The authors present an approach to quantify the effect of forest on a (slow) moving avalanche. To this end, they study the detrainment and braking  due to trees by using a 3d model approach based on the material point method and a rheology previously proposed by one of the author.  

They study varing forest stand composition  and derive an empirical formula for practical use. The newly proposed formula is compared to one proposed  by Feistl (2015). 

The paper presents an important step to describe and quantify the interaction between avalanches and and the efficiency of a forest to mitigate moving avalanches.

General commnts:

The authors refer to the the approach by Feistl (2015). At this point it would be valuable for the reader to get some more information about this approach without to have to look  the full thesis. 

To enhance the practical usefulness, it would be nice, if the parameter study would cover more typical parameter combinations of forest stands. Firstly  a tree diameter of 1 m refers to a rather very mature forest. Secondly, the stand density index  (Reinke, 1933)  in their example (figure 9)  covers a range from  SDI = [900, 3600], whereby the later sound rather high..Using a combination of  1 m diameter and 400 trees per hectare suggests an efficiency that a natural forest probably doesn't  fulfill.

The SDI would, properly, serve also better as fixed value for the comparison in figure 8 than the forest density.

By the way, for practitioners it is properly  more common to speak  of number, N, of trees per hectare , instead of density.

Instead of using the ambiguous expression forest cover, it is the basal surface area per hectare that is meant here.

Otherwise, the paper is well written and is a valuable contribution to an important question in respect to avalanche hazards and its mitigation.

This manuscript discussed the snow avalanche protection efficiency of the forests with applying the 3D MPM combined with the modified cam Clay model. This approach developed by the authors’ group looks very powerful and promising to break through various aspects of snow avalanches from its initiation to dynamics. In actual, 3D MPM provides overwhelming useful information comparing to the previous depth averaged model. Further, once the model has been established it can be applicable under the various conditions. Taking into conceivable factors, the deduced relations in this study will be quite useful for the practical applications, I believe. Although it is out of scope here, I hope the authors proceed the research on the other aspect as well: how the forest stabilizes the snowpack and prevent from the snow avalanche release.  

All the methodologies and discussions are well organized and carefully described. So, I believe this article is worth publishing. However, I am glad if the authors can clarify and improve some of the points listed below before the publication.   

Line 47: K is used for not only the detrainment coefficient but the material bulk modulus in eq. (5).

Please check fonts of variables. They are not always unified in the text, the figure and figure captions: italic or vertical, such as spacing of trees “e”.

Line 102: “CFL” means Courant-Friedrichs-Lewy Condition? Since it is not so common outside the numerical simulation field, the brief explanation is preferable, if you dare to use.

Line 121: M=0.8 snow, defined as warm shear regime, agreed well with the field observations. On the other hand, Case 3 of M=1.2 is also set as the warmer case in Table 2. So, the Case 2 of M=0.8 snow correspond to the snow which is dry but the temperature is close to zero? I am curious whether you have got the information of snow properties by Feistl et al.? Are these reasonably agree with the physical parameters given in this study? In this study snow properties are designated with snow friction coefficient: M, the tension compression ratio:β , the hardening factor ζ, and initial consolidation pressure p⁰_ini. Although the general features of snow defined with these parameters are explained briefly, it will be glad if the authors clarify the relations more specifically with the snow properties we usually observe in the field.   

Further, do you have any idea how you can validate that the model is also appliable for the dry snow?

Table 2: The hardening factor ζ is set the same for both dry and wet snow. Is this reasonable?

Figure 2: No snow depositions are found in (b) after the rectangular domain. Does it mean all the snow went through?

Table 2: Density of Case 1 which is explained as cold “dense” regime is still 200 kg/m³?

It is the same as other two warmer cases? I do have an impression that the density of the dry avalanche is usually lighter than the wet one. In particular, densities of granules and blocks in Case 3 are still 200 kg/m³? I wonder densities described here perhaps show bulk densities including air and snow?

Line 185: Although it does not matter much, I am a bit worried that authors use the word “impact” frequently. Since this article deals with the avalanche impact on the forest in actual, I prefer rewording such as “action”, “affect” and “influence” to avoid the misleading.

Figure 6: Eq. 3.5 and 3.4 in the figure must be Eq. 8 and 9.

Is it just a coincidence that Case 1 maximum and Case 2 final agrees quite well? Further, please specify the reason why Case 3 is not shown here.

Figure 8: Again, here why case 1 is not introduced?

Figure 9: Please explain physically why the detrainment mass is proportional to the third power of the forest density.

Table 3: According to Figure 8, the relation between the detrainment mass and tree diameter for Case 2 and Case 3 are obviously different even though the front velocities are almost the same (11.2 m/s and 10 m/s). Thus, I do not understand the reason why you can use the same p3 and p4 for all three types of snow as shown in Table 3. Further, although no results are not introduced in 4.2.2, I am wondering the snow type does not give any effect on the forest density consequence.

Line 273: Please explain why the detrainment energy, when the avalanche reaches the bottom of the valley, is similar between the random and the regular staggered arrangements, in spite of the fact that the final stopped mass with both arrangements are largely different.

Line 281: Random arrangements is the most effective to stop the avalanche. I am curious how you suggest to people in charge who take care of and manage the forest? Do you say the forest should leave as it is without artificial maintenance? Foresting should be done randomly?  

The manuscript “Detrainment and braking of snow avalanches interacting with forests” by Vedrine et. Al. is a computational study on how detailed numerical modelling approaches can contribute to investigate how gravitaitonal mass flows interact with obstacles. The forest (obstacles) can offer a protective effect which reduces the size or frequency of avalanches by stopping the formation of avalanches or reducing the magnitude of an event. This work focuses on quantifying the mass and energy reduction capabilities of forest (detrainment and braking) in the transit zone of a small or medium sized avalanches by detrainment, which reduces the kinetic energy of the avalanche by removing mass.

The work highlights the possibility of using purely numerical methods (MPM) to quantify the potential effect of forests and parameterize the forest snow interaction within simple relationships of terrain (slope), flow (velocity) and forest parameters (density). The simulation experiments were carried out on a generic slope with a constant slope angle, examining the influence of mainly avalanche type/velocity and different forest formations/density with respect to mass/energy reduction. The parameters of the MPM avalanche model are defined by prior experiments to resemble the behavior of colder to warmer flow regimes and calibrated with regards to snow forest interactions based on a single documented field observation.  The single event validation could be considered as weakness of the study. However it is known that corresponding data is sparse – but it would be interesting to comment on other the possibility of other parameter combinations that might lead to similar results, or how they would change for another observation example. Another clarification would be desirable for the definition (and numerical implementation) of detrained mass (see specific comments below) in the MPM model and how changing boundary conditions (slope angle) would influence the results.

 Generally, the manuscript is well written and well organized, providing suitable figures and supplementary material. Some possible enhancements include the figures in the energy analysis and the consistency between equations and figures (e.g. fig 5, “velocity” = “v_f” in eq. 7, more examples in the specific comments (e. g. Fig 10)).

Specific comments:

• l 11: “wet compared to dry snow”: Since this is a numerical study i would suggest to rephrase (or is there evidence in field observations?): “for the parametrizations of cold to warm snow”
• l 36: What about the study of “Brožová, N., Fischer, J. T., Bühler, Y., Bartelt, P., & Bebi, P. (2020). Determining forest parameters for avalanche simulation using remote sensing data. Cold Regions Science and Technology, 172, 102976 (11 pp.). https://doi.org/10.1016/j.coldregions.2019.102976”. Does it relate or include relevant data to evaluate the results of this study?
• Table 2 “Case 1..3”: I think it could be beneficial to name the cases “cold/intermediate/warm” here and throughout the paper to make it easier for the reader (and please check consistency of warm/wet and cold/dry throughout the paper).
• l 143, “some arches appear in case 3”: Can you comment on how “arches” (surges?) are defined in this context?
• l 165 “detainment mass”: Does this mean snow is considered detrained if its velocity<0.5m/s and adds to “M_stopped” – how does it relate to (frictional) stopping – are these numerical of flow model quantities? A clarification on the definition of “M_stopped” seems to be crucial for the paper and could be included at this point, particularly the difference between “stopped” (Fig 5), “maximum” and “final” (Figs 5,6) or “stored” (Fig 7). Please also check the corresponding units [kg] or [kg/m^2] used for “M_stopped”.
• l 192: Does maximum detrained mass refer to the maximum over time (detrained snow = v> 05m/s?, see comment above)?
• l 214: Should this not be p_3 and p_4?
• l 243: This sentence is confusing, please clarify: decreases linearly, as function of ..?
• l 281: Is the statement that the random distribution has a higher protective effect valid after checking one specific distribution?
• l 301: Please double check the argument with low/high velocities.

 Equations:

• Why Is “.” Sometimes used as mathematical symbol for multiplication in the manuscript (e.g. eq. 7-11)?

 Figures:

• Fig 2: “d” and “e” are used twice once for tree diameter and spacing and once for the forest arrangements. “snow profile” should rather be “vertical velocity profile”?
• Fig 6: legend wrong? 3.5 and 3.4 are the ones in Feistl et al. And eq. 3.4 is the same as eq.8? 
• Fig 7: is this for case 2?
• Fig 10: is “M_d” from MPM the same as “M_stopped” in the previous figures (same, “M_d” from eq. 11 = “m_d”). What kind of r^2 is used? Is it possible to comment on how the different cases (1-2) are distributed in this figure?
• Fig 11: Do both avalanches reach the bottom after 9s (effect of forest on front velocity)?