Round 1

Reviewer 1 Report

Please see attached file with comments - Overall I rated it as acceptable for publication with minor review needed.  There were some clarifications needed where I did not understand terms - which were generally later in text.  Also I thought some more background information on river transport, overall goals of the project and how the results would be used would help.   I have not followed this field so did not know the term frazil ice for instance.

THank you for your work.

Comments for author File: Comments.docx

Author Response

Please see attached discussion letter.

Author Response File: Author Response.pdf

Reviewer 2 Report

1. The abbreviations throughout the manuscript MUST be corrected. E.g, GA and PSO have been abbreviated many times.

2. SVM is very slow and many better/fast machine learning techniques are available. Why do authors choose SVM?

3. Why PCA, though many other good options are available.

4. Authors must compute the execution time and write about the trade-off between different performance parameters. E.g, accuracy is achieved at the cost of computation overhead, etc, etc. 

Author Response

Please see the attached discussion letter.

Author Response File: Author Response.pdf

Reviewer 3 Report

The purpose of this study is for assessing heat balance state and using a machine-learning approach to assess it. Based on the title of the paper, it appears to be an application paper. By reading the paper, it seems like a methodological paper for PCA. There are good parts to be like regarding improved PCA analysis. It is more appropriate to consider changing the title to something like "Environmental variables contributing to heat balance state .." or “Using PCA to analyze environmental variables contributing to heat balance state...” The PCA method is appropriate to reduce parameter dimension and apply to machine learning models. However, I did not see the authors talk about the application of the machine learning model to predict the change of heat state in the water transport channel. Is this a future goal? The paper sent a confusing message to the readers. There are some major problems, which the authors need to address and improve the paper.  

1. The purpose of the study is to assess heat balance state. To me it sounds like an assessment of the ice state or under what condition ice will form, but most parts of the paper is to discuss the PCA method. PCA is a common method. Improving PCA is important, but does not fit the purpose of the paper as I don't see the assessment of the heat balance state. 

2. The method section was not well presented. The length of the channel is 1267 km. The authors did not explain where these data were observed and the data sources, as well as how many measurements were collected. It looks that the data set X is the selected number of measured parameters and measurement records. Using one station measurement is not feasible to represent the Channel.  The weakness of the MS is that the authors did not talk about the temperature measurements (with and without forming ice), the analysis focused on the contribution of environment variables, but did not talk about the correlation between environmental variables and heat balance. 

3. I don't know if Eq. 1 and 2 were used in the analysis and if they are related to the data used for analysis, and if it is related to the data of Eq.3? What is the purpose of presenting the equation?  The authors did not clearly explain the approach in the method section. 

4. Page 232-327, the authors talk about winter data from 2015-2021. It is not clear to me what data the authors are talking about, where these data were collected. Has this data set been used? These details have not been presented in the method part. If the authors used it for model training and test, the results need to be presented clearly. 

5. The authors talked about the contribution of environment variables but did not talk about how it is related to ice formation, or used them to predict temperature. 

6. It looks like the data used for PCA is an example of the data. The good part of the paper is to present the PCA method and use it to analyze the contribution of variables. However, based on the results I don't see much difference between different approaches. It is fine just present method of PCA, but it may not fit for the scope of "Water" 

Author Response

Please see attached discussion letter.

Author Response File: Author Response.pdf

Reviewer 4 Report

This study is concerned with the exploration of the heat balance state of the water-transfer of  the main channel of the middle route of the South-to-North Water Transfer Project in China. The principal component analysis method is used to reduce the dimension of the eigenvector and a new approach for judging the heat loss or heat absorption of flowing water in a channel during winter period is developed employing the Gaussian radial basis. The grid search, the particle swarm optimization and the genetic algorithm methods are the main optimization ways of the parameters. Machine learning process proves that the air-water temperature difference and thermal conditions are the key factors affecting the heat loss or heat absorption of water body. Hence, the water temperature changes are shown to be well predicted by means of the proposed method together with the state of water heat balance. The technique can be promising for controlling the ice problems in channels for water transfer in cold regions.

In view of important contributions to the specific topic, the paper can be published in the MDPI: Water, after adressing the following main issues:

A) Language and typing are fine overall. Only some typos are present.

B) Abstract can be trimmed a bit for more focus on the present attempts only with no details.

C) Introduction is Okey. A few more recent efforts can be added.

D)  It is better to make a Table for the main parameters of the model 1&2. Also, provide references for these equations, though well-known.   

E) Differential heat equations 1&2 demand initial and boundary conditions, right after the model. This is essential to characterize the physical mechanism of the heat transfer of the water body during a winter period. The publications “Heat Balance Calculation and Energy Efficiency Analysis for ... MDPI (2021)”,

“Heat transfer from warm water to a moving foot in a footbath (DOI: 10.1016/J.APPLTHERMALENG.2015.12.027)”, “Energy Balance Approach to Study the Role of Perspiration in Heat ... Hindawi (2020)”

and “Heat transport in shear-driven flow with axial conduction (DOI: 10.1016/J.JTICE.2021.05.038)” can be benefited to enrich the text in this direction.

F) Give proper references for the formulas used.

G) - It is heuristic to reduce the problem into Eq.(13). How many parameters are pertinent here and what are the expected values of them in real applications? Are they compatible with the simulations of the collected data?

H) It is concluded that with the increases in the number of principal component that extracted, the prediction accuracy of the model increases accordingly. Are there missing components in the model?

K) Recommendations for further works are expected for the young scholars.

L) How can one adjust the current predictions to other water-ice problems?

Author Response

Please see attached discussion letter.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Quality of all figures is very bad, it MUST be improved. Authors are suggested to use the vector for of images; like, ps, eps, pdf, etc.

Reviewer 3 Report

The revision is improved.