General comment

Overall, I believe this is an interesting work. The authors studied the water and energy budget in several larger rivers on both short and long time scales. The manuscript could be accepted after major revisions. 

Specific comment

1. Please label the river basins in the Figure 1. 

2. The boundary of the Amur River is not correct, which would make following results not right. Please check different maps to use the correct boundary.

3. Please use appropriate font size and keep consistent in each figure. The font is too small to be readable. 

4. Lines 374-381. It seems these are methodology, and should not be placed in the results.

5. Lines 419-427. This part is not well written. Each paragraph has only two or three lines. Please rearrange the text.

6. Line 471. References are needed to support your statement.

7. When talking about optimization, we always cannot forget some popular optimization algorithms, such as SCE, DDS, GA, etc. What are the differences between your method and these popular ones?

8. When reading paper, we always want to see the differences between your study and previous ones. Lines 457-470 stressed the similarities but not the differences. Please dig a little bit more to show the differences. 

9. From the conclusion, I can see the main contribution from your study is that you introduced a sequential optimisation approach. Other than this, is there any new findings that different from other studies? There are a lot of optimization method can do the similar job. I want to see new findings that can advance our understanding of the hydrological processes. 

10. A better judgment of the selections of the river basins should be given. Is it because the observation data in these rivers are better than others? Or other reasons. Some important river basins, such as the Mekong River, are not selected. No rivers in Western Europe are selected. I don’t mean you have to select all the rivers, but an appropriate reason should be given. 

Comment uploaded as supplement

General comments

Petch et al presented a new method to derive monthly water and energy flow estimates consistent with observed water and energy budgets. The paper is generally well-written, and the topic is highly relevant to the HESS readership. However, I do have some concerns and suggestions:

1. The authors appear to claim that their optimization method works well by evaluating the results with GRACE - a product that was used in the optimization process. Please consider validation/evaluation with an independent product and/or different time periods. 
2. The authors aim to present better water and energy data and methods. For the effort to be impactful and meaningful, please share the data and the scripts (the scripts were shared, but I could not not find any content in the readme file).
3. Since the paper argues that the produced method constitutes an improvement upon current optimisation methods, it would be useful if the evaluation/comparison figures and results section could show a clearer distinction between comparisons with products that are “optimized” datasets and those that are not. 
4. Since the paper explicitly aims to improve optimization at all time scales (monthly, interannual, trend), it would be useful if the figures and results section could clearly and explicitly show the improvements at each of those time scales. 

Specific comments

L53: “is these” should be “in these”.

L106: Instead of “short and long time scales”, please consider being more precise (e.g., monthly, interannual, long-term trend). Other parts of the paper suggest that the aim is to both produce optimized estimates and an optimisation method/methodology. Please include all study aims in this “aim” paragraph. 

Introduction section: Please consider adding a table providing an overview of optimisation methods. The text already contains a literature review, but it is difficult to gain an overview. Since this paper proposes a methodological advancement, it would be useful to at a glance see in what way this paper presents an advancement. 

Table 1: “present” is ambiguous, it would be clearer if you simply state the years that were downloaded for use in this study. Also make sure that the capitalisation of the headings are consistent. “Parameter” should be “Variable”, I think. In addition, please consider adding a column describing the dataset type (e.g., satellite, in-situ measurements etc). For GRACE, should the variable be “water storage anomaly”?

Methods section: Please consider adding an overview figure of the methodological steps. For variable symbols, please consider using single-letter symbols rather than multi-letter symbols.  

Figure 4 (and elsewhere), please check -  “total water storage” or “total water storage anomaly”?

L350 First use of ITCZ, write out. 

L461 Please consider providing the relative error in the unit of % for Amazon as well. 

L468 Since the imbalances of the Amazon and Amur were explained by the lack of measurements, it seems odd that Congo is presented in this context as the basin with lowest imbalance without further explanation. Between the lines, the text seems to imply that the lack of measurements is not as much an issue in the Congo, which is not true. If any, the lack of measurements is even a bigger issue in this region. Please consider a revision of the paragraph. 

Sect 5.1. Consider moving relevant parts to the Methods.

L551. Could the authors also share the optimized results?

I could not find any content in the readme.md file beside a single row stating “Water-and-energy-budgets”. I have attempted to view it both by downloading it and opening it using a text editor, and by previewing it on GitHub. Please check.