Authors analyze possibility to retrieve the particle size distribution from the measurements of space based HSRL lidar, using inversion with regularization. Lidar perform measurements at 3 wavelengths 532 nm, 1064 nm, 1572 nm and authors assume that 3 backscattering and 3 extinction coefficients are available.

This inversion technique is widely used for ground based lidars, but it is really a challenge to use it for satellite measurements. The main problem is to provide high quality of input data, because measurements from space are characterized by high noise. So, anybody, who tries to present such inversion, first of all should demonstrate profiles of aerosol backscattering and extinction coefficients with corresponding uncertainties. This is what I miss in this manuscript. Authors should explain how they calculate backscattering and extinction at 1064 and 1572 nm. I could also provide other comments, but question about input data quality is the main. I think, without it  manuscript cannot be published.

The manuscript represents the application of the regularization algorithm to the first spaceborne HSRL lidar ACDL, and enabling the retrievals of vertically resolved aerosol microphysical parameters. Although there is potential to improve the retrieval of the fine-mode particles, this work shows a valuable contribution by obtaining AMP from the spaceborne lidar and it is interesting. Before the manuscript can be publication, the following questions need to be addressed.

1. The author’s choice of wavelengths in the inversion process differs from the commonly scheme (3α+2β). Please explain the basis for the selection of the input data combination in this paper.

2. In the actual atmosphere, the refractive index of the atmosphere varies significantly due to changes of humidity and the type of aerosols, and there is a lack of discussion on the sensitivity of the inversion results to the choice of refractive index.

3. Please provide a further explanation for the increase in the bimodal inversion errors in the simulation (volume concentration reaching 60%).

4. There is a lack of quantitative description of the ACDL data errors shown in Fig. 10, as well as the other two sets of comparison data.

5. It would be better to add the display of parameters for the ACDL system.