Optimizing the Formation of DMAs in a Water Distribution Network through Advanced Modelling
Round 1
Reviewer 1 Report
The authors present a methodology for the management of pressure and water quality in water distribution networks. For this purpose they develop a method that performs the division of the WDN into areas by using a Geometric Partition method based on the Recursive Coordinate Bisection (RCB). An algorithm is then used to select the isolation valves that define the DMAs. The method uses a Gaussian Mixture Model and a Genetic Algorithm in combination, analyzing each of the options through a hydraulic analysis of the network.
The paper in general lines is written correctly. Both the subject and the methodology presented are adequate and the results that appear seem hopeful. However, in my opinion it would be necessary to include some improvements in the article before proceeding to its publication.
The improvements required are:
1. In the introduction there are very few references on WDN clustering. At present this is a main subject of which there are numerous references. I would suggest that the authors review the existing scientific literature and make an effort to frame their work within the overall framework of the papers published so far.
2. Lines 36-42. The authors should specify explicitly and clearly what the objective of the work is.
3. Line 48. They use the concept of Geometric Partition (GP) as a clearly defined method of dividing the network. Is there any kind of reference about it? Any antecedents? Please, clarify this.
4. Lines 50-56. The authors present the RCB algorithm. In my opinion it is not clear how the authors apply this algorithm. Therefore, I would suggest that you expand on this section and explain it in more detail.
5. Line 50. In the sentence ".. The algorithm is based on ....", what algorithm is it referring to?
6. Line 62. There are references to different applications of Gaussian Mixture Modeling (speech data, image segmentation, biometric systems, weather observation). In my opinion it would be interesting to provide some bibliographical reference of this type of applications.
7. Line 108. Equation is too small
8. Line 113. Figure 1. Labels in the graph are too small.
9. Equations 9-14 are very small.
10. The results are presented in section 3 of the work. However, an important part of the content of this section is the methodology developed. For this reason I think it is necessary to separate the proposed methodology from what is its application to the case study.
11. One of my biggest concerns related to the paper is that the methodology does not explain how uniformity of pressures and quality are obtained. How is this uniformity treated? How is it evaluated? Equations 15 and 16 define part of the objective function related to water pressure and quality (age). In the case of pressure, it is considered not only the pressure. It also considers the demand of the node. Likewise, for the pressure its evaluation is additive; that is, the greater the number of nodes, the greater the value obtained. On the other hand, in the case of water age, the maximum value is selected. My biggest concerns in this regard are three. The first is why the mathematical treatment is different: in one case it is additive and in another case only the maximum value is obtained. The second is why in the case of pressure the demand is considered and in the case of water age the demand is not considered. The third is whether the size of the network (number of nodes) will not affect the way in which these values are valued. In my opinion, this is an essential part of the work that should be clarified.
12. Line 150. The authors propose a value of k = 4. Why is that value adopted? Is the best option? Would not it be necessary to carry out a sensitivity analysis? In my opinion, the selection of the number of subregions is important in the proposed method. Therefore it should be clarified a little better how this parameter is selected and the influence that this can have on the final result.
13. The case study selected is extremely simple, since it has four clearly differentiated sectors and 4 is the number of subregions proposed. My biggest concern is whether the proposed method would work with a more complex network or with a topology not so clearly defined. In other words, the division of this network into four sectors is trivial in view of its topology. What does the method contribute in this case that a preliminary analysis made by any engineer could not provided?
14. From my point of view figure 3 has several deficiencies. The first is that the content texts are too small to be read correctly. The second is the content of the figure. It is a succession of case study scenarios that should be explained in greater detail in the text. That is, my proposal would be to divide the figure into several different figures and make a detailed explanation of the content of each of them.
15. It would be important to know the data of the network in order to leave the possibility that other researchers could reproduce the results. Is there any reference to this network in the literature? The authors just give information on the scope of the network (sizes, diameters, flows).
16. Figure 4 does not contribute with relevant information. This figure can be summarized in a line.
17. The conclusions are very scarce and hardly indicate the real contributions of the work. I would invite the authors to do a little more emphasis on the novelty of their work, the differences with previous works and how the results presented validate the proposed method.
18. Finally, I would like to comment on the references used. In general, the references used are too old. There are many papers related to WDS clustering during the last ten years. The work gives the sensation that it has not taken into consideration the advances experienced in this field during the last years.I would recommend the authors update these references.
Author Response
Response to reviewer 1
We thank the reviewer for the time he/she took to read our paper and the very useful comments he/she brought forward. We have taken all of the reviewer's suggestions into account. In particular:
1. In the introduction there are very few references on WDN clustering. At present this is a main subject of which there are numerous references. I would suggest that the authors review the existing scientific literature and make an effort to frame their work within the overall framework of the papers published so far.
We apologise for the poor introduction. We have enriched the introduction and cited the existing references on WDN clustering.
2. Lines 36-42. The authors should specify explicitly and clearly what the objective of the work is.
We have explained the main objective of our work in the introduction. In section 2, we have also added a brief explanation of the model.
3. Line 48. They use the concept of Geometric Partition (GP) as a clearly defined method of dividing the network. Is there any kind of reference about it? Any antecedents? Please, clarify this.
We have added some references related to GP based network partitioning, namely.
4. Lines 50-56. The authors present the RCB algorithm. In my opinion it is not clear how the authors apply this algorithm. Therefore, I would suggest that you expand on this section and explain it in more detail.
We have added a more extensive explanation of RCB algorithm in subsection 2.1.
5. Line 50. In the sentence ".. The algorithm is based on ....", what algorithm is it referring to?
We are sorry for this omission. We have added " The Geometric Partitioning algorithm is based on …".
6. Line 62. There are references to different applications of Gaussian Mixture Modelling (speech data, image segmentation, biometric systems, weather observation). In my opinion it would be interesting to provide some bibliographical reference of this type of applications.
We have added more references concerning to other applications employing GMMs, as you suggested.
7. Line 108. Equation is too small
We have corrected the size of the equation.
8. Line 113. Figure 1. Labels in the graph are too small.
We have increased the size of the graph labels.
9. Equations 9-14 are very small.
We have corrected the size of all equations.
10. The results are presented in section 3 of the work. However, an important part of the content of this section is the methodology developed. For this reason, I think it is necessary to separate the proposed methodology from what is its application to the case study.
We have substantially restructured the paper sections 2 and 3 according to your proposal.
11. One of my biggest concerns related to the paper is that the methodology does not explain how uniformity of pressures and quality are obtained. How is this uniformity treated? How is it evaluated? Equations 15 and 16 define part of the objective function related to water pressure and quality (age). In the case of pressure, it is considered not only the pressure. It also considers the demand of the node. Likewise, for the pressure its evaluation is additive; that is, the greater the number of nodes, the greater the value obtained. On the other hand, in the case of water age, the maximum value is selected. My biggest concerns in this regard are three. The first is why the mathematical treatment is different: in one case it is additive and, in another case, only the maximum value is obtained. The second is why in the case of pressure the demand is considered and in the case of water age the demand is not considered. The third is whether the size of the network (number of nodes) will not affect the way in which these values are valued. In my opinion, this is an essential part of the work that should be clarified.
Regarding the water age, the factor ‘Age’ in the fitness function includes all the factors that are relating with the calculation of the water age and are automatically generated by the problem. Also, we added the calculations for a second network (Aiani), that is real and more complex, and the mathematical treatment gave positive results regardless the size of the network.
12. Line 150. The authors propose a value of k = 4. Why is that value adopted? Is the best option? Would not it be necessary to carry out a sensitivity analysis? In my opinion, the selection of the number of subregions is important in the proposed method. Therefore, it should be clarified a little better how this parameter is selected and the influence that this can have on the final result.
We have added new sets of experiments, corresponding to more k values. We have used five different values, k=1, …,6. We show numerical results for all different k values in Table 1, indicating that the best choice is k=4.
13. The case study selected is extremely simple, since it has four clearly differentiated sectors and 4 is the number of subregions proposed. My biggest concern is whether the proposed method would work with a more complex network or with a topology not so clearly defined. In other words, the division of this network into four sectors is trivial in view of its topology. What does the method contribute in this case that a preliminary analysis made by any engineer could not provided?
We have added a new set of experiments based on an external network, so called Aiani, that is more complex network concerning the number of nodes and its topology.
14. From my point of view figure 3 has several deficiencies. The first is that the content texts are too small to be read correctly. The second is the content of the figure. It is a succession of case study scenarios that should be explained in greater detail in the text. That is, my proposal would be to divide the figure into several different figures and make a detailed explanation of the content of each of them.
Thank you, we have made corrections and clarifications in Figure 3 according to all of your suggestions
15. It would be important to know the data of the network in order to leave the possibility that other researchers could reproduce the results. Is there any reference to this network in the literature? The authors just give information on the scope of the network (sizes, diameters, flows).
The network is included as an example in the free lessons of Watergems V8i program (lesson 6). We should have mentioned that more specifically.
16. Figure 4 does not contribute with relevant information. This figure can be summarized in a line.
We have summarized Figure 4 in a line that you suggest.
17. The conclusions are very scarce and hardly indicate the real contributions of the work. I would invite the authors to do a little more emphasis on the novelty of their work, the differences with previous works and how the results presented validate the proposed method.
We apologize for the inaccuracy of the conclusion section; indeed, it is quite misleading. We have emphasized the contributions our work and we discuss in more detail the evaluation results of the proposed models with respect to alternative state of the art approaches.
18. Finally, I would like to comment on the references used. In general, the references used are too old. There are many papers related to WDS clustering during the last ten years. The work gives the sensation that it has not taken into consideration the advances experienced in this field during the last years. I would recommend the authors update these references.
We apologize for the old references. We replaced the existing references with new ones corresponding to the last ten years state of the art works considering the WDS problem.
Reviewer 2 Report
DearEditor,
the paper describes a hybrid two stage approach to divide water distribution network in District Metered Areas. The proposed optimization procedure takes accounts not only the hydraulic performance of the water system but also the quality aspects related to water age. However, some major revisions are required to improve the manuscript and explain same important details of methodology and the obtained results.
Major revisions
1) The title should be improved because the paper deals with the design of DMA and not to “Water pressure and water age management”…
2) The introduction is too poor. It needs to be extended by providing more details about main advantages and drawbacks of DMAs; including a state of the art about DMAs and water network partitioning or sectorization; reporting a brief description of the proposed methodology and advantages of Student’s t-mixture model compared to other optimization algorithms to design the optimal DMAs.
Some important papers are suggested:
D. Gilbert, E. Abraham, I. Montalvo, O. Piller, (2017). Iterative Multistage Method for a Large Water Network Sectorization into DMAs under Multiple Design Objectives. Journal of Water Resources Planning and Management, 143(11), 04017067.
Di Nardo A, Di Natale M, Giudicianni C, Greco R, Santonastaso G.F, (2016) Water supply network partitioning based on weighted spectral clustering. Studies in Computational Intelligence: Complex Networks & Their Applications, vol. 693, 797-807. doi: 10.1007.
Di Nardo, A.; Di Natale, M.; Giudicianni, C.; Santonastaso, G.; Savic, D. Simplified Approach to WaterDistribution System Management via Identification of a Primary Network. Journal of Water Resources Planning and Management 2018, 144, 04017089.
Di Nardo, A., Michele Di Natale, Giovanni Francesco Santonastaso: A comparison between different techniques for water network sectorization. Water Science & Technology Water Supply 12/2014; 14(6):961-970., DOI:10.2166/ws.2014.046
Herrera M, Izquierdo J, Pérez-García R, Montalvo I. (2012). Multi-agent adaptive boosting on semi-supervised water supply clusters. Advances in Engineering Software.; 50:131-136.
Herrera, M, Canu, S, Karatzoglou, A, Pérez-García, R, Izquierdo, J (2010) An Approach To Water Supply Clusters by Semi-Supervised Learning, Proceedings of International Environmental Modelling and Software Society (IEMSS).
Herrera, M.,Abraham, E., and Stoianov, I.(2016). "A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks." Water Resources Management, 10.1007/s11269-016-1245-6, 30(5):1685–1699.
K. Diao, R. Farmani, G. Fu, M. Astaraie-Imani, S. Ward, D. Butler (2014). Clustering analysis of water distribution systems: identifying critical components and community impacts. Water Sci Technol., 70(11): 1764-1773.
Tzatchkov, V.G., Alcocer-Yamanaka, V.H., Rodriguez-Varela, J.M., 2006. Water Distribution Network Sectorization Projects in Mexican Cities along the Border with USA. In: Proc. of the 3rd International Symposium on Transboundary Water Management, Ciudad Real, Spain, pp. 1-13.
3) Lines 12-18: “The current study presents a hybrid, two-stage approach, towards an optimal division of a WDN in District Metered Areas (DMAs), enhancing both water age and pressure as critical parameters. The first stage aims to divide the WDN into smaller areas via the method of Geometric Partitioning, which is based on Recursive Coordinate Bisection (RCB). Subsequently, Student’s t-mixture model (SMM) is applied to each area, providing an optimal placement of isolation valves and separating the network in DMAs.”In the last years, some other authors have proposed a water network partitioning based on two phases strategy: e.g.
L.S. Perelman, M. Allen, A. Preis, M. Iqbal, A.J. Whittle, Automated sub-zoning of water distribution systems, Environ. Model. Softw. 65 (2015) 1-14.
Di Nardo, A., Michele di Natale, Dino Musmarra, Giovanni Santonastaso, FrancescoTuccinardi, Giancarlo Zaccone: Software for partitioning and protecting a water supply network. Civil Engineering and Environmental Systems 12/2015; 33(1)., DOI:10.1080/10286608.2015.1124867
Bruno M. Brentan, Enrique Campbell, Gustavo L. Meirelles, Edevar Luvizotto Jr., and Joaquín Izquierdo, Social Network Community Detection for DMA Creation: Criteria Analysis through Multilevel Optimization, Mathematical Problems in Engineering Volume 2017, Article ID 9053238, 12 pages.
4) The section 2, Proposed Methods, should include a general description of proposed methodology also with the help of a flow chart.
5) Some other details have to be provided about the Recursive Coordinate Bisection (RCB). RCB algorithm could generate disconnected subdomains,in other words it could generate DMAs that are not contiguous. Have the authors considered the possibility to apply other algorithms that improve quality of partitioning?
6) In the section 2, Proposed Methods, the authors should add a new sub-section 2.4 in which describe the Genetic Algorithm, the optimization strategy and the objective functions to minimize or maximize.
7) Lines 138-146: to better understand the proposed methodology the description of objectives functions should be included in section 2, Proposed Methods, e not in section 3, Results.
8) Do the authors minimize or maximize the objective function of Eq. (15) and Eq. (16)?
9) The authors have to clarify how they define the boundary pipes, that connect different DMAs, in which install flow meters (open pipes) and isolation or gate valves (closed pipes). Then, starting from “cluster of highest mean value being marked in green” (Figure 3) how do they define pipes to isolate and where place PRV valve? Maybe a flow chart of whole procedure could help the reader to understand the proposed method.
10) Line 156-157: “Therefore, the total Pressure*Demand product is being reduced by 52,72% compares to the initial value”Which is the initial value? Is the value of the original network? Please specify it.
11) In Figure 3.d the red lines represent the pipes in which the isolation valves are installed. One isolation valve is installed on pipe P-17 which is inner the DMA. Why do the authors consider the closure of a pipe inner DMA? Generally, to divide a network in DMAs it is advisable install isolation valves only on boundary pipes.
12) To better understand the performances of the proposed methodology, it is recommended to compute the objective functions for the original network layout and report all computed values not only as percentage but also as absolute terms. In addition, to improve the comparison between SMM, GMM and GA, same hydraulic performance indices could be evaluated such as the resilience (Todini E. 2000 Looped water distribution networks design using a resilience index based heuristic approach. Urban Water 2, 115–122.) and the deviation of resilience or other indices reported in (A. Di Nardo M. Di Natale G. F. Santonastaso V. G. Tzatchkov V. H. Alcocer-Yamanaka. Performance indices for water network partitioning and sectorization Water Science and Technology: Water Supply (2014) 15 (3): 499-509.).
13) Before the paper is prepared for publication, some grammar errors should be corrected.
Minor revision
1) Eq. (2) define the term: Pnk
2) Describe the terms of Eq. (16).
3) In the caption of Figure 3 there is no the description of figure 3.e and 3.f
4) In Figure 3.d, there is a black line on pipe P-248, what do that symbol represent? Please describe it.
5) Improve the English Language
Author Response
Response to reviewer 2
We thank the reviewer for his/her extensive report on our paper, and the many useful comments
and suggestions he/she brought forward. We have considered and integrated all of the
suggestions the reviewer mentions in his/her report.
In particular:
1) The title should be improved because the paper deals with the design of DMA and not to “Water pressure and water age management”
Thank you for your suggestion. We have replaced the existing title with “Optimizing the formation of DMAs is a water distribution network through advanced modelling”.
2) The introduction is too poor. It needs to be extended by providing more details about main advantages and drawbacks of DMAs; including a state of the art about DMAs and water network partitioning or sectorization; reporting a brief description of the proposed methodology and advantages of Student’s t-mixture model compared to other optimization algorithms to design the optimal DMAs.
We apologize for the poor introduction. We have extended this section by providing an extensive explanation of the proposed approach, adding advantages and disadvantages of DMAs and more references about the subject.
3) Lines 12-18: “The current study presents a hybrid, two-stage approach, towards an optimal division of a WDN in District Metered Areas (DMAs), enhancing both water age and pressure as critical parameters. The first stage aims to divide the WDN into smaller areas via the method of Geometric Partitioning, which is based on Recursive Coordinate Bisection (RCB). Subsequently, Student’s t-mixture model (SMM) is applied to each area, providing an optimal placement of isolation valves and separating the network in DMAs.” In the last years, some other authors have proposed a water network partitioning based on two phases strategy: e.g.
We have cited the suggested references concerning hybrid approaches dealing with water network partitioning in the introduction section.
4) The section 2, Proposed Methods, should include a general description of proposed methodology also with the help of a flow chart.
We now explicitly define the proposed methods, and have added a flow chart.
5) Some other details have to be provided about the Recursive Coordinate Bisection (RCB). RCB algorithm could generate disconnected subdomains, in other words it could generate DMAs that are not contiguous. Have the authors considered the possibility to apply other algorithms that improve quality of partitioning?
DMAs have been created after the second algorithm we used (GMM-EM, SMM-EM or GA). RCB does not create DMAs, but it divides the network in some nominal sub-areas to help the second algorithm process the network faster. Thus, in the first step no pipe is closed to create isolated areas. We are sorry if it wasn’t so clear in the article and have corrected it.
6) In the section 2, Proposed Methods, the authors should add a new sub-section 2.4 in which describe the Genetic Algorithm, the optimization strategy and the objective functions to minimize or maximize.
We have added a discussion of the Genetic algorithm on subsection 2.4.
7) Lines 138-146: to better understand the proposed methodology the description of objectives functions should be included in section 2, Proposed Methods, e not in section 3, Results.
We have added an extensive explanation of the objective functions as you suggested.
8) Do the authors minimize or maximize the objective function of Eq. (15) and Eq. (16)?
We clarify that the objective functions of Eq. 15 and 16 are minimized.
9) The authors have to clarify how they define the boundary pipes, that connect different DMAs, in which install flow meters (open pipes) and isolation or gate valves (closed pipes). Then, starting from “cluster of highest mean value being marked in green” (Figure 3) how do they define pipes to isolate and where place PRV valve? Maybe a flow chart of whole procedure could help the reader to understand the proposed method.
The boundary pipes are emerging from the algorithm. By comparing the mean average value of each generated cluster, we get the one with the highest μκ value and after placing an isolation valve on each pipe or a combination of them within the specific cluster, we check the total product Pressure*Demand for a period of the 24-hour (PD).
10) Line 156-157: “Therefore, the total Pressure*Demand product is being reduced by 52,72% compares to the initial value” Which is the initial value? Is the value of the original network? Please specify it.
We have added an explanation concerning the initial value of the original network.
11) In Figure 3.d the red lines represent the pipes in which the isolation valves are installed. One isolation valve is installed on pipe P-17 which is inner the DMA. Why do the authors consider the closure of a pipe inner DMA? Generally, to divide a network in DMAs it is advisable install isolation valves only on boundary pipes.
We have noticed that with the placement of an extra PRV to this pipe, there reduction of the Fitness function is greater, so this import leads to greater optimization of the problem.
12) To better understand the performances of the proposed methodology, it is recommended to compute the objective functions for the original network layout and report all computed values not only as percentage but also as absolute terms. In addition, to improve the comparison between SMM, GMM and GA, same hydraulic performance indices could be evaluated such as the resilience (Todini E. 2000 Looped water distribution networks design using a resilience index based heuristic approach. Urban Water 2, 115–122.) and the deviation of resilience or other indices reported in (A. Di Nardo M. Di Natale G. F. Santonastaso V. G. Tzatchkov V. H. Alcocer-Yamanaka. Performance indices for water network partitioning and sectorization Water Science and Technology: Water Supply (2014) 15 (3): 499-509.).
We have added the absolute terms of the objective functions for all methods and ,also some more details about the process.
13) Before the paper is prepared for publication, some grammar errors should be corrected.
We now explain the Pnk parameter, we describe the terms of Eq. 16, we have added descriptions of figures 3e and 3f, and we have added a brief description of the black line in figure 3d.
Round 2
Reviewer 1 Report
First of all I want to thank the authors for having tried to answer my questions about the initial version of the paper. In this version, many of my suggestions have been included. From my point of view, the paper continues to have some deficiencies in format and in the way in which some graphics are presented. The two case study figures are presented with different aspects. It is not understood how one of the networks has element's IDs while the other does not. In addition, one has a legend to represent junctions, reservoirs, tanks and pipes and the other does not. It would be interesting to have a consistency in the representation of networks. However, I think that this more technical question (resolution, legibility, size of the texts). So, I will leave the decision on these aspects to the editor.
Regarding the content of the work, I am grateful to the authors for the effort made in improving the state of the art and updating the references. Undoubtedly, in this way the article is better framed the current context.
However, some of the concerns I had in my first review continue. These concerns are basically four.
From my point of view, Case studies must be separated from the methodology. Therefore, the networks on which the proposed methodology is applied should be in a different section (Case studies, Results or whatever it is called). This section could, in my opinion, collect both the definition of the examples and the results.
In my previous review I showed my concern about the uniformity of the variables of a DMA. How is this uniformity treated? How is it evaluated? The authors make some clarification about the treatment that is carried out on water quality (age). However they omit references to the uniformity of pressures.
My previous comments indicated the need to explain the treatment that was carried out with restrictions of the problem. In the case of pressure, only the pressure defect, transformed into power, is considered, since this pressure is multiplied by the demand. Likewise, pressure evaluation is additive. That is, the greater the number of nodes, the greater the value. On the other hand, in the case of the water age, only the maximum value is selected. Why is the treatment different in the two parameters? Can the authors say that the result does not depend on the number of nodes? I think this aspect should be explained.
Finally, the authors have ignored my recommendation to improve the conclusions. From my point of view, the conclusions are a fundamental part of a paper. They highlight the main aspects of the work and how the proposed methodology is valid through the selected case studies. In my opinion, the conclusions as they are written do not reflect this objective. That is why I repeat my recommendation to write them again.
Author Response
We do thank the reviewer for the comments he/she made during the first review. We tried to do our best and incorporate all the necessary data to reply to any matter raised.
Regarding the second review though, we do have some argumentation refering tofurther changes requested.
COMMENT
First of all I want to thank the authors for having tried to answer my questions about the initial version of the paper. In this version, many of my suggestions have been included. From my point of view, the paper continues to have some deficiencies in format and in the way in which some graphics are presented. The two case study figures are presented with different aspects. It is not understood how one of the networks has element's IDs while the other does not. In addition, one has a legend to represent junctions, reservoirs, tanks and pipes and the other does not. It would be interesting to have a consistency in the representation of networks. However, I think that this more technical question (resolution, legibility, size of the texts). So, I will leave the decision on these aspects to the editor.
REPLY
We fully agree with the reviewer, that this is just a technicality. We think that the choice to present the two case studies in a different way is up to the authors.
COMMENT
Regarding the content of the work, I am grateful to the authors for the effort made in improving the state of the art and updating the references. Undoubtedly, in this way the article is better framed the current context.
REPLY
We have tried to do our best
COMMENT
From my point of view, Case studies must be separated from the methodology. Therefore, the networks on which the proposed methodology is applied should be in a different section (Case studies, Results or whatever it is called). This section could, in my opinion, collect both the definition of the examples and the results.
REPLY
Respecting the point of view of the reviewer, we would like to stress out that we have chosen another way to structure the paper, believing that this would have been better for the reader to follow our point.
COMMENT
In my previous review I showed my concern about the uniformity of the variables of a DMA. How is this uniformity treated? How is it evaluated? The authors make some clarification about the treatment that is carried out on water quality (age). However they omit references to the uniformity of pressures.
REPLY
In each DMA a joint optimization was attempted combining he average operating pressure and the average water age. So, the uniformity of pressures was an equal task handled.
COMMENT
My previous comments indicated the need to explain the treatment that was carried out with restrictions of the problem. In the case of pressure, only the pressure defect, transformed into power, is considered, since this pressure is multiplied by the demand. Likewise, pressure evaluation is additive. That is, the greater the number of nodes, the greater the value. On the other hand, in the case of the water age, only the maximum value is selected. Why is the treatment different in the two parameters? Can the authors say that the result does not depend on the number of nodes? I think this aspect should be explained.
REPLY
regarding the water age factor, the max value is the decisive parameter as it is an indiction of how "fresh" the water is actually. So the water age should be treated in a different way compared to the PD product. Regarding the latter, the final outcome might seem to result from an additive impact, depending on the number of nodes. But this is not actually he case. As the network remains the same (with the same number of nodes) the comparison and optimization is being done in a normalised way (the nodes do not have an impact). The paper tries to show that it is not only the pressure that by default should be optimised. It is the combined result of the supplied volumes of water and of the pressure in which it is supplied.
COMMENT
Finally, the authors have ignored my recommendation to improve the conclusions. From my point of view, the conclusions are a fundamental part of a paper. They highlight the main aspects of the work and how the proposed methodology is valid through the selected case studies. In my opinion, the conclusions as they are written do not reflect this objective. That is why I repeat my recommendation to write them again.
REPLY
We tried to improve the conclusions' section.
Reviewer 2 Report
The authors improved significantly the paper that now can be accepted for the publication.
Author Response
We really want to thank the reviewer for acknowledgimg out efforts to improve the quality of our paper
