A New Dam-Break Outflow-Rate Concept and Its Installation to a Hydro-Morphodynamics Simulation Model Based on FDM (An Example on Amagase Dam of Japan)

Round 1

Reviewer 1 Report

A developed dam-break discharge rate equation intended for sudden-partial gate opening/breaching, not depending on the storage-depth curve, is presented, experimentally validated and applied. The tsumami/flooding model of Ca et al., 2010 is used to study the flooding downstream of the Amagase Dam.

The manuscript needs to be better written, the message delivered to the reader is somewhere quite hard to understand. English language and style check is required. Proofread is then recommended. Reference style must be coherent with the Reference list. Methods need to be better presented and explained. The Amagase Dam case study is just an application, a simulation exercise of the proposed output hydrograph model, coupled with the Ca et al., 2010 model. The feasibility of the proposed methodology should be better emphasised.  Validation against real cases is therefore recommended. The conclusions should summarise the effectiveness of the proposed methodology.

Abstract. Need to be improved in terms of readability. For instance “The proposed equation is extensively affected by a dam-break shape. This incident is investigated …” The meaning of “incident” here, is not clear.

The Intoduction need proper care as well, e.g. “. (dot mark is not required) especially, when densely populated cities are located downstream of a dam” could be better rephrased. Again: “the routing of the in-flow flood through a reservoir”. Inflow hydrograph could be seen as a boundary condition to the reservoir, hence the term “through” is not appropriate. This in turn finds me not in agreement with the statement “hydrograph is affected by the bathymetry of a dam, valley shape, dam height and shape, and extension of the breach” unless referring to the outflow hydrograph.

LINE 105. How can possible D be much grater than the dam’s height? “? is the imaginary depth from the dam crown height as shown in Fig. (1. b) and it is assumed many times the depth of a dam”

Eq. 5. The reason why the Authors switch from “H” (Eq. 3) to “H – dh/dt T” (Eq. 5) needs to be stated.

LINE 117 “for tsunami simulations”? The model, expressed by eqs (15) – (19) must be better presented, along with related working hyphoteses.

LINE 122 “?0 is the weighted average roughness co-132 efficient of areas like farms, roads, and waste & wetlands”. Is this the case?

Fig.3.a Use the same digits for precision, e.g. 9.50 not 9.5.

LINE 250. I believe that it would be better to develop fewer study cases, focusing in more detail on them.

I understand the reason which moved the Author to investigate the Amagase Dam. However, how can the collapse mechanism be simulated adequately with the proposed methodology, as it is made of concrete? Why give room to flooding simulation if the paper's key idea consists of a newly proposed outflow dam hydrograph?

Author Response

Thank you very much for your time and considerations. Please see the attachment for responses to the comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

I appreciate the work done to improve the paper and I can see that the current version is clearer than the previous one. Therefore, I recommend the paper for publication in the revised form.

Author Response

Thank you very much for your time and considerations.

Reviewer 3 Report

GENERAL COMMENTS

This manuscript aims to purpose a novel dam-break outflow rate equation, applicable to concrete dam types.

Existing hydrodynamic and morphodynamic numerical models are used to assess the coefficients of the outflow rate equation and show the application of the model in two real-world examples.

This is not a cutting-edge scientific work, it is even quite limited in terms of original content, but it addresses a topic that is worth researching. The results of a dam-break simulation are in fact very dependent on the dam-break cross-section and the breaking time. 

This work proposes an equation to take into account the dam-break cross-section while maintaining a high subjectivity. On the other hand, sudden dam-break is considered, which is also not entirely realistic.

The experimental work (section 3.1), if new, should be better explored, with identification of the correlations and standard deviations of the different cases. In general, the experimental data seem very scattered and, therefore, without great statistical relevance.

In addition, significant sections appear to be taken from previously published material.
In fact, excluding section 2.1 and part of the experimental work (section 3.1), all other contents appear in publications, some of the authors' own works.

Subsections 2.2.1 and 2.2.2, section 3.2 and Figure 9, among other contents, all appear to be "copy and paste" from other publications by the same authors, especially Ahmadi et al. (2020) [J. Mar. Sci. Eng. 2020, 8, 762; doi: 10.3390 / jmse8100762].

Review citations and the List of Reference carefully. All citations and several references do not meet the Water journal standards.

Aiming at a possible reformulation of the manuscript, in addition to the General Comments above, I may suggest the following Specific Remarks.

SPECIFIC REMARKS

- Mathematical formulations must be carefully checked. Especially, check equation (2) and the units of all terms in equations (16) and (17). It appears that something does not match. In fact, according to equation (3), Q has units [L³T^-1], and according to eq.(21), f_c is dimensionless. Therefore, all terms of eqs. (16) and (17) have units [L²T^-2], excepting the last term of each equation, which has units [L³T^-2].

- In eqs. (15)-(17), q_x and q_y are horizontal fluxes in the x and y directions, which are defined by eqs. (18) and (19), respectively. Why has the notation changed in eq. (20), with the velocities V and U in the x and y directions, respectively? 

- In eq. (22), how are the deposition and the entrainment rates, Cs and Cut, calculated? 
As these quantities depend on the suspended sediment concentration, C, how is this unknown obtained? The model must be completed.

- Figures 5-7 are very limited and cannot be used together. In fact, Figure 5 is valid for uniformity coefficients (U) in the range of 1.5-3, and Figure 7 is valid for U = 20.1. In addition, Figures 5 and 6 are only valid for dry densities around 1.5 g/cm³.

- Figure 9 caption reads "Relative accuracy of the topography-change along line (A) on the measured and reproduced simulation results." What is "line (A)" and where is it?

- The verification and application examples are, essentially, acceptable. The Conclusions also reflect the core content of the manuscript. Anyway, some recommendations for future research should be considered.

- Citations and References (list) must be properly written according to the Water standards. In addition, check the following citations/references:
  . Aureli et al. (2014) does not appear in the List of References.
  . Kurishiru (1996) does not appear in the List of References.
  . Kurishiru et al. (1996) is not cited.
  . Ribberink (1998) is not duly cited.
  . Van Rijn (1993) is not duly cited.
  . Bates (1993) does not appear in the List of References.
  . Bates and De Roo (2000) is not cited.
  . Amicarelli (2020) does not appear in the List of References.
  . Amicarelli et al. (2020) is not cited.
  . Kocaman (2020) does not appear in the List of References.
  . Kocaman and Dal (2020) is not cited.
  . Hervouet (1999) does not appear in the List of References.
  . Hervouet and Petitjean (1999) is not cited.
  . Valiani (2002) does not appear in the List of References.
  . Valiani et al. (2002) is not cited.

Finally, careful proofreading is highly recommended.

Author Response

Thank you very much for your time and considerations. Please see the attachment for responses to the comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I'm satisfied with the revisions made

Author Response

Thank you very much for your time and feedback. We appreciate your kind decision about our manuscript.

Reviewer 3 Report

I find this manuscript with interest and useful for WATER readers; the first version has been slightly improved.

Admittedly, some explanatory material has been added and some of my concerns have been clarified; however, there are still some errors, flaws and omissions already pointed out in the first review, which must be properly considered; I note some of them: 

- It appears that equation (2) is still wrong; it should be (2g)^0.5 instead of (2gh)^0.5.
- Redraw equation (22), as the exponent 1.65 is not positioned correctly. 
- Correlations and standard deviations of the curves shown in Figure 4 must be provided. These statistical parameters are important for the reader to assess the quality/dispersion of results. This issue is equally valid for the graphs shown in Figures 5, 6, and 7.

On the other hand, other issues were not properly answered, or were answered but only partially; I note the following:

- Lines 182-163 read "?(?) is the suspended load concentration (adapted from the Soulsby (1997)[21]"; why is this equation (supposedly the Rouse profile) not given? Also, how is C obtained (for the equation Cs)?
- The analytical formulations needed for the applications should be provided, rather than leading the reader to the bibliography.
- Citations are numbered but the author(s) and year of publication are equally presented in most of them, i.e., they are double cited; I note just a few:
. Line 32: Wahl, (1997)[2]
. Line 48: Bazin, (1865)[7] following which, Ritter, (1892)[8]
. Line 55: Aureli et al., (2013)[10] 
. Lines 59-60:  Pilotti et al., (2010)[3], Saberi and Zenz, (2015)[11], Basheer et al., (2017)[12], and Hakimzadeh et al., (2014)[13]
. Line 63: Piloti et al., (2010)[3]
. Lines 65-66:  Piloti et al. (2010)[3] and Aureli et al, (2013) [10]
. Line 67: Aureli et al., (2013)[10] and equation (19) of Pilotti et al., (2010)[3]
. Line 80: Aureli et al. (2013) [10]
. and many more.

Therefore, I recommend that authors carry out a more careful review and in full compliance with the journal's guidelines.

Author Response

Thank you very much for your comments. We have accordingly revised our manuscript. Please refer to the attached file. A point-by-point response is provided. 

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The paper interestingly verifies the validity of a two-dimensional (2D) dam-break hydro-morphodynamic simulation model with a newly proposed outflow rate equation on the 2011 great Tohoku tsunami in the Sendai-Natori coast of Japan and the Japan’s Amagase Dam. The manuscript is well written, despite some inaccuracies highlighted in the original manuscript and commented along the lines.

However, below are some suggested improvements:

1. In the introduction, the Authors might make their description of the existing literature more complete by including other numerical models, such as the SPH models, currently used to study dam-break floods (see Amicarelli A., Manenti S., Albano R., Agate G., Paggi M., Longoni L., Mirauda D., Ziane L., Viccione G., Todeschini S., Sole A., Baldini L.M., Brambilla D., Papini M., Khellaf M.C., Tagliafierro B., Sarno L., Pirovano G. 2020. SPHERA v.9.0.0: A Computational Fluid Dynamics research code, based on the Smoothed Particle Hydrodynamics mesh-less method. Computer Physics Communications 250, 107157). In addition, they should highlight the innovative aspects of the present research.
2. In paragraph 3, the authors do not well explain how they choose the values of the empirical coefficients to include in the Bed-load Transport Rate and outflow rate equations, despite it being a fundamental part of their work. For example, they choose 0.35 as the value of the flow rate coefficient justifying it as the average value. An error analysis might be needed here, considering that the range of the coefficient is quite wide (see Table 1).
3. In the paragraph “Verification Simulations”, the authors should better justify the choice of the four cases and a more critical analysis of the results is advised.

Comments for author File: Comments.pdf

Reviewer 2 Report

A deep review of the manuscript is highly recommended. Among other reasons:

• The introduction is not clear. The main reasons for your research are not presented.
• The applicability of the newly proposed equation relies exclusively on 2 study cases. The authors may consider testing the same problems with a hydraulic modelling software (e.g., OpenFOAM).
• What happens to your equation when you consider a rectangular section (i.e., D->∞)?
• The bibligraphy must be further completed with the vast existing research material.
• An extensive editing of English language and style is required.

Reviewer 3 Report

The message delivered to the reader is confusing, e.g.: “albeit, because of the complexity of the phenomenon, it is very difficult to anticipate a dam breach formation. and”.

Methods are not clearly presented. The discussion of results is not well-structured. Proofreading is required. Some sentences are clumsy, hard to read, while others need grammatical checks. The abstract would benefit a brief presentation of results, with key, concrete values. The literature review needs to broaden and better discussed as it is really poor in the present form.

LINE 38. “a model that is based on the finite-difference method is a need”

Why? I do not understand this sentence. Are other schemes less reliable? Please clarify.

LINE 81-82. “?? & ?? are the x & y direction ratios of the wet portion”, “? is the area ratio of the wet portion” “in a calculation mesh”

Better state the meaning of these parameters.

LINE 90. ?0 is the weighted average roughness coefficient of areas like farms, roads, and waste & wetlands, ?1,2,&3

There are many reasons for which weighting irregularities do not work. Why 3 areas?

LINE 109. Are the Authors assuming the Shield criterion?

Position expressed in Eq. (17) need to be justified.

Captions of Figs 3, 4 and 5 are pasted (same, later on), together with the images. I would suggest major care in preparing the manuscript.