Hydrometeorological Forecast of a Typical Watershed in an Arid Area Using Ensemble Kalman Filter

Round 1

Reviewer 1 Report (New Reviewer)

This manuscript addresses an important hydrological problem and adopts a new approach to forecasting watershed parameters. As such, the manuscript is aligned with the journal's scope and aims. However, several important issues will require addressing and revision before the manuscript can be considered for publication. 

Overall - The manuscript needs major proofreading and language editing. 

The resolution and quality of some of the figures are relatively low and authors should consider improving picture quality. 

The structure of the manuscript is fine but you need to avoid the numbered points in your manuscript and instead blend the points in the text (e.g. conclusions).

Abstract: This is fine - you may want to highlight the methodological novelty in the abstract. 

Keywords: avoid odd and long keywords e.g. Hydrological parameter simulation and prediction, and Wavelet analysis and wavelet decomposition. revise the keywords. 

Introduction: the storyline of the intro is fine and the content is fine. Authors can dedicate more text to discussing the influence of climate change on the hydrology and hydraulics of catchments, and the effects on extreme climatic events (10.1016/j.agrformet.2020.108150). The changes in water cycles influenced by inland floods (10.1016/j.watres.2022.119100) is another topic that can be discussed and this can broaden the readership of your paper (also applies to L40 discussions).

L32 - 'Many studies have observed the impact of climate change on the hydrological system and are expected to persist in the future [1].' - if there are many studies, why do you have only one reference? add additional work to show a broader perspective. 

You correctly mentioned that future rises in global temperature may affect the distribution of water resources availability, but I think it's important to also mention the effects on water processing such as purification and treatment processes (10.1016/j.jwpe.2020.101411) or natural process-ponds (10.1016/j.ecoleng.2022.106702). 

2. Overview of the research area: adequate description and discussions. If you can, improve the quality of Fig.1.

3.1. Data: Please provide the dataset as an appendix or provide a link to the data portal, this is to ensure the reproducibility of your model/outcomes.

3.2 Algorithm: the method should elaborate more on the underlying equation and how disturbance and uncertainty are accounted for (10.1016/j.heliyon.2022.e08768). You should also highlight the methodological robustness and novelties. 

3.2.5 Accuracy verification: How can you justify using only one index of NSE for model verification? why further statistical measures are not used? I think this must get improved and further developed in the revision to provide comprehensive metrics for model verifications. 

4.2 Stationarity test and periodic decomposition: I think Fig 2 needs further numeric input and description to clarify the findings presented in the figure. 

Fig.3 - vertical axis, what is [/a]? if you mean annual here, then why not use the common phrase 'year'? 

Fig.5 - two problems to address here: (1) method rely on a heavy number of data for training (2) underpredictions of your model (e.g. precipitation, evaporation)  - how can you overcome these problems and how one can go about uncertainty quantifications should be discussed in the paper with the view of how reliable are such methods (10.1038/s41598-022-08417-4). 

Conclusions: are mostly fine, I suggest changing the writing style from numbered concluding points, as this is more close to a dissertation writing style, and instead, blend these points into the section's discussions. 

Following the above revisions, the manuscript can be considered for publication. 

Author Response

Dear reviewer:

Thanks you for your valuable review comments. Next, I will make a one-to-one response to the questions in the comments.

1, The resolution and quality of some of the figures are relatively low and authors should consider improving picture quality.

Ans: We used the original file to output a higher resolution sketch map. We have remade Table 2, improved its resolution and adjusted the font size.

2, The structure of the manuscript is fine but you need to avoid the numbered points in your manuscript and instead blend the points in the text (e.g. conclusions).

Ans: We modified the expression in the conclusion part and incorporated the numbered points into the text, including inappropriate expressions in section 3.2.4 and section 5. A discussion on the impact of additional data on the optimal estimate has been added in 3.2.4. (See Appendix C).

3, Abstract: This is fine - you may want to highlight the methodological novelty in the abstract.

Ans: We emphasized the innovation of the article in the abstract

4, Keywords: avoid odd and long keywords e.g. Hydrological parameter simulation and prediction, and Wavelet analysis and wavelet decomposition. revise the keywords.

Ans: We modified the keywords to make it easier to retrieve.

5, Introduction: the storyline of the intro is fine and the content is fine. Authors can dedicate more text to discussing the influence of climate change on the hydrology and hydraulics of catchments, and the effects on extreme climatic events (10.1016/j.agrformet.2020.108150). The changes in water cycles influenced by inland floods (10.1016/j.watres.2022.119100) is another topic that can be discussed and this can broaden the readership of your paper (also applies to L40 discussions).

Ans: We have studied some of the extended information you've introduced. These materials are very valuable, and these studies reflect a high level of professionalism and credibility. With regard to the impact of climate change on catchment areas, there are abundant research on the impact of extreme climate events, especially the impact of inland floods on the water cycle. We have added discussion on these materials in the introduction.

6,L32 - 'Many studies have observed the impact of climate change on the hydrological system and are expected to persist in the future [1].' - if there are many studies, why do you have only one reference? add additional work to show a broader perspective.

Ans: The impact of climate change on the hydrological system is a fairly broad topic, including quantitative research, statistical inference, distributed modeling, climate models and many other valuable research directions. We believe that although the quality of the articles cited is fine, they may lack a wide perspective. According to your suggestion, we have supplemented references and added discussion appropriately.

7, You correctly mentioned that future rises in global temperature may affect the distribution of water resources availability, but I think it's important to also mention the effects on water processing such as purification and treatment processes (10.1016/j.jwpe.2020.101411) or natural process-ponds (10.1016/j.ecoleng.2022.106702).

Ans: The availability of water resources on the basin scale mainly refers to the part of water resources that can be adjusted and utilized through engineering measures and has a certain assurance rate under the conditions of technical feasibility and economic rationality. For example, it is obvious that glaciers and bedrock fissure water are not an efficient way to collect water resources. Different physical processes will lead to changes in the existing form and location of water, while the existing form and location of water will lead to changes in its availability. For example, when the total water volume of the system remains unchanged, the melting of glaciers will improve the availability of water resources and increase the risk of extreme climatic hydrological events.

The purification and treatment process can also significantly improve the availability of water resources. We believe that these studies are valuable. Although we are not familiar with this field, we can still feel the solid and reliable quantification methods and analysis experiments in the article. As large-scale meteorological activities (such as monsoon and ocean current) and micro hydrological activities (such as leakage flow and infiltration) are difficult to be directly controlled by people, developing water purification and treatment processes may be an effective way to solve the availability problem of water resources

7, Section2. Overview of the research area: adequate description and discussions. If you can, improve the quality of Fig.1.

Ans: We have added descriptions and discussions in Section 2 and improve the quality of Fig. 1

8, Section3.1. Data: Please provide the dataset as an appendix or provide a link to the data portal, this is to ensure the reproducibility of your model/outcomes.

Ans: We have provided data sources in the Data Availability Statement (Line470).

9, Section3.2 Algorithm: the method should elaborate more on the underlying equation and how disturbance and uncertainty are accounted for (10.1016/j.heliyon.2022.e08768). You should also highlight the methodological robustness and novelties.

Ans: We have added the description of the details of the basic equation, and added the calculation method of uncertainty (ensemble variance based on wavelet decomposition). See Appendix B. To illustrate the robustness of the method, we start from the perspective of new data and observe its impact on the system equation and measurement equation. See Appendix C.

10, Section3.2.5 Accuracy verification: How can you justify using only one index of NSE for model verification? why further statistical measures are not used? I think this must get improved and further developed in the revision to provide comprehensive metrics for model verifications.

Ans: We added BCIP test and K-S test to increase persuasiveness. BCIP ensures the robustness of the model from the perspective of likehood。K-S test study the maximum difference of the joint probability density function between reality and predictions.

11, Section4.2 Stationarity test and periodic decomposition: I think Fig 2 needs further numeric input and description to clarify the findings presented in the figure.

Ans: According to your suggestion, we directly used the test statistics of MK and ACF tests rather than the test results, and added the description of the stationarity test as well.

12, Fig.3 - vertical axis, what is [/a]? if you mean annual here, then why not use the common phrase 'year'?

Ans: Generally, a is used to indicate the period. For example, "There is change in temperature cycle of about 12a”(10.1007/BF02648545), the vertical coordinate of the wavelet power diagram represents the frequency. Since 12a represents the period of a process, 1/12a represents the frequency of the process. In fact, this unit is only a constant multiple of Hz, and we can even change the unit to Hz directly. However, if this is done, the value will be unreadable. A more important advantage of the original expression is that it can intuitively see the main period （also called principal period), and study the magnitude of the main period changing with time.

13, Fig.5 - two problems to address here: (1) method rely on a heavy number of data for training (2) underpredictions of your model (e.g. precipitation, evaporation)  - how can you overcome these problems and how one can go about uncertainty quantifications should be discussed in the paper with the view of how reliable are such methods (10.1038/s41598-022-08417-4).

Ans: You mentioned an article about ANN. I am also a fan of neural networks. It is generally believed that statistical methods cannot catch up with neural networks when we only talk about efficiency. The prediction ability of neural network is quite strong, and this process is achieved through over fitting. The generalization ability sacrificed by over fitting can be recovered with simple techniques, such as early stop, regularization and batch normalization.

Compared with neural network, it is obviously that EnKF does not rely on a large number of data for training. In terms of prediction ability, our results are fine. From a practical point of view, further improvement depends on higher resolution data and greater number of  parameters. The quantification of uncertainty is simulated through the error covariance matrix (See Appendix B). Neural networks are also known for their high uncertainty, while data assimliation algorithm can control the uncertainty with priori hypotheses and matrix analyze.

14, Conclusions: are mostly fine, I suggest changing the writing style from numbered concluding points, as this is more close to a dissertation writing style, and instead, blend these points into the section's discussions.

Ans: We modified the expression in the conclusion according to your suggestion.

Author Response File: Author Response.pdf

Reviewer 2 Report (Previous Reviewer 1)

The revise file is OK.

Author Response

Thank you!

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (New Reviewer)

The authors have revised the manuscript. Although some of my comments and concerns are addressed, there remain further comments to get addressed. I believe following the proposed revision below, the manuscript should be in a good format to get published. 

Sections 1 and 2 are improved, and I dont have any further comments. 

Section3.2 Algorithm: the authors have reflected on my comment about the elaboration of the method and the underlying equations but did not use recent references, especially for considering disturbance and uncertainty (10.1016/j.heliyon.2022.e08768). You should also highlight the methodological robustness and novelties.

Fig.5 - two problems to address here: (1) method rely on a heavy number of data for training (2) underpredictions of your model (e.g. precipitation, evaporation) - how can you overcome these problems and how one can go about uncertainty quantifications should be discussed in the paper with the view of how reliable are such methods (10.1038/s41598-022-08417-4). - here I am not convinced by your response about ANNs and the claim that they are good in prediction because of overfitting. I think you can find many researchers/ and papers in the literature disagreeing with you on this matter! On the other hand, I am supportive of the idea of using EnKF as this could be a novel approach for the context of the problem discussed in this research. However, I think a bit more comprehensive overview of existing approaches can be provided to the readers. 

It appears that you deleted some of the figures' captions - e.g, Fig.6 and 7.

The English should be improved. 

It is difficult for me to understand what is changed in the revision as there are very many changes in track-changes and not sure if the formatting is correct. for the next revision, please make sure you upload both track changes and final versions for easier assessment of the manuscript.  

Author Response

Dear reviewer:

Thanks you for your valuable review comments. Next, I will make a one-to-one response to the questions in the comments.

1,Section3.2 Algorithm: the authors have reflected on my comment about the elaboration of the method and the underlying equations but did not use recent references, especially for considering disturbance and uncertainty (10.1016/j.heliyon.2022.e08768). You should also highlight the methodological robustness and novelties.

Ans:We learned about the valuable article you've recommended(10.1016/j.heliyon.2022.e08768), where the Sliding Mode Observers (SMO) were adopted to mitigate the effects of disturbance in the system and uncertainties in the parameters, which is a reliable method to measure the system's resistance to disturbances. Unscented Kalman Filter (UKF) and Ensemble Kalman Filter (EnKF) have been adopted to improve the forecast in the flow estimation of a lowland conceptual hydrologic model. We think these methods are very practical and worth further discussion.

In Section 3.2, acorrding to the recent references, we discussed the disturbance and uncertainty in more detail. Based on these analyses, we have more confidence in the robustness and novelties of the usage of wavelet decomposition in EnKF.

2,Fig.5 - two problems to address here: (1) method rely on a heavy number of data for training (2) underpredictions of your model (e.g. precipitation, evaporation) - how can you overcome these problems and how one can go about uncertainty quantifications should be discussed in the paper with the view of how reliable are such methods (10.1038/s41598-022-08417-4). - here I am not convinced by your response about ANNs and the claim that they are good in prediction because of overfitting. I think you can find many researchers/ and papers in the literature disagreeing with you on this matter! On the other hand, I am supportive of the idea of using EnKF as this could be a novel approach for the context of the problem discussed in this research. However, I think a bit more comprehensive overview of existing approaches can be provided to the readers.

Ans:I agree with you about overfitting. There might be something wrong in my expression. When we talk about overfitting, we always regard it as a defect. Overfitting only shows that the model is suitable for the training set, while may not have good performance in actual prediction. The regularization method and the trick of model learning, including the structure of the network, are indispensable for ANNs. With the support of optimization algorithm and computer performance, the ability to find the extreme value of high-dimensional function becomes stronger, so that the expression ability of neural network learning can be enhanced (https://doi.org/10.3758/PBR.15.2.256). ANNs and other deep learning technologies have strong expression ability, and good results have been achieved(10.1038/s41598-022-08417-4).

In section 4.3, we provided more comprehensive overviews of existing schemes, including some machine learning algorithms, to provide a broader perspective.

4,It appears that you deleted some of the figures' captions - e.g, Fig.6 and 7.

Ans:According to your suggestion, we presented the results of MK test and ACF test in the form of numerical value in the last revision. Therefore, Figure 2 has been modified into a table (it is not common to fill in so many numbers in the figure). The number of all later figures has been reduced by 1. However, the content of the pictures has not been changed.

5,The English should be improved.

Ans:We carefully checked the usage of English and correct some grammatical errors/misspells . We are sure that these revisions do not change the meaning of the manuscript.

6,It is difficult for me to understand what is changed in the revision as there are very many changes in track-changes and not sure if the formatting is correct. for the next revision, please make sure you upload both track changes and final versions for easier assessment of the manuscript.  

Ans:We provide both track changes and final versions for easier assessment of the manuscript.

Author Response File: Author Response.docx

Round 3

Reviewer 1 Report (New Reviewer)

The authors have revised the manuscript and improved the quality of the text and discussions. I think the paper can be published in its present form. 

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Take a close look at the recommendations.

Comments for author File: Comments.pdf

Reviewer 2 Report

This study selected precipitation, evaporation, temperature, and runoff as model variables, builds a model, tests and analyzes the stationarity of the hydrometeorological parameters of the Manas River, and forecasts the selected parameters based on the ensemble Kalman filter (EnKF) equation. The manuscript looks technically correct, but here are several issues that I am concerned about.

First, I cannot find significant contributions and novelty. Hydrometeorological parameter prediction based on EnKF is quite basic and well designed. Therefore, the contribution of this study lies in the application in the Manas River. However, I did not see any new findings in this case study.

Second, the manuscript also appears that the bulk of the text introduces and explains materials well-known in EnKF. However, the presentation is very chaotic. The authors even don't know how to introduce the variables in equations.

Third, the EnKF assumes that system and observation models are both linear and that the state belief is Gaussian distributed. The authors should provide evidence to justify it.

I think this manuscript cannot meet the requirement of Water. The publication of such a work is not helpful.