General comments: The authors numerically simulated single-wavelength lidar multiple scattering signals by the Monte Carlo method, and focuses on the impacts of cloud multiple scattering on the lidar return signals in the cloud-free molecular atmosphere between cloud layers or outside a cloud layer. The author reported some interesting results, for example, the ratio of multiple scattering contributions to single scattering signals in the molecular atmosphere near the cloud edge is even larger than the ratio in the cloud (i.e., stepwise jump phenomena), and the multiple scattering effects are decreasing with the increase of the distance from the cloud edge (i.e., escape effects), and so on. It is worth publishing. However, there are several shortcomings in this paper. First, why did the authors set the altitude of the cloud base to 8km? It is too high for water clouds. Why is the extinction coefficient of the water cloud set to 1.0 km^{-1}? It is too small. It is not representative for water clouds. The authors should give a reasonable explanation for this. Secondly, the simulation results are particularly noisy. Is it convincing? Thirdly, there is logical confusion in the interpretation of the simulation results in Section 3.1.1, which is misleading. For example, the authors stated that the stepwise jump phenomenon is simply caused by the stepwise jump in the phase function at scattering angles close to 180 degrees. In my opinion, other factors (such as the molecular extinction coefficient) also might have effects on this. The validation results in Fig 3a and 3b can only show that the free atmospheric signal is mainly affected by the forward scattering of clouds. The author mentioned pulse stretching many times and emphasized that their explanations are different from pulse stretching explanations. Can the author specifically point out the difference between the two? Finally, this paper is rather lengthy, and the simulation description is repeated many times. It is suggested that the author refine the text to improve the reading experience.

Specific comments:

Line 62-66 in Section 1: “results of MC simulations published in the literature evidenced the following. As it is expected, lidar signals from regions of the cloud-free molecular atmosphere … are affected by the scattered light emerging from clouds.” Has the literature analyzed this multiple scattering effect in detail? If so, what is the difference between the results discussed by the authors and them? The authors should make a detailed discussion on this, which is the main contribution of this paper.

Section 2.1: Subscript “MS” is used in several physical quantities and has different physical meanings, which are easy to cause misunderstanding. For example, it denotes total order-scattering in the lidar signal S_{MS}, while the contribution of single scattering is excluded in the ratio R_{MSto1}. In contrast, the ratio R’_{MS} contains the contribution of single scattering.

Section 2.1: I suggest providing a simple schematic diagram to describe the lidar sounding of the cloud-free atmosphere outside the clouds. It will be especially helpful for understanding formulas (especially Eq. (8-14)).

Line 92-95 in Section 2.2: As seen from Fig. 1, the phase function f_{ch2} is the same as the f_{ch1} except for the backscattering directions. Does this mean that f_{ch2} does not meet the normalization condition? If so, it would significantly increase the backscattering contribution of lidar signals, and the difference between Figs. 3a and 3b will be easily understood. See the comment “Line 265-293 in Section 3.1.1”. The author should briefly elaborate on it.

Line 209, 215, and 386-387: Why is the extinction coefficient of the water cloud set to 1.0 km^{-1}? It is too small. It is not representative for water clouds. Why did the authors set the altitude of the cloud bottom to 8km? It is too high for water clouds. The authors should give a reasonable explanation for this. Alternatively, the authors at least emphasize the scope of application of the conclusions made in this paper in the abstract or conclusion.

Fig. 2 in Section 3.1: The simulation results are particularly noisy in Fig. 2. Is it convincing? Can the authors reproduce the simulation results using other Monte Carlo programs?

Line 261-262 in Section 3.1.1: “It means that only the range 𝑑 ∈]3., 3.02] km of 𝑅2𝑡𝑜1(𝑑) can be somewhat affected by the pulse-length stretching.” Why is only the range in [3,3.02] affected by a little pulse-length stretching? According to Miller and Stephens, 1999, if multiple scattering (except the exact forward scattering with zero scattering angle) occurs, the half of light path length will be greater than the sounding ranges under the single scattering approximation, and pulse stretching will occur. From this point of view, the multiple scattering signals in the cloud-free atmosphere can be considered as caused by pulse stretching, but the influence degree is different.

Line 262-264 in Section 3.1.1: “Thus, it is safe to assume that the stepwise jump of 𝑅𝑀𝑆𝑡𝑜1(𝑑) and 𝑅2𝑡𝑜1(𝑑) is due to the stepwise jump in phase-function properties at angles close to 180° (the phase function of particles within the cloud and the Rayleigh scattering within the free atmosphere).” It is too vague to be misleading. Do the authors mean that the stepwise jump of 𝑅_{𝑀𝑆𝑡𝑜1} is caused by the stepwise jump in the phase function of the water cloud within the scattering angles close to 180 degrees or the significant difference between the phase function of the water cloud and the Rayleigh scattering at scattering angles close to 180 degrees? I prefer to think of it as the latter. However, I think other factors (such as the molecular extinction coefficient) also have effects on this.

Line 265-293 in Section 3.1.1: “That assumption is confirmed by the plots in Figs. 3a and b”. It's not convincing. It can only show that the phase function of the water cloud at scattering angles close to 180 degrees can affect the lidar multiple scattering signals in the cloud, but not in the cloud-free atmosphere. Therefore, it can show that the free atmospheric signal is mainly affected by the forward scattering of clouds. However, it is hard to demonstrate that the stepwise jump pattern occurring in the cloud-free atmosphere is due to the stepwise jump in phase-function properties at angles close to 180°.

In my opinion, it can be more clearly explained by the small-angle forward scattering theory, i.e., the lidar signal is contributed by the light that experiences a series of forward scattering from the emitter, then a single backward scattering, and finally a series of forward scattering back to the receiver. The forward scattering is roughly the same for both the cloud and the free atmosphere. They all occur in the cloud. The difference is the backscattering events, one occurring in the cloud and one occurring in the free atmosphere. Therefore, I claim that both the molecular extinction coefficients and phase function are the main reason for the stepwise jump in the 𝑅_{𝑀𝑆𝑡𝑜1}.

In addition, the author mentioned pulse stretching many times and emphasized that their explanations are different from pulse stretching explanations. Can the author specifically point out the difference between the two?

Line 294-302 in Section 3.1.1: The explanation of the “escape effect” is incomplete. In addition to the large forward diffraction ring relative to the field of view, the particularly small cloud extinction coefficient should also be a major reason. This is because if the extinction coefficient is large, the average free path length of light is short, and it is difficult to escape from the sampling volume even after many times of scattering. That's why I asked the authors to explain why they chose this special case.

Line 309-314 in Section 3.1.1: “the pulse stretching is the cause of the jump” This judgment seems to be too subjective. Although the field of view is large, the extinction coefficient is too small and thus the free path length is large, so the light may not be able to experience enough scattering to produce obvious pulse stretching.

Line 408-410 in Section 4.1.1: “Thus, the stepwise jump in those cases is not only due to the stepwise jump in phase-function properties for angles close to 180°. We can suggest that the range 𝑑 ∈]3., 3.1] km is somewhat affected by the pulse stretching.” This judgment seems to be too subjective. Can the authors specifically show the difference between the two explanations? It is the same question in the comment “Line 265-293 in Section 3.1.1”

Line 430 Section 4.1.2: “The NUBF effect is so high in such conditions that it has to be shown in terms of lidar signals.” It's expected, I think, and it's easy to predict. Can the author provide the lidar single scattering signal results in the case of a three-dimensional cloud field? This may be more interesting.

Technical corrections:

Line 52 in Section 1: “Using some cases as examples, good performance of approximate models was underlined by their authors.” It is too vague to provide any useful information.

Line 75 in Section 1: “because multiple integrals are in its core. Therefore, it is an easy matter to develop the corresponding code.” It seems that there is no logical relationship between the two, so it is suggested to modify it clearly.

Line 156 in Section 2.2: “matrixes” can be corrected to “matrices”.

Line 191 in Section 2.2: “The Gaussian component 𝐺2(𝜃) is large” need be corrected to “The width of …”.

Line 261 in Section 3.1.1: “the distance from the lidar to particles of the cloud layer is quite low” It is “short” not “low”.

Line 337 in Section 3.1.2: “when and 𝜀𝑝 ≤ 0.2 km-1.” The word “and” may need to be deleted.

The detailed analyses are clear and important in this manuscript. The authors have taken novel piece of work, which is of great interest to focus on peculiarities of MS effect in regions of the cloud-free molecular atmosphere and to evaluate performance of an approximate model with the focus on cloud-free regions. For this reason, I felt and consider the subject of this paper is interesting. The results are relevant, and appropriate for the journal. The whole paper is straight forward, the conclusion is convincing but not well written. I believe the manuscript can be made publishable, but will require significant revisions.

Is there any limitation for the model used in this manuscript? In the instrumentation/method part, the uncertainties and precision of datasets obtained from LIDAR (ground mounted-space-borne) should be elaborately discussed. It is suggested to include the limitations, accuracy levels with some of its values (scattering characteristics of LIDAR signals, which leads to resolve the uncertainties) in tabular form.

As I found some mismatch, so suitable tools/formats should be followed thoroughly e.g., math tool should be used to write parameters of equations, non-italic. In addition, different formats of braces and square brackets were found; it should be presented in a consistent way. Spelling errors (may be typo) should be omitted e.g. Mont-Carlo simulations or Monte-Carlo simulations (see section 2.2). Numerous different corrections and suggestion are made in PDF form so have a look on them and carry on accordingly.

It is just on a lighter note: are the authors in position to present extinction coefficient vertical profiles of LIDAR, if any, I urge to have certain studies that definitely make the studies worth more. The authors should use and cite updated research work, not before 2010. It should include more details on the specific algorithms or techniques used to differentiate between single and multiple-scattering events.

Is there any scope to present the statistics of interesting results in tabular form? If so, i urge to include in the revised version. I suggest the authors to devote adequate time to proof read the manuscript correcting typos and grammar. Also the level of language used could be improved to depict some scholarly writing.