Generation of Synthetic Series for Long-Term Analysis of Optimal Operation Policies of a Cascade Hydroelectric Dam System
Round 1
Reviewer 1 Report
Please revise the manuscript according to the attached file.
Comments for author File: 
Comments.docx
Author Response
Response to Reviewer 1
Dear reviewer, attached we send the responses to your thoughtful comments and we have highlighted the changes in the modified article with green color.
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MS: WATER-2219100 OVERVIEW As remarked in the abstract, in this study synthetic biweekly series of 1000 years of record were generated to simulate the behavior of the Grijalva river dam system using the optimal operation policies for each alternative. The Grijalva River is approximately 700 km long, and it is the second largest in Mexico. It originates in Guatemala - giving rise to a binational basin, the Middle and Upper Grijalva cover the central area of Chiapas and the lower Grijalva is located in the plains of Villahermosa, Tabasco. In the middle reaches of the Grijalva River, a hydroelectric system of four cascading dams was built. By stressing the dam system by simulating its behavior with synthetic series longer than the historical record but preserving the same statistical characteristics of the historical series on the synthetic ones, it was possible to factually evaluate each operating policy considering the frequency and magnitude of spills and deficits that occurred at each dam. Overall, the manuscript is interesting as well as the related applications. However, I seem to find the following critical points: (i) Novelties and advancements in knowledge should be better clarified especially in terms of new methodologies and novel results in comparison to similar papers on Grijalva dam system; Answer Modifications were made to the document to address these comments from the reviewers. (ii) It is unclear how the results of this study are (or can be) validated; Answer Modifications were made to the document to address these comments from the reviewers.
(iii) It is unclear how the results of this study can be extended to other real cases in the world; Answer Information was added to the article to explain this doubt about the generality of the method.
(iv) Finally, references should be carefully revised. Several of them are uncomplete and/or incorrect! Answer
Information was added to the paper to explain this doubt about the generality of the method. The references were reviewed and those that the reviewers detected as incomplete were modified. In conclusion, I believe this manuscript could be worthy of publication in Water journal; however, it presents significant weaknesses (general in nature) in present form. Here below, some specific comments (major and minor revisions) are provided in the hope they can be useful to refine the manuscript.
Answer We appreciate your thoughtful suggestions and the modifications to the paper were made and each question made by the reviewers was answered.
SPECIFIC COMMENTS [Title] At the end of the title I would emphasize that this is a Case Study. Therefore, I would write something like this “…dam system: The Case Study of Grijalva River in Mexico”.
Answer
We appreciate the comment; however, the authors consider that the methodology can be used other cascading systems, in addition to the fact that the title would be too long.
[Abstract] I would suggest to add some quantitative results in this section. In current form, this section is rather qualitative.
Answer
The abstract was modified to address this comment.
[Keywords] Maybe the keyword “Grijalva system” should be better specified as “Grijalva dam system”; analogously, I would specify “Reservoir spills” instead of “spills” alone and “Reservoir deficits” instead of “deficits” alone.
Answer
The change was made in the keywords.
[Introduction] (i) In this section often one reads sentences like “[17], proposed” or “[19], applied”. I would avoid this kind of style trying to be more explicit. For instance, the above examples should read as “Silva and Portela [17]” or “Airton de Sousa and Belmino [19]”; (ii) At the end of this section the Authors should highlight the major gaps on the topic they are dealing with and emphasize how these gaps are overtaken in this study. Answer
Authors were added and the reference was cited.
[Case study] (i) It would be helpful to provide the main characteristics of the four dams considered in this study and their appurtenant hydraulic structures; (ii) The text at the end of this section, from line 156 to line 171, is typical of the final part of the section Introduction. I will therefore move it at the end of the Introduction.
Answer
(i) We provide the main features of the dams in the paragraphs that correspond to each explanation of the simplification of the system and in the handling of the data. (ii) the change was made from the paragraph to the suggested introduction area.
[Results and Discussion] (i) It remains unclear hod did the Authors validate their results; (ii) It also unclear how the results of this study can be transferred to another real case in the world.
Answers
(i) The purpose of the manuscript was to obtain optimal operation policies and select some of them through the simulation of the operation of the reservoir joint simulation using records, first historical records, but since no events of spills and deficits were found, the above justified and motivated the generation and simulation of synthetic records that when simulating them created conditions of greater stress to the system by observing events of deficit and spillovers for some of the optimal policies tested, which helped in the selection of the most convenient policy for its use in the long term. (ii) The methodology is general enough to apply it to other reservoir systems if the information from the reservoirs described in this study is available.
[References] (i) [Ref.#11] This reference is uncomplete for several aspects. It should read “Thomas, Jr., H.A.; Fiering, M.B. Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation. In Design of Water Resources-Systems, edited by Mass et al., Harvard University Press: Cambridge, UK, 1962; pp. 459493; (ii) [Ref.#12] It reads “Matalas, N. Mathematical assessment of synthetic hydrology, 1967. Water Resources 3 (4), pp.937-94.”, but it should read “Matalas, N.C. Mathematical assessment of synthetic hydrology. Water Resour. Res. 1967, 3, 937-945.”!
Answer
Fixed references 11 and 12. |
TYPOS [but the list could be longer]
[At line 220] It reads “kmín and kmáx”, but it should read “kmin and kmax”.
Answer
The correction was made in the requested line.
[Equation (7)] It reads “Máx”, but it should read “Max”.
Answer
The correction was made in the requested line.
[At line 248] It reads “máxk1,k2”, but it should read “max k1,k2”.
Answer
The correction was made in the requested line.
[At line 172] It reads “2. Methodology”, but it should read “3. Methodology”. Analogously, the section numbering should be updated in the following.
Answer
The correction was made in the requested line.
[Table 12] It reads “Relative Difference, In %”, but I would write “Relative difference [%]”.
Answer
The correction was made in the requested line.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Please see the file attached.
Comments for author File: Comments.docx
Author Response
Response to Reviewer 2
Dear reviewer, attached we send the responses to your thoughtful comments and we have highlighted the changes in the modified article with yellow color.
By taking the dams of the Grijalva system as a study case, this paper applied stochastic dynamic programming and modified Svamidze method to optimize the operation policies. This study is interesting and is significant to the optimization of operation policies of hydroelectric dam system. However, there are some problems in the present paper. The comments that should be addressed are listed as follows.
- In line 174, the abbreviation “SPD” should be changed to “SDP”. This mistake reappears in lines 288 and 289. The authors should proofread the whole paper carefully to avoid this kind of mistake.
Answer
The correction was made in the requested line.
- Line 196, as the year can also be disaggregated by monthly or weekly scale, why did the authors divide the year into groups of consecutive fortnights? Please expound the consideration the authors took when deciding the interval for dividing.
Answer
The main reason for dividing into 7 stages per year was the decrease in the dimensioning of the problem. In addition to the fact that such division of the year into stages attended to the value of the historical averages of the grouped fortnights. The foregoing is expressed in line 289 of the modified document.
- Line 210, what is the meaning of the abbreviation “NS”? It should be noted that the meaning of each abbreviation should be added in the paper when first use them.
Answer
NS means number of states, the correction was made.
- Line 274-276, the probability distribution function of historical total volume must be important in this research and impact the reliability of the generated synthetic volume. Please introduce the method applied to obtain the probability distribution function.
Answer
Added the requested information.
- Line 289-292, please expound the reason for dividing the years into seven stages, and the consideration of setting the volume increment of 200 hm3to discretize the state variables.
Answer
The main reason for dividing into 7 stages per year was the decrease in the dimensioning of the problem. In addition to the fact that said division of the year in stages attended to the value of the historical averages of the grouped fortnights. The foregoing is expressed in line 289 of the modified document.
The useful capacity of each dam was divided using a DV=200 hm3 because we wanted to refine the analysis with respect to previous studies that considered DV=600 hm3.
Information was added to the requested lines.
- Line 294-298, why can the turbine capacity of La Angostura and Malpaso be equivalent to 1412.5 hm3and 1866 hm3? What is the basis for determining the values of kmin and kmax for each stage in Table 2? Please add explanations.
Answer
The flow through turbines of each dam was multiplied by the seconds of a fortnight to obtain the biweekly flow through turbines volume. The maximum extraction kmax was obtained by dividing the fortnightly flow through volume by the DV considered in the analysis and approximating the most logical integer. Subsequently, the kmax of a fortnight was multiplied by the fortnights of the stage.
The kmin was obtained in a similar way starting from a flow destined to drinking water for each dam; subsequently, this flow was converted to a fortnightly volume considering the time in seconds of a fortnightly period, and later the fortnightly kmin was multiplied by the number of fortnightly periods in the stage.
- Table 3, the values of the penalty coefficients should be important to evaluate the test results, while it is not clear what standard the authors took to determine the values of these coefficients, the authors should add explanations to clarify the basis or standard for determining these penalty coefficients.
Answer
Information was added on said coefficients that do not have a monetary value and whose intention is to decrease the value of the expected benefit per generation each time an undesired event of deficit, spillage or volumes exceeding guide curves occurs.
The increase or decrease in the coefficients is valued with the results of the simulation of different optimal policies.
- Figure 2, “MOWL”, refer to comment 3.
Answer
Added maximum operating water level (MOWL) definition inline when referring to figure 2.
- Table 4, the caption of this table is incorrect, which is identical with table 3.
Answer
The correction was made in the requested line.
- Table 9, “Average historical record of 61 years” is repeated 5 times in table 9, which is improperly.
Answer
The correction was made in the requested line.
Author Response File: Author Response.pdf
Reviewer 3 Report
By taking the dams of the Grijalva system as a study case, this paper applied stochastic dynamic programming and modified Svamidze method to optimize the operation policies. This study is interesting and is significant to the optimization of operation policies of hydroelectric dam system. However, there are some problems in the present paper. The comments that should be addressed are listed as follows.
1. In line 174, the abbreviation “SPD” should be changed to “SDP”. This mistake reappears in lines 288 and 289. The authors should proofread the whole paper carefully to avoid this kind of mistake.
2. Line 196, as the year can also be disaggregated by monthly or weekly scale, why did the authors divide the year into groups of consecutive fortnights? Please expound the consideration the authors took when deciding the interval for dividing.
3. Line 210, what is the meaning of the abbreviation “NS”? It should be noted that the meaning of each abbreviation should be added in the paper when first use them.
4. Line 274-276, the probability distribution function of historical total volume must be important in this research and impact the reliability of the generated synthetic volume. Please introduce the method applied to obtain the probability distribution function.
5. Line 289-292, please expound the reason for dividing the years into seven stages, and the consideration of setting the volume increment of 200 hm3 to discretize the state variables.
6. Line 294-298, why can the turbine capacity of La Angostura and Malpaso be equivalent to 1412.5 hm3 and 1866 hm3? What is the basis for determining the values of kmin and kmax for each stage in Table 2? Please add explanations.
7. Table 3, the values of the penalty coefficients should be important to evaluate the test results, while it is not clear what standard the authors took to determine the values of these coefficients, the authors should add explanations to clarify the basis or standard for determining these penalty coefficients.
8. Figure 2, “MOWL”, refer to comment 3.
9. Table 4, the caption of this table is incorrect, which is identical with table 3.
10. Table 9, “Average historical record of 61 years” is repeated 5 times in table 9, which is improperly.
Author Response
Response to Reviewer 3
Dear reviewer, attached we send the responses to your thoughtful comments and we have highlighted with blue color the changes in the modified article.
Reviewer 3
The manuscript presents an investigation on a methodology in generation of synthetic data for operation policy of hydroelectric dam systems. The study is interesting, however I observed some shortcomings throughout the manuscript. The authors are recommended to revise the manuscript based on the following remarks:
- The 'Abstract' is too long. In my view, the authors can remove some senetnces from paragraphs 1 and
Answer
The abstract was modified.
- Line 20: Is the available data long enough to generate 1000 years of record? It is necessary to have a long term dataset for your Please clarify this issue in the manuscript.
Answer
The authors consider that the historical series of 62 years is statistically representative of the behavior of the system to generate 10 synthetic series of 1000 years.
- Line 32: I think the "optimal policy" is an important part of your It is worthwhile to describe it in a few lines in 'Abstract'.
Answer
Added optimal policy description.
An optimal policy is understood to be the selection of volumes of water to be extracted from each reservoir in the system that guarantees in the long term the greatest expected benefit from electricity generation and, on the other hand, that reduces possible unwanted events of spills, deficits, as well as volumes. exceeding the guide curves imposed by the system operator body.
- Line 55: Please add a few sentences about the performance and advantages of Fiering's
Answer
The Thomas Fiering method has the advantage of its ability to preserve the first three statistical moments of the analyzed series; but it is not ensured that these statistics can be preserved in the case of synthetically generating several time series with crossed autocorrelations.
- Lines 63 to 66: Did [15] compare the mentioned model to suggest any of those model for reservoir operation?
Answer.
What the author [16] indicates is that these synthetic generation methods can be used in the design of reservoirs.
Later, Mc Leod [16], studied the application of synthetic series to avoid bias in data sequences of stochastic processes using random initial values with the objective of avoiding bias. He also developed some simulation procedures with synthetic records obtained from Box Jenkins models; the author indicates that these synthetic generation methods can be used in the design of reservoirs.
- Line 74: I think generation of 1200 series in not practically In general, a convergence of the results is expected after generation of less than 100 series. Is there any reason for such large number of data generation?
Answer
The authors pointed out that the generated series reproduced the statistics of the original series.
For our part, 10 series of 100 years each were generated in order to find flow events of greater or lesser magnitude than the historical ones, which did occur and this helped the occurrence of spills and deficits in the system by simulating the different operating policies. , so this number of generated series was considered useful.
- lines 92 to 96: Do the authors believe that a combination of an AI method (like GP) with a conventional stochastic model (like SARIMA) can significantly improve the results? Is it worthy? Please include your idea based on the results of [22].
Answer
We consider that for the generation of periodic series with cross autocorrelation, the proposed modified Svanidze method was the ideal one, since the distribution function of the total annual sum volume and the fortnightly behavior that the data have historically reported are preserved, while with a technique of AI combined with the ARIMA model, it must be validated that these properties of the series are satisfied.
- line 102: I noticed that in the following articles, generated data is utilized to develop a model in prediction of scour depth and sediment I suggest the authors to use these two papers to mention other application of generated data in water engineering:
- New stochastic modeling strategy on the prediction enhancement of pier scour depth in cohesive bed materials
- New formulations for prediction of velocity at limit of deposition in storm sewers based on a stochastic technique
Answer
We appreciate the reviewer's suggestion, but we consider that the subject of the research is different from that of the indicated references, so we did not appreciate adding them to this article.
- Line 146: Is "guide curves" a technical term in water allocation? Please check it with some
Answer
We have added the reference that establishes the technical concept of guide curve.
- Lines 182 to 185: The authors state require criteria to consider the inflows as random In my opinion, more criteria is needed to ensure a parameter is random variable. Please check more references and complete that paragraph.
Answer
The paragraph was modified.
- Lines 196 and 197: Is there any methodology in the literature in order to correctly divide the year into groups of consecutive fortnights. Please explain this issue with more
Answer
We have added brief details of why the year was divided into 7 stages in line the first paragraph of section 3.4
- Lines 236 to 238 is Please rewrite it in simple sentences.
Answer
The sentences were rewritten.
- Lines 269 to 274: The sentence is as long as 6 lines! Please split it into several It is ambiguous in current form.
Answer
The paragraph was modified and the sentences were splitted.
- Line 277: How did you select a random year? Do your results change if another year is selected randomly? Is there any specific rule in that selection?
Answer
Random selection with replacement was made, using uniformly distributed numbers to select from historical data with a linear relationship.
If the selected year changes, the behavior of the fortnightly data obtained synthetically does change, but its value also depends on the total volume, which is also randomly generated, but according to its probability distribution function.
- Lines 284 to 286: Is it common to choose October as the first month of a water year? In many parts of the world such years start from
Answer
In the analyzed region, the lowest correlation of inflow volumes was identified when going from the selected fortnight of October to the following fortnight: For this reason, a hydrological year was used with said beginning and end.
- There are many tables in the Some tables are not necessary for a scientific paper. Please remove less important tables (like Table 5).
Answer
We consider that Table 5 is important to highlight that a lower maximum storage is obtained in Malpaso for the purposes of protecting the population downstream of the last dam in the system.
- Line 324: how do the authors define the "proposed high guide curve"? What is the application of that curve in water policy?
Answer
The proposed high guide curves appear in Figure 2 and Figure 11, they were referenced as Test 1 to Test 4.
Section 3.2 talks about guide curves; the high guide curve refers to the conservative curve managed by the operating agency.
“3.2. Guide curves
The guide curves are maximum elevations and storage suggested by the operating agencies that can reach the main dams of a country, their purpose is to avoid undesired events, mainly spills [27,30,36]. They are represented as elevation-time or volume-time graphs.”
- Please add a new paragraph into the "conclusions" including the novelty and improvements of your results with respect to the previous The current version of "conclusions" only demonstrates results of the selected case.
Answer
A new paragraph was added.
- Lines 482 to 486: Please rephrase that It is a bit unclear to the reader.
Answer
The paragraph was modified.
- The manuscript needs to be edited by a native English
Answer
The manuscript was reviewed and the modifications are highlighted in gray
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The manuscript is acceptable in present form.
Reviewer 2 Report
Overall, the Authors addressed my concerns. The manuscript in present form is worthy of publication in Water journal.
Reviewer 3 Report
You revised your paper well.
