Hybrid ITSP-LSTM Approach for Stochastic Citrus Water Allocation Addressing Trade-Offs Between Hydrological-Economic Factors and Spatial Heterogeneity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1- The integration of the ITSP and LSTM frameworks demonstrates a forward-thinking approach to handling both temporal and spatial uncertainty in agricultural water management. However, a question emerges about how sensitive are the results to the assumptions made about the probability distributions of water inflow levels (i.e., 0.2 for low and high, 0.6 for medium)? Would a different assumption—such as a skewed distribution reflecting more frequent dry years due to climate change—alter the optimal allocation decisions significantly?

2- The study presents a commendable effort in quantifying irrigation demands using LSTM models trained on decades of meteorological data. Yet, the model appears to use a static set of citrus crop coefficients across growth stages. A question here in that could incorporating real-time satellite imagery or IoT sensor data into the LSTM model provide dynamic crop coefficients (Kc) to reflect actual field conditions, thereby improving prediction accuracy?

3- One of the appropriate aspects is the translation of hydrological uncertainty into interval-based profit optimization. However, the study assumes a fixed benefit-to-penalty ratio of 1:1.3. This leads to an issue about how robust is this ratio across different economic or market conditions? For example, if market citrus prices plummet or penalty costs rise due to droughts, would the current allocation scheme still be economically optimal?

4-  While the ITSP model allows for adaptive decision-making, the use of a fixed 2:1 ratio favoring local water sources over external ones may oversimplify economic trade-offs. Has a cost-benefit analysis been performed to test whether a more flexible or dynamic ratio (adjusted per scenario or crop value) would lead to more efficient or profitable outcomes?

5-  The zoning strategy employed (A, B, and C zones) is grounded in water availability and planting area size, yet it remains static. This raises a methodological question that can the zoning be made dynamic by including seasonal labor availability, pest pressure, or changing market access conditions? What would be the computational implications of introducing such multidimensional zoning within the ITSP-LSTM framework?

6-  The model optimizes for expected benefits but seems to underplay risk aversion strategies that real-world farmers might adopt. How might the inclusion of a farmer’s risk preferences or risk aversion constraints (e.g., via utility functions or CVaR—Conditional Value at Risk) change the final water allocation outcomes? Could this make the model more applicable in participatory irrigation planning?

7-  The economic coefficients in the study rely on projected yield, price, and water use per unit area. However, citrus yield is notoriously sensitive to both water stress and timing of irrigation. A operational question is that could incorporating sub-seasonal water stress indices into the penalty function (instead of using annualized deficits alone) better capture the real agronomic and economic consequences of water misallocation? How feasible is this in a computationally tractable ITSP framework?

 

Author Response

Dear editor and reviewer,

Thank you very much for taking the time to review our manuscript and providing insightful comments and constructive feedback. We highly appreciate your suggestions, which have helped us improved the quality of our paper significantly, the revised parts have been marked in red in the text. Please find below our point-by-point responses to your comments:

 

Comment 1: The integration of the ITSP and LSTM frameworks demonstrates a forward-thinking approach to handling both temporal and spatial uncertainty in agricultural water management. However, a question emerges about how sensitive are the results to the assumptions made about the probability distributions of water inflow levels (i.e., 0.2 for low and high, 0.6 for medium)? Would a different assumption—such as a skewed distribution reflecting more frequent dry years due to climate change—alter the optimal allocation decisions significantly?

 

Response: We sincerely appreciate the reviewer’s insightful question regarding the sensitivity of our results to the assumed probability distribution of water inflow levels. This is a critical consideration, particularly in the context of climate change, and we are pleased to provide additional clarification and analysis to address this concern.

The initial probabilities (0.2/0.6/0.2 for low/medium/high inflow) were carefully selected based on long-term hydrological records from the study area Zhijiang City. Historical data spanning 30 years (1993-2022) revealed that medium inflow conditions (e.g., annual precipitation between 1,200-1,500 mm) occurred approximately 60% of the time, while extreme low (≤1,000 mm) or high (≥1,800 mm) inflow years were less frequent (around 20% each). This distribution aligns with regional climatic patterns observed in subtropical monsoon zones where seasonal variability dominates but prolonged droughts or floods are relatively rare. By adopting these probabilities as a baseline, we aimed to reflect the statistical reality of the study area while enabling comparison with existing ITSP frameworks that often use symmetric distributions.

 

Comment 2: The study presents a commendable effort in quantifying irrigation demands using LSTM models trained on decades of meteorological data. Yet, the model appears to use a static set of citrus crop coefficients across growth stages. A question here in that could incorporating real-time satellite imagery or IoT sensor data into the LSTM model provide dynamic crop coefficients (Kc) to reflect actual field conditions, thereby improving prediction accuracy?

 

Response: We sincerely appreciate the reviewer’s thoughtful suggestion regarding the integration of real-time satellite imagery or IoT sensor data into the LSTM model to generate dynamic crop coefficients (Kc). This is an innovative and promising direction, as field conditions such as canopy development, soil moisture, and phenological stage can significantly influence Kc values. We fully agree that incorporating such data could enhance prediction accuracy by capturing real-time variability in crop water requirements.

In our study, the static Kc values used for citrus were derived from a 7-year field experiment conducted at our citrus research base, which involved meticulous monitoring of evapotranspiration rates across growth stages under diverse climatic and management practices. These data formed the foundation for the locally adopted citrus irrigation standards, ensuring their scientific rigor and applicability to the study region. While these coefficients provide a reliable baseline, we acknowledge their limitations in capturing spatial and temporal heterogeneity in large-scale or fragmented orchards.

To address this, we have recently initiated exploratory research on hyperspectral infrared remote sensing to monitor citrus canopy health and water stress indicators. This technology enables high-resolution mapping of physiological parameters, which can be integrated with LSTM models to derive dynamic Kc estimates in future work. We are actively exploring partnerships with remote sensing experts to refine this approach and plan to incorporate IoT-based soil moisture sensors in the next phase of our research. The reviewer’s idea aligns closely with our long-term goals, and we look forward to opportunities for collaboration or knowledge exchange on this topic.

 

Comment 3: One of the appropriate aspects is the translation of hydrological uncertainty into interval-based profit optimization. However, the study assumes a fixed benefit-to-penalty ratio of 1:1.3. This leads to an issue about how robust is this ratio across different economic or market conditions? For example, if market citrus prices plummet or penalty costs rise due to droughts, would the current allocation scheme still be economically optimal?

 

Response: We sincerely appreciate the reviewer’s thoughtful question regarding the robustness of the fixed benefit-to-penalty ratio (1:1.3) used in our profit optimization framework. This is a critical consideration, as economic and market conditions can significantly influence the trade-offs between irrigation benefits and penalty costs.

The penalty-to-benefit ratio of 1.3 was established through expert judgment. This value reflects the trade-off between economic losses from water deficits (penalty) and gains from efficient allocation (benefit), as advised by agricultural economists and local water managers familiar with citrus farming in Anfusi Town. While no direct field survey or literature explicitly provides this exact ratio, its selection is grounded in the following rationale: (1) Agricultural economists and local water managers in Anfusi Town, who have extensive experience with citrus farming, emphasized that water deficits during critical growth stages can reduce yields by 15-20% under drought conditions. To mitigate such risks, the penalty coefficient was calibrated to reflect the proportional economic loss associated with unmet irrigation needs relative to the gains from efficient allocation. A ratio of 1.3 implies that penalties for water shortages are 30% higher than the benefits of surplus allocations, aligning with regional practices where water deficits are prioritized over over-allocation to avoid crop failure. (2) The ratio of 1.3 draws parallels to methodologies in interval optimization models, where penalty coefficients are often set based on stakeholder input and historical data. For instance, in crop water management, ratios between 1.0 and 1.5 are frequently adopted to account for variability in irrigation efficiency and crop resilience. In Anfusi Town, the slightly elevated ratio (e.g., 1.3) accounts for the high economic value of citrus crops and the need to prioritize water during peak demand periods. (3) The penalty-to-benefit ratio was adjusted to reflect the seasonal variability of water availability in Anfusi Town, where summer irrigation demands must be met despite limited reservoir capacity. A lower ratio (e.g., 1.0-1.2) might encourage over-allocation during dry periods, risking long-term reservoir depletion, while a higher ratio (e.g., >1.5) could excessively penalize minor deficits, reducing flexibility for adaptive management. The chosen value of 1.3 strikes a balance, ensuring both economic viability and resource sustainability.

 

Comment 4: While the ITSP model allows for adaptive decision-making, the use of a fixed 2:1 ratio favoring local water sources over external ones may oversimplify economic trade-offs. Has a cost-benefit analysis been performed to test whether a more flexible or dynamic ratio (adjusted per scenario or crop value) would lead to more efficient or profitable outcomes?

 

Response: Thank you for raising this important point. The initial 2:1 ratio was determined based on regional economic and logistical constraints in Zhijiang City, where local reservoirs and weirs have historically been prioritized due to (1) lower transportation costs (estimated at ¥0.15/m³ for local sources vs. ¥0.35/m³ for external sources), (2) policy incentives for self-sufficiency in water-stressed zones, and (3) infrastructure limitations in long-distance pipeline networks. A cost-benefit analysis was indeed conducted during determination of this ratio, we regret that it was not explicitly detained in the original manuscript due to space constraints and a focus on presenting core methodological outcomes.

Specifically, we conducted a cost-benefit analysis by recalibrating the ratio to three alternative scenarios: (1) 3:1 (stronger local preference), (2) 1.5:1 (balanced allocation), and (3) 1:1.5 (external source preference). The results revealed significant variations in economic efficiency: Under the 3:1 ratio, total costs decreased by 8% for high-value citrus blocks due to reduced reliance on expensive external water, but this came at the risk of over-extraction from local reservoirs during dry seasons; The 1.5:1 ratio yielded a 4% net profit increase compared to the baseline, as it allowed strategic use of external water during peak demand periods without exceeding local supply capacities; The 1:1.5 ratio improved resilience in drought scenarios but increased operational costs by 12%, highlighting the trade-off between flexibility and economic efficiency.

According to the reviewer’s suggestion, we have revised the manuscript and added a paragraph explaining the regional basis for the 2:1 ratio as follows:

• Section 3.3 Target value of citrus water allocation in advance (Lines 491-505）

To optimize water resource allocation while minimizing external supply costs, a 2:1 ratio of local to external water sources was calibrated based on regional economic data, including significantly lower transportation costs (¥0.15/m³ for local vs. ¥0.35/m³ for external sources), infrastructure limitations, and policy priorities favoring self-sufficiency in water-stressed zones. To optimize water resource allocation while minimizing external supply costs, this ratio was adopted to prioritize cost-effective utilization of local reservoirs and weirs over expensive inter-basin transfers. A cost-benefit analysis evaluated multiple scenarios (e.g., 3:1, 1.5:1, and 1:1.5 ratios) and revealed critical trade-offs between cost efficiency, drought resilience, and operational flexibility. For instance, a 3:1 ratio reduced costs for high-value citrus zones but risked over-extraction during dry seasons, whereas a 1.5:1 ratio improved profitability without exceeding local supply capacities. These findings underscored the 2:1 ratio as a balanced compromise for the study region, effectively harmonizing economic feasibility with sustainable water management under regional constraints.

 

Comment 5: The zoning strategy employed (A, B, and C zones) is grounded in water availability and planting area size, yet it remains static. This raises a methodological question that can the zoning be made dynamic by including seasonal labor availability, pest pressure, or changing market access conditions? What would be the computational implications of introducing such multidimensional zoning within the ITSP-LSTM framework?

 

Response: We sincerely thank the reviewer for raising this methodological question regarding the static zoning strategy in our study. While we fully agree that dynamic factors such as seasonal labor availability, pest pressures, and market access could enhance zoning adaptability, we would like to emphasize that the current zoning approach (A, B, and C zones) is designed for robust applicability under the study region’s prevailing conditions. 

We fully acknowledge the potential benefits of dynamic zoning, integrating such multidimensional factors into the ITSP-LSTM framework would introduce computational challenges. First, the model would need to process additional temporal datasets, increasing input complexity and potentially requiring higher-resolution data. Second, dynamic zoning would necessitate nonlinear interactions between variables, as labor availability might correlate with pest pressures or market demands in non-trivial ways. This could escalate computational costs, particularly for large-scale applications, and may require advanced optimization techniques to maintain tractability. We deeply thank the reviewer for providing valuable research directions, which we will incorporate into our future water resources studies.

 

Comment 6: The model optimizes for expected benefits but seems to underplay risk aversion strategies that real-world farmers might adopt. How might the inclusion of a farmer’s risk preferences or risk aversion constraints (e.g., via utility functions or CVaR—Conditional Value at Risk) change the final water allocation outcomes? Could this make the model more applicable in participatory irrigation planning?

 

Response: We sincerely thank the reviewer for this insightful question regarding the integration of risk aversion strategies into our model. In this study, we focused on Zhijiang City, where farmers exhibit relatively homogeneous risk preferences due to the region’s simplified agricultural structure and uniform policy guidelines. Most farmers cultivate citrus as a primary crop under similar contractual arrangements , and their decision-making aligns closely with the locally mandated water-use standards. These factors reduce the variability in risk attitudes among farmers.

However, we fully agree with the reviewer that incorporating risk aversion could enhance the model’s realism in more heterogeneous contexts. For instance, in regions with diverse crop portfolios, fluctuating market prices, or variable access to insurance, such features would be critical. In another study focused on large watershed scales, we are currently developing a two-layer water management model that explicitly separates government-level constraints and farmer-level risk preferences. This dual-layer framework will integrate participatory feedback mechanisms to quantify trade-offs between efficiency and risk tolerance, enabling more adaptive and inclusive planning. We look forward to future discussions and guidance on this work.

 

Comment 7: The economic coefficients in the study rely on projected yield, price, and water use per unit area. However, citrus yield is notoriously sensitive to both water stress and timing of irrigation. A operational question is that could incorporating sub-seasonal water stress indices into the penalty function (instead of using annualized deficits alone) better capture the real agronomic and economic consequences of water misallocation? How feasible is this in a computationally tractable ITSP framework?

 

Response: We sincerely appreciate the reviewer’s suggestion to incorporate sub-seasonal water stress indices into the ITSP framework. This approach could indeed improve the model’s ability to capture the timing-sensitive impacts of water misallocation on citrus yields, which are highly sensitive to irrigation timing during critical growth stages. However, the current study is constrained by data resolution (e.g., annual yield statistics and monthly water records) and computational tractability, as sub-seasonal modeling would require fine temporal disaggregation , nonlinear stress-yield relationships, and significantly increased problem complexity.

Based on our current research experience, we are uncertain whether this approach is entirely accurate, but we share it here for scholarly discussion and feedback purposes. While incorporating sub-seasonal water stress indices into the penalty function could improve agronomic realism, the model calibration may become less robust, as short-term stress events (e.g., sudden droughts) are inherently more variable and harder to generalize across scenarios. We are actively exploring hybrid approaches to address these issues in future work. Thank you for your thoughtful feedback, which has inspired us to refine our methodological balance.

 

 

Thank you very much for your time and consideration. We sincerely hope that our revised manuscript and responses to the reviewers' comments meet your expectations. Looking forward to your further feedback.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript is focused on optimizing water resources for fragmented citrus planting areas in Anfusi Town. A combined ITSP-LSTM method is proposed, offering research value for water resource management. However, the manuscript is characterized by deficiencies in innovation, inadequate discussion and format error.The specific issues and suggested modifications are as follows:

1. There have been studies on water resource allocation considering uncertainty. The author takes Citrus as the research object. Compared with other crops, what are the special features of this crop in the water resource allocation model?  
2. What are the water resource management challenges caused by the heterogeneity of dispersed planting spaces mentioned in this article? Spatial heterogeneity is a core research element, but there has been no in-depth exploration of research methods. In line 254 of the manuscript, it is mentioned that 'spatially heterogeneous water supply capacity may lead to defects'. What specifically does' defects' refer to? What is the targeted work of this manuscript?
3. In line 252 “considering spatially varying water supply capacity and stochastic demand”, it mentions "stochastic demand", but there is no relevant discussion on demand randomness in subsequent work.
4. Some variables in the text have confusing definitions: S_ij represents crop area in formula (1) , while S_ij represents water deficit in formula (4a). It is necessary to ensure that each variable maintains a unique and unambiguous meaning throughout the entire manuscript
5. Should the cumulative variable of formula (4d) be j instead of i?
6. Table 3 and Table 2 have some overlapping content, it is recommended to integrate and streamline them.
7. Should the title "1.1" in line 418 be changed to "3.4"?
8. There are numerous citation issues in the text, such as lines 165 and 203.

Author Response

Dear editor and reviewer,

Thank you very much for taking the time to review our manuscript and providing insightful comments and constructive feedback. We highly appreciate your suggestions, which have helped us improved the quality of our paper significantly, the revised parts have been marked in red in the text. Please find below our point-by-point responses to your comments:

 

Comment 1: There have been studies on water resource allocation considering uncertainty. The author takes Citrus as the research object. Compared with other crops, what are the special features of this crop in the water resource allocation model?

 

Response: Thank you for your insightful question regarding the unique characteristics of citrus crop in our water resource allocation model. The integration of citrus-specific characteristics into the water allocation model addresses critical challenges unique to this crop. Unlike staple crops cultivated in contiguous flatlands, citrus is predominantly grown in fragmented mountainous regions, necessitating zonal partitioning to account for spatially variable water supply and demand. The model incorporates distinct phenological stages (e.g., blooming, maturation) with stage-specific irrigation requirements, leveraging the Penman-Monteith method and LSTM predictions to align with climate variability. Citrus’s high economic value and sensitivity to water stress further differentiate it, as penalties for shortages (1.3 times the benefit coefficient) drive prioritization of local over external water sources to minimize financial risks. Additionally, its decadal lifespan requires long-term planning to ensure resilience against seasonal deficits, achieved through inter-zonal redistribution and interval analysis to balance stochastic inflows and economic-ecological trade-offs. These adaptations highlight the necessity of tailoring water allocation strategies to citrus’s spatial fragmentation, phenological complexity, and economic significance, advancing sustainable management in fragmented agricultural systems. Overall, we have revised the manuscript to explicitly address citrus-specific features in the Introduction section:

• Section1 Introduction (Lines 130-140)

Despite the predominant focus of agricultural irrigation water allocation research on staple crops like rice, wheat, and maize (Liu et al., 2023; Yu et al., 2022), citrus crops (a critical economic crop in southern China) have received limited attention in optimization frameworks. Unlike short-cycle annual crops, citrus exhibits long-term growth cycles (10 to 20 years) and stage-specific water requirements (e.g., blooming, fruit maturation), necessitating allocation strategies that balance immediate yield stability with long-term orchard health. Furthermore, staple crops cultivated in contiguous flat lands, whereas citrus is predominantly grown in fragmented mountainous regions, requiring zonal partitioning to account for spatially variable water supply and demand.

 

Comment 2: What are the water resource management challenges caused by the heterogeneity of dispersed planting spaces mentioned in this article? Spatial heterogeneity is a core research element, but there has been no in-depth exploration of research methods. In line 254 of the manuscript, it is mentioned that 'spatially heterogeneous water supply capacity may lead to defects'. What specifically does 'defects' refer to? What is the targeted work of this manuscript?

 

Response: We sincerely appreciate the reviewer’s insightful questions regarding the spatial heterogeneity challenge. We have revised the manuscript to clarify these aspects, below is a detailed response:

The spatial heterogeneity of dispersed citrus planting zones in fragmented mountainous areas introduces significant water resource management challenges. Unlike staple crops grown in contiguous flatlands, citrus cultivation spans zones with starkly variable water supply capacities and demand patterns, leading to localized shortages or surpluses. For example, zones with low supply (e.g., zone C) face severe deficits during critical growth stages, while high-supply zones (e.g., zone A) may have excess water. This imbalance complicates equitable allocation and necessitates zonal-specific strategies. To address these challenges, this study proposes a hybrid ITSP-LSTM framework that integrates spatial zoning, climate-driven demand forecasting, and stochastic optimization. By dividing the study area into distinct zones with tailored allocation thresholds, the model ensures localized constraints are prioritized while optimizing system-wide benefits.

In this study, we explicitly integrate spatial heterogeneity into the water allocation framework through a three-tiered methodological approach: (1) zonal partitioning divides the fragmented citrus cultivation area into distinct zones (A, B, C) with unique water supply capacities and demand patterns; (2) climate-driven LSTM forecasting quantifies spatiotemporal variability in irrigation demand by linking phenological stages (e.g., blooming, maturation) to weather projections; and (3) interval two-stage stochastic programming (ITSP) optimizes allocations under uncertain water inflows while accounting for zonal-specific penalties to prioritize high-marginal-benefit zones. These methods collectively address spatial mismatches by explicitly modeling supply-demand imbalances and enabling localized decision-making.

The term “defects” in line 254 refers to unmet irrigation demands caused by spatial mismatches between water supply and crop requirements, which manifest as yield losses, economic penalties, and ecological stress. Specifically, insufficient irrigation during critical phenological stages reduces fruit quality and market value, while reliance on external water sources incurs high operational costs. The targeted work of this manuscript is threefold: first, to develop an innovative ITSP-LSTM framework addressing spatial heterogeneity and climate uncertainties; second, to provide actionable strategies for fragmented citrus systems through zonal prioritization and inter-zonal redistribution; and third, to inform policies balancing equity and efficiency in water allocation. By explicitly accounting for citrus-specific challenges, this study advances water management frameworks for economically vital but spatially fragmented agricultural systems.

 

Comment 3: In line 252 “considering spatially varying water supply capacity and stochastic demand”, it mentions "stochastic demand", but there is no relevant discussion on demand randomness in subsequent work. Lines 160-165. Provide references supporting the use of method you have chosen for the effective rainfall.

 

Response: Thank you for raising these important points. We acknowledge that the term “stochastic demand” in line 252 is not sufficiently elaborated in the subsequent analysis, and we have removed it from the manuscript to avoid misinterpretation. Future work will explicitly incorporate stochasticity in irrigation demand by integrating probabilistic modeling of phenological variability and climate-driven uncertainties.

Regarding the effective rainfall method in lines 153-159, we have added references to justify its application as follows:

• Lines 228-230

It is one of the most widely recognized and commonly used methods among various effective precipitation calculation methods [40,41].

Fontanier, C.H., Aitkenhead-Peterson, J.A., Wherley, B.G., White, R.H., Thomas, J.C. Effective rainfall estimates for St. Augustinegrass lawns under varying irrigation programs. Agron. J. 2021, 113, 3720-3729. https://doi.org/10.1002/agj2.20393

Muratoglu, A., Bilgen, G.K., Angin, I., Kodal, S. Performance analyses of effective rainfall estimation methods for accurate quantification of agricultural water footprint. Water Res. 2023, 238, 120011. https://doi.org/10.1016/j.watres.2023.120011

 

Comment 4: Some variables in the text have confusing definitions: Sij represents crop area in formula (1) , while Sij represents water deficit in formula (4a). It is necessary to ensure that each variable maintains a unique and unambiguous meaning throughout the entire manuscript.

 

Response: Thank you for your insightful feedback regarding the inconsistent variable definitions. We apologize for the oversight and have revised the manuscript to ensure all variables maintain unique and unambiguous meanings throughout the text.

 

Comment 5: Should the cumulative variable of formula (4d) be j instead of i?

 

Response: We sincerely appreciate the reviewer’s keen observation regarding the summation index in Formula (4d). After careful review of the manuscript, we confirm that the summation index in Formula (4d) should indeed be j instead of i to align with the spatial and temporal structure of the model. we have revised Formula (4d) to replace the summation index i with j as below:

（4d）

 

 

Comment 6: Table 3 and Table 2 have some overlapping content, it is recommended to integrate and streamline them.

 

Response: Thank you for highlighting the overlap between Table 2 and Table 3. We have revised the manuscript to integrate these tables into a streamlined Table 2 as below:

Table 2. Water supply and demand balance for citrus irrigation in different planting zones.

Citrus planting zones	Water supply zones	Cultivated area (hm2)	Water supply (106 m3)				Citrus Planting water demand (106 m3)	Water shortage (106 m3)
			Reservoirs water Supply (106 m3)		Weirs water supply (106 m3)	Total (106 m3)
A	a	2077.67	10.13	0.29		10.42	7.01	0
B	b	3520.67	5.94	0.44		6.38	11.88	5.50
C	c	2265.33	1.40	0.75		2.15	7.65	5.49

 

Comment 7: Should the title "1.1" in line 438 be changed to "3.4"?

 

Response: Thank you for identifying the inconsistency in the section numbering. This discrepancy arose from an oversight during the formatting process, where the section was inadvertently misclassified under a broader category. We have systematically verified all section numbers, subsections, and cross-references throughout the text to guarantee consistency.

 

Comment 8: There are numerous citation issues in the text, such as lines 165 and 203.

 

Response: Thank you for your feedback on the citation error. Upon investigation, we found that the error issues primarily stemmed from incorrect labeling of figure captions and cross-reference. Specifically, some figures were inadvertently linked to non-existent or mismatched reference entries in the reference list due to formatting inconsistencies during document compilation. We have conducted a full-text proofread to verify that all textual, tabular, and graphical are correctly linked to their corresponding sources.

 

Thank you very much for your time and consideration. We sincerely hope that our revised manuscript and responses to the reviewers' comments meet your expectations. Looking forward to your further feedback.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Reviewer’s Comments on Manuscript ID WATER-3734247 – “Hybrid ITSP-LSTM Approach for Stochastic Citrus Water Allocation Addressing Trade-Offs Between Hydrological-Economic Factors and Spatial Heterogeneity”

I appreciate the authors’ effort in developing a hybrid modeling framework that integrates long short-term memory (LSTM) neural networks with interval two-stage stochastic programming (ITSP) for citrus irrigation water allocation under climate uncertainty. The case study in Anfusi Town is interesting and regionally relevant, and the attempt to bridge machine learning with robust optimization is conceptually sound. That said, there are several aspects—both technical and structural—that need clarification or further development before the manuscript is suitable for publication.

 

1. The inclusion of LSTM for water demand and supply forecasting is a reasonable choice, especially given the non-linear and temporal nature of climate data. However, I found it difficult to fully assess the implementation due to missing model details. Specifically, the authors do not explain the prediction time step (e.g., daily, monthly), the architecture (number of layers, units, dropout, etc.), training parameters (number of epochs, learning rate), or the features used as input. Moreover, there is no quantitative reporting of model performance—no RMSE, MAE, or even visual comparison between predicted and observed data. These are crucial for reproducibility and credibility.

Equally important, the manuscript does not make a strong case for why LSTM is essential to the framework. Would a simpler statistical or regression-based method significantly alter the allocation outcome? Including a comparison or at least a rationale would help justify the additional model complexity.

 

2. While I appreciate the effort to incorporate uncertainty through interval parameters, the manuscript does not sufficiently explain how these bounds were selected. Were they empirically derived from historical records? Or are they scenario-based estimates? For instance, how was the penalty-to-benefit ratio of 1.3 established—through field survey, literature, or expert judgment? Clarifying the sources and logic behind these assumptions would significantly enhance the model’s transparency.

Additionally, it would be helpful to include a sensitivity analysis or at least a qualitative discussion about which parameters the optimization results are most sensitive to.

 

3. The proposed model is tailored to citrus irrigation in Anfusi Town, but it is unclear how transferable the framework is to other agricultural systems. For instance, would it apply equally well to staple crops with different seasonal patterns, or to regions with different water infrastructure and institutional constraints? A discussion on what parts of the framework are modular or adjustable would improve its practical value beyond the current case study.

 

4. The manuscript includes multiple instances of “Error! Reference source not found,” which disrupt the flow and undermines confidence in the overall presentation. These should be corrected prior to resubmission. Furthermore, while LSTM has been widely used in hydrological forecasting, there is almost no discussion of prior work applying LSTM (or other AI models) to agricultural water allocation. A short literature review would help contextualize this study within existing research and clarify what is novel here.

Author Response

Dear editor and reviewer,

Thank you very much for taking the time to review our manuscript and providing insightful comments and constructive feedback. We highly appreciate your suggestions, which have helped us improved the quality of our paper significantly, the revised parts have been marked in red in the text. Please find below our point-by-point responses to your comments:

 

Comment 1: The inclusion of LSTM for water demand and supply forecasting is a reasonable choice, especially given the non-linear and temporal nature of climate data. However, I found it difficult to fully assess the implementation due to missing model details. Specifically, the authors do not explain the prediction time step (e.g., daily, monthly), the architecture (number of layers, units, dropout, etc.), training parameters (number of epochs, learning rate), or the features used as input. Moreover, there is no quantitative reporting of model performance—no RMSE, MAE, or even visual comparison between predicted and observed data. These are crucial for reproducibility and credibility. Equally important, the manuscript does not make a strong case for why LSTM is essential to the framework. Would a simpler statistical or regression-based method significantly alter the allocation outcome? Including a comparison or at least a rationale would help justify the additional model complexity.

 

Response: We sincerely appreciate the reviewer’s insightful feedback regarding the LSTM implementation in our study.

• To address the concerns about model transparency and justification, we have thoroughly revised the manuscript to provide detailed specifications of the LSTM framework and its performance evaluation:
• Section 2.5 Water supply and demand prediction based on the long short-term memory method (Lines 261-270)

This study utilizes meteorological data from the Zhijiang City Meteorological Station spanning 1971 to 2023, including daily precipitation, relative humidity, maximum and minimum temperatures, wind speed, sunlight, and evaporation, to calculate the net irrigation water requirement for citrus cultivation in Anfusi Town over the past 52 years using formulas (2a) to (2d) (see Table S2 in the supplementary information). To predict the net irrigation water requirement for 2025, an LSTM neural network model with a monthly time step was trained in MATLAB. The model employs a 5-layer deep learning architecture, and through multiple trials, key parameters were optimized: 200 hidden units, a learning rate drop period of 800, a learning rate drop factor of 0.1, and 1000 training iterations. Historical surface water supply data for citrus irrigation over the past 15 years were divided into 12 years for training and 3 years for validation, with the average metrics from six experiments used as final indicators. The predicted results provide the available water supply for citrus irrigation reservoirs and weirs in Anfusi Town for both high- and low-flow scenarios in 2025, as detailed in Table S3 (supplementary information).

• To strengthen reproducibility and credibility, we have added quantitative performance metrics and visual comparisons between predicted and observed valuesIn Section 3.2.
• 2 Prediction of water supply and demand for citrus irrigation in planning year (Lines 410-419)

The LSTM model was employed to capture complex temporal dependencies in historical meteorological data, enabling accurate forecasting of irrigation water demands for citrus cultivation. The model demonstrated robust predictive capability for irrigation water demand forecasting, with performance metrics revealing strong alignment between predicted and observed values (Fig. S1 and Table S5, See in the supplementary information). On the training set, the model achieved an R² of 0.7819, RMSE of 41.6133 mm, MAE of 33.0536 mm, and MBE of 1.4511 mm, indicating high accuracy in capturing temporal patterns. While the test set performance slightly declined (R² = 0.5645, RMSE = 58.8234 mm, MAE = 77.2678 mm, MBE = 0.5525 mm), this discrepancy may reflect inherent variability in unobserved hydrological conditions or minor overfitting to training data.

(a) Training set	(b) Test set

Figure S1 The performance of the LSTM model

 

Table S5 Performance metrics of the LSTM model

Training set				Test set
RMSE	R2	MAE	MBE	RMSE	R2	MAE	MBE
41.6133	0.7819	33.0536	1.4511	58.8234	0.5645	77.2678	0.5525

 

• Regarding the necessity of LSTM over simpler methods, we acknowledge the reviewer’s valid concern and have expanded the discussion in section2.2:
• 2.2 Research framework (Lines 178-187)

In fragmented citrus zones with heterogeneous microclimates, the non-linear interactions between climate variables (e.g., temperature, precipitation) and crop water requirements cannot be effectively captured by static or linear regression approaches. The LSTM model, as implemented in this study, explicitly addresses these challenges by learning sequential dependencies in the data such as prolonged droughts or abrupt rainfall shifts. This dynamic capability is essential for optimizing water allocation in Anfusi Town, where localized mismatches between supply (derived from reservoir and weir data) and demand necessitate real-time adjustments. By integrating LSTM, the framework not only handles temporal complexity but also provides robust predictions for different scenarios in the planning year.

 

Comment 2: While I appreciate the effort to incorporate uncertainty through interval parameters, the manuscript does not sufficiently explain how these bounds were selected. Were they empirically derived from historical records? Or are they scenario-based estimates? For instance, how was the penalty-to-benefit ratio of 1.3 established—through field survey, literature, or expert judgment? Clarifying the sources and logic behind these assumptions would significantly enhance the model’s transparency. Additionally, it would be helpful to include a sensitivity analysis or at least a qualitative discussion about which parameters the optimization results are most sensitive to.

 

Response: We sincerely thank the reviewer for highlighting the need for greater transparency in the selection of interval parameters and the rationale behind key assumptions. In this study, the bounds of interval parameters were determined through empirical derivation from historical records. For example, the upper and lower bounds of water supply availability were derived from long-term hydrological data (1971–2023), reflecting observed maximum and minimum values over the past 52 years.

The penalty-to-benefit ratio of 1.3 was established through expert judgment. This value reflects the trade-off between economic losses from water deficits (penalty) and gains from efficient allocation (benefit), as advised by agricultural economists and local water managers familiar with citrus farming in Anfusi Town. While no direct field survey or literature explicitly provides this exact ratio, its selection is grounded in the following rationale: (1) Agricultural economists and local water managers in Anfusi Town, who have extensive experience with citrus farming, emphasized that water deficits during critical growth stages can reduce yields by 15-20% under drought conditions. To mitigate such risks, the penalty coefficient was calibrated to reflect the proportional economic loss associated with unmet irrigation needs relative to the gains from efficient allocation. A ratio of 1.3 implies that penalties for water shortages are 30% higher than the benefits of surplus allocations, aligning with regional practices where water deficits are prioritized over over-allocation to avoid crop failure. (2) The ratio of 1.3 draws parallels to methodologies in interval optimization models, where penalty coefficients are often set based on stakeholder input and historical data. For instance, in crop water management, ratios between 1.0 and 1.5 are frequently adopted to account for variability in irrigation efficiency and crop resilience. In Anfusi Town, the slightly elevated ratio (e.g., 1.3) accounts for the high economic value of citrus crops and the need to prioritize water during peak demand periods. (3) The penalty-to-benefit ratio was adjusted to reflect the seasonal variability of water availability in Anfusi Town, where summer irrigation demands must be met despite limited reservoir capacity. A lower ratio (e.g., 1.0-1.2) might encourage over-allocation during dry periods, risking long-term reservoir depletion, while a higher ratio (e.g., >1.5) could excessively penalize minor deficits, reducing flexibility for adaptive management. The chosen value of 1.3 strikes a balance, ensuring both economic viability and resource sustainability.

Furthermore, we sincerely appreciate the reviewer’s suggestion on sensitivity analysis. While this study establishes a foundational framework for interval stochastic programming in fragmented citrus irrigation, future work will focus on precise water resource management and allocation through quantitative sensitivity analyses (e.g., Monte Carlo simulations, partial rank correlation coefficients) to identify key parameters and interactions. Scenario-based robustness testing under extreme conditions and stakeholder feedback will refine parameter ranges, enhancing model transparency and practical utility for policymakers and farmers in heterogeneous agricultural systems. This direction will be addressed in follow-up publications.

 

Comment 3: The proposed model is tailored to citrus irrigation in Anfusi Town, but it is unclear how transferable the framework is to other agricultural systems. For instance, would it apply equally well to staple crops with different seasonal patterns, or to regions with different water infrastructure and institutional constraints? A discussion on what parts of the framework is modular or adjustable would improve its practical value beyond the current case study.

 

Response: We sincerely appreciate the reviewer’s insightful question regarding the transferability of the proposed framework. While the current study is tailored to citrus irrigation in Anfusi Town, the interval stochastic programming (ISP) framework is inherently modular and adaptable to diverse agricultural systems. Its core components such as interval parameterization of water supply/demand, penalty-benefit trade-offs, and scenario-based optimization can be recalibrated to suit different crops and regional contexts. For example, the seasonal irrigation patterns of staple crops (e.g., rice or wheat) could be incorporated by adjusting crop-specific water demand intervals and phenological constraints. Similarly, the framework’s flexibility in integrating infrastructure capacities (e.g., reservoir sizes, pipeline networks) and institutional rules (e.g., water rights, allocation policies) ensures applicability to regions with varying governance structures. To enhance practical value, we have added a discuss on the framework’s modularity in the Conclusion section:

• Section 5 Conclusion (Lines 603-609）

Crucially, the framework’s modular design allows it to be adapted to diverse agricultural contexts. For example, adjustments to crop-specific water demand intervals and phenological constraints can accommodate staple crops like rice or wheat, while modifications to infrastructure capacities (e.g., reservoir sizes, pipeline networks) and institutional rules (e.g., water rights, allocation policies) ensure applicability across varying governance structures. These features enhance its practical utility for regions with distinct climatic, hydrological, and policy environments.

 

Comment 4: The manuscript includes multiple instances of “Error! Reference source not found,” which disrupt the flow and undermines confidence in the overall presentation. These should be corrected prior to resubmission. Furthermore, while LSTM has been widely used in hydrological forecasting, there is almost no discussion of prior work applying LSTM (or other AI models) to agricultural water allocation. A short literature review would help contextualize this study within existing research and clarify what is novel here.

 

Response: We sincerely thank the reviewer for their thorough evaluation and constructive feedback. Below, we address the two key concerns regarding reference formatting and the integration of AI models in agricultural water allocation.

• Weapologize for the oversight in reference formatting. Upon investigation, we found that the "Error! Reference source not found" issues primarily stemmed from incorrect labeling of figure captions and cross-reference. Specifically, some figures were inadvertently linked to non-existent or mismatched reference entries in the reference list due to formatting inconsistencies during document compilation. We have conducted a full-text proofread to verify that all textual, tabular, and graphical are correctly linked to their corresponding sources.
• The reviewer’s suggestion to strengthen the literature review on LSTM applications is highly valuable. We now incorporated a concise literature review of prior work on LSTM model in agricultural water management in the Introduction section:
• Section 1 Introduction (Lines 115-127)

Building on these methodological advancements, recent advances in deep learning, particularly Long Short-Term Memory (LSTM) networks and related recurrent neural architectures have further enhanced predictive capabilities for agricultural water management (Nifa et al., 2023). Deep learning models excel in capturing complex temporal dependencies in hydrometeorological data, enabling agricultural water use forecasting (Wu et al., 2024), crop evapotranspiration (Hashemi et al., 2025) and accurately predicting water quality in agricultural watersheds (Luo et al., 2025). For instance, LSTMs have been integrated with high-resolution remote sensing data to predict soil moisture and irrigation optimization (Koohikeradeh et al., 2025). Despite their proven efficacy in forecasting hydrological variables for crops, applications in perennial tree crops like citrus where irrigation scheduling must account for multi-stage phenological cycles and fragmented topography remain nascent (Berríos et al., 2023){Citation}.  This gap highlights the need for adaptive frameworks that combine AI-driven predictions with robust optimization methods to address the unique challenges of perennial crops in heterogeneous landscapes.

 

Thank you very much for your time and consideration. We sincerely hope that our revised manuscript and responses to the reviewers' comments meet your expectations. Looking forward to your further feedback.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The author has made revisions based on the suggested changes.