Has it<em> really</em> stopped? Interplay between rheology, topography and mesh resolution in numerical modelling of snow avalanches

Goodwin, Saoirse Robin; Faug, Thierry; Chambon, Guillaume

doi:https://doi.org/10.5194/nhess-2024-123

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https://doi.org/10.5194/nhess-2024-123

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29 Jul 2024

| 29 Jul 2024

Status: this discussion paper is a preprint. It has been under review for the journal Natural Hazards and Earth System Sciences (NHESS). The manuscript was not accepted for further review after discussion.

Has it really stopped? Interplay between rheology, topography and mesh resolution in numerical modelling of snow avalanches

Saoirse Robin Goodwin, Thierry Faug, and Guillaume Chambon

Abstract. Depth-averaged models of snow avalanches have hitherto lacked an objective arrest criterion. In this study, we investigate the stoppage mechanisms of simulated avalanches, considering the interplay between mesh resolution, simple/complex topographies, and cohesion. We use a second-order depth-averaged model including a modified Voellmy model with cohesion and a physical yielding criterion. Simulated results were found to be sensitive to the mesh resolution, until the cell width is less than 20 % of the characteristic flow depth. The yielding criterion is sufficient to unambiguously define flow arrest for highly cohesive avalanches, even on the complex topography with feature sizes comparable to the typical flow depth. In contrast, for weakly-cohesive avalanches on the complex topography, a fully static state is never reached, due to numerical diffusion enhanced by local non-zero slopes. We hence investigated different global and local arrest criteria applied during post-processing, complementing the yielding criterion. Most of these criteria require setting ad-hoc thresholds, the values of which depend on numerous factors. However, tracking the evolution to a static state of the highest point of the flow material in the runout zone appears to offer an objective and practical solution to indicate when the model enters a numerical-diffusion-dominated regime, whereupon simulations can reasonably be terminated.

Received: 29 Jun 2024 – Discussion started: 29 Jul 2024

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Saoirse Robin Goodwin, Thierry Faug, and Guillaume Chambon

Status: closed

RC1:
'Comment on nhess-2024-123', Stefan Hergarten, 01 Sep 2024

The manuscript describes the extension of a depth-averaged flow model that uses Voellmy's rheology by a physically-based stopping criterion. To be honest, I am not convinced by the manuscript in its present form. There are too many aspects not explained or justified sufficiently.
(1) There is only a vague promise to disclose the codes used for the simulation and for the analysis after acceptance of the paper. This makes

assessing the correctness of the manuscript difficult.
(2) It does not become clear whether the issue addressed in the paper is a general problem of Voellmy's rheology (and then also of similar rheologies) of just a deficiency of the implementation used here (and perhaps of some other implementations). In the beginning of Sect. 2.2, it reads as if Voellmy's rheology itself would not let the material come to rest. This is not true since material will finally come to rest if the tangent of the slope angle of the free surface is smaller than the coefficient of friction μ. This means that spreading of the deposits in the runout zone should stop completely. Otherwise, there may be a problem with the numerical implementation of the friction term. I was involved in two model developments. One of them (based on Gerris, doi 10.5194/nhess-15-671-2015) lets the fluid accelerate first an the uses a fully implicit scheme for the friction term, which leads to a permanent creeping and some artificial spreading of the deposits. The other (MinVoellmy, doi 10.5194/gmd-17-781-2024, already cited) uses a mixed scheme for the friction term and stops reasonably well in the runout zone. I do not know whether the model used here includes a 'good' or a 'bad' implementation of the friction term.
(3) It is true that some models include am empirical (non-physical) stopping criterion. However, there is no illustration or discussion how strong the effect of such a criterion is practically and whether it might be relevant for hazard assessment.
(4) The stopping criterion (Eq. 6) is not explained completely since a proper definition of τ_{b,test} is missing. Is the criterion just that the actual momentum could be consumed entirely in the actual time step, as implemented in MinVoellmy? Or is it something more elaborate?
(5) The authors often refer to numerical diffusion as the source of the issues addressed in this manuscript. This is not clear to me, in particular since the simple implementation in MinVoellmy does not include any measures against numerical diffusion, but shows little spreading of the deposits.
As a second aspect, the manuscript discusses the effect of an additional cohesion term in Voellmy's rheology. In contrast to the points discussed above, this aspect becomes clear, but is not very surprising. As mentioned above, Voellmy's rheology without cohesion lets the material move permanently if the fluid surface is steeper than the tangent of the coefficient of friction μ. This results in an ongoing, but small flow into the runout zone and finally lets the runout zone grow a bit. Cohesion just results in an increase of my by a term τ_c/(ρ g_z h), which is inversely proportional to the thickness h. So flow on the slope stops if the thickness falls below a threshold that depends on cohesion.
From my point of view, publishing the manuscript as a research paper would require much more explanation of the approach and convincing arguments that the problem addressed here is important for practical applications and that it is a general problem and not just a deficiency of the implementation used here.
Since these points are quite fundamental for me, I do not write line-by-line comments at the moment, but look forward to reviewing a revised version. I would also like to point out that my rating of the manuscript refers to the 'worst-case scenario' and would be much higher if the points raised above can be addressed.
Best regards,

Stefan Hergarten

Citation: https://doi.org/10.5194/nhess-2024-123-RC1
- AC1: 'Reply on RC1', Saoirse Goodwin, 22 Oct 2024
  
  The comment was uploaded in the form of a supplement: https://nhess.copernicus.org/preprints/nhess-2024-123/nhess-2024-123-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/nhess-2024-123-AC1
RC2:
'Comment on nhess-2024-123', Anonymous Referee #2, 02 Sep 2024

In this paper, the authors aim to define criteria for when material truly stops in depth-averaged models, distinguish between physical stopping mechanisms and issues related to numerical diffusion, and discuss or propose best practice guidelines to address these challenges. The manuscript examines the interplay between three key variables affecting avalanche arrest: mesh resolution, topographic complexity, and snow cohesion. The authors use a second-order depth-averaged model as a test framework, incorporating a modified Voellmy model with cohesion and a physical yielding criterion. To the best of the reviewers' knowledge, this complete form of the model has not been tested before.
Defining criteria for when material truly stops in depth-averaged models is challenging from both physical and numerical perspectives. Numerical diffusion depends on factors such as the numerical scheme, grid resolution, and time-stepping methods. Additionally, physical stopping mechanisms are a matter of debate and vary from model to model. The choice of stopping condition is closely linked to the specific output the model is intended to produce. As a result, there isn't a one-size-fits-all criterion for determining when material has truly stopped moving in a numerical model. Each model's unique characteristics mean that numerical diffusion can have varying impacts, requiring tailored criteria to accurately assess stopping conditions. This issue also extends to different mechanical deposition criteria.
In this respect, I’m not yet convinced that the paper will have a significant impact on the international community, as the results appear specific to the models used by the authors and lack broader evidence of global relevance. The proposed global arrest criteria are not entirely new or convincing. For example, the role of calculation grid resolution has already been established in previous work, and the other criteria can also be questioned (see comments below). The authors need to strengthen their arguments in this regard.

Furthermore, I feel the paper lacks a discussion or analysis regarding the overall relevance of the stopping issue in relation to the final outputs. Ultimately, what really matters is how much the runout distance or the impact pressure at a specific location can be influenced by these issues. Understanding this impact is crucial for assessing the practical implications of the stopping criteria.
Finally, although the paper’s main aim is not focused on the model’s performance, the extensive description of the model and the impact of cohesion raises questions about the physical appropriateness of the model. For example, the cohesion values used in the simulations (1-100 Pa) are relatively small compared to the broader range of possible values mentioned in the paper (0-2300 Pa). Despite this, the model shows a strong response to variations in cohesion. Is this behavior physically realistic? This is particularly important to discuss because cohesion take an important role in your conclusions.
Other comments:
Abstract, line 1: I disagree with the assertion that 'depth-averaged models of snow avalanches have hitherto lacked an objective arrest criterion.' The paper does not adequately test or consider existing methods—many of which are mentioned in your bibliography but not further analyzed—making such a blanket statement misleading. Furthermore, it’s important to clarify what differentiates an objective criterion from a subjective one. For instance, a limit based on the physical threshold of a variable is, in my opinion, also an objective criterion.
Figure 2: The captions are generally very small; please ensure they are easily readable. Additionally, the legend describing the green-brown color is missing.
Line 136: At the beginning of a sentence, 'Figs. 3a' should be written out in full as 'Figure 3a' for proper academic style. This issue occurs multiple times throughout the paper, so I suggest a thorough review.
Line 137: How are the center of mass and the tip of flow defined (CoM) exactly? In depth-averaged modeling, defining the avalanche tip and the center of mass is not entirely straightforward and can be complex due to several factors.
Line 138: you mean substantial flow stoppage? not substantive
Figure 3. The figure shows 6 visible lines, but there are 10 items in the legend, for each graph. Please mention in the caption that some of the curves are overlaid? Or are they just missing?
Line 139: It is observed that grid sizes of 320x160 and coarser significantly influence simulation results. Do you mean 160x80? I think the 320x160 is not visible in the graphics. Additionally, the 160x80 grid shows only around a 2% difference, which is relatively minor. Providing these percentages helps clarify the magnitude of the error we are discussing.
Lines 147-150: The flow is described as stopping 'from the bottom up.' Could you clarify whether this refers to a back-propagating shock or if you are indicating that material stops first on gentler slopes and, in more cohesive scenarios, even on steeper slopes? The terms 'bottom-up' and 'bottom-down' seem unclear and could be misleading in this context.
Caption figure 4: (f) τc = 10 Pa should be τc = 100 Pa. I’m wondering: The cohesion values used in your simulations (1-100 Pa) are relatively small compared to the broader range of possible values mentioned in the paper (0-2300 Pa). Despite this, the model shows a strong response to variations in cohesion. Is this behavior physically realistic? Could you provide an explanation for why the model reacts so significantly to these relatively small changes in cohesion?
Line 203: As shown in the previous section, relying on the physically-based yielding criterion is generally insufficient for defining avalanche arrest objectively when a realistic, complex topography is considered. These assertion may not be entirely accurate. This conclusion could be influenced by the specific yielding criterion used in this study, which might not be the most suitable for the scenarios considered. Consequently, this raises questions about the extent to which the results obtained from this analysis can be generalized to other models. This need to be discussed in the paper.
Figure 5 and Lines 168-178: : In my understanding the higher the cohesion, the slower should be the flow, the longer should be the simulations time to allow all material to come to a natural rest. This effect is reinforced on complex topography because the random acceleration and decelerations phases. Therefore, it is crucial to define when the avalanche has truly physically stopped, before compare results. For example: What happens to the curves with complex topography and high cohesion if the simulation is extended to 30 seconds? Specifically, how much time does it take for all the material to reach the flat slope and come to a complete stop? At what point does numerical dissipation begin to affect the results? I do not believe this distinction is adequately addressed in the paper.
Line 183 At time t = 2 s, is it observed that cohesion τc and the topographical complexity only weakly affect the results … The maximum difference is around 1m/s ( 8 to 9 m/s velocity maximum) corresponding to around 10 %., so, not so small.
Line 225_226. Potentially, it could thus offer a more objectivecriterion to define effective flow arrest, although it would still require to be manually pinpointed on the curves. This would mean applying a different criterion for each individual simulation and scenario, which may not simplify the process. I do not believe this would make things easier or that it represents an applicable rule.
Line 251-252. For simple and complex topographies, Figs. 9 and 10 show time-histories of different metrics relating to the highest point of the flow material on the runout zone: It is unclear what is meant by 'the highest point of the flowing material in the runout zone.' Are you referring to the location of the point with maximum flow or deposition depth at each time step in the lower part of the track (x > 20 m)?
Figure 9 shows metrics related to the highest point (hp). However, the figure does not specifically reference the 'highest point' but rather shows flow depth. It would be clearer to use the term "maximum flow depth" in the caption to accurately match what is presented in the figure. This change should also be reflected in the main text.
Additionally, it is unclear why mesh resolution is considered again, given that its major impact was already established. Furthermore, the symbols for the curves, especially for velocity, are difficult to distinguish. Improving the differentiation of these symbols would be helpful. Only two subplots are labeled with letters. All subplots that are discussed should be labeled, and each description should clearly indicate which subplot it refers to.
Lines 259-260: Why is the discussion returning to mesh resolution, which was already addressed and fixed in Section 3.1? The paper is complex enough, and mixing processes can lead to more confusion. It would be better to keep the discussions on different processes as separate as possible.
Lines 272-273: The statement suggests that certain metrics related to the highest point in the runout zone—specifically, the first transition to a static state and the cancellation of its velocity—serve as objective criteria for defining avalanche arrest. However, I find this problematic. In real-world avalanches, the first point that stops in the runout zone can be overrun by material still in motion along the avalanche path, often reaching the deposition zone with a slight delay compared to the leading front. Therefore, this stopping criterion is only valid when the entire mass moves as a cohesive front, which is rarely the case in practice.
In depth-averaged modeling, "overrunning" cannot be directly accounted for, but material from behind can still push the already deposited material. Could this be a possible reason for the observed shift in maximum depth, as shown in Figures 9 and 10? If I’m misunderstanding, it might be due to the lack of straightforward visualization in this part of the paper. Perhaps the authors could provide a video to better illustrate the processes involved?
Lines 278-279: The statement 'However, sufficiently robust and objective arrest criteria are hitherto lacking' in the paper is questionable. Many models already have established stopping criteria, and the paper does not provide sufficient evidence to demonstrate their lack of robustness. Additionally, it is debatable whether truly universal robust criteria can be developed that are effective across all models, given the diverse nature of numerical diffusion and stopping conditions.

Lines 337-338: The claim that 'mesh resolution affects simulated flow properties if the cell size is larger than about 20% of the characteristic flow depth, typically for both simple and complex topographies' cannot be generalized. These values are specific to your particular setup and should be clearly stated as such. Furthermore, this aspect is already well established in the literature.
Lines 341-345: The statement regarding large cohesion values promoting a full transition of the material to a static state …..and following lines, seems more aligned with the conclusions of a different study. The influence of cohesion on snow mobility is a distinct topic from the primary focus of your paper. Furthermore, numerical dissipation can be seen as a weaker effect compared to strong physical processes like cohesion. It is obvious that when cohesion is high, it plays a dominant role in stopping the material, reducing the significance of numerical dissipation. Dissipation effects may only become prominent when physical forces, such as cohesion, are weaker. Maybe you can discuss on that.
Lines 355-358: The statement that 'identifying when/whether avalanches are arrested is of paramount importance for, e.g., hazard zoning or designing mitigation measures' is too general. Such a claim should only be made when there is a clear understanding of how these arrest criteria impact key variables, such as runout distance and pressure. Additionally, it is important to note that models are primarily used to generate scenarios, which are then compared to historical data and evaluated by avalanche experts before the final danger assessment.

Citation: https://doi.org/10.5194/nhess-2024-123-RC2
- AC2: 'Reply on RC2', Saoirse Goodwin, 22 Oct 2024
  
  The comment was uploaded in the form of a supplement: https://nhess.copernicus.org/preprints/nhess-2024-123/nhess-2024-123-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/nhess-2024-123-AC2

Status: closed

RC1:
'Comment on nhess-2024-123', Stefan Hergarten, 01 Sep 2024

The manuscript describes the extension of a depth-averaged flow model that uses Voellmy's rheology by a physically-based stopping criterion. To be honest, I am not convinced by the manuscript in its present form. There are too many aspects not explained or justified sufficiently.
(1) There is only a vague promise to disclose the codes used for the simulation and for the analysis after acceptance of the paper. This makes

assessing the correctness of the manuscript difficult.
(2) It does not become clear whether the issue addressed in the paper is a general problem of Voellmy's rheology (and then also of similar rheologies) of just a deficiency of the implementation used here (and perhaps of some other implementations). In the beginning of Sect. 2.2, it reads as if Voellmy's rheology itself would not let the material come to rest. This is not true since material will finally come to rest if the tangent of the slope angle of the free surface is smaller than the coefficient of friction μ. This means that spreading of the deposits in the runout zone should stop completely. Otherwise, there may be a problem with the numerical implementation of the friction term. I was involved in two model developments. One of them (based on Gerris, doi 10.5194/nhess-15-671-2015) lets the fluid accelerate first an the uses a fully implicit scheme for the friction term, which leads to a permanent creeping and some artificial spreading of the deposits. The other (MinVoellmy, doi 10.5194/gmd-17-781-2024, already cited) uses a mixed scheme for the friction term and stops reasonably well in the runout zone. I do not know whether the model used here includes a 'good' or a 'bad' implementation of the friction term.
(3) It is true that some models include am empirical (non-physical) stopping criterion. However, there is no illustration or discussion how strong the effect of such a criterion is practically and whether it might be relevant for hazard assessment.
(4) The stopping criterion (Eq. 6) is not explained completely since a proper definition of τ_{b,test} is missing. Is the criterion just that the actual momentum could be consumed entirely in the actual time step, as implemented in MinVoellmy? Or is it something more elaborate?
(5) The authors often refer to numerical diffusion as the source of the issues addressed in this manuscript. This is not clear to me, in particular since the simple implementation in MinVoellmy does not include any measures against numerical diffusion, but shows little spreading of the deposits.
As a second aspect, the manuscript discusses the effect of an additional cohesion term in Voellmy's rheology. In contrast to the points discussed above, this aspect becomes clear, but is not very surprising. As mentioned above, Voellmy's rheology without cohesion lets the material move permanently if the fluid surface is steeper than the tangent of the coefficient of friction μ. This results in an ongoing, but small flow into the runout zone and finally lets the runout zone grow a bit. Cohesion just results in an increase of my by a term τ_c/(ρ g_z h), which is inversely proportional to the thickness h. So flow on the slope stops if the thickness falls below a threshold that depends on cohesion.
From my point of view, publishing the manuscript as a research paper would require much more explanation of the approach and convincing arguments that the problem addressed here is important for practical applications and that it is a general problem and not just a deficiency of the implementation used here.
Since these points are quite fundamental for me, I do not write line-by-line comments at the moment, but look forward to reviewing a revised version. I would also like to point out that my rating of the manuscript refers to the 'worst-case scenario' and would be much higher if the points raised above can be addressed.
Best regards,

Stefan Hergarten

Citation: https://doi.org/10.5194/nhess-2024-123-RC1
- AC1: 'Reply on RC1', Saoirse Goodwin, 22 Oct 2024
  
  The comment was uploaded in the form of a supplement: https://nhess.copernicus.org/preprints/nhess-2024-123/nhess-2024-123-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/nhess-2024-123-AC1
RC2:
'Comment on nhess-2024-123', Anonymous Referee #2, 02 Sep 2024

In this paper, the authors aim to define criteria for when material truly stops in depth-averaged models, distinguish between physical stopping mechanisms and issues related to numerical diffusion, and discuss or propose best practice guidelines to address these challenges. The manuscript examines the interplay between three key variables affecting avalanche arrest: mesh resolution, topographic complexity, and snow cohesion. The authors use a second-order depth-averaged model as a test framework, incorporating a modified Voellmy model with cohesion and a physical yielding criterion. To the best of the reviewers' knowledge, this complete form of the model has not been tested before.
Defining criteria for when material truly stops in depth-averaged models is challenging from both physical and numerical perspectives. Numerical diffusion depends on factors such as the numerical scheme, grid resolution, and time-stepping methods. Additionally, physical stopping mechanisms are a matter of debate and vary from model to model. The choice of stopping condition is closely linked to the specific output the model is intended to produce. As a result, there isn't a one-size-fits-all criterion for determining when material has truly stopped moving in a numerical model. Each model's unique characteristics mean that numerical diffusion can have varying impacts, requiring tailored criteria to accurately assess stopping conditions. This issue also extends to different mechanical deposition criteria.
In this respect, I’m not yet convinced that the paper will have a significant impact on the international community, as the results appear specific to the models used by the authors and lack broader evidence of global relevance. The proposed global arrest criteria are not entirely new or convincing. For example, the role of calculation grid resolution has already been established in previous work, and the other criteria can also be questioned (see comments below). The authors need to strengthen their arguments in this regard.

Furthermore, I feel the paper lacks a discussion or analysis regarding the overall relevance of the stopping issue in relation to the final outputs. Ultimately, what really matters is how much the runout distance or the impact pressure at a specific location can be influenced by these issues. Understanding this impact is crucial for assessing the practical implications of the stopping criteria.
Finally, although the paper’s main aim is not focused on the model’s performance, the extensive description of the model and the impact of cohesion raises questions about the physical appropriateness of the model. For example, the cohesion values used in the simulations (1-100 Pa) are relatively small compared to the broader range of possible values mentioned in the paper (0-2300 Pa). Despite this, the model shows a strong response to variations in cohesion. Is this behavior physically realistic? This is particularly important to discuss because cohesion take an important role in your conclusions.
Other comments:
Abstract, line 1: I disagree with the assertion that 'depth-averaged models of snow avalanches have hitherto lacked an objective arrest criterion.' The paper does not adequately test or consider existing methods—many of which are mentioned in your bibliography but not further analyzed—making such a blanket statement misleading. Furthermore, it’s important to clarify what differentiates an objective criterion from a subjective one. For instance, a limit based on the physical threshold of a variable is, in my opinion, also an objective criterion.
Figure 2: The captions are generally very small; please ensure they are easily readable. Additionally, the legend describing the green-brown color is missing.
Line 136: At the beginning of a sentence, 'Figs. 3a' should be written out in full as 'Figure 3a' for proper academic style. This issue occurs multiple times throughout the paper, so I suggest a thorough review.
Line 137: How are the center of mass and the tip of flow defined (CoM) exactly? In depth-averaged modeling, defining the avalanche tip and the center of mass is not entirely straightforward and can be complex due to several factors.
Line 138: you mean substantial flow stoppage? not substantive
Figure 3. The figure shows 6 visible lines, but there are 10 items in the legend, for each graph. Please mention in the caption that some of the curves are overlaid? Or are they just missing?
Line 139: It is observed that grid sizes of 320x160 and coarser significantly influence simulation results. Do you mean 160x80? I think the 320x160 is not visible in the graphics. Additionally, the 160x80 grid shows only around a 2% difference, which is relatively minor. Providing these percentages helps clarify the magnitude of the error we are discussing.
Lines 147-150: The flow is described as stopping 'from the bottom up.' Could you clarify whether this refers to a back-propagating shock or if you are indicating that material stops first on gentler slopes and, in more cohesive scenarios, even on steeper slopes? The terms 'bottom-up' and 'bottom-down' seem unclear and could be misleading in this context.
Caption figure 4: (f) τc = 10 Pa should be τc = 100 Pa. I’m wondering: The cohesion values used in your simulations (1-100 Pa) are relatively small compared to the broader range of possible values mentioned in the paper (0-2300 Pa). Despite this, the model shows a strong response to variations in cohesion. Is this behavior physically realistic? Could you provide an explanation for why the model reacts so significantly to these relatively small changes in cohesion?
Line 203: As shown in the previous section, relying on the physically-based yielding criterion is generally insufficient for defining avalanche arrest objectively when a realistic, complex topography is considered. These assertion may not be entirely accurate. This conclusion could be influenced by the specific yielding criterion used in this study, which might not be the most suitable for the scenarios considered. Consequently, this raises questions about the extent to which the results obtained from this analysis can be generalized to other models. This need to be discussed in the paper.
Figure 5 and Lines 168-178: : In my understanding the higher the cohesion, the slower should be the flow, the longer should be the simulations time to allow all material to come to a natural rest. This effect is reinforced on complex topography because the random acceleration and decelerations phases. Therefore, it is crucial to define when the avalanche has truly physically stopped, before compare results. For example: What happens to the curves with complex topography and high cohesion if the simulation is extended to 30 seconds? Specifically, how much time does it take for all the material to reach the flat slope and come to a complete stop? At what point does numerical dissipation begin to affect the results? I do not believe this distinction is adequately addressed in the paper.
Line 183 At time t = 2 s, is it observed that cohesion τc and the topographical complexity only weakly affect the results … The maximum difference is around 1m/s ( 8 to 9 m/s velocity maximum) corresponding to around 10 %., so, not so small.
Line 225_226. Potentially, it could thus offer a more objectivecriterion to define effective flow arrest, although it would still require to be manually pinpointed on the curves. This would mean applying a different criterion for each individual simulation and scenario, which may not simplify the process. I do not believe this would make things easier or that it represents an applicable rule.
Line 251-252. For simple and complex topographies, Figs. 9 and 10 show time-histories of different metrics relating to the highest point of the flow material on the runout zone: It is unclear what is meant by 'the highest point of the flowing material in the runout zone.' Are you referring to the location of the point with maximum flow or deposition depth at each time step in the lower part of the track (x > 20 m)?
Figure 9 shows metrics related to the highest point (hp). However, the figure does not specifically reference the 'highest point' but rather shows flow depth. It would be clearer to use the term "maximum flow depth" in the caption to accurately match what is presented in the figure. This change should also be reflected in the main text.
Additionally, it is unclear why mesh resolution is considered again, given that its major impact was already established. Furthermore, the symbols for the curves, especially for velocity, are difficult to distinguish. Improving the differentiation of these symbols would be helpful. Only two subplots are labeled with letters. All subplots that are discussed should be labeled, and each description should clearly indicate which subplot it refers to.
Lines 259-260: Why is the discussion returning to mesh resolution, which was already addressed and fixed in Section 3.1? The paper is complex enough, and mixing processes can lead to more confusion. It would be better to keep the discussions on different processes as separate as possible.
Lines 272-273: The statement suggests that certain metrics related to the highest point in the runout zone—specifically, the first transition to a static state and the cancellation of its velocity—serve as objective criteria for defining avalanche arrest. However, I find this problematic. In real-world avalanches, the first point that stops in the runout zone can be overrun by material still in motion along the avalanche path, often reaching the deposition zone with a slight delay compared to the leading front. Therefore, this stopping criterion is only valid when the entire mass moves as a cohesive front, which is rarely the case in practice.
In depth-averaged modeling, "overrunning" cannot be directly accounted for, but material from behind can still push the already deposited material. Could this be a possible reason for the observed shift in maximum depth, as shown in Figures 9 and 10? If I’m misunderstanding, it might be due to the lack of straightforward visualization in this part of the paper. Perhaps the authors could provide a video to better illustrate the processes involved?
Lines 278-279: The statement 'However, sufficiently robust and objective arrest criteria are hitherto lacking' in the paper is questionable. Many models already have established stopping criteria, and the paper does not provide sufficient evidence to demonstrate their lack of robustness. Additionally, it is debatable whether truly universal robust criteria can be developed that are effective across all models, given the diverse nature of numerical diffusion and stopping conditions.

Lines 337-338: The claim that 'mesh resolution affects simulated flow properties if the cell size is larger than about 20% of the characteristic flow depth, typically for both simple and complex topographies' cannot be generalized. These values are specific to your particular setup and should be clearly stated as such. Furthermore, this aspect is already well established in the literature.
Lines 341-345: The statement regarding large cohesion values promoting a full transition of the material to a static state …..and following lines, seems more aligned with the conclusions of a different study. The influence of cohesion on snow mobility is a distinct topic from the primary focus of your paper. Furthermore, numerical dissipation can be seen as a weaker effect compared to strong physical processes like cohesion. It is obvious that when cohesion is high, it plays a dominant role in stopping the material, reducing the significance of numerical dissipation. Dissipation effects may only become prominent when physical forces, such as cohesion, are weaker. Maybe you can discuss on that.
Lines 355-358: The statement that 'identifying when/whether avalanches are arrested is of paramount importance for, e.g., hazard zoning or designing mitigation measures' is too general. Such a claim should only be made when there is a clear understanding of how these arrest criteria impact key variables, such as runout distance and pressure. Additionally, it is important to note that models are primarily used to generate scenarios, which are then compared to historical data and evaluated by avalanche experts before the final danger assessment.

Citation: https://doi.org/10.5194/nhess-2024-123-RC2
- AC2: 'Reply on RC2', Saoirse Goodwin, 22 Oct 2024
  
  The comment was uploaded in the form of a supplement: https://nhess.copernicus.org/preprints/nhess-2024-123/nhess-2024-123-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/nhess-2024-123-AC2

Saoirse Robin Goodwin, Thierry Faug, and Guillaume Chambon

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This paper considers how we can objectivity define stoppage of numerically-modelled snow avalanches. When modelling real topographies, numerically-modelled avalanche snow velocities typically do not converge to 0, so stoppage is defined with arbitrary criteria, which must be tuned on a case-by-case basis. We propose a new objective arrest criterion based on local flow properties, in tandem with a newly-implemented physical yielding criterion.


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