Inclusion of Narrow Flow Paths between Buildings in Coarser Grids for Urban Flood Modeling: Virtual Surface Links

Round 1

Reviewer 1 Report

Comments and suggestions for the Authors

The reviewer’s brief summary of the paper

1D/2D computational models are now being used extensively and successfully for urban flood modelling. There are however, a number of issues for on-going research. One is balancing the runtime of models with the accuracy of the results for different grid sizes: the smaller the grid size, the longer the runtime, yet, the coarser the grid size, the flow results are more likely to be less accurate and therefore can become unacceptable. A second issue concerns the details of furnishing the cells for a particular area of flow with terrain data. The authors are concerned about details of the flow in narrow gaps between buildings, which are included explicitly in a basic model with a 2m grid, and are missing when resampling the topography for flow models with a 5m or 10m grid and simulating the same events. The authors propose a solution to this problem by introducing ‘Virtual Surface Links’ in the coarser grid models which convey flows that compensate for the missing flows between the buildings. The VSLs are virtual 1D rectangular channels which convey flows between storage nodes and outfall nodes defined in the coarse models. The authors demonstrate that the VSLs can help to adjust the predicted flows in the coarser models to maintain the accuracy of the simulations as produced in the basic  model.                                                                                                                                                                                                                                                  Comments

1.  LiDAR data for (national) urban surface topography is widely available in some countries, such as Britain and The Netherlands, and can be provided by government agencies at a resolution between 2m and 0.25m. Analysis of the data can lead to a Digital Terrain Model (DTM) specifically for the interpolated natural surface of the (urban) terrain without any urban structures. These can be modelled separately and an estimated porosity can be assumed for each structure at ground level. The DTM for the terrain surface is independent of the flow modelling grid. The authors suggest ‘resampling’ the terrain data when moving from one model grid to a coarser grid. (It would be helpful if the authors could define what they mean by ‘sampling’ and ‘resampling’. These terms give the impression that the terrain model for the 2m grid is different from the terrain models for the coarse grids). The reviewer suggests that the terrain data, at a suitable (fine) resolution, can be applied independently of the flow modelling: the data for the buildings can be loaded for flow modelling along with the terrain data to explore the influence of existing and/or new urban structures on the flow. This approach requires the derivation in each cell of a given grid model, of the two values of hydraulic roughness from the roughness values of the surface elements in the cell, and the ‘form’ roughness across the whole cell. Provided appropriate care is taken, the concept of the VSLs could possibly be adopted in the coarse grid flow models, as in the paper, by artificially removing the geometric features for flow between buildings, though the advantage is probably minimal.
2. The authors rightly make much of the topography of the urban area in modelling flow over the ground surface. However, they only mention briefly the hydraulic roughness of the ground surface texture. This could be because of restrictions on the range of values that can be taken by the hydraulic roughness ‘n’ in the commercial 1D/2D software, and the values of n are at best small compared with typical river modelling values. A river model may have Manning ­n values typically between 0.02 and 0.2 associated with varying amounts of sediment and vegetation which form the texture of the channel and flood plain cross sections along a short model reach, and such values can be used with confidence in 2D modelling of urban areas. Some river modellers also include ‘form’ roughness in deriving the Manning n values. There is also evidence that the irregular geometry of a river with inundated flood plains contributes its own effect on the dynamic attenuation of peak flows. The authors should also note that the roughness for a grid cell can vary according to the direction across the cell. This implies that roughness can have at least two distinct values over a 2D coarse grid cell: one in the x-direction, say, and one in the y-direction. The authors should state their assumptions about the hydraulic roughness in the paper.
3. The authors admit in the paper that calibration of the VSLs may be required. This calibration appears to involve some subjective choices and decisions. Can the authors deduce a more robust and less user-dependent procedure for carrying out the calibrations?

Author Response

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Reviewer 2 Report

1. It is mentioned VSL method is used. What are the advantages of adopting this particular method over others in this case? How will this affect the results? More details should be furnished.
2. For readers to quickly catch your contribution, it would be better to highlight major difficulties and challenges, and your original achievements to overcome them, in a clearer way in abstract and introduction and especially in conclusion.

3. There is a serious concern regarding the novelty of this work. What new has been proposed?

4. Conclusions needs to modify and to be revised to be more quantitative. You can absorb readers' consideration by having some numerical results in this section.
5. The authors have to add the state-of-the art references in the manuscripts.

Author Response

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Reviewer 3 Report

The manuscript is carelessly prepared with regard to the description of basic ideas, terms and equations. In many places the text is imprecise or even incomprehensible.

1)    The manuscript concerns a flash flood modeling, where the Authors mainly focus on the presentation of the Virtual Surface Links (VSL) technique aimed at eliminating inaccuracies that arise as a result of coarsening of 2D grid. However, in Section 2.1, a brief description of the proposed procedure is too general and incomprehensible. For example, there is no mathematical description of how this method is implemented at the level of the flow equations.

2)    The manuscript contains inaccuracies and obvious errors regarding the basic flow equations and models.    

• In the Saint-Venant model, the dynamic equation (Eq. (8)) is incorrect.
• In description of the 2D diffusive wave model (lines 221-222), the Authors claim that „ the momentum equation of the SWE is simplified by neglecting the pressure and friction term”. Of course, such a statement is untrue, because it is quite the opposite - the simplified dynamic equation (Eq. (11) in manuscript) contains only the pressure and friction terms.
• For what purpose was Eq. (6) presented in manuscript? This equation is written in a non-conservative form, which is not recommended due to the balance errors generated in the numerical solutions.
• The description of the coupling 2D surface flow model (diffusive wave model) with the 1D the drainage system model (Saint-Venant model) is not clear. Why is there no source term in the continuity equation (Eq. (4)) of the Saint-Venant model?  
• There is a certain lack of consistency in description of the methods. The Authors presented an algebraic equation (Eq. (12)) which is an approximation of the continuity equation (Eq. (10)), while such approximations for the simplified dynamic equation (Eq. (11)) and for the Saint-Venant equations (Eqs. (4-5) have not been presented.

Minor remarks:

1)    Errors in reference to the numbering of the equations: line 211 and line 239.

2)    Error in the applied units:  flow velocity U should be in m/s (line 212).

3)  Lack of description for the variables and parameters used in equations:

•  Area, Depth in Eq. (8),
•  z in Eq. (11),
•   t, t+Δt in Eqs. (9) and (12),  
•    indexes i, j, ij in Eqs. (12-14),  
•    n_ij  in Eq. (12).

4) Is Eq. (7) is dimensionally consistent? Asn is a storage surface area, but Asl is a length of conduit.

Concluding, I do not recommend the manuscript in its current form for publication in Water MDPI.

Author Response

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Round 2

Reviewer 1 Report

I thank the authors for revising their manuscript in response to the comments of the reviewers. I accept the end result of the review process which is that the paper is now ready for publication, pending a final check on the language, and references to journal papers that address another class of 2D simulation models which do not need to make special treatment of narrow flow paths between buildings as the 2D models become coarser

The alternative class of models do this by defining a basic square grid for the terrain model with resolution (say 0.25m) finer than the resolutions for the flow grids (say 1m, 2m 5m, 10m). Suppose the computational time for the 2m grid is unacceptable and you need to run the flow model with a coarser grid which, under your coarsening of the terrain model grid through resampling, leads to the disappearance of such fine terrain features as the narrow gaps between buildings. But there is an alternative approach in which the terrain model data remains untouched with the fine terrain details preserved and included in the coarser models. The 2D calculations depend on constructing linear data tables for the accurate non-linear interpolation of the instantaneous volume stored in a cell and the corresponding surface area, taking into account the detailed terrain geometry, and with the water depth above the lowest point in the terrain data for the cell. This process is repeated for the sectional areas of flow at the interfaces between adjacent cells. At each interface there are two flow sections either side of the grid line because a section is determined only from the terrain data for its cell. Again, the 2D calculations depend on constructing linear data tables for the non-linear interpolation of the instantaneous components of the conveyance for the flow section. The flow at the two sections are often the same, but they can be different. The depth of flow at the interface is defined by the average water level for the cells either side of the interface; the flow can be super-critical in one direction or blocked. In particular, any narrow channel which would not show on any coarse cell as being significant, will still be present and contribute to the dependent variables and therefore to the flow calculations. The data tables speed up the calculations of the flow in a coarse grid, and the gain in speed opens up   procedures using flow models with different coarseness in analysing and simulating urban flood alleviation/protection schemes. 

Thank you for including in your paper the map of the distribution of surface roughness for your application area. Incidentally the reference for the map was not found. Could you please explain how you deal with two or more roughness values in a cell.

P-DWave 2D ignores the inertia terms in the Saint Venant equations. In that some of the flows round buildings and through narrow gaps could be near critical, how can you guard against modelling errors due to the neglect of inertia terms?

Please ensure as much as possible that your paper has an up-to-date list of state-of-the-art models and papers on 2D urban flood modelling.

Comments for author File: Comments.docx

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Reviewer 2 Report

Authors revised properly.Should accept now.

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Reviewer 3 Report

Unfortunately, the manuscript is still unacceptable in the present form for publication, because the Authors did not make appropriate corrections according to my major remarks presented in previous review.

1)  There is still no mathematical description of the Virtual Surface Links method and how this method is implemented at the level of the equations. For this reason, a description of the proposed procedure is incomprehensible. It is worth noting that the proposed method is the basis of the manuscript.

2)  The Authors still do not explain how the 2D surface flow model is coupled with the 1D the drainage system model. If the continuity equation (in the Saint-Venant model) does not have to include the source term, then how does this coupling work?

3)    The Authors still do not explain why they use Eq. 6 in the non-conservation form. It is not a very good idea to refer only to the software manual without thoroughly understanding the problem.

Author Response

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Round 3

Reviewer 3 Report

The manuscript has been accordingly corrected.