Round 1

Reviewer 1 Report

The Authors propose a new model emphasizing the shallow water equations which are able to predict this phenomenon and minimize its impacts. The study is comprehensive and benefit practical engineers and other researchers. Some revisions are required to improve the quality of the manuscript. 

1. Flood maybe related to the increase of river level. The river level increase due to sedimentation. Please review the following paper on sediment transport.

https://doi.org/10.3390/fluids7080277

2. Please remove the sentences in Lines 257-258. Those are from the template of the journal

3. Figure number is line 266 in the text refer to figure 3, but there is no figure 3

4. Figure 4 is blur. Please improve the resolution of the drawing. Provide scale.

5. Check figure numbering in the paper. The figure number start from figure 4 in the paper.

6. Please review the following paper to understand a good and proper presentation of map for showing spatial distribution of data

https://doi.org/10.3390/atmos13050772

7. Scale of figure 6?

8. What are the justifcation of the selection of three vaues of rainfall intensities?

9. Conclusions are too long. Some sentences are repetition of background, research methodology and discussion. Revise conclusions to be more concise

10. References format need to be amended according to journal formating style

Author Response

1.             Reviewer #1 Comments and Author Responses

 

The Authors propose a new model emphasizing the shallow water equations which are able to predict this phenomenon and minimize its impacts. The study is comprehensive and benefits practical engineers and other researchers. Some revisions are required to improve the quality of the manuscript. 

• Flood maybe related to the increase of river level. The river level increases due to sedimentation. Please review the following paper on sediment transport. https://doi.org/10.3390/fluids7080277

 

Authors’ Response:

 

The authors thank you for this important remark as well as for the suggestion document which enriches our bibliography.  We do need to clarify though that the objective of this first study was to assume that the catchment is relatively free from developed surface water sources.  Thus, at the start of the simulation, there is no stream, no lake, no building.  Rather, given space constraints, the primary goal is to better appreciate the sensitivity of the model to primary watershed properties. The watershed has been divided into Cartesian coordinate xyz through the surfer software and at each point we have assigned an index such as (a) for the points that belongs to the river, (b) for those in the cultivated area and so one to better integrate our input parameters according to different zones. Knowing that the height of water in the watercourse is about 8 m, we have therefore taken this into account to subtract from the simulated water height in that area. It was an assumption in order to be able to assess the potential water level as well as the potentially floodable areas in the entire watershed. In our future work, we are planning to evaluate the sensitivity of the model for a more realistic case of urban drainage in a watershed that includes the obstruction of buildings, or urbanization, and of existing streams and rivers. We will be honored to hope to share, exchange and benefit again from your rich experience in the subject as part of this next challenge.

 

• Please remove the sentences in Lines 257-258. Those are from the template of the journal

 

Authors’ Response:

 

The sentences have been removed.   Sorry we missed this holdover from an earlier draft the first time!

 

 

• Figure number is line 266 in the text refer to figure 3, but there is no figure 3

 

Authors’ Response:

 

It was an error; figure 4 was the intended reference. The error has been corrected.

 

 

• Figure 4 is blur. Please improve the resolution of the drawing. Provide scale.

 

Authors’ Response:

 

 

Thanks.   Good point. The resolution of the figure 4 has now been improved. We have exchanged the old figure for one with better resolution

 

• Check figure numbering in the paper. The figure number start from figure 4 in the paper.

 

Authors’ Response:

 

Thanks again. The authors were able to make corrections to the entire figure from Figure 3 to Figure 13.

 

 

• Please review the following paper to understand a good and proper presentation of map for showing spatial distribution of data .https://doi.org/10.3390/atmos13050772

Authors’ Response:

 

All the maps contained in the paper have been modified in order to present them with a better resolution.

 

• Scale of figure 6?

 

Authors’ Response:

 

The figure 6 is an illustration of the watershed at initial condition provided by surfer 13 software. There is no scale at that point just an illustration of the watershed in the orthonormal frame at the initial condition.  We have tried to clarify this.

 

• What are the justification of the selection of three values of rainfall intensities?

Authors’ Response:

 

 

We chose three consecutives values of rain intensity in order to better evaluate the sensitivity of the model in the relation to rainfall intensity on long simulation time. The authors wanted to clearly show that the higher the rainfall intensity, the easier it is for the soil to lose its water retention potential and more potentially floodable areas increase.  We were particularly interested to see of the non-linearities in the flow equations and in the watershed representation produced any surprises.

 

• Conclusions are too long. Some sentences are repetition of background, research methodology and discussion. Revise conclusions to be more concise

 

 

Authors’ Response:

 

Good point.  The conclusion has been revised and improved.

 

 

• References format need to be amended according to journal formatting style

 

Authors’ Response:

 

 

All references contained in the paper have been modified in accordance with the requirements of journal.

 

Author Response File: Author Response.docx

Reviewer 2 Report

This work is within the scope of the journal Applied Science; however, I still have two comments for the authors.

Comments:

1.      Many previous researches related to the present study should be considered in the Introduction section, e.g., Chen et al., 2019. An Operational Forecasting System for Flash Floods in Mountainous Areas in Taiwan. Water, 11(10), 2100; Chang et al., 2020. An Operational High-Performance Forecasting System for City-Scale Pluvial Flash Floods in the Southwestern Plain Areas of Taiwan. Water, 13(4), 405. Their results could provide useful information for the present study.

 

2.      Does the flooding model developed by the authors simulate riverine and pluvial flooding?

Author Response

1.             Reviewer #2 Comments and Author Responses

 

This work is within the scope of the journal Applied Science; however, I still have two comments for the authors.

Comments:

• Many previous researches related to the present study should be considered in the Introduction section, e.g., Chen et al., 2019. An Operational Forecasting System for Flash Floods in Mountainous Areas in Taiwan. Water, 11(10), 2100; Chang et al., 2020. An Operational High-Performance Forecasting System for City-Scale Pluvial Flash Floods in the Southwestern Plain Areas of Taiwan. Water, 13(4), 405. Their results could provide useful information for the present study.

 

 

Authors’ Response:

 

The two rich and informative publications noted by the reviewer have been integrated into the introduction part of the paper.  Thanks for the suggestion,

 

 

• Does the flooding model developed by the authors simulate riverine and pluvial flooding?

 

Authors’ Response:

 

The flooding model designed by the authors has the ability to simulate pluvial flood and that is what we did here with different rainfall intensity and that was just our first case study but in the next work we are planning to evaluate the sensitivity of the model in the case of urban drainage.

Author Response File: Author Response.docx

Reviewer 3 Report

Dear authors.

Please find my comment in the attached file.

Best regards

Comments for author File: Comments.pdf

Author Response

1.             Reviewer #3 Comments and Author Responses

 

         I consider the manuscripts’ content interesting since it has potential applications to a real-life problem, such as flooding. However, several drawbacks make the paper quite hard to read. Therefore, the authors should improve many grammatical issues and address the following concerns before any consideration for publication:

 

1. Introduction

 Lines 120-125, What do the authors mean by preventing spurious oscillations? The oscillations can appear with sharp gradients in pressure and velocities, making the numerical algorithm unstable. Please, clearly explain the relationship between oscillations and the MUSCL scheme.

 

 

Authors’ Response:

 

Having in the past conducted work with shallow water equations for 1D dam break, the authors have always associated the MUSCL scheme to the FVM-Godunov in the way to prevent the potential oscillations that may arise on the computation of the water height, pressure, discharge or velocity. But the main goal of combining FVM-Godunov type with MUSCL scheme is “to replace the piecewise constant approximation of Godunov's scheme by reconstructed states, derived from cell-averaged states obtained from the previous time-step. For each cell, slope limited, reconstructed left and right states are obtained and used to calculate fluxes at the cell boundaries (edges)”. (Line: 145-149)

 

Reviewer:

 

2. Numerical model

1. Why is it more appropriate using FVM than FDM for this problem?

 

 

Authors’ Response:

 

There are several points that might be made to this question, but we’ll be brief:

 

• The Finite Volume Method (FVM) is straightforward to implement on non-uniform/unstructured grid, differently from Finite Difference Method (FDM) that requires a specific type of grid.
• The most relevant issue is theoretical: the FVM discretizes the integral form of the equations. It can be shown that is equivalent to use a weak formulation, the only one that can adopt for non-regular solutions. FDM cannot be used because the derivatives cannot be defined across a discontinuity. This gives an advantage of being conservative without special cares (mass conservative or momentum conservative) in FVM is more natural and guaranteed compared to FDM. Moreover, the discretization form with FVM is set of small cells, namely finite volume.
• FVM is more conservative than FDM

 

1. I suggest explaining the deduction of the formulas (6)-(10) more clearly. In the current form, it is not apparent how to go from one to another.

 

Authors’ Response:

 

Thanks for the good suggestion.  The authors now show in more detail the resolution of the equations 6 to 10. The new resolution process has been integrated in the paper (6-13). (Line: 198-202)

 

1. Lines 179-180, What do the authors mean by FVM applying to a steady-state?

 

Authors’ Response:

 This was certainly not initially as clear as it should have been.  The sentence has been reformulated as follows.

H is a constant and this state physically corresponds to the state of equilibrium of the water course or steady-state. To preserve this state of equilibrium, the authors have used a FVM scheme which consists of a hydrostatic reconstruction as proposed by Audusse (2004) as follow.

 

1. How is possible a hydrostatic reconstruction in this problem?

 

Authors’ Response:

 

Yes, we could have been clearer about this, so thanks for the question.  In essence, the hydrostatic reconstruction proposed by Audusse et al. (2004), coupled with a positive numerical flux, allowed us to verify several important mathematical and physical properties in the simulation.  A key factor was to maintain the positivity of the water height and, thus, to avoid instabilities when dealing with dry zones.

 

1. In lines 216-217, the authors mentioned in the abstract and introduction the use of HLLC, but in the later lines mention the use HLL scheme. Could you please clarify this point?

 

 

Authors’ Response:

 

Our apologies.  In this study, the authors had to use HLL scheme and not HLLC.  Sorry for the confusing typo. The corrections have been made on the paper.

 

 

1. What is the Jacobian matrix associated with the system of equations? Please, write it explicitly.

 

 

Authors’ Response:

 

Thanks.   In the x direction, the term  with  j=1,2,3 is the eigenvalues of the Jacobian of F and can be expressed as :

 

 

 

In the y direction, the term  with  j=1,2,3 is the eigenvalues of the Jacobian of G and can be expressed as :

 

 

 

 

1. The definition of the CFL is not entirely correct. Please, refine the definition and clearly explain how to obtain the expression for the CFL. Why is the value of CFL 0.9? Is that related to a stability criterion?

 

Authors’ Response:

 

Thanks for pushing on this point.  The definition of the Courant is as follow: “The Courant-Frieddrichs-Lewy or CFL condition expresses that the disntance that any information travels during the time step length within the mesh must be lower than the distance between mesh elements. In other words, information from a given cell or mesh element must propagate only to its immediate neighbors (https://www.simscale.com/knowledge-base/what-is-a-courant-number/)” (Line: 278-287).

The CFL has been equal to 0.9 for the stability criterion of the model in this case study

 

 

3. Initial conditions and Numerical results

 

• The initial conditions are not clear. Please, explain in detail how to create the initial watershed. Also, please mention the boundary conditions and their effects on the problem.

 

 

   Authors’ Response:

 

           

The process of creating the initial watershed has now been detailed in section 3.1.1 Map processing and the figure 6 illustrates the figure at the initial condition, seen by the surfer software. Among the input we have considered the velocities in x and y directions are zero and the water at initial condition was also assumed as 0, the watershed has been considered as essentially dry without surface water initially. Our future goal is to include these features in order to be able to evaluate the sensitivity of the model for a more realistic case of urban drainage with building obstructions, subsurface and surface water conveyance.

 

 

• Please, use Fig. or Figure everywhere, do not mix both.

 

   Authors’ Response:

 

Thanks.  All the “fig.” present in the paper has been changed to “figure”

 

 

• Lines 344-345, Why is the watershed sensitive to rainfall intensity and simulation time?

 

 

       Authors’ Response:

 

The soil has the potential to retain surface water that infiltrates to recharge the water table during the periods of short rainfall and low intensity. But the retention threshold can be quickly reached during the heavy rains and over a long period of time, then the amount of water that could not be infiltrated will turn into runoff water and cause flooding. The more rainfall intensity increases over a long period of time, the greater the area occupied by runoff.

 

4. Conclusions

 

 

• Lines 445-447: What do the authors mean by the ghost cell approach integrated to maintain a uniform solution in interior and boundary cells? Is this related to the boundary conditions?

 

Authors’ Response:

 

The ghost cell formula mentioned in this paper had been proposed by (Zhou et al. 2017) by assuming that the flow of information in the virtual cells is the same as at the boundaries, namely and , where  and are obtained by coupling the Riemann invariant with a head-flow boundary relation at time n. the  head-flow boundary is expressed by

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have addressed the comments from reviewers

Reviewer 2 Report

The authors have addressed all my comments; this manuscript can be accepted for publication in its present form.

Reviewer 3 Report

Dear Authors.

I appreciate the effort to address all my concerns. Now, I accept the paper for publication.