is below 0.005 (Di Biagio, Atmos. Chem. Phys., 19, 15503–15531, 2019) for dust of different origin. Will it influence the inversion?

In Table 7 the parameters of the coarse mode obtained from the lidar measurements are not provided. Any reason?

Fig.1. Axis title fonts should be increased.

Authors presented a study of aerosol microphysical retrievals from HSRL-2 instrument using both simulated data and real lidar measurements. The used iterative algorithm is based on Phillips-Tikhonov regularization. It is very unfortunate for the algorithm that quality of its results depends on the choice of prior and first guess. Retrieval errors increase when the prior deviates too much from the truth value that is a disadvantage for the real lidar data processing. At the moment, there is no way to have a good first guess for parameters like complex refractive index (especially, its imaginary part) or column number in the mass production mode.

Overall, this paper is well written and can be published after minor corrections:

- I would suggest renaming the "alpha" variable (mode component coefficient) in Eq. 2. Throughout the paper, "alpha" means aerosol extinction and only in Eq. 2 there is a confusing turn.

- There is no need to use blue color in figures at all. The blue curves in Fig. 3 can be dashed to be more friendly to people who have access only to black-and-white printer.

- Line 105 says:

"ii) Instead of performing a linear uncertainty/information content analysis, we apply an iterative retrieval scheme, that can be used to perform actual retrievals." The use of word "Instead" makes me think that the "iterative retrieval scheme" is somehow better compared to the "information content analysis" and have to replace the information content analysis. These two things are doing completely different job and can't be done instead of each other. I would say something like "Keeping in mind the results of uncertainty/information content analysis, we apply an iterative retrieval scheme..." to avoid the negative connotations of the word "instead".

Now let's talk about the results of information content analysis.

Authors mentioned that "3β + 2α combination of measurements provides about 3-4 independent pieces of information" (line 100). Also, Authors are saying that "In addition to the underdeterminedness of the inversion problem, limitations to the forward model can further inhibit the retrieval of the microphysical properties" (line 165). At the same time "With this parameterization, the total number of parameters free to vary in the retrieval is six for each mode, thereby twelve in total for the bimodal setup we use" (line 150).

Let's forget about dust and consider only spherical particles. Depolarization is zero and useless in this case. So, 3β + 2α lidar measures 5 numbers that gives Authors only 3-4 independent pieces of information. At the bottom line, Authors would like to use 3-4 pieces of information to retrieve 12 independent parameters and it sounds like a miracle. It is clear that the inverse solution is not unique, and Authors experience massive issues in Their retrievals, but Authors don't want to talk about it. I would like Authors to directly acknowledge this issue in Their paper. It can be done be adding several solid sentences clearly discussing the non-uniqueness of inverse solution due to the simple 3-4/12 math and the ways that Authors offer to increase the information content. Iterative algorithm by itself is not increasing the information content at all.

I also would suggest:

Line 5

"high spectral resolution lidar (HSRL)" instead of "High Spectral Resolution Lidar (HSRL)"

Line 15

"higher aerosol optical depth (AOD)" instead of "higher AOD"

Line 20

- MAEs are shown for all the input parameters except effective variance. Effective variance also deserves to be shown here. Please show the effective variance in all the tables with results (if available).

- Please include also relative errors for effective radius and effective variance [0.038/??% (0.025/??%)].

Line 30

"Spectropolarimeter for Planetary Exploration (SPEX) and Research Scanning Polarimeter (RSP)" instead of "SPEX and RSP".

Line 50

"AOD and SSA" instead of "Aerosol Optical Depth (AOD) and Single Scattering Albedo (SSA)".

Line 60

- Acronym "POLDER" needs to be defined.

- "Measurements using HSRL techniques" instead of "Measurements using high spectral resolution lidar (HSRL) techniques".

Line 75

Acronym "ATLID" needs to be defined.

Line 90

"the 3β + 2α setup" instead of "the 3α + 2β setup".

Line 100

"used in MAP retrievals" instead of "used in Multi-Angle Polarimeter (MAP) retrievals".

Line 110

"during the ACEPOL campaign" instead of "during the Aerosol Characterization from Polarimeter and Lidar (ACEPOL) campaign".

Line 115

"onboard (CPL (McGill et al., 2002))" instead of "onboard (Cloud Physics Lidar (CPL) (McGill et al., 2002))".

Line 120

"(i.e. AOD)" instead of "(i.e. the aerosol optical depth (AOD))".

Line 220

"from HSRL measurements" instead of "from high spectral resolution lidar measurements".

Line 225

"and the RSP" instead of "and the Research Scanning Polarimeter (RSP)".

Figure 1

Please add the plots for effective variance and remove the redundant "Retrieval" in the right two columns to increase the font size. The font size in plots is normally 2 pt smaller compared to the main text.

Figure 3

"Metric" is redundant in the right column of plots and can be removed to increase the font size.

Tables 3-6

Effective variance is definitely missing here.

The authors describe an iterative algorithm for the retrieval of aerosol microphysical properties from atmospheric lidar sounding based on damped Gauss-Newton method including Tikhonov-Phillips regularization. They assume a bimodal-log-normal distribution of a mixture of spheroids and spherical particles. First a simulation study is done. Finally a measurement case is evaluated and compared with the SPEX and RSD retrievals.

The results are interesting, although a few limitations, questions and drawbacks are open.

List of remarks in random order:

• The under-determinedness of the retrieval yields in non-uniqueness. The authors observed the following property:

“A study of the sensitivity of retrievals to the choice of prior and first guess showed that, on average, the retrieval errors increase when the prior deviates too much from the truth value.”

This is a well-known phenomenon of iterative methods in case of non-uniqueness. Depending on the initial value the algorithm converges to another “solution”.

This is the main drawback of the presented method.

• Question: How many iteration steps were made until the algorithm stops?
• Please, explain all abbreviations.
• “The coarse-mode contribution to the measurements is negligible, thus only the fine-mode microphysical properties are presented”. Why? Please, include the values.
• Line 145: I am wondering about the variable n which was not introduced before.
• (8) and (9): I am wondering that MAE is the same as bias?
• “The correlation between the truth and retrieval for both real and imaginary refractive

 index components is rather poor, as exemplified by the r values of 0.349 and 0.251, respectively.”

This was observed even in retrieval techniques for spherical particles, see Mueller et al, AMT 9 (2016) 5007-5035. The authors should compare their simulation studies with those techniques.

• The pt-font in all Fig. is too small.
• The main results of Tables 3-6 should be summarized, additionally, in a Figure for the conveniences of the readers. The presentation is boring.
• Table 7 caption: The authors should provide more information about:” …what is to be expected from biomass burning, see for example Nicolae et al. (2013)”
• It was interesting to learn that using the presented algorithm one gets:

            “However, the difference between the super-lidar and HSRL-2 configuration is not so clear where measurement noise is included, as overall the results are quite similar in that case.”

This means in case of measurement errors more input information does not result in a more accurate retrieval. May be this regularization method is not the best one for this retrieval or the regularization parameter was not selected appropriate? Please, regard this point.