The paper presented by Shcherbakov et al. aims to establish an empirical relationship to account for the effects of multiple scattering on lidar measurements from the ground, aircraft and satellite. As stated by the authors, there have already been many studies to take this effect into account. Some have directly used Monte Carlo modelling; others have used radiative transfer codes allowing the development of phase functions over several orders. From these previous studies, parameterizations have already been developed, in particular to take into account the forward scattering which is preponderant in the multiple scattering for large particles.

The proposed parameterization is based on cases where the optical thickness (OT) remains below 7, which is indeed an upper limit for the vast majority of lidars. It explores mainly FOVs of 0.25 and 1 mrad which may appear somewhat limiting for existing ground-based and airborne lidar systems. The contribution of this study is not sufficiently demonstrated. It is clear that the definition of a lidar system is generally carried out taking into account the constraints linked to the observation geometry and that Monte Carlo simulations are performed by the designers, as was done for CALIOP and is done for airborne and ground-based lidars. This aspect of Monte Carlo simulation is therefore not original in itself and many models exist in laboratories around the world. It is a basic design tool.

There are several points that need to be better explained in this article, such as

1) The justification of the optical properties considered as initial conditions for the modelling. Are they common, extreme?

2) The sensitivity of the parameterization to the adjusted parameters (a1, a2 and a3),

3) Better justify the choice of an altitude interval of 8 to 11 km which is not optimal for aerosol layers. It would have been preferable to choose realistic layers such as a Saharan boundary layer that can extend from the surface to 3-5 km above.

4) Clarify the results on 𝜂𝑀𝑆(ℎ), the parameter initially defined by Platt. At the entrance to the scattering layer, the multiple scattering is small and 𝜂𝑀𝑆 = 1 (Eq. 7), but this is not the case when looking at the figures. Is it really the in-cloud distance that is on the x-axis? Or maybe I have misunderstood, and better explanations are needed.

5) The results should be presented in a more synthetic way in order to lighten the reading of the article. It could be interesting to make 2D figures 𝜂𝑀𝑆 = f(FOV,OT).

6) It is difficult to properly assess the robustness of the parameterization. In the case of CALIOP corrections are applied and it would be interesting to compare them to those proposed via the parametrization.

Other aspects:

P4. How are the number of realizations (photons) chosen? How are the results degraded?

P5. Degassing feathers = ash feathers?

Table 1. Define the parameters in the caption table.

P8. The number of significant scattering orders is closely related to the number of photons. It would be nice to see this relationship.

P10L160. For figs 3,5 and 8 it is R that is used while the adjustment is made on G. In order to make it more understandable for the reader, it would be better to present G or to adjust on R. At this stage of the paper, there is nothing to justify such a model. Why this choice?

Eq.18. Development to 2nd order of arctan whereas before it was 1st order

P11L292. This is an important result for the paper and should be in the body of the paper or at least in an appendix. Furthermore, it would have been nice to show graphically the fits on an example and a sensitivity study to these fits against the coefficients a1,a2 and a3.

Figure 3: What explains the difference in the spread of points between the layer types?

P14L330. Why 5%?

P14L336. 8 km of higher = 8 km or higher?

Table 2. The values in the table are in %?

Appendix A. It is not clear what the authors are trying to demonstrate here. The functions are indeed different, but they remain related. It depends on the initial hypothesis that is considered. Is this appendix useful?

The paper presented by Shcherbakov et al. aims to establish an empirical relationship to account for the effects of multiple scattering on lidar measurements from the ground, aircraft and satellite. As stated by the authors, there have already been many studies to take this effect into account. Some have directly used Monte Carlo modelling; others have used radiative transfer codes allowing the development of phase functions over several orders. From these previous studies, parameterizations have already been developed, in particular to take into account the forward scattering which is preponderant in the multiple scattering for large particles.

The proposed parameterization is based on cases where the optical thickness (OT) remains below 7, which is indeed an upper limit for the vast majority of lidars. It explores mainly FOVs of 0.25 and 1 mrad which may appear somewhat limiting for existing ground-based and airborne lidar systems. The contribution of this study is not sufficiently demonstrated. It is clear that the definition of a lidar system is generally carried out taking into account the constraints linked to the observation geometry and that Monte Carlo simulations are performed by the designers, as was done for CALIOP and is done for airborne and ground-based lidars. This aspect of Monte Carlo simulation is therefore not original in itself and many models exist in laboratories around the world. It is a basic design tool.

There are several points that need to be better explained in this article, such as

1) The justification of the optical properties considered as initial conditions for the modelling. Are they common, extreme?

2) The sensitivity of the parameterization to the adjusted parameters (a1, a2 and a3),

3) Better justify the choice of an altitude interval of 8 to 11 km which is not optimal for aerosol layers. It would have been preferable to choose realistic layers such as a Saharan boundary layer that can extend from the surface to 3-5 km above.

4) Clarify the results on η𝑀𝑆(ℎ), the parameter initially defined by Platt. At the entrance to the scattering layer, the multiple scattering is small and η𝑀𝑆 = 1 (Eq. 7), but this is not the case when looking at the figures. Is it really the in-cloud distance that is on the x-axis? Or maybe I have misunderstood, and better explanations are needed.

5) The results should be presented in a more synthetic way in order to lighten the reading of the article. It could be interesting to make 2D figures η𝑀𝑆 = f(FOV,OT).

6) It is difficult to properly assess the robustness of the parameterization. In the case of CALIOP corrections are applied and it would be interesting to compare them to those proposed via the parametrization.

Other aspects:

P4. How are the number of realizations (photons) chosen? How are the results degraded?

P5. Degassing feathers = ash feathers?

Table 1. Define the parameters in the caption table.

P8. The number of significant scattering orders is closely related to the number of photons. It would be nice to see this relationship.

P10L160. For figs 3,5 and 8 it is R that is used while the adjustment is made on G. In order to make it more understandable for the reader, it would be better to present G or to adjust on R. At this stage of the paper, there is nothing to justify such a model. Why this choice?

Eq.18. Development to 2nd order of arctan whereas before it was 1st order

P11L292. This is an important result for the paper and should be in the body of the paper or at least in an appendix. Furthermore, it would have been nice to show graphically the fits on an example and a sensitivity study to these fits against the coefficients a1,a2 and a3.

Figure 3: What explains the difference in the spread of points between the layer types?

P14L330. Why 5%?

P14L336. 8 km of higher = 8 km or higher?

Table 2. The values in the table are in %?

Appendix A. It is not clear what the authors are trying to demonstrate here. The functions are indeed different, but they remain related. It depends on the initial hypothesis that is considered. Is this appendix useful?

This paper develops simple functions to characterize the impacts of multiple scattering on lidar observations, based on simulations from a physics-based Monte Carlo multiple scattering code.  The simulations are performed for one type of coarse aerosol, one water cloud case, and two cirrus cases, for typical configurations of ground-based and airborne lidars and for the CALIOP and ATLID spaceborne lidars. 

I think this paper is a useful introduction to and overview of lidar multiple scattering effects.  I disagree with the comment from RC2, who says “This aspect of Monte Carlo simulation is therefore not original in itself and many models exist in laboratories around the world. It is a basic design tool.”  Not every lidar group considers multiple scattering or applies corrections. Multiple scattering codes should be a basic design tool, but it is often not considered in lidar retrievals under an assumption that the lidar design ensures they are insignificant.  The results presented in this paper are helpful to groups which haven’t previously considered multiple scattering, and to users of lidar data who want to understand under what conditions the impacts should be considered and perhaps apply corrections to the data which is not already corrected.

The discussion of the method is sufficiently detailed but the discussion of the results is mostly a factual description of the simulations and fitting results.  Some interpretation and synthesis of the results into general conclusions and guidance is needed.  The major goal of the paper seems to be to identify conditions where multiple scattering are small enough they can be ignored.  The paper identifies these conditions for the four particle types considered and two ‘standard’ FOVs.  The authors should use their results to make more general statements.  Only a few specific lidar viewing geometries and particle cases are considered.  What are the limitations in using these fitting equations to estimate multiple scattering for other conditions (range, FOV, extinction, particle size).  Are the aerosol, water cloud, and cirrus types defined in a way that they predict typical multiple scattering effects?  Are the conclusions valid over expected variations in particle size?  There is some variability in cirrus phase functions due to differences in particle habit.  Would you expect variations in habit to change these conclusions?   

Specific comments

Line 23: The authors should quantify here what is meant by “acceptable”

Line 126: Is “coarse aerosol” meant to represent dust?  More details should be provided on the model for coarse aerosol:  index of refraction, shape (spheres, spheroids, aspect ratio),  and size.  Why was this particular model chosen, is it generally representative of coarse aerosol?  Is multiple scattering different for desert dust or hydrated sea salt aerosol of similar size?  How sensitive are the results to changes in aerosol optical properties?

Line 321: Explain why 5% is selected as the threshold where the multiple scattering contribution must be considered.  Because 5% is smaller than other sources of error typically found in lidar retrievals?

Technical corrections

Line 24 and 40: “of 1 km”  does this mean ‘equals 1 km’, ‘less than 1 km’?

Line 65: “techniques” should be “technique”?

Line 77: when “the” impact

Line 100: “The” other two …

Line 265, 383, 409, and 452: “again” rather than “another time”

Line 632: “drown” should be “shown”?

Line 637: “the shown in Fig. A1b function” should be “the function shown in Fig. A1b”, I think