General comments

I apologize for the time it took to review this paper. This paper includes advanced content covering extensive elements of global water resources. It took much more time than I had initially estimated to review it (I read through it three times).

This paper is ambitious in that it attempts to estimate the amount of water withdrawn and consumed for agricultural, industrial, and domestic sectors for 300 geographical units globally. It calculates the costs and benefits in each unit by water source and maximizes the net benefits for the entire world. While the conventional method of calculating the amount of water withdrawn by sector is to use a regression model, this research proposes a new technique that is suitable for advanced scenario analyses.

The manuscript is well prepared, but I felt that there were issues with the following: in the introduction section, there was no reference to earlier research by GCAM, which has long propelled economics-based global water resources studies; in the methods section, there was room for improvement in the expression of mathematical formulas; and in the methods, results, and discussion sections, there was no description of the balance between supply and demand of goods and services. For details, please see below.

Specific comments

Lines 52-68: It is surprising to me that the authors do not refer to any works of GCAM (e.g., Kim et al., 2016; Dolan et al., 2021; Niazi et al., 2024). Niazi et al. (2024) are cited in this manuscript but not in the review part. Their works must be referred to, and this study must be contextualized well in the development history of economics-based global water resources modeling.

Line 151 “each headwater gauge”: What is the headwater gauge? I assume it is the uppermost river discharge gauge, but Equation 1 has the inflow term (I_h,t).

Line 189 “but it is considered a more expensive water supply source compared to surface water and renewable groundwater”: Is this relationship static (irrelevant) to groundwater table depletion?

Line 213 “water application per ha, b_a,j,k”: I expect this is a weather-/climate- dependent term, but the text implies this is a tuning parameter. If this term is not weather-/climate-specific, the projected change in irrigation water requirements due to global warming (e.g., Wada et al. 2013) cannot be implemented in this modeling framework. Elaborate on this issue.

Line 265 “alpha_1,a,g,j,k is…”: Do you mean the alpha_1 is negative? Equations 22 and 23 are expressed in general forms, but I guess the authors assume a declining and a convex upward function, respectively. This should be conveyed more clearly.

Line 290 Equation 25: Maximizing the sum of net benefit is understandable, but I wonder whether the supply and demand of goods and services equilibrate with this approach. Another concern is what the author assumes on international trade. These points are critically important in interpreting the results part.

Line 307-307 “1410 river gauges nodes and 1128 demand nodes”: Clarify why they become 282*5 and 282*4.

Line 376 “For irrigated agriculture, country-specific prices of 13 crops”: Do you mean the market price of agricultural products from irrigated cropland? I wonder whether such a price is distinguishable between rainfed and irrigated agriculture.

Line 413 “for the base year 2010. The calibration process consists in adjusting model parameters such as irrigation efficiency…”: Was calibration conducted only for one year? If this is the case, the validation should ideally be done for a different year other than 2010. If addressing is technically tricky, at least the authors can discuss challenges.

Line 524 “the ENV scenario would reduce cereals (wheat, maize, and other cereals) by 36-45%, cotton by 32%, oil crops by 27%, roots by 26%, fruit by 24%, vegetables by 21%, and rice by 14% in 2050”: First, which do you mean reduction in the total crop production or irrigation water? If the former is the case, how will humanity be fed by smaller calorie production than today (see discussion in Gerten et al. 2020)? If the latter is the case, would it accompany a considerable expansion in rainfed cropland (see discussion in Rosa et al. 2018)?

Line 571 “while the agricultural sector has a smaller share of 7% (23 billion USD/year)”: By reading this point, I started to wonder about the role of governments (the public sector). Agricultural water is often subsidized, and its infrastructure is usually built and managed by central/local governments. Does the public sector cover the cost included in Equations 21-22, and how?

Line 601-604 “Strong et al. (2000)…”: The discussion sounds blurry. Clarify whether their findings/estimates are similar to (support) the authors’ findings or not.

Line 612-615 “Strong et al. (2000)…”: Ibid.

Line 622 “Demand management options can reduce withdrawals by 27% compared to BAU”: Was goods and service supply maintained? Won't a 27% reduction create other problems?

Line 639 “unregulated groundwater pumping could increase substantially by 160% in BAU by 2050”: The claim contrasts that of Niazi et al. (2024). If I understand correctly, the difference stems from the treatment/assumption in the groundwater table. If it is explicitly considered, groundwater pumping becomes, sooner or later, economically unaffordable.

Editorial comments

Line 90 Figure 1: The acronyms used (PMP and BCU) should be explained in the caption.

Line 114 “across subbasins within river basins at the global scale”: I feel this part is a bit awkward. Subbasins are always within river basins…

Line 117 “from inverse water demand functions estimated using the Point Expansion approach (Griffin, 2016)”: This part is not very informative. I understand that readers should read Griffin (2016), but it would be helpful for us if the authors added more understandable information.

Line 120 “using the positive mathematical programming (PMP) procedure to address regional-scale aggregation and overspecialization problems (Baccour et al., 2022; Dagnino and Ward, 2012)”: ibid.

Line 151 “local runoff r_h,t, and inflow from upstream BCUs I_h,t”: The authors use “X” for flows in general, while here, r and I are also used for “flows (in contrast to stocks).” These expressions are confusing to me, which is one of the reasons why I needed three times of reading.

Line 158 “and -1 for nodes that reduce flow”: How streamflow can be reduced? Do you mean “diverted flow?”

Line 164 Equation 4: This expression is very confusing to me. Here, X is used both to express release and evaporation. It is odd to see that S (Storage) and X(Flow/Flux) have the same dimension (kg).

Line 222 Equation 14: Why does the form of the equation differ from Equation 12? I expected the difference to be only with/without the irrigation efficiency term.

Line 266 ”based on the first-order conditions of the agricultural profit maximization problem following the PMP procedure (Dagnino and Ward, 2012)”: This phrase is too technical and not informative. Provide a bit more understandable information.

Line 268 “M&I”: What’s this for?

Line 277 “Then beta_2,M&I is expected to be large and negative”: What does “large” mean?

Line 397 “a more sustainable scenario (RES)”: Maybe it reads ENV.

References

Kim, S. H., Hejazi, M., Liu, L., Calvin, K., Clarke, L., Edmonds, J., Kyle, P., Patel, P., Wise, M., and Davies, E.: Balancing global water availability and use at basin scale in an integrated assessment model, Climatic Change, 136, 217-231, 10.1007/s10584-016-1604-6, 2016.

Dolan, F., Lamontagne, J., Link, R., Hejazi, M., Reed, P., and Edmonds, J.: Evaluating the economic impact of water scarcity in a changing world, Nature Communications, 12, 1915, 10.1038/s41467-021-22194-0, 2021.

Gerten, D., Heck, V., Jägermeyr, J., Bodirsky, B. L., Fetzer, I., Jalava, M., Kummu, M., Lucht, W., Rockström, J., Schaphoff, S., and Schellnhuber, H. J.: Feeding ten billion people is possible within four terrestrial planetary boundaries, Nature Sustainability, 3, 200-208, 10.1038/s41893-019-0465-1, 2020.

Niazi, H., Wild, T. B., Turner, S. W. D., Graham, N. T., Hejazi, M., Msangi, S., Kim, S., Lamontagne, J. R., and Zhao, M.: Global peak water limit of future groundwater withdrawals, Nature Sustainability, 7, 413-422, 10.1038/s41893-024-01306-w, 2024.

Rosa, L., Rulli, M. C., Davis, K. F., Chiarelli, D. D., Passera, C., and D’Odorico, P.: Closing the yield gap while ensuring water sustainability, Environmental Research Letters, 13, 104002, 10.1088/1748-9326/aadeef, 2018.

Wada, Y., Wisser, D., Eisner, S., Floerke, M., Gerten, D., Haddeland, I., Hanasaki, N., Masaki, Y., Portmann, F. T., Stacke, T., Tessler, Z., and Schewe, J.: Multimodel projections and uncertainties of irrigation water demand under climate change, Geophys. Res. Lett., 40, 4626-4632, 10.1002/grl.50686, 2013.

In this paper, Kahil et al. present the development of ECHO-Global version 1.0, a global hydro-economic model designed to assess the economic and environmental performance of water management options at the subbasin (BCU) scale. By integrating a detailed representation of water flows from multiple sources, including surface water, groundwater, and non-conventional supplies, with advanced economic benefit functions calibrated via positive mathematical programming, the model simulates future water management scenarios under climate and socio-economic changes. The study offers valuable insights into changes in water withdrawals, irrigated crop areas, and associated economic impacts, and its outputs are broadly consistent with previous global assessments. Although the work represents an important advancement in global water resource modeling, I have several comments (see below).

Section 2 – Modeling framework

1. The authors make extensive use of multiple indices (e.g., i, a, u, j, k, w) and a variety of binary or proportional coefficients (bᵢ, bₐ, etc.) to capture the system’s complexity. While this is understandable, clarity would be improved by providing a comprehensive table that summarizes all indices, variables, and coefficients—including their definitions and units.

2. Equation 1 (Headwater Inflow): For BCUs, a critical omission in the headwater inflow representation is the lack of consideration for direct evaporation from natural surface water bodies. While Equation 1 accounts for local runoff and upstream inflows, it doesn't factor in evaporative losses from rivers, lakes, and wetlands prior to reaching the headwater gauge. This can represent substantial water losses, especially in arid regions, leading to significant overestimation of available surface water. While this might be negligible in some BCUs, it becomes critically important in others, for instance, in the Sudd swamp (potentially located in a BCU between Sudan and the Nile polygon), where studies suggest up to 50% of surface water can be lost annually through evaporation. I suggest that the authors either add an evaporation term in Equation 1 or provide a clear justification for why its omission does not affect the overall accuracy of water availability estimates.

3. Equation 4 (Reservoir Storage): The current formulation expresses reservoir dynamics as a net release (outflow minus inflow), which obscures the separate contributions of inflows and outflows and makes tracking mass conservation problematic. A formulation that explicitly distinguishes between inflows, outflows, and evaporation would offer a more transparent representation of reservoir operations.

4. When discussing water stocks, the explicit focus on reservoirs raises the question: what about the natural lakes, aren’t they sources of water for irrigation and other purposes in many parts of the globe? which can be substantial water stocks in many regions.

2.2.3 Groundwater pumping

5. Although the model distinguishes renewable from non-renewable groundwater pumping, it currently assumes no interaction between groundwater and surface water. Given that groundwater recycling, induced recharge, and lateral exchanges often play pivotal roles in water resource sustainability, especially under climate change scenarios, a more nuanced representation of groundwater-surface water interactions would be highly beneficial. Even if such dynamics are slated for future improvements, acknowledging current limitations and discussing potential impacts on long-term resource sustainability would enhance the study.

Section 2.2.7 Economics

6. The coupling of water supply dynamics with economic benefit functions (calibrated via the positive mathematical programming procedure) is strength of the methodology. However, the calibration of these economic functions and the underlying demand and cost parameters inherently introduces uncertainty. The paper would be strengthened by a clearer discussion or sensitivity analysis regarding the impact of parameter uncertainty, especially given that water pricing, elasticity, and sectoral cost estimates play a critical role in determining net benefits. A discussion on how these uncertainties propagate through the model would help evaluate the robustness of the policy simulations

Section 2.3 – Spatial delineation and node-link network

7. The pragmatic choice of using BCUs, defined as intersections of river basins with country administrative boundaries, effectively balances computational demands with spatial detail. However, this approach leads to heterogeneous spatial resolution, with some countries (e.g., the USA) represented in much finer detail than others. Such differences may influence the accuracy and policy relevance of country-specific outputs. While I am not suggesting a change to the model’s fundamental structure, I recommend that the authors discuss how this heterogeneity might affect results and if there are any plans to explore alternative BCU delineations that could mitigate resolution bias, particularly in regions where aggregated representation may obscure important subnational variability.

2.4 Model database

8. Regarding Table 1, the reservoir area‐capacity function slope is based on Yigzaw et al. (2018). Notably, there has been some critical review of this dataset—especially regarding the ‘area-depth’ relationship (see Shrestha et al., 2024, Figure 8). Although area-volume comparisons with other methods appear reasonable, it is unclear how sensitive the model is to potential flaws in this dataset. I recommend that the authors double-check this dataset and verify whether any uncertainties in the area-depth relationship might have implications for their work.

Section 3: Water management scenarios

9. Scenario rationale and uncertainty: The paper presents an extensive set of 2050 water management scenarios under SSP2-RCP6.0. However, the exclusive focus on SSP2-RCP6.0 warrants further justification. Given the uncertainties in water supply prediction alongside those in water demand projections influenced by economic assumptions, the authors should discuss how these uncertainties might affect model outcomes. It would be useful to know whether alternative SSP-RCP combinations were considered or if sensitivity analyses were performed, with these insights ideally integrated into the discussion section.

10. Interdependencies in policy constraints and management strategies: Table 2 outlines detailed policy constraints for the scenarios (BAU, ENV, DM, NC, RES), yet the interplay between supply management and demand management strategies is not fully explained. I recommend that the authors provide a brief clarification on how these various constraints and the associated optimal allocation methods interact. This addition would enhance transparency in how water is allocated among sectors without altering the model’s fundamental structure.

The review comments on Kahil et al. “Development of the global hydro-economic model (ECHO-Global version 1.0) for assessing the performance of water management options”

This manuscript presents ECHO-Global, a global hydroeconomic model that integrates physical water flows and economic optimization to assess cross-sectoral water allocation under multiple water management scenarios. The model operates at the scale of 282 basin-country units (BCUs) and captures sector-specific water allocation and use in agriculture, domestic, and industrial sectors, constrained by water availability and infrastructure, while maximizing net economic benefits. The scenario analysis explores supply- and demand-side interventions, including efficiency improvements, land and water reallocation, environmental flow protection, and the use of non-conventional water sources.

The manuscript makes a valuable contribution to the field of global water modeling. ECHO-Global distinguishes itself by combining hydroeconomic balance constraints with economic decision-making across sectors. The application of Positive Mathematical Programming (PMP) to calibrate agricultural land allocation adds credibility to modeled crop choices. Its flexible structure allows for scenario-based assessments aligned with SSP–RCP narratives, providing policy-relevant insights into future water challenges. In this manuscript, the authors demonstrate multiple water management scenarios under the SSP2-RCP6.0 scenario.

The study is timely and addresses an important set of questions regarding the feasibility and trade-offs of water management strategies in the context of climate and socioeconomic change. The model structure is thoughtfully designed, and the manuscript is generally well written and organized.

However, there are some points that I would like the authors to address; Some aspects of the model formulation, scenario design, and interpretation would benefit from further clarification. In particular, additional transparency in how assumptions are specified, how key parameters are derived or constrained, and how results should be interpreted in light of modeling limitations would strengthen the overall contribution. Moreover, the presentation of results could be improved in terms of clarity and consistency, and the structure of the methods section might be adjusted to enhance readability. Some scenario implications may also merit broader contextual discussion.

In summary, this is a promising and ambitious study that contributes to advancing the field of integrated global water resource assessment. With improved clarity in model assumptions, explanation of methods, and framing of results, the manuscript will offer valuable insights to both scientific and policy audiences.

<< Major comments >>

P.6, L140: Although the model equations are defined over time-steps (Section 2.2), monthly water demand inputs are described in Section 2.4.1, and apparently, the total surface water inflow to each BCU is defined as annual value, the model's temporal resolution (e.g., whether it solves monthly or annually) is not explicitly stated. I recommend clearly stating the model time-step and temporal resolution in Section 2.1 or 2.2 to avoid ambiguity.

P.7: While the model includes reservoir evaporation, initial storage levels, and dead storage as components of the reservoir mass balance (e.g., equations 4–7), the description of how these quantities are parameterized remains unclear. For example, evaporation is said to depend on reservoir and climatic features, but no equation or calibration method is provided. Similarly, the sources of initial storage and dead storage values are not described. I recommend that the authors provide additional details on the estimation or data sources for these parameters—particularly for evaporation, which can significantly affect water availability in arid regions.

P.11, L260: While the model optimizes land allocation variables L_ag,j,k,t​, it remains unclear whether these represent irrigated land area or total crop area. Given their direct link to irrigation water application, they likely refer to irrigated land, but this should be explicitly clarified in the variable definitions.

P.11, L265-267: While the model adopts a Positive Mathematical Programming (PMP) approach to optimize agricultural land allocation, the manuscript lacks a clear description of how irrigated land areas are derived within this framework. Given the importance of irrigated area changes in explaining scenario results (e.g., reductions in agricultural water withdrawal), a more detailed explanation of the PMP calibration steps—including observed activities, cost functions, and land-use constraints—would greatly improve transparency and reproducibility, especially for readers unfamiliar with PMP.

P.11, L265-267: The current modeling framework optimizes irrigated land area based on economic profitability and water availability, but it does not appear to account for key drivers of future land-use change such as shifts in food demand or climate-induced changes in land suitability (e.g., aridification due to a warmer climate, crop viability under warming). These factors can strongly influence future irrigation patterns, and their exclusion limits the applicability of the model under broader climate–socioeconomic scenarios. I suggest that the authors briefly discuss this limitation, particularly in the context of scenarios (e.g., SSP2–RCP6.0) where food trade is expected to play a key role.

Also, the model appears to omit international trade in agricultural commodities. Since the economic decisions in the model depend on crop profitability at the national level, and since global trade flows can substantially influence land allocation and irrigation demand, the absence of trade dynamics may limit the realism of the scenario outcomes. I also suggest the authors to discuss this limitation as well briefly.

P,10 Eq20, P.17 L376-376: The model appears to use fixed crop prices based on historical FAOSTAT averages for 2006–2015 (Section 2.4.3), without projecting changes in agricultural commodity prices under future scenarios. Since crop prices are a major driver of land allocation and water use decisions, omitting price projections may limit the ability of the model to reflect plausible economic dynamics under SSP2–RCP6.0 or other scenarios. A discussion of this limitation and its potential effects on model outcomes (i.e., projection uncertainty) would be helpful.

P.12, L291: The objective function of the model uses a discount rate to calculate the net present value of benefits (Eq. 25, Section 2.2.8), but, probably, the specific value used for the discount rate, and its data source or justification, are not mentioned in the manuscript. Given the central role of the discount rate in determining long-term investment and benefit evaluations, I suggest that the authors specify the discount rate used and explain the rationale behind its selection, particularly in relation to standard assumptions in SSP or IAM frameworks.

P.17: While the model considers 13 major irrigated crops, the manuscript does not provide sufficient detail on how crop composition or land allocation changes under different scenarios. Including a summary table or plot showing crop-specific land area shifts would enhance interpretability.

P18, L400: The manuscript states that the ENV scenario minimizes the use of non-renewable groundwater (p.18). However, it remains unclear how this is implemented in the model. Is this achieved via explicit constraints, penalization in the objective function, or higher supply costs? Since this assumption plays a central role in shaping water allocation outcomes under the ENV scenario, it would be helpful if the authors provided more detailed explanation of the modeling formulation underlying this restriction.

P18, L402-403: The manuscript states that the DM scenario "identifies an optimal allocation of water and land to enhance agricultural water use efficiency" (p.18). However, this statement may be somewhat misleading. The optimal allocation of water and land (driven by economic value) primarily serves to maximize economic benefits, not necessarily to increase water use efficiency. Only the direct increase in irrigation efficiency (i.e., reaching the technical maximum in each basin) leads to a clear and quantifiable improvement in agricultural water use efficiency. I suggest rephrasing this sentence to more clearly distinguish between these different mechanisms.

P.19: The manuscript describes the Demand Management (DM) scenario as involving “optimal allocation of water” among sectors based on the economic value of water use. While this formulation (or expression) may be reasonable within the model, it may appear supply-side oriented to some readers—since it does not directly modify water demand behavior, but rather reallocates supply. I suggest clarifying how this approach qualifies as "demand management" in the context of the scenario narrative, perhaps by distinguishing it from infrastructure expansion or other supply-side interventions. The expression, “Optimal water demand allocation”, may be straightforward?

P.19, Table 2: The scenarios DM, NC, and RES assume that irrigation efficiency will be increased to a “maximum efficiency level” for each basin. However, the definition and source of this maximum value remain unclear. It would improve transparency to clarify whether these maximum values are technically feasible (e.g., drip irrigation), economically viable, or derived from empirical benchmarks (e.g., FAO-AQUASTAT or literature-based potential efficiencies). Furthermore, the estimation method and data sources used to determine these maximum efficiency values are not described. Providing such clarification, including potential regional differentiation or reference benchmarks (e.g., FAO-AQUASTAT or literature-based ranges), would greatly improve the transparency and credibility of the scenario assumptions.

P20. L411-413: The manuscript states that the model was both calibrated and validated for the base year 2010 (Chapter 4, first sentence). ① However, it is unclear how the model outputs for year 2010 prior to calibration were computed, and what metrics were used to assess the calibration’s effectiveness. ② Moreover, performing both calibration and validation on the same year raises concerns regarding overfitting and the robustness of the model’s predictive capacity. I recommend that the authors clarify the calibration procedure and consider including a validation step based on out-of-sample data or a different time period.

P.26, L507: Under the SSP2–RCP6.0 scenario, the reported reduction in irrigated land area warrants further discussion. Does this outcome align with other studies projecting land-use responses under similar scenarios? Including such a discussion would help readers better assess the realism and policy relevance of the model’s scenario results.

P20., L409: Broadly, the scenario results are presented without uncertainty ranges, confidence intervals, or sensitivity analyses. Given the strong influence of parameters like willingness to pay, irrigation efficiency, and non-conventional water costs, this deterministic presentation may limit the policy relevance of the results. Including uncertainty bands or conducting a robustness check across plausible parameter ranges would enhance the credibility of the scenarios for decision-makers.

P28, L568-569: The manuscript states that the domestic sector accounts for 55% of gross benefits in 2010, exceeding those of the industrial sector. This result may seem counter-intuitive, as industrial activities typically generate substantial economic outputs per unit of water use. While the manuscript explains that marginal benefits in domestic use are high for essential needs, the specific parameter values or demand curve assumptions used to generate these results are not clearly shown. I recommend the authors elaborate on the assumptions behind sectoral benefit estimation, especially regarding the benefit functions for the domestic and industrial sectors.

P33, L621: The manuscript states that a combination of water management options can help satisfy water demand. However, under the ENV scenario, both environmental flow requirements and constraints on non-renewable groundwater use are expected to reduce the water available for irrigation. Probably, this leads to substantial decreases in agricultural water withdrawals compared to BAU. It would be helpful for the authors to clarify whether this description is correct and whether these reductions result from unmet water demand due to supply constraints, or from economically optimal decisions under restricted water availability.

P34, L657: While the model provides a detailed representation of water allocation across BCUs within river basins, it does not appear to incorporate institutional or policy-based constraints such as transboundary water treaties or cooperative water management. Similarly, international trade in agricultural products is not modeled, despite its potential impact on regional cropping patterns and water demand. Clarifying these limitations would help define the scope and appropriate applications of the modeling framework.

<< Minor comments >>

P2 L41-46: Would you elaborate or rephase “appropriate water management options … consistent across spatial scales”?

General: I suggest reorganizing Sections 2.2–2.4 so that the spatial delineation and data sources (currently in Sections 2.3 and 2.4) are presented before the model formulation (Section 2.2). This would help readers understand the origins and meaning of key parameters or assumptions—such as willingness to pay and irrigation efficiency—before encountering them in the description on equations. Presenting the data context first would improve the overall readability of the modeling framework.

P.12, Eq. 25: the net present value (NPV) is defined as a summation over time ttt, yet the notation "Max NPV" is somewhat ambiguous. It might be clearer to explicitly show the double summation over both ttt and uuu, and to define NPV as a function of ttt, to clarify that it accumulates time-discounted net benefits across periods.

Figure 3: The colorbar needs unit.

Figure 5(a): Groundwater is shown as a single aggregated category. However, since the model differentiates between renewable and non-renewable groundwater—both conceptually and in terms of cost and sustainability—it would be more informative to distinguish these sources in the figure. This would also better support the interpretation of the ENV scenario, which specifically aims to reduce non-renewable groundwater use. I suggest disaggregating groundwater into renewable and non-renewable components to enhance the clarity and policy relevance of the figure.

Figure 6: Maps appear to be vertically compressed, which may hinder the geographic interpretation of spatial patterns. The aspect ratio does not reflect the natural proportions of the Earth’s latitude–longitude grid, making it difficult to compare regions and assess spatial trends accurately. I recommend adjusting the map projection or aspect ratio to improve visual clarity and ensure accurate geographic representation.