Hierarchical Statistics-Based Nonlinear Vertical Velocity Distribution of Debris Flow and Its Application in Entrainment Estimation
Round 1
Reviewer 1 Report
This paper deals with debris flow using particle method and compares the results with experimental results. The model employed in this paper seems powerful and phenomena investigated in the paper are of interest. However, there are some comments on the paper and the authors are suggested to consider those.
Comments for author File: 
Comments.pdf
Author Response
This paper deals with debris flow. Experimental results were reproduced in the present model. The fluid of the experiment is composed of 56% gravel, 37% sand and 7 mud fine particles. On the other hand, the debris flow in the simulation was treated as uniform particle. Authors are suggested to explain how the debris flow is modeled in the simulation (e.g. particle side and density).
Response: Thanks for your critical comment. In the revised manuscript, we have added a discussion of reducing debris flows containing rocks of various sizes to a single uniform particle. ”Debris flow shows complex physical characteristics because of its complex particle size composition. Many studies show that the physical characteristics of debris flow are related to its particle size composition [19,20]. Due to the limitations of SPH numerical simulation methods, it is difficult to simulate non-Newtonian fluids with multiple particle sizes. In this paper, in order to reduce computational complexity, a compromise method is adopted. Debris flow is treated as a single uniform particle, and its complex rheological properties are described by HBP non-Newtonian fluid constitutive model. The strong phase separation in debris flows by uneven particle size in fluid is not thoroughly considered. The effects of this simplification require further study.” This information can be found in Page 14, Line 418-426.
For the application of the present simulation, erosion process was calculated in the present work. In the erosion process, there are so many factors which govern the phenomena in the experiment. Moreover, these factors may be affected by the bed material, size, density and so on. In the simulation, how the authors tune the simulation parameters? It may be important information for readers.
Response: Thank you for your detailed suggestion. In the revised manuscript, we added an introduction to the calculation formula of erosion rate and the detailed description of parameter selection. Please see Page 11, Line 326-Page 12, Line 356 for the detailed revision.
Author Response File: Author Response.pdf
Reviewer 2 Report
Please revise the manuscript according to the attached file.
Comments for author File: Comments.pdf
Author Response
We appreciate your kind and detailed revision on our manuscript. The feedback and constructive comments helped us strengthen our manuscript. Based on the comments we received, careful modifications have been made to the early version of the manuscript. All changes are highlighted in the manuscript. We hope the revised manuscript will meet your standard. Below you will find our point-by-point responses to your comments/questions.
The reviewed manuscript presents an investigation on simulation of velocity profile in a debris flow. The study is overall interesting and may be published as a new article if the authors address all the following remarks and revise the manuscript, accordingly.
- Line 17: The term "HBP" is unclear to the reader. Please add the complete phrase.
Response: We must thank you for your positive feedback and kind recommendation for publication in Water. It is appreciated that our manuscript could meet your standard. In the current revision round, we have added the complete phrase of the term “HBP”. Please see the revision in Page 1, Line 15. We hope the revision could strengthen our manuscript.
- Line 22: Please replace "And we apply" with "We also applied".
Response: Apologize for the mistake. It has been fixed. Please see the detailed revision in Page 1, Line 20.
- Line 47 to 49: In general, the flow velocity is larger in the middle of fluid under narrow channel condition. In the aforementioned papers, do you think that it was due to narrow channel conditions or debris flow effects?
Response: We appreciate your insightful comment. According to your comment, we have added statements: “This phenomenon can be explained in part by the Manning-Strikler equation, that flow depth along the thalweg is usually greater than both sides, leading to a greater velocity according to Ferguson [10].” Please see the revision in Page 2, Line 48-50.
- Lines 57 to 59: Do linear distribution models of Drago et al. study predict the experimental data accurately? In my view, use of linear models may lead to notable errors.
Response: Thank you for pointing this out. In the revised manuscript, we have added more description on this aspect: “Generally, the linear model is able to represent the velocity distribution feature through flow depth, however, as we demonstrated in our previous study [18], the linear model shows obvious error at the free surface and the bottom of the fluid.” You could find the revision in Page 2, Line 61-64.
- Lines 102 and 103: Please also add a note about disadvantages of SPH method. I think in high Reynolds numbers (like debris flow), SPH results would be erroneous.
Response: Thank you for pointing this out. We appreciate your insightful comments. In the revised manuscript, we have added a note about disadvantages of SPH method. “Many previous studies have substantiated that the SPH method shows a better performance for simulating laminar flow with low Reynolds number, while it may be insufficient to resolve turbulent flow with high Reynolds number, e.g., Price [38] and Meister et al.[39]. In general, the Reynolds number is critical for determine the laminar or turbulent regimes of fluids. The fluidity of a debris flow varies by grain size and relative flow depth. As demonstrated by Sakai and Hotta [40], debris flow with relative flow depth of approximately 10 is entirely laminar, while it becomes partially turbulent water flow with a greater relative flow depth. In this sense, many previous studies with respect to the SPH numerical simulation, assumed the debris flow as viscous laminar regimes fluid. Remarkable studies can be referred to Jakob et al. [41], Li et al. [42], and Huang et al. [43]. We developed a three-dimensional SPH numerical model based on the Herschel-Bulkley-Papanastasiou (HBP) constitutive model from the perspective of debris flow rheology, which effectively simulated the dynamic process of debris flow and the erosion process of loose deposits in gully beds [20,29]. The above studies demonstrate that the three-dimensional SPH approach can effectively mimic the dynamic process and flow pattern of debris flow, providing support for analyzing the vertical velocity distribution of debris flow.”. Please see the revision in Page 3, Line 113-129. We hope the revision could strengthen our manuscript.
- Lines 109 to 114: What is the novelty of your study with respect to Huang et al. [35]?
Response: Thank you for your insightful comment. Huang et al. used Bingham model to study debris flow. In this paper, we chose the more effective HBP model, which can more accurately simulate the complex flow characteristics of debris flow.
- Line 139: What is the real role of Mohr-Coulomb criterion in Eq. (6)?
Response: Thank you for pointing this out. In the revised manuscript, we have added an explanation of Mohr-Coulomb criterion in Equation (6). “The Mohr-Coulomb yield criterion is responsible for the energy dissipation when debris flow is propagating. [39]”. Please see the revision in Page 4, Line 153-155.
[39] Naef, D.; Rickenmann, D.; Rutschmann, P.; McArdell, B.W. Comparison of flow resistance relations for debris flows using a one-dimensional finite element simulation model. Nat. Hazards Earth Syst. Sci. 2006, 6, 155-165. https://doi.org/10.5194/nhess-6-155-2006
- Please add a reference for Figure 1 if you have taken from somewhere else.
Response: Thank you for pointing this out. We appreciate your insightful comments. In this paper, we checked Figure 1 of the paper again and confirmed that we drew it by ourselves without citing other literatures.
- Line 203: Please add the USGS flume width.
Response: Thank you for pointing this out. According to your comments, some information about the USGS flume has been added in the revised manuscript. Please see the revision in Page 6, Line 216-218.
- Line 244: Why does velocity profile change from non-linear to linear as time passes? What is the physical/scientific reason?
Response: We appreciate your insightful comment. However, it is a difficult question to answer why the velocity profile changes from nonlinear to linear. We have discussed this issue separately in the revised manuscript, and it is necessary to conduct further research on this issue in the future. However, it is a difficult question to answer as to why the velocity profile changes from nonlinear to linear. Please see the revision in Page 13, Section 6.1.
- Lines 263 and 264: Did you perform any preliminary simulations to choose an optimum number of particles? If yes, it is interesting to insert your results into the paper.
- Lines 263 and 264: Did you perform any preliminary simulations to choose an optimum number of particles? If yes, it is interesting to insert your results into the paper.
Response: Thank you for pointing this out. Since Questions 11 and 12 are repeated, we reply together here. However, we have checked the line 263-264 and found that there was no preliminary simulation to choose an optimum number of particles. The large number of particles in Figure 5 was selected according to the results in Figure 4(a).
- Section "5. Application in entrainment estimation" is insufficient. The methodology employed to predict erosion was not properly described. Please add more details on mathematical formulations.
Response: Thank you for your detailed suggestion. In the revised manuscript, we have added some more details about the entrainment estimation in Section 5. Please see the revision in Page 11, Line 340-346 and Page 12, Line 363-369. We hope the revision could strengthen our manuscript.
- Figure 11 is ambiguous to the reader. Please present it in a better form.
Response: Thank you for pointing this out. According to your comments, we have modified Figure 11 (Figure 10 in the revised manuscript). You could find the revision in Page 12, Figure 10. We changed the picture to horizontal according to the orientation of the water tank and marked the erosion area and the uneroded area. We hope the improved figure will be easy for readers to understand.
- I found three papers that velocity profiles were numerically simulated. I suggest the authors to use the following three papers to emphasis the accuracy and reliability of numerical models in prediction of different hydraulic phenomena.
- Experimental and numerical study of free-surface flows in a corrugated pipe
- Flow pressure behavior downstream of ski jumps
- Large eddy simulation of the turbulent flow field around a submerged pile within a scour hole under current condition
Response: Thank you for your detailed suggestion. According to your comments, we have cited the above three papers in the revised manuscript to emphasis the widespread use of numerical simulation methods. You could find the revision in Page 3, Line 95-96.
- Please lay emphasize on the novelty or improvements of your study in comparison with the previous studies in "6. Conclusion and discussion". That section looks slim and needs to be significantly improved.
Response: Thank you for pointing this out. We appreciate your insightful comments. According to your comments, the conclusion section has been improved. Please see the revision in Page 14, Line 443-Page 15, Line 448 and Page 15, Line 457-459.
- Line 386: I agree that a 'three-dimensional model' was developed for the simulation, but actually the considered flow has been 'two-dimensional'. Can you name your modeling three dimensional?
Response: We appreciate your insightful comment. In the revised manuscript, we have removed the three-dimensional simulation in Line 386. Please see the revision in Page 14, Line 443.
Author Response File: Author Response.pdf
Reviewer 3 Report
Dear Authors,
I have read and carefully evaluated your manuscript "Hierarchical statistics‐based nonlinear vertical velocity distribution of debris flow and its application in entrainment estimation", which I found botentially worth for publication, should you be prepared to include moderate revisions. Please, consider my suggestions below.
Abstract: I suggest some modifications to make it more infromative and more spcific, I suggest adding some numerical details, expecially concerning the reults.
You investigate debris flows, which may have very different characteristics (under the tag "debris flow" you can place very different flows). More information on the debris flow characteristics should appear in the manuscript. And also the information on the experiment is not very precise. E.g. at line 210 you state gravel, sand, mud.... but it would be better to provide a granulometic curve and some other geomechanic characteristics. And also water content, what are the water content values used? To sum up, I recommend adding in the text more details and also summarize the main geomechanical properties of the experiment/model in a table.
The discussion of the results could be improved. E.g., looking at fig12, I think that it could be interesting to measure the differences between the curves and to provide some statistics about the discrepancy between simulation and experimental data. It could be useful also to evaluate the integrals below the curves and to compare them.
L219-223 I don't think this information is useful.
I recommend not mergning Discussion with Conclusion. Maybe the discussion can be merged with the results, buth conclusion would better stand out alone.
Author Response
I have read and carefully evaluated your manuscript "Hierarchical statistics‐based nonlinear vertical velocity distribution of debris flow and its application in entrainment estimation", which I found potentially worth for publication, should you be prepared to include moderate revisions. Please, consider my suggestions below.
Abstract: I suggest some modifications to make it more informative and more specific, I suggest adding some numerical details, especially concerning the results.
Response: We must thank you for your positive feedback and kind recommendation for publication in Water. It is appreciated that our manuscript could meet your standard. In the current revision round, we have added a numerical description of the results. You could find the revision in Page 1, Line 22-24. We hope the revision could strengthen our manuscript.
You investigate debris flows, which may have very different characteristics (under the tag "debris flow" you can place very different flows). More information on the debris flow characteristics should appear in the manuscript. And also the information on the experiment is not very precise. E.g. at line 210 you state gravel, sand, mud.... but it would be better to provide a granulometric curve and some other geomechanics characteristics. And also water content, what are the water content values used? To sum up, I recommend adding in the text more details and also summarize the main geomechanically properties of the experiment/model in a table.
Response: Thank you for pointing this out. According to your comment, more information about the debris flow and the experiment have been added. And the table of key parameters used in numerical simulation has also been added into the paper. This information can be found in Page 6, Line 210-214 and Page 6, Table 1. However, we have not found the information about the grading curve and water content of the sand and gravel in the test debris flow from the literature [1].
[1] Iverson, R.M.; Reid, M.E.; Logan, M.; LaHusen, R.G.; Godt, J.W.; Griswold, J.P. Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment. Nat. Geosci. 2011, 4(2), 116-121. https://doi.org/10.1038/ngeo1040
The discussion of the results could be improved. E.g., looking at Fig12, I think that it could be interesting to measure the differences between the curves and to provide some statistics about the discrepancy between simulation and experimental data. It could be useful also to evaluate the integrals below the curves and to compare them.
Response: We appreciate your insightful comment. According to your comment, a histogram containing the calculated depth error percentage of erosion at each location has been added as Figure (b). Using this histogram, we have analyzed quantitatively the simulation results of erosion depth. This information can be found in Page 12, Line 361- Page 13, Line 380 and Page 13, Figure 11(b).
L219-223 I don't think this information is useful.
Response: Thank you for pointing this out. According to your comment, we have removed the information.
I recommend not merging Discussion with Conclusion. Maybe the discussion can be merged with the results, but the conclusion would better stand out alone.
Response: We appreciate your insightful comment. According to your comment, we have separated the discussion section from the conclusion and added the discussion on uniform particle simplification. You could find the revision in Page 13, Line 388-Page 14, Line 426.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The manuscript may be published in present form.
Reviewer 3 Report
Dear Authors,
thank you for the revised manuscript. You addressed all my comments and the paper is almost ready to be published.
I just suggest to add a few details in the conclusion, to make it more informative. It is almost the same comment I did for the abstract in the previous round of review. Just add a few number to provide evidence and you're al set.
Best regards.
Author Response
I just suggest to add a few details in the conclusion, to make it more informative. It is almost the same comment I did for the abstract in the previous round of review. Just add a few number to provide evidence and you're al set.
Response: Thank you for pointing this out. According to your comments, we have modified the conclusion and added a few details in the revised manuscript. Please see the revision in Page 15, Line 457-459.
