A Copula-based interval linear programming model for water resources allocation under uncertainty

Assessing the option water-saving willingness of irrigation areas considering farmers' risk tolerance

Water option trading could facilitate water conservation in irrigation areas to achieve optimal allocation of agricultural water resources. However, the risk associated with water-saving decisions increases due to the uncertainties of tradeable water and water-saving benefits, which makes farmers in the irrigation area with heterogeneous risk tolerances exhibit varied option water-saving willingness (OWSW) in response to the water option contract. Thus, this article provides a novel framework for prior assessing the OWSW in the irrigated area that considers farmers' heterogeneous risk tolerance and proposes the optimal contractual water demand to stimulate the OWSW. First, a multiobjective optimal allocation model for cropping water is constructed to predict tradeable water, and then risk trust, risk-return perception and reference are integrated into water-saving return analysis for proposing a willingness calculation model involving forecast information. Finally, the influence of heterogeneous risk tolerance on farmers' water-saving path choices and the irrigation area's OWSW is analyzed with three sets of comparative data from 2014 to 2021. Results indicate that the intensity and stability of OWSW in water-scarce irrigation areas increase as farmers' risk tolerance rises, but the enhancement utility exhibits a diminishing marginal trend. When both prediction accuracy and farmers' risk tolerance are low, contracts with relatively adventurous and differentiated water demands are more likely to stimulate OWSW. This study provides insights into activating water options trading and stimulating water conservation in agriculture from a risk management perspective.

Copula-based analysis of socio-economic impact on water quantity and quality: A case study of Yitong River, China

Socio-economic development has a significant impact on both water quantity and quality. However, few studies have considered the complex relationship between water quantity and quality when evaluating such impact. In this study, three indicators based on copula model were proposed, namely, water quantity improvement degree (WQID_w), water quality improvement degree (WQID_q) and water quantity and quality joint improvement degree (WQJID). These indicators were used to assess the impact of social economy on water quantity and quality, and applied to a case study in Yitong River in Northeast China from 2021 to 2025. Four scenarios were set to explore the impact of socio-economic development and water resources protection on WQID_w, WQID_q and WQJID. The maximum WQID_w, WQID_q and WQJID were <1 under the business-as-usual scenario, which showed that the present socio-economic pattern caused great damage to river water quantity and quality. The combined effect of socio-economic development and water resources protection increased the WQJID of COD and NH₃-N by 1.67 and 1.30. This showed that attention should be paid to water resources protection while developing social economy. Compared with comprehensive evaluation, separate evaluation of water quality will underestimate the impact of social economy on rivers, while separate evaluation of water quantity will overestimate the impact. The relationships between WQID_w, WQID_q and WQJID were quantified. Meanwhile, the uncertainty of the evaluation was controlled by the selection of water quality indicators. The WQID_q, WQID_w and WQJID proposed in this study provide a comprehensive assessment tool for guiding water resources management.

A Method of Multi-Objective Optimization and Multi-Attribute Decision-Making for Huangjinxia Reservoir

The objectives of flood control, power generation, water supply and ecology for reservoir operation are neither completely coordinated nor completely opposed, and its optimal operation and decision-making is very complicated. This study proposed a method of multi-objective optimization and multi-attribute decision making for reservoir operation (MODRO). The correlation analysis method was used to analyze the competitive relationship among the extracted objectives, and the multi-objective optimal operation model was constructed. The NSGA-II-SEABODE algorithm was applied to solve the MODRO problem. The objective extraction, model construction, optimization solution and scheme selection were coupled to form a multi-objective optimization and multi-attribute decision making method with the whole process of “Objective-Modeling-Optimization-Selection”. Huangjinxia Reservoir, which is located in Shaanxi, China, was selected as the case study. The results show that: (1) Quantifying the degree of conflict among objectives makes the construction of the multi-objective optimal operation model more reasonable. (2) The NSGA-II-SEABODE algorithm are used to obtain the decision-making scheme, which provides decision-making basis for managers. (3) For Huangjinxia Reservoir, water diversion is negatively related to power generation and ecology, and power generation is positively related to ecology. The results can promote the efficient utilization of water resources, improve the comprehensive benefits of reservoirs, and provide decision-making support for actual reservoir operation.

Multi-Stakeholder Coordinated Operation of Reservoir Considering Irrigation and Ecology

In traditional ecological operation, it is difficult to coordinate the balance among the interests of stakeholders, and stakeholders find it difficult to accept the operation scheme. To address these problems, this study proposed a method of multi-stakeholder coordinated operation of reservoir (MSCOR). By comprehensively considering the interest demands of stakeholders, the multi-stakeholder interval coordination mechanism (MSICM) for reservoir operation was established. The multi-stakeholder coordinated operation model (MSCOM) was constructed. The multi-stakeholder solution algorithm based on the MSICM, the non-dominated sorting genetic algorithm II, and the approach of successive elimination of alternative schemes based on the k-order and p-degree of efficiency (MSIC-NSGA-II-SEABODE) were applied to solve the MSCOR problem. The coordination mechanism, model construction, multi-stakeholder optimization, and multi-attribute decision making were coupled to establish a multi-stakeholder coordinated operation method, comprising the whole process of mechanism–modeling–optimization–decision making. Taking Baojixia Reservoir as an example, the performance of the coordinated operation method was compared with that of the traditional optimal operation method, and the relationship between the irrigation benefits and ecological benefits of the reservoir was explored. The results show that: (1) On the premise of the same satisfaction degree of basic irrigation interests, the ecological AAPFD value of coordinated operation decreased by 0.184, 0.469, and 0.886 in a normal year, dry year, and extraordinary dry year, respectively. The effect of coordinated operation on balancing various stakeholders was more obvious with the decrease in water inflow. (2) The MSICM ensures that the multi-stakeholder operation of the reservoir conforms to the principles of comprehensiveness, balance, and sustainability. (3) The coordination scheme obtained by the MSIC-NSGA-II-SEABODE algorithm is more reasonable and feasible. The research results provide a new idea and method to address the MSCOR problem.