This paper emphasizes the issue of decreasing data confidence at the watershed scale in the era of big data, caused by the non-closure of water budget from multiple data sources. In their analysis, the total water budget residuals were quantitatively decomposed into two components, inconsistency and omission residuals, to account for different drivers of water budget non-closure phenomenon. This is an interesting addition, as previous studies have typically given little or only qualitative consideration to the water imbalance caused by omissions in the original water balance equation.

Attempting to close the water balance is valuable, both hydrological inference under climate change and hydrological modeling require data that satisfy the basic assumption of water balance. The PHPM-MDCF proposed in this work employ hydrological model to constrain multisource datasets, which is reasonable because hydrological models are well-known for their water balance capabilities. The correction also seems to be effective, which comes from the validation with results from large sample basins.

However, there are still some concerns that need to be explained in the response or addressed in the manuscript. The authors have observed the typical seasonal pattern of non-closure phenomena but lack corresponding explanations. In addition, although the authors decomposed the closure residuals into two parts, it seems that only the inconsistency residuals were corrected. What is the rationale behind this approach? Why were the omission residuals not corrected?

In summary, this paper is innovative and aligns with the interests of potential readers of the HESS. After careful consideration and revision, this work has the potential to make a significant contribution to this field. As they described, the underlying Bayesian philosophy is an approach for aligning our understanding of natural processes with real-world observations.

Major concerns:

1. Sect. 4.1, the patterns of the Res are of interest to me. The authors identified typical spatial distributions and compared them with previous studies in Sect. 4.4, explaining these patterns through hydro-meteorological conditions and watershed area. From a physical perspective, this explanation is consistent with common sense and is sufficient for me. However, the temporal patterns of the Res are also of interest (Fig. 5). The authors should provide further explanation in this regard or compare them with previous studies, as this could offer valuable insights into the causes of the non-closure of water balance.
2. From Fig. 6, it appears that the Res and Resi have been effectively corrected, but the Reso have not changed significantly. Is this merely a specific case for this basin or a general situation? If it is a general situation, dose this imply that PHPM-MDCF only corrects for Resi and does not account for Reso? I believe that further explanation of this treatment could improve the transparency of the methods used in the paper.
3. Although the author has clearly articulated the main scientific problem of the paper, there are still areas that could be further improved, which I have listed in the specific issues.

Specific issues

1. Line 22-25: According to the results, it seems that humid/wet basins are also prone to larger closure residuals, which needs to be emphasized here.
2. Line 36-46: I believe this section should place greater emphasis on the issues of scale mismatch and difficulty in obtaining reference data.
3. Line 58-60: It is recommended to cite the review by Beven (2002).
4. Line 83-84: It is recommended to add references to support the argument.
5. Line 119: "Res" does not appear to be in italics.
6. Line 126-127: It is recommended to change it to: “(a) How can the total water budget residuals be quantitatively decomposed into inconsistency and omission residuals based on Eq. (3)?”
7. Table1: The “period” should be “Original Period”.
8. Figure5: The figure caption seems to contain an error. There are no other subfigures.
9. Line 332-334: The argument here doesn't seem to correspond with the figure. Could it be that the figure has been updated?
10. Line 418: add “which are” before “implemented”.
11. Line424-426: Change the sentence to “The fact that simultaneous corrections of other variables during extreme runoff noise corrections did not significantly differ from OS-based corrections further enhances our confidence in PHPM-MDCF.”
12. Line 417: It is necessary to further emphasize the issue of the non-closure phenomenon in humid regions.
13. Figure 12: There seems to be a mistake with the R2 values.
14. Line 639: Humid regions is a better expression.

The paper presents an interesting concept, and its organization and writing are well done. However, I have some differing views regarding the underlying assumptions and principles of the proposed method. My main comments are as follows:

Major Comments:

(1) I do not agree with the two underlying assumptions of the PHPM-MDCF method, nor with the significance of using Equation 4 to calculate omission errors. My main reasons are as follows:

Firstly, the errors in hydrological models are non-negligible and represent the sum of both omission errors and data errors, rather than omission errors alone. The paper assumes that hydrological models have no data errors (inconsistency errors) and only omission errors, which is evidently unreasonable. This assumption is particularly problematic because hydrological models are typically validated against observed runoff, often neglecting the validation of ET (Evapotranspiration) and TWSC (Terrestrial Water Storage Change) simulation accuracy. As a result, using Equation 4 to calculate omission errors is not justified. Due to the complexity of hydrological models and the impact of errors in driving variables, the water imbalance caused by errors in the hydrological model may be substantial. Even if the inputs to the hydrological model are observational data and the model itself is developed based on the principle of water budget, the primary contributor to water imbalance errors between input and output might still be data errors.

Secondly, the total residual is calculated using multiple sources of data, and omission errors are calculated using data that drive the hydrological model as per Equation 4. The difference between these is then used to calculate data inconsistency errors. However, this approach might introduce uncertainties due to data inconsistency.

(2) The validation of results should include a comparison between the PHPM-MDCF method and existing methods. The paper repeatedly emphasizes the inadequacy of current methods in distributing residuals, yet no comparison with existing methods is provided in the results to verify the accuracy of the PHPM-MDCF method. The goal of closing the water budget is to reduce residuals while improving the accuracy of water cycle variables. Therefore, the credibility of the model should not be judged solely by the reduction of residuals (Figure 6). A comparison with existing methods would be more convincing. I strongly recommend supplementing the results with a comparison against existing correction methods, particularly CKF, PR, and MCL methods. For instance, the accuracy of the datasets after calibration using these methods, including P (Precipitation), ET (Evapotranspiration), Q (Runoff), and TWSC (Terrestrial Water Storage Change).

(3) The description of the reference datasets is unclear. It is necessary to specify which observational system datasets were used for P (Precipitation), ET (Evapotranspiration), Q (Runoff), and TWSC (Terrestrial Water Storage Change), and why these datasets can be considered observational data. I recommend clarifying this in the text.

(4) Only a single product was selected for each water cycle variable. I believe that selecting multiple products is crucial for validating the proposed PHPM-MDCF method. This is because different datasets have different sources of error, leading to varying inconsistency residuals depending on the data combination. If the proposed method can be used to identify inconsistency residual error, using multiple data combinations would better verify the reliability of the proposed method in this study.

(5) In Step 2 at line 250, please explain why is it reasonable to allocate residuals based on the difference between simulated values and reference values? It is worth noting that the simulated ET (Evapotranspiration) and TWSC (Terrestrial Water Storage Change) by the hydrological model may not have been validated for accuracy and may contain significant uncertainties. If their errors are used to allocate residuals, substantial uncertainties could lead to unreasonable allocation of residuals to ET and TWSC. The formula for residual allocation needs to be supplemented. Additionally, if Step 3 determines that the residual allocation is unreasonable, can simply halving the residual solve the issue? The underlying principles need to be clarified, or an example should be provided.

(6) Please clearly state the scope and spatiotemporal scale of this study. Most studies investigate water budget closure at the monthly scale rather than the daily scale. Aside from data availability, I believe this is mainly due to larger data errors and the lag effect of hydrological processes at the daily scale. If this study focuses on water budget closure at the daily scale, how were these issues addressed?

(7) At line 320, it is necessary to explain the reasons behind the spatial distribution of Res. How does the difference in spatial patterns indicate that inconsistency residuals and omission residuals are driven by different factors? Please provide a detailed explanation. The most likely reason for Resi and Res having the same spatial pattern is that the former was calculated based on the latter. Their difference from Res0 is due to the different error sources used in calculating Res0 and Res, which does not necessarily demonstrate the reliability of the method for separating inconsistency residuals from omission residuals. Additionally, the residual values in Figure 4 differ significantly from those reported in previous studies. What is the reason for this discrepancy?

(8) In the multi-source dataset correction framework for achieving water budget closure, what is the rationale for setting the initial correction rate to 0.5? Why is the correction rate halved when the model produces unreliable simulations? Is there a potential proportional relationship between the adjustment of the correction rate and the magnitude of bias in unreliable simulations that could allow for more efficient correction rate adjustments? Additionally, what is the basis for setting the conditions for iteration and termination of the correction process as “the inconsistency residuals decreases to 10% of its initial value or the correction rate falls below 4%”?

Minor Comments:

(1) Please provide additional explanation on how Section 4.3.1 demonstrates the reliability of the PHPM-MDCF method.

(2) The paper does not validate the accuracy of the Res_o, Res_i, and Res separation method in the results.

(3) At line 310, can KGE ≥ −0.41 really indicate that the hydrological model accurately represents the observed hydrological system?

(4) In Figure 5, Res_o is closer to 0. Can we attribute this to the principle of water budget in the development of the hydrological model, rather than merely to omission errors? Since Res_i = Res - Res_o, and Res_o is relatively small, it is evident that the values and spatial patterns of Res_i and Res are more similar. What does this imply?

(5) Please explain from a theoretical standpoint why the PHPM-MDCF method has such advantages over previous methods: “It suggests that the soft constraints based on physical hydrological processes will not lead to compensatory errors, as seen in traditional methods due to the rigid allocation of water budget residuals.”.

(6) I do not find this statement reasonable: “When the hydrological model calibrated against multiple variables measured by the multisource datasets and achieves reliable performance, we consider the simulation system approaching the measurement system.”.

(7) At line 255, please clarify the data sources for the observed values of P, ET, Q, and TWSC used in this study. Without this information, it is difficult to judge whether the deviation between the simulation system and the measurement system is calculated reasonably.

(8) I personally feel that the discussion in Section 5.1 would be more effective if it were more closely aligned with the scope of this study.

(9) The limitations discussed in Section 5.2 are not explained from a theoretical perspective. I hope that some convincing explanations can be supplemented from this standpoint.

(10) The structure of the article lacks a keywords section. Please add keywords.

(11) Please add references related to the water budget equation.

(12) The text states “as illustrated in Fig. 3” but the caption provided is “Figure 3”. The authors should ensure that all figure captions are consistent with the text descriptions. Please carefully check the rest of the article for similar errors and make the necessary corrections.