Simulation of Titicaca Lake Water Level Fluctuations Using Hybrid Machine Learning Technique Integrated with Grey Wolf Optimizer Algorithm

Round 1

Reviewer 1 Report

General comment

A hybrid Support Vector Regression (SVR) model coupled with Gray Wolf Optimizer (GWO) was implemented to assess its capability for predicting Lake water level of Titicaca Lake located between Peru and Bolivia in the manuscript “Simulation of Titicaca lake water level fluctuations using hybrid machine learning technique integrated with gray wolf optimizer algorithm”. A performance comparison of the original support vector regression algorithm with the hybrid algorithm was the main aim of the research. Three input data pre-processing tools Relief (RL), Random Forest (RF), and Principal component analysis (PCA) were combined with the regression algorithms to create six scenarios. The authors from the research have concluded that; (1) using gray wolf optimizer increased performance of the original SVR model; (2) From the three preprocessing techniques RF is better performing; (3) The combination of RF with The hybrid SVRGWO algorithm resulted the best performance.

The writing is simple but there are a lot spelling errors and editorial issued. As an example I mentioned some in the specific comments below.

The effort of the authors to present the preprocessing methods and the predictor’s methods are not replicable.

The discussion of the result is too shallow and did not incorporate other research results as a comparison. The hybrid SVR-GWO method has been implemented in other researches such as;

• Buyukyildiz, M., Tezel, G. & Yilmaz, V. Estimation of the Change in Lake Water Level by Artificial Intelligence Methods. Water Resour Manage 28, 4747–4763 (2014). https://doi.org/10.1007/s11269-014-0773-1
• Li, B., Yang, G., Wan, R., Dai, X. and Zhang, Y., 2016. Comparison of random forests and other statistical methods for the prediction of lake water level: a case study of the Poyang Lake in China. Hydrology Research, 47(S1), pp.69-83.
• Tikhamarine, Y., Souag-Gamane, D. & Kisi, O. A new intelligent method for monthly streamflow prediction: hybrid wavelet support vector regression based on grey wolf optimizer (WSVR–GWO). Arab J Geosci 12, 540 (2019). https://doi.org/10.1007/s12517- 019-4697-1

Throughout the document the term “lake water level” has been written as, “water lake level” (Section-3.1 Par-5 Line 14, Section 2.2.3 Par-2 line 10), and sometimes as “Lake water Level” (Introduction section Par-1 Line 1), whereas the abbreviation is presented as ‘LWL’. So it is wise to use consistent term throughout the document

In paragraph 4 of introduction section, the detailed site description is not appropriate in this section and it needs to be referenced. Specially the figures about the depth, surface area, etc. The authors can create sub section for description of the study area under materials and methodology section.

In the result and discussion section of the manuscript (i.e. section 3.2, line 6) it has been narrated as “SVR-GWO2 is a strong model for prediction lake water level.” Which is too general, expressing that this model can be used for Lake water level prediction at all sites. This is incorrect, since the time series data of such hydrological data may vary from location to location. Additionally the quoted statement contradicts with the statement stated on line 5 presenting SVR-GWO3 is the better performing model than others in all scenarios (“the performance of SVR-GWO3 was better than other scenario.”).

Specific Comments

In section 2.1.1 line 13-14 “In this study, the main components of the first one……” it is not clear enough. It would be good with additional explanation is given to what does ‘main components of the first one” mean.

Starting from section 2.3 the word ‘januvia’ is used and miss-written for “January”. Correct it accordingly.

Line 43: consider replacing the singular verb has with plural have

Line 61: consider changing the verb form is into plural are (this error is repeated throughout this article consider revising to make changes)

Line 106: consider removing the word the

Line 132: Full stop is missing at the end of the first sentence.

Line 244: consider changing the word Januvia into January

Line 271: consider removing unnecessary comma here and apply the same throughout the document

Line 322: consider changing the word that into than

Line 353: consider changing the word base into based

Caption of Table 1 does not inform what type of data? Is it water level? Please five enough caption description for Tables and figures. For example, figure 6 and 7: what is the broken line indicating? It is not given information in the caption.

Author Response

The authors would like to thank the referees for their objective and thorough review of our manuscript. We have addressed all the reviewers’ comments in the following point-by-point response and prepared the revised manuscript. This report is prepared to highlight the reply to the comments, to make it clear for the reviewers. We indicate our reply in different colours to differentiate between the comments and the authors’ reply as Black and Blue respectively.

All changes made to accommodate the Reviewers' comments are highlighted by red font in the revised manuscript.

The authors hope that you will kindly consider this paper again for possible publication in Water.

Thank you for your patience and support in this process.

Yiqing Guan

Corresponding author

(On behalf of the authors)

September 2020

Reviewer 2 Report

There are deficiencies in the paper that must be corrected before publication but these are easily remedied.  

(1) The paper never states what time period the forecast of lake level is for – it appears to be one month but this is not stated.  There is  no justification for the choice of forecast period or how this period relates to management decisions that might be made based on forecast lake levels.

(2) There is also no direct statement as to what data the forecast is based on and why this data and no other data were selected for use in forecasting. The paper lists the many variables that affect lake levels of which monthly precipitation on the watershed area of the lake and monthly evaporation from the lake are the most prominent. The paper mentions watershed models in the introduction but does not explicitly state that for this study the only data used was past waterlevel measurements.

(3) There should be a section on data available that provides the source of the monthly-mean lake water level data and for the meteorological data used in the paper

Editing Suggestions

Line 19                 power, AND FOR environmental, agricultural and industrial PURPOSES. Undoubtedly In 

Line 23                  (GWO) ARE used

Line 40                  remove climate                 climate is not an input or output like rest of list   

Line 77                  deepEST

Line 79  `               150 25’ and 160 35’

Line 81                  8560 km²

Line 92                  In order to better understand the present-time dynamic of Lake Titicaca, studies have been made regarding Paleo lake water levels. Since there is important knowing in better the Titicaca Lake dynamic, some approaches were 92 applied for finding lake water levels, also regarding Paleo lake levels.

Line 103                 It is not clear in Line 103 whether the decline in lake level of one metre is for Lake or Lake Poopo.  Rewrite sentence to identify which lake is referred to.

line 159                the term “face data” is used I don’t recognize this term – is discrete data meant

Line 244 and 246                              January

Line 246 247                       Are the temperatures listed air temperatures or water temperatures ???

Line 275                                approaches relies heavily significantly relayed  on …

Author Response

The authors would like to thank the referees for their objective and thorough review of our manuscript. We have addressed all the reviewers’ comments in the following point-by-point response and prepared the revised manuscript. This report is prepared to highlight the reply to the comments, to make it clear for the reviewers. We indicate our reply in different colours to differentiate between the comments and the authors’ reply as Black and Blue respectively.

All changes made to accommodate the Reviewers' comments are highlighted by red font in the revised manuscript.

The authors hope that you will kindly consider this paper again for possible publication in Water.

Thank you for your patience and support in this process.

Yiqing Guan

Corresponding author

(On behalf of the authors)

September 2020

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Title:

Simulation of Titicaca lake water level fluctuations using hybrid machine learning technique integrated with gray wolf optimizer algorithm

Authors:

Babak Mohammadi 1, Yiqing Guan 1, *, Danrong Zhang 1, *，Pouya Aghelpour 2, Samad Emamgholizadeh 3, Ramiro Pillco Zolá 4

In this study, the authors developed a hybrid model that combines the support vector regression (SVR) and the gray wolf algorithm (GWO) to predict the lake water level fluctuations. Also, three types of data preprocessing method, i.e., Principal component analysis, Random forest, and Relief algorithm were used for finding the best input variables. This is an interesting and relevant paper. For further improved quality of this paper before publication, some comments and suggestions are listed as follows.

1.1. In Introduction, the authors mentioned that accurate prediction of lake water level within short-scale intervals has always been one of the challenges faced by hydrologists. Prediction of the lake water level (LWL) fluctuations at various time intervals is a challenging task in water resources management. Hydrologists concerned about the accurate prediction at specific locations with affordable time and cost. Generally speaking, the computational cost would be a critical issue in real-time forecasting (hourly prediction, i.e., short-scale intervals mentioned above) especially for disaster prevention. These descriptions might cause misunderstanding to the readers. In fact, this paper targeted at a monthly-scale simulation of lake water level. Transition between paragraphs can be modified/improved for better linkage.

1.2. For the literature review, Condom et al. (2004) combined a soil routine model with lake routing using an input time step of three months. The focus was on reproducing the 100 m drop in the lake levels or by the time Paleo-Lake Tauca disappeared. The studies of water levels for the paleolake or under climate change scenarios are not closely relevant to this study. Also, the format for citation is not consistent. Condom et al. (2004) cannot be found in the section of References.

1.3. Since this study conducted time series predictions of lake water level, the conventional time series analysis approaches should be reviewed, i.e., ARIMA, ARMAX.

1.4. The authors also mentioned that changes in lake levels are affected by many factors such as precipitation, direct and indirect runoff. Later in section 2.3 data used, the authors also mentioned that the average yearly precipitation of the Titicaca lake basin is 609.5 mm/year. The monthly precipitation data can be included in the model.

1.5. The authors mentioned that the performance of the SVR model can be enhanced by hybridization with the Gray Wolf Optimizer algorithm (GWO) [36]. Some details can be provided for better understanding. Unlike artificial neural networks, the SVR would find an exact solution using quadratic programming with given/tunable parameters, e.g., the regularization parameter. Was the Gray Wolf Optimizer algorithm simply used to replace quadratic programming? The key point to improve SVR can be emphasized.

2. In Materials and Methods, the algorithms should be clearly addressed. It is suggested that the learning/training algorithm for SVR should be included. Fig. 3 shows the flow chart between pre-processing methods and predictor methods. One or two figures can be used to clearly describe the algorithm of SVR and GWO. Particularly, the GWO for updating SVR weight (the highlights of this study) can be better illustrated. In equations, the dot operation (like a period) is not clear.

3.1. In Results and Discussion, PCA1 can be further examined. Since PCA1 only account for about 85% of variability, poor prediction is expected. PCA1-PCA4 can be included in the model for further comparisons and discussion. The meanings of the coefficient of RF and RL should be addressed. How to decide the threshold value to select a proper lag number?

3.2 From Table 4, the comparison between SVR-GWO2 and SVR-GWO3 shows that more lag times would not further increase the prediction accuracy. It seems that the results have been converged. Minor discrepancy might result from optimization. Some discussions can be made.

3.3 MAPE used in this paper would mislead the readers (i.e., 0.001%) because of the high water level (e.g., 3810 m). The mean variation range (e.g., about 1 m) or another suitable variable can be considered in Eq. (10). Also, the regression in Fig. 8 would cause misunderstanding although these equations are correct. In regression analysis, y is the regressand (i.e., the target value or measured value here) and x is the regressor (i.e., the predicted value). For demonstration of the results, the predicted time series of water levels and residual errors can be presented first. From the viewpoint of statistics, the box-plot and histogram analysis can be discussed together.

4. In Conclusion, the authors mentioned that the performance of the RF pre-processing method was better than PCA and RF methods for finding the best input for predictor models. However, this is not consistent to those in results and discussion.

5. For this manuscript, there are some mistakes in English writing, including grammar issues and misuse of vocabularies. The authors should go through the whole manuscript again to carefully revise these problems. Some examples are listed as follows.

Line 244: Januvia 2017; Line 280: PCA1 has selected; Line 381: the compassion of different models

Comments for author File: Comments.pdf

Author Response

The authors would like to thank the referees for their objective and thorough review of our manuscript. We have addressed all the reviewers’ comments in the following point-by-point response and prepared the revised manuscript. This report is prepared to highlight the reply to the comments, to make it clear for the reviewers. We indicate our reply in different colours to differentiate between the comments and the authors’ reply as Black and Blue respectively.

All changes made to accommodate the Reviewers' comments are highlighted by red font in the revised manuscript.

The authors hope that you will kindly consider this paper again for possible publication in Water.

Thank you for your patience and support in this process.

Yiqing Guan

Corresponding author

(On behalf of the authors)

September 2020

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The water-level forecast discussed in this paper is for one month ahead.  

The description of the forecast should always include the time period involved i.e. be stated as one-month-ahead forecast throughout the text.  The current draft only states the period of the forecast once - near the end of the conclusions.

With the additional of the one-month time step added throughout the text I find the paper suitable for publication.

Author Response

Reviewer #2

The water-level forecast discussed in this paper is for one month ahead. 

The description of the forecast should always include the time period involved i.e. be stated as one-month-ahead forecast throughout the text.  The current draft only states the period of the forecast once - near the end of the conclusions.

With the additional of the one-month time step added throughout the text I find the paper suitable for publication.

Reply

Thank you for your opinion about our work. We have checked again whole of manuscript and we have fixed some small errors.

Author Response File: Author Response.docx

Reviewer 3 Report

omments and Suggestions for Authors

Title:

Simulation of Titicaca lake water level fluctuations using hybrid machine learning technique integrated with gray wolf optimizer algorithm

Authors:

Yiqing Guan 1, * , Babak Mohammadi 1, Danrong Zhang 1, *，Pouya Aghelpour 2, Samad Emamgholizadeh 3, Ramiro Pillco Zolá 4

The authors have modified the framework and provided more details in this revised manuscript. However, it seems that the authors did not fully catch the points raised by this reviewer. Also, some mistakes in English writing still exist in this revision. I do hope that an improved quality can be achieved before possible publication in Water. The minor and major parts of my comments are listed below.

Minor (about English writing):

Line 42: The accurate prediction of lake water lake intervals, has always been one of the challenges faced by hydrologists.

à lake water level …

Line 68: but it can be enhanced by the performance of the SVR model by hybridization with the Grey Wolf Optimizer algorithm (GWO) [23].

à the performance of SVR model can be enhanced by …

Line 85: the Grey Wolf Optimizer model used to improve the prediction of Titicaca lake water level

à the Grey Wolf Optimizer model is used to improve …

The authors should carefully read the manuscript again or require English editing to avoid this type of mistakes.

Major (about the content):

1. As mentioned in the manuscript, SVR minimizes structural error to obtain an “optimal” solution. In the introduction, the authors can address the reason “Why” SVR needs further improvement and “How” SVR can be enhanced.

Line 183: “This technique implements the principle of inductive minimization of structural error in order to attain a general optimal solution”.

Besides, see my previous comments. The SVR would find an exact solution using quadratic programming with given/tunable parameters, e.g., the trade-off parameter. Was the Gray Wolf Optimizer algorithm simply used to replace quadratic programming? Were the parameters in SVR also optimized by GWO, too? Some details can be provided for better understanding. In addition to the values of parameters, “the key points” to improve SVR should be emphasized.

2. The use of pre-processing methods is an important part for model development. The authors tried to find a proper set of lags. As mentioned in this paper (Line 143), the PCA changes the input variables to the main components that are independent and linear combinations of input variables. Therefore, what is this linear combination of inputs, e.g., a*L(t-1) + b* L(t-2) or a*L(t-1) + b* L(t-2) + c* L(t-3)? PCA1 can be further examined in terms of the lags. More in-depth discussion can be made. Since PCA1 only account for about 85% of variability, poor prediction is expected. Since four or five lags suggested by RF and RL methods were used, similarly, PCA1 to PCA4 can be included in the model for further accuracy.

3. MAPE used in this paper would mislead the readers (i.e., 0.001%) because of the high water level (e.g., 3810 m). In fact, MAPE with a range between 0.008% to 0.001% makes no sense/meaning. The mean variation range (e.g., about 1 m) or another suitable variable can be considered in Eq. (10). Also, the regression (e.g., y = 0.6381*x + 1378.5) in Fig. 8 would cause misunderstanding. This indicated that y can be predicted when x is known. Note that y is the result from SVR prediction and x is the measured value. Typically, we would use the estimation from SVR as an indicator (or regressor) to predict the target value (i.e., measured value). In other words, the lake water level is about 1.85 (1/0.63) times SVR estimation.

Comments for author File: Comments.pdf

Author Response

Reviewer #3

The authors have modified the framework and provided more details in this revised manuscript. However, it seems that the authors did not fully catch the points raised by this reviewer. Also, some mistakes in English writing still exist in this revision. I do hope that an improved quality can be achieved before possible publication in Water. The minor and major parts of my comments are listed below.

Reply

The authors would like to sincerely thank the Reviewer 3, for his/her positive opinion of our research contribution presented in this manuscript. We have done it all mentioned parts revised the manuscript accordingly.

Line 42: The accurate prediction of lake water lake intervals, has always been one of the challenges faced by hydrologists.

à lake water level .

Reply

It has done.

Line 68: but it can be enhanced by the performance of the SVR model by hybridization with the Grey Wolf Optimizer algorithm (GWO) [23].

à the performance of SVR model can be enhanced by .

Reply

It has done.

Line 85: the Grey Wolf Optimizer model used to improve the prediction of Titicaca lake water level

à the Grey Wolf Optimizer model is used to improve .

The authors should carefully read the manuscript again or require English editing to avoid this type of mistakes.

Reply

It has done.

As mentioned in the manuscript, SVR minimizes structural error to obtain an “optimal” solution. In the introduction, the authors can address the reason “Why” SVR needs further improvement and “How” SVR can be enhanced.

Line 183: “This technique implements the principle of inductive minimization of structural error in order to attain a general optimal solution”.

Besides, see my previous comments. The SVR would find an exact solution using quadratic programming with given/tunable parameters, e.g., the trade-off parameter. Was the Gray Wolf Optimizer algorithm simply used to replace quadratic programming? Were the parameters in SVR also optimized by GWO, too? Some details can be provided for better understanding. In addition to the values of parameters, “the key points” to improve SVR should be emphasized.

Reply

The authors agree with reviewer, then we have added some details about mentioned topic:

L 307-309: The parameter settings of the SVR-GWO model have selected by trial and error method; whereas, the population size set to 20 and the max number of iterations is set to 500.

L 329-332: The optimal parameters of the SVR ranged between γ (Radial basis function parameter) = 0.45 ‒ 20.2 and C (Trade-off parameter) = 1.68 ‒ 19.14. Also, for running the GWO used 500 as the maximum number of iterations, 50 as the number of agents.

The use of pre-processing methods is an important part for model development. The authors tried to find a proper set of lags. As mentioned in this paper (Line 143), the PCA changes the input variables to the main components that are independent and linear combinations of input variables. Therefore, what is this linear combination of inputs, e.g., a*L(t-1) + b* L(t-2) or a*L(t-1) + b* L(t-2) + c* L(t-3)? PCA1 can be further examined in terms of the lags. More in-depth discussion can be made. Since PCA1 only account for about 85% of variability, poor prediction is expected. Since four or five lags suggested by RF and RL methods were used, similarly, PCA1 to PCA4 can be included in the model for further accuracy.

Reply

For further information we have provided linear combination of inputs for PCA1:

PCA1= =0.1117*L1+0.1138 *L2 +0.1155 *L3 +0.1169 *L4+0.1179 *L5+0.1183 *L6 +0.1183 *L7+0.1179 *L8 +0.1169 * L9+0.1155 *L10 + 0.1138 *L11+0.1117 *L12 -5287.7

According to the mentioned above table: PCA1 was covered 85% of whole variance, PCA2 was covered 8% of whole variance, PCA3 5% of whole variance, PCA4 1% of whole variance, so on.

Then in compression PCA method result the first component (PCA1) is the best variables for considering as the input of models. More information is provided in manuscript text.

MAPE used in this paper would mislead the readers (i.e., 0.001%) because of the high water level (e.g., 3810 m). In fact, MAPE with a range between 0.008% to 0.001% makes no sense/meaning. The mean variation range (e.g., about 1 m) or another suitable variable can be considered in Eq. (10). Also, the regression (e.g., y = 0.6381*x + 1378.5) in Fig. 8 would cause misunderstanding. This indicated that y can be predicted when x is known. Note that y is the result from SVR prediction and x is the measured value. Typically, we would use the estimation from SVR as an indicator (or regressor) to predict the target value (i.e., measured value). In other words, the lake water level is about 1.85 (1/0.63) times SVR estimation.

Reply

Thanks, we have removed MAPE result. Then we have used RMSE, MAE, and R² as the statical indexes.

Author Response File: Author Response.docx

Round 3

Reviewer 3 Report

This reviewer appreciates the authors’ efforts for the revision. I would recommend acceptance of this article for publication in Water. Before publication, discussion of PCA1 should be presented in the manuscript. Again, this reversion still needs further English editing.

Comments for author File: Comments.pdf

Author Response

The authors would like to thank the referees for their objective and thorough review of our manuscript. We have addressed all the reviewers’ comments in the following point-by-point response and prepared the revised manuscript. This report is prepared to highlight the reply to the comments, to make it clear for the reviewers. We indicate our reply in different colours to differentiate between the comments and the authors’ reply as Black and Blue respectively.

All changes made to accommodate the Reviewers' comments are highlighted by red font in the revised manuscript.

The authors hope that you will kindly consider this paper again for possible publication in Water.

Thank you for your patience and support in this process.

Yiqing Guan

Corresponding author

(On behalf of the authors)

September 2020

Author Response File: Author Response.docx