The manuscript investigates the drivers of changes in lake dynamics using an integrated modelling framework that combines hydrological modelling, machine-learning approaches, and the Budyko framework. The methodology is applied to disentangle the dominant drivers on the water balance of Lake Balkhash (Kazakhstan). The authors identify three distinct periods characterized by differing hydroclimatic and anthropogenic influences, showing that human interventions strongly affected the water balance during the second period, while recent wetting trends are largely offset by increased human pressures.

Overall, the paper is interesting, novel, and clearly written. The methodological approach is sound, and the figures and tables are appropriate and informative. However, some methodological details regarding data and methods are insufficiently described and would benefit from clarification. In addition, the Discussion section introduces new results on lake level projections that are not presented or motivated earlier in the manuscript. These results are interesting and relevant, and in my view would be better integrated into the main Results section or more clearly introduced in the earlier parts of the paper. Detailed comments are provided below.

General comments

• I recommend removing “integrated attribution modelling” from the title and being cautious with the use of the term “attribution” throughout the manuscript. This terminology may cause confusion with established climate and impact attribution studies (e.g. Pietroiusti et al., 2024), which are not conducted here. More neutral wording such as “disentangling drivers” or “assessing relative contributions” would be clearer.
  
  
  
  Pietroiusti, R., Vanderkelen, I., Otto, F. E. L., Barnes, C., Temple, L., Akurut, M., Bally, P., van Lipzig, N. P. M., & Thiery, W. (2024). Possible role of anthropogenic climate change in the record-breaking 2020 Lake Victoria levels and floods. Earth System Dynamics, 15(2), 225-264. https://doi.org/10.5194/esd-15-225-2024
• The manuscript would benefit from a clearer description of observed climatic changes in the basin, including precipitation characteristics (mean annual values and seasonality) and documented trends such as warming or enhanced glacier melt in upstream mountain regions. Where possible, summary statistics or maps (e.g. in an appendix) would improve context.
• The role of the machine-learning component following the hydrological model simulations requires clearer justification. At present, it appears to function primarily as a bias-correction step. The manuscript should explain why this additional step is necessary, how overfitting is avoided, and why the direct hydrological model outputs are insufficient.
• The analysis of future lake level projections is introduced for the first time in the Discussion section. Given its relevance, this analysis should be presented in the Results section and clearly introduced in the Introduction and Methods. The climate data sources (e.g. selection of CMIP6 models) should be explicitly described and referenced, and model performance in simulating precipitation and evaporation in the basin should be assessed or supported by existing literature. The role of glacier melt in future changes also warrants more explicit discussion.
• The frequent use of the term “runoff” appears inconsistent with the processes described, where “inflow” (i.e. water actually entering the lake after upstream losses) would often be more appropriate. This distinction should be clarified and terminology applied consistently throughout the manuscript.
• The multi-step procedure used to derive naturalized streamflow is not sufficiently clear. In particular, using parameter sets calibrated for the first period (including snow and glacier parameters) may not capture climate-driven changes in snow and glacier dynamics in the most recent period. This assumption and its implications should be discussed more explicitly.
• The manuscript uses overly strong or promotional language throughout the results, discussion and conclusion section (e.g. “powerful,” “massive increase,” “overwhelmingly,” “immense,” “enormous potential,” “exceptionally favorable”). I recommend moderating this wording and adopting a more neutral, quantitative scientific tone throughout the manuscript.

Specific comments

Title: I suggest removing “integrated attribution modelling”. This is not a standard modelling term, and given the existence of established fields such as climate attribution and climate impact attribution, its use may be confusing for readers (see also general comment above).

Title: Please consider adding the country or region to the lake name to help readers geographically locate the study area, e.g. “Lake Balkhash (Kazakhstan)”.

L90–99: Are lake level observations available for Lake Balkhash? If not, please state this explicitly and explain why. If such data exist, a plot of lake level and/or lake extent evolution and variability over this period would be highly informative. Datasets such as DAHITI or G-REALM may be relevant.

L87–89: Could you provide quantitative information or maps on mean annual precipitation (e.g. in an appendix) and precipitation seasonality? In addition, a description of observed climatic changes in the region is missing (e.g. warming, enhanced glacier melt in upstream mountain ranges, changes in precipitation patterns). Where possible, briefly mentioning projected future changes under different scenarios would further strengthen the context.

Table 2 (datasets): Please provide full references for all datasets listed under Source. In line with HESS guidelines, these datasets should also be included in the reference list, and their URLs should be provided in the Data availability section.

Table 2: Please clarify what is meant by “~2000 snapshot” for the glacier dataset.

L123: The phrase “enhance precision” should be replaced by “increase resolution”, as downscaling does not increase the precision of the original dataset. Please also clarify whether the downscaling approach is validated against precipitation observations and whether total precipitation amounts are conserved.

L126: Please provide more details on the observed streamflow dataset, including which stations are available (preferably shown on a map) and their periods of record. If historical lake level or extent data are unavailable, could the streamflow observations be used to illustrate the periods defined in Table 1?

L146: Streamflow and runoff are not equivalent terms; please clarify and use consistent terminology.

L150: Please clarify why overfitting is not an issue in the machine-learning approach. As implemented, it appears to function as a form of bias correction—this should be stated explicitly and justified.

L176: How is the parameter n calculated? Is it static in time? What data sources are used to determine n?  Please also specify which data are used to estimate potential evaporation and actual evaporation.

L188: Please explicitly describe how lake precipitation and lake evaporation are determined, including data sources and assumptions.

L191: For the level-to-area conversion, please provide the conversion function or a plot of the hypsometric relationship. Additional methodological details from Wang et al. (2022) should also be summarized.

L207: This equation appears to repeat a previous one; please update to the correct formulation.

L239: Please be precise about which input data are used here and repeat the product names (either here or in the Methods; see also comment above).

L274: Please clarify how the deltaic water consumption method works and which data sources are used.

L276: The multi-step procedure is not sufficiently clear. Moreover, using the same parameter set (including snow and glacier module parameters) calibrated for an early period (1931–1969) may not account for climate-driven changes in snow and glacier dynamics in later decades. As a result, the naturalized streamflow may implicitly assume pre-1970 climatic conditions, despite substantial climate change in more recent decades. This assumption and its implications should be discussed.

L279: For how many years does this apply? An overview figure showing data availability by year and tributary would be helpful.

Figure 6: The term “real runoff” is confusing and potentially misleading (e.g. with respect to observed values). Please revise this terminology. In addition, “inflow” may be more appropriate than “runoff” here and throughout the manuscript.

L296: What evidence supports the statement regarding “more extreme events”? Please clarify or provide supporting references or analysis.

L284–295: The reported values in km³ yr⁻¹ do not appear to correspond to the absolute values shown in Figure 6; please check for consistency.

Table 3: Does x represent precipitation (P) here? If so, please replace x with P and add units to the relevant columns.

L341: Please provide the exact sources of the water level and lake area data. What data are used prior to the remote-sensing period? Also indicate the data sources explicitly in the caption of Figure 8.

L364: For additional context, it would be useful to provide an estimate of basin-wide warming over the study period.

Figure 11: would the lake dry up in the most extreme scenario? What is the uncertainty?

Textual comments

• L117: Please verify whether the dataset is CRU JRA v3.5 rather than v2.5.
• L134: Missing H in the AAF flowchart; please also check figure caption font consistency.
• L136: PIML is used without being introduced (already appears in L60).
• L143–145: Sentence is missing a main verb; please also repeat the input data products used for each variable.
• L169–170: Use P instead of x to avoid confusion.
• L174: Equation 1 uses E, while ET is used elsewhere—please ensure consistency.
• L207: Equation is repeated; please update to the correct formulation.
• L292: At this stage, attribution should not yet be stated, as the corresponding analysis follows later.
• L297 and L371: Consider adding a white line or spacing to better delineate paragraphs.
• L341: Please provide exact sources for water level and lake area data and indicate these explicitly in the caption of Figure 8.
• L392: Replace “quantify” with the appropriate verb for clarity.

The manuscript “Revealing the Driving Factors of Water Balance in Lake Balkhash Through Integrated Attribution Modeling” developed a hydrological attribution and analysis framework to quantify the contribution of climatic and anthropogenic drivers to the Lake Balkhash water storage. The research topic is important, and the overall framework is reasonable. However, the manuscript in its current form lacks sufficient clarity and rigor in several critical aspects. In particular, the use of the term Physics-Informed Machine Learning (PIML) is conceptually inconsistent with commonly accepted definitions, the claimed research gap relative to existing hydrological and attribution studies is not clearly articulated, and essential details regarding model calibration, validation, and evaluation are insufficiently documented. Addressing these issues is necessary to improve the transparency, reproducibility, and scientific importance of the work. Therefore, I recommend major revision before the manuscript can be considered for publication.

Major comments:

1. Inappropriate terminology regarding the PIML.

The manuscript characterizes the proposed model as Physics-Informed Machine Learning (PIML); however, it looks more like a ML-corrected SEGSWAT+ to me. In this study, the physics-based model (SEGSWAT+) run independently, and a ML model is subsequently trained to predict the discrepancy between the simulated outputs and observations. While this strategy can improve predictive skill, it does not incorporate physical laws, constraints, or governing equations into the learning process itself. As such, the ML component operates as a statistical correction to the physics model rather than being informed by physics during model training or optimization. 

Under commonly used definitions, PIML frameworks require explicit physical constraints to be embedded within the model architecture, loss function, or parameter evolution (see Raissi et al., 2019; Shen et al., 2023). The proposed method would therefore be more accurately described as ML-corrected SEGSWAT+ or a hybrid model rather than a PIML. I would suggest the authors change the terminology in order to avoid conceptual ambiguity and ensure consistency with established definitions in the literature.

Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys., 378, 686–707. doi: 10.1016/j.jcp.2018.10.045

Shen, C., Appling, A. P., Gentine, P., Bandai, T., Gupta, H., Tartakovsky, A., ...Lawson, K. (2023). Differentiable modelling to unify machine learning and physical models for geosciences. Nat. Rev. Earth Environ., 4, 552–567. doi: 10.1038/s43017-023-00450-9

1. Research gap

Line 50-60: The research gap is not clearly explained. Previous studies have already developed multiple models to quantify the contributions of different drivers to lake water balance changes. For example, Yu et al. (2025) developed a distributed Geomorphology-Based Hydrological Model (GBHM) to quantify the contributions of multiple drivers. What is the key difference or advancement of your approach compared to GBHM in terms of the study objective (i.e., driver attribution)? The authors claim that previous models did not “integrate their findings with the lake’s terminal water balance,” but this statement is vague. What does the “terminal water balance” mean exactly? Does this imply that previous studies did not directly simulate lake water levels or storage changes? 

In addition, the authors state that data scarcity, particularly limited lake inflow observations, is a major challenge for existing hydrological models. It is unclear why this limitation would affect physics-based hydrological models and machine-learning models, but not the proposed hybrid model. If the uncertainty arises from insufficient data for model calibration, this limitation would appear to be a general issue for all modeling approaches rather than one unique to existing models. 

It’s very important (perhaps the most important) to clearly and explicitly articulate the specific research gap, the limitations of previous studies, and how the proposed approach meaningfully advances beyond existing models.

3. Calibration details

Section 2.3.1 requires additional detail regarding the model calibration strategy. Specifically:

(1) The calibration (training), validation, and testing periods should be clearly specified here.

(2) Based on Figure 3, the overall strategy appears to involve pre-calibrating SEGSWAT+ using gauge station observations, followed by training the machine-learning model to correct the residuals. If this interpretation is correct, it should be stated explicitly in Section 2.3.1 to avoid confusion.

(3) What’s the hyper parameter selection strategy for each ML/DL model (e.g., number of layers for ANN, sequential length for LSTM)? 

(4) A table summarizing the SEGSWAT+ parameters used for calibration, as well as the machine-learning hyperparameters, is essential. This table could be placed in the appendix.

(5) A comparative table reporting NSE, KGE, PBIAS, and R² for the raw SEGSWAT+ outputs and the final ML-corrected model across the calibration (training), validation, and testing periods should be provided to clearly demonstrate the performance improvement achieved by the ML correction.

(6) Section 2.3.4 could be merged into Section 2.3.1. Dedicating an entire section to explaining KGE, NSE, and PBIAS is unnecessary, as these metrics are widely used and well understood in hydrological modeling.

(7) Multiple evaluation metrics are used in this study. If these metrics yield conflicting assessments, how is the optimal parameter set selected?

Minor comments:

Line 27-31: These texts do not explain the environmental issue well. “This balance is under pressure..” on which direction? Increasing or decreasing water storage… Please state the issue clearly. Consider use simple sentences: “Decreasing water storage has become a widespread issue for these lakes, posing a significant threat to their ecological health (reference). The decline in water storage is driven by two primary factors: climate change and human activities. (reference).”

Line 41: omit “Lake Balkhash has no outlet”.

Line 43: “It signals a long-term depletion of solid water reserves”. What does that mean? Do you mean the increasing evaporation outweighs the glacier melt? If yes, it is important to add references to support your statement. Consider “While increasing glacier melt can temporarily raise inflow, the associated increase in evaporation outweighs this effect and leads to overall water depletion.” 

Line 67: Swap “To achieve this” with “Specifically”

Figure 1: Consider remove political borders and just focus on watershed boundaries.

Table 1: I appreciate this style! Just a minor suggestion: consider place references in “Source” column instead of simply saying it’s from Zenodo.

Figure2: Spell AAF in the caption. Figure and table captions should be self-explanatory. All acronyms must be fully spelled out in the captions, even if they have already been defined in the main text. Also, check the font style of the caption. 

Line 140: “The SWAT model and its improved versions are widely used in hydrological simulation processes.”, such as? Add references of the original literature of the SWAT model and other publications of the model application.

Line 141: Swap “Iteration” with “variant”. 

Figure 3: Need a higher-resolution figure, the Q_final figure is blurred. Also, this flow diagram is not explained well in the main text. What’s the relationship between Qsim and Qres. What’s Qres? Is it the discharge into reservoir or the residual of simulated discharge? Consider explain this figure component by component in section 2.3.1.

Line 189: Is “A” static? Or it was calculated by a hypsometric curve between Area and Storage?

Line 194: I understand including groundwater component is challenging. However, groundwater table decline is also a major contributor to water scarcity in arid regions. Therefore, evidence supporting the claim that groundwater has a relatively minor contribution in this study area should be provided here (e.g., relevant observations, previous studies, or sensitivity analyses).

Figure 5: The figure resolution needs to be improved. In addition, consider segmenting the time series into calibration and validation periods using shaded boxes. The figure caption should also be revised to “Comparison between observed and simulated streamflow.” Note that runoff in an open channel should be referred to as streamflow, not runoff.

Line 341: Which satellite altimetry & optical data was used to validate the reconstructed water storage? This needs to be clearly stated in section 2.2.