Dual-Interval Two-Stage Optimization for Flood Management and Risk Analyses

In this study, a dual interval two-stage restricted-recourse programming (DITRP) method is developed for flood-diversion planning under uncertainty. Compared with other conventional methods, DITRP improves upon them by addressing system uncertainties with complex presentations and incorporating subjective information within its optimization framework. Uncertainties in DITRP can be represented as probability distributions and intervals. In addition, the dual-interval concept is presented when the available information is highly uncertain for boundaries of intervals. Moreover, decision makers’ attitudes towards system risk can be reflected using a restricted-resource measure by controlling the variability of the recourse cost. The method has been applied to a case study of flood management. The results indicate that reasonable solutions for planning flood management practice have been generated which are related to decisions of flood-diversion. Several policy scenarios are analyzed, assisting in gaining insight into the tradeoffs between risk and cost.     

Agricultural Multi-Water Source Allocation Model Based on Interval Two-Stage Stochastic Robust Programming under Uncertainty

Numerous uncertainties and complexities exist in the agricultural irrigation water allocation system, that must be considered in the optimization of water resources allocation. In this paper, an agricultural multi-water source allocation model, consisting of stochastic robust programming and two-stage random programming and introducing interval numbers and random variables to represent the uncertainties, was proposed for the optimization of irrigation water allocation in Jiamusi City of Heilongjiang Province, China. The model could optimize the water allocaton to different crops of groundwater and surface water. Then, the optimal target value and the optimal water allocation of different water sources distributed to different crops could be obtained. The model optimized the economic benefits and stability of the agricultural irrigation water allocation system via the introduction of a the penalty cost variable measurement to the objective function. The results revealed that the total water shortage changed from [18.6, 32.3]?×?10⁸ m³ to [15.7, 26.2]?×?10⁸ m³ at a risk level ω from zero to five, indicating that the water shortage decreased and the reliability improved in the agricultural irrigation water allocation system. Additionally, the net economic benefits of irrigation changed from [287.21, 357.86]?×?10⁸ yuan to [253.23, 301.32]?×?10⁸ yuan, indicating that the economic benefit difference was reduced. Therefore, the model can be used by decision makers to develop appropriate water distribution schemes based on the rational consideration of the economic benefit, stability and risk of the agricultural irrigation water allocation system.     

An Integrated Approach of System Dynamics,Orthogonal Experimental Design and Inexact Optimization for Supporting Water Resources Management under Uncertainty

An integrated approach of system dynamics (SD), orthogonal experimental design (OED) and inexact optimization modeling was proposed for water resources management under uncertainty. The developed method adopted a combination of SD and OED to identify key scenarios within multiple factors, through which interval solutions for water demands could be obtained as input data for consequential optimization modeling. Also, optimal schemes could be obtained in the combination of inexact two-stage stochastic programming and credibility constrained programming. The developed method was applied to a real-world case study for supporting allocation of multiple-source water resources to multiple users in Dalian city within a multi-year context. The results indicated that a lower credibility-satisfaction level would generate higher allocation efficiency, a higher system benefit and a lower system violation risk. The developed model could successfully reflect and address the variety of uncertainties through provision of credibility levels, which corresponds to the decision makers’ preference regarding the tradeoffs between system benefits and violation risks.     

基于鲁棒规划方法的农业水资源多目标优化配置模型

在干旱半干旱地区,调整种植结构可以促进农业水资源的高效利用。农业水资源配置需要在多个目标间权衡博弈,对各目标的偏好和赋权直接影响着优化模型的输出和决策方案的制定,但以往研究往往忽略了权重确定过程中因主观等因素的影响而普遍存在的不确定性。针对农业水资源多目标规划中存在的权重不确定性难题,建立了基于鲁棒优化方法的农业水资源多目标优化配置模型方法(MRPWU)。该方法可以把权重中蕴含的复杂不确定性信息纳入建模过程,产生可靠的模型结果;并能提供效益值及风险值均定量化的方案集,便于决策者在权衡效益与风险后确定最优方案。模型以作物种植经济收益和碳吸收量最大化为目标、以水土资源供需平衡等为约束条件,并应用于农业水资源供需矛盾突出的甘肃省民勤县。优化结果表明,随着保护度水平的提高,生态效益上升,经济效益和综合效益下降,系统面临的风险也随之下降。相比于权重为确定参数的模型,MRPWU模型可以在综合效益下降3.7%的同时,较大地提高系统应对权重不确定性以及风险的能力。与2017年的实际情况相比,MRPWU模型可以减少种植面积1.6%、节省灌溉用水3.9%,同时提高生态效益1.6%。     

Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSP) method was developed for water resources management under uncertainty. As a new extension of mathematical programming methods, the developed ITSSP approach has advantages in uncertainty reflection and policy analysis. In order to better account for uncertainties, the ITSSP approach is expressed with discrete intervals, functional intervals and probability density functions. The ITSSP method integrates the two-stage stochastic programming (TSP), interval programming (IP) and semi-infinite programming (SIP) within a general optimization framework. The ITSSP has an infinite number of constraints because it uses functional intervals with time (t) being an independent variable. The different t values within the range [0, 90] lead to different constraints. At same time, ITSSP also includes probability distribution information. The ITSSP method can incorporate pre-defined water resource management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a water resource management system with three users and four periods (corresponding to winter, spring, summer and fall, respectively). Solutions of the ITSSP model provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable interval solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flow. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system reliability criteria.     

Application of Integrated Hydrologic and River Basin Management Modeling for the Optimal Development of a Multi-Purpose Reservoir Project

Multi-purpose reservoir development have been always a big challenge for the management of water resources. This paper describes an integrated approach for investigating catchment hydrology in the development of a hydropower and a canal irrigation system based on model analyses. The investigation aims to adequately determine an optimal domestic and irrigation water resources allocation scheme based on an assessment of the reservoir water balance and capacity for hydropower. The soil and water assessment tool (SWAT) which characterizes basin hydrology and the water management and planning model MODSIM which provides a decision support system for water allocation optimization, were used in this study. The integrated approach was applied to Prek Te River basin in Cambodia. The water demand aspect was examined based on domestic water use, irrigation water, environmental flow, and water losses. An operational rule curve was developed for hydropower operation with respect to a power potential of 13 MW. Hydrologic modeling revealed 90 % dependable water of about 2.7 m³/s during the dry season and 214.3 m³/s during the wet season, indicative of a wet-season dependent reservoir for storage. Results from the 26-years simulation period also showed that diversions for domestic water and irrigation water supply were 92.3 % dependable for a 13 MW capacity hydropower development. The integrated approach was shown to be a valuable decision support tool for water resources management with the determination of an optimum policy for multi-purpose reservoir operation based on available basin water supply.     

缺水型灌区水资源优化调度模型研究

长江针对缺水型灌区的供水特点,以云南曲靖灌区为例,应用大系统分解协调原理,将整个系统设计为两层递阶控制结构;以运行费用和系统缺水量最小作为目标函数,建立了灌区库群系统水资源优化调度模型;对模型权重系数进行了率定;根据系统目标重要性的优先次序,确定了灌区优化配水矩阵;并采用模拟技术与优化技术相结合的途径,进行优化模型的求解,给出了优化决策算法的程序框图,所建模型符合曲靖灌区的实际情况,研究成果可为同类灌区水资源调度运行提供依据.     

A Multi-objective Linear Programming Model with Interval Parameters for Water Resources Allocation in Dalian City

Water resources management has been of concern for many researchers since the contradiction between increased water demand and decreased water supply has become obvious. In the real world, water resources systems usually have complexities among social, economic, natural resources and environmental aspects, which leads to multi-objective problems with significant uncertainties in system parameters, objectives, and their interactions. In this paper, a multi-objective linear programming model with interval parameters has been developed wherein an interactive compromising algorithm has been introduced. Through interactive compromising conflicts among multi-objectives, a feasible solution vector can be obtained. The developed model is then applied to allocation of multi-source water resources with different water qualities to multiple users with different water quality requirements for the Dalian city for 2010, 2015 and 2020 planning years. The model pursues the maximum synthesis benefits of economy, society and the environment. The results indicate that the proportion of reused water to the total water amount is gradually increasing, and the proportion of agricultural water consumption to the total water consumption is gradually decreasing. The allocation of multi-source water resources to multiple users is improved due to incorporation of uncertain factors into the model that provide useful decision support to water management authorities.     

A Fuzzy Robust Nonlinear Programming Model for Stream Water Quality Management

An interval-parameter fuzzy robust nonlinear programming (IFRNP) approach was developed for stream water quality management under uncertainty. The interval and fuzzy robust programming methods were incorporated within a general framework to address uncertainties associated with the nonlinear objective and the left- and right-hand sides of the constraints. A piecewise linearization approach was developed to deal with the nonlinear cost function. IFRNP could explicitly address complexities of various system uncertainties, where parameters were represented as both interval numbers and fuzzy membership functions. Furthermore, the dual uncertain information associated with the lower and upper bounds of each interval parameter could be effectively tackled through the concept of fuzzy boundary interval. The proposed IFRNP method was applied to a case of water quality management in the Guoyang section of the Guo River in Anhui province, China. A number of cost-effective schemes for water quality management were generated, and allowable wastewater discharge amounts were recommended. The results indicated that IFRNP was applicable to water quality management problems, where high nonlinearities and dual uncertainties exist.     

作物优化灌溉制度的研究

文中对非充分灌溉条件下作物优化灌溉制度如何制定进行了研究。其特点是将作物产量模型、耗水规律模型和土壤水分变化动态模型相结合，以产量最高为目标函数，建立了计算机优化决策系统。该研究成果可使有限的水量在作物生育期内发挥最大的效率，对优化配置水资源，实现农业高效用水具有重要作用。实例研究结果说明，所建模型及求解方法是合理与可行的。     

A user-oriented and quantifiable approach to irrigation design

A new user-oriented approach is presented to apply marketing research techniques to quantify perceptions, preferences and utility values of farmers. This approach was applied to design an improved water distribution method for an irrigation scheme in Mendoza, Argentina. The approach comprises two subprocesses. The first one consists of a diagnostic analysis and the identification of an alternative water distribution system as a concept solution to the regional irrigation problems. In contrast to the rigid current system, the alternative system allows farmers, within some limitations, to design their own monthly allocation of water. The second, user-oriented subprocess consists of three stages: a perception, a preference and a utility analysis. Perception and preference analyses show that the farmers perceive the alternative (not yet in existence) system as the preferable one, with respect to control and sufficiency. Analysis also reveals that the flow rate and irrigation interval that farmers currently receive influence their perceptions. A utility analysis determines the utility values of farmers for different levels of flow rate, irrigation interval and the possibility of designing their own monthly allocation of water. The Mendoza case indicates that by using this approach the farmers' perceptions, preferences and utility values of technical features of the irrigation system are quantified. Thus, management and designers alike can be provided with recommendations on vital design elements.     

Assumption-Simulation-Feedback-Adjustment (ASFA) Framework for Real-Time Correction of Water Resources Allocation: a Case Study of Longgang River Basin in Southern China

Water resources allocation is subject to uncertain future conditions and therefore needs real-time correction. This study develops a framework of “assumption-simulation-feedback-adjustment” (ASFA) for real-time correction of water resources allocation. The assumption component constructs a water resources allocation model and generates initial allocation solution (IAS); the simulation component applies IAS in a real-time hydrological scenario; the performance information is input into the feedback component. Three feedback functions, including gain function, correlation function, and least square function, are employed to deal with the information, and the value of output gain is determined for the adjustment component. The result then is a feedback allocation solution (FAS). This study applied ASFA to Longgang River basin, China, as a case study, compared FASs generated by three different feedback functions as well as IAS. Results showed that FAS generated by the gain function (FAS_GF) performed better with a higher assurance rate and less risk of continuous water shortage. Results also showed that to achieve the same management requirement, FAS_GF had a lower requirement of the amount of diverted water, indicating that the ASFA framework can make better use of water resources and reduce the pressure of diverted water. The ASFA framework builds a feedback mechanism for real-time correction of water resources allocation, provides a novel perspective for addressing the challenge of future uncertainty, which significantly improves the solutions of water allocation.     

灌区多目标供水优化调度模型及其求解

针对灌区水资源供需矛盾十分突出的问题，以云南曲靖灌区为研究对象，应用大系统分解协调原理，建立了两层递阶水资源优化调度模型，并采用模拟技术与优化技术相结合的途径，进行优化模型的求解，给出了优化决策算法的程序框图，合理解决了多水源、多目标、多用户、多保证率的供水调度问题。研究结果可为同类灌区水资源调度运行提供依据。     

Optimal Long-term Operation of Reservoir-river Systems under Hydrologic Uncertainties: Application of Interval Programming

Long-term basin-wide reservoir-river operation optimization problems are usually complex and nonlinear especially when the water quality issues and hydrologic uncertainties are incorporated. It is due to non-convex functions in water quality modeling and a large number of computational iterations required by most of stochastic programming methods. The computational burden of uncertainty modeling can be reduced by a special combination of uncertainty modeling and interval programming, though the problem solution is still a challenge due to model nonlinearity. In this paper, an integrated water quantity-quality model is developed for optimal water allocation at river-basin scale. It considers water supply and quality targets as well as hydrologic, water quality and water demand uncertainties within the nonlinear interval programming (NIP) framework to minimize the slacks in water supply and quality targets during a long-term planning horizon. A fast iterative linear programming (ILP) method is developed to convert the NIP into a linear interval programming (LIP). The ILP resolves two challenges in NIP, first converting the large non-linear programming (NLP) into a linear programming (LP) with minimum approximation and second reducing the iterations needed in interval programming for NLP into just two iterations for the upper and lower limits of decision variables. This modeling approach is applied to the Zayandehrood river basin in Iran that has serious water supply and pollution problems. The results show that in this river basin at dry conditions when available surface water resources are below 85 % of normal hydrologic state and water demands are 115 % of current water demands, the total dissolved solids (TDS) concentration can be reduced by 50 % at the inlet of the Gavkhuni wetland located downstream of the river basin.     

应用大系统递阶模型优化配置区域农业水资源

以经济效益最大为目标，建立灌溉供水量最优分配的分解协调模型。以作物子系统为第一层，建立求解单作物非充分灌溉条件下灌水量在各生育期的最优分配的动态规划模型。然后以区域大系统作为第二层，建立不同作物之间水量最优分配的模型。在此基础上，提出了协调模型求解方法步骤。根据作物布局和地下水分布给出了不同作物在各生育期地下水的最优分配量，以提高区域农业水资源承载能力。     

Socially-Optimal and Nash Pareto-Based Alternatives for Water Allocation under Uncertainty: an Approach and Application

This study has proposed a methodology by enhancing an interactive algorithm to multi-objective optimization problems with interval parameters, in an attempt to reach the tradeoff between quality and reliability of the resultant optimum solutions. The earlier algorithm could turn into a prolonged procedure that deals with several players with different aspirations at different reliability, or risk, levels under non-deterministic conditions. Hence, it is not a pertinent approach to solve problems of water allocation between competing parties. The enhanced methodology aims to alleviate the burdens of the procedure and generate a unique set of solutions (i.e., near-Pareto-optimal alternatives), instead of a myriad of compromise solution sets. We have investigated a real-world hydro-environmental problem, the allocation of water between Dorudzan-Korbal irrigation networks and Bakhtegan Lake in Fars Province, Iran to assess feasibility of this methodology. In order to reach a consensus concerning the stakeholders’ individual preferences, we identified the compromise alternatives from the obtained sets of non-dominated solutions by taking advantage of various social choice rules and the Nash bargaining model. The results demonstrated that the developed methodology could incorporate the risk of system constraints violations (i.e., planning reliability under uncertainty) into the process of approximating the optimal tradeoff set of solutions. It also gave policymakers a chance to acquire perception into the potentially best compromise for land and water allocation schemes regarding the preference profiles of the involved interest groups.     

A Conditional Value-at-Risk Based Inexact Water Allocation Model

A conditional value-at-risk (CVaR) based inexact two-stage stochastic programming (CITSP) model was developed in this study for supporting water resources allocation problems under uncertainty. A CITSP model was formulated through incorporating a CVaR constraint into an inexact two-stage stochastic programming (ITSP) framework, and could be used to deal with uncertainties expressed as not only probability distributions but also discrete intervals. The measure of risks about the second-stage penalty cost was incorporated into the model, such that the trade-off between system economy and extreme expected loss could be analyzed. The developed model was applied to a water resources allocation problem involving a reservoir and three competing water users. The results indicated that the CITSP model performed better than the ITSP model in its capability of reflecting the economic loss from extreme events. Also, it could generate interval solutions within which the decision alternatives could be selected from a flexible decision space. Overall, the CITSP model was useful for reflecting the decision maker’s attitude toward risk aversion and could help seek cost-effective water resources management strategies under complex uncertainties.     

Conjunctive Water Use Planning in an Irrigation Command Area

In the present study, an integrated soil water balance algorithm was coupled to a non-linear optimization model in order to carry out water allocation planning in complex deficit agricultural water resources systems based on an economic efficiency criterion. The LINGO 10.0, optimization package has been used to evolve at optimal allocation plan of surface and ground water for irrigation of multiple crops. The proposed model was applied for Qazvin Irrigation Command Area, a semi-arid region in Iran. Various scenarios of conjunctive use of surface and ground water along-with current and proposed cropping pattern have been explored. Some deficit irrigation practices were also investigated. The results indicate that conjunctive use practices are feasible and can be easily implemented in the study area, which would enhance the overall benefits from cropping activities. The study provides various possible operational scenarios of the branch canals of the command area in the common and dry condition, which can help managers in decision making for the optimum allocation plans of water resources within the different irrigation districts. The findings demonstrate that for deficit irrigation options, the mining allowance of ground water value of the command area is greatly reduced and ground water withdrawal may be also restricted to the recharge to maintain the river–aquifer equilibrium.     

不确定性多目标模糊规划在水资源优化配置中的应用

在充分考虑水资源系统中供需水不确定性的基础上,基于多目标规划、模糊规划和区间规划原理,以经济效益、社会效益和环境效益最大为目标,以需水量、可供水量和不同子区用水部门间的用水公平性为主要约束,构建一种适用于多水源、多子区、多用户的考虑供需水不确定性的多目标模糊规划模型,以期通过平衡水资源配置系统中用户配置水量、缺水风险与系统收益三者的关系,实现系统综合效益最大。模型以衡水市历年供水、用水及社会经济等数据确定规划年的水资源参数及经济参数,采用区间参数反映系统中的不确定性,通过引入模糊隶属度函数,利用两步交互式算法,将多目标规划转化为单目标规划进行求解,以2025年为衡水市规划水平年,得到规划水平年下的11个子区、4种水源、4个用水行业的最优配水方案。结果表明：本研究制定的水资源优化配置方案可实现“外调水优先利用、地下水控制利用”,同时考虑用水的公平性约束后,在缺水条件下可有效控制水资源向每立方米水效益高的区域和部门流动,有利于多区域、多部门共担缺水风险;该水资源优化配置方案可有效缓解衡水市水资源供需矛盾,实现多水源和多目标之间的协同互补。研究成果可为河北省其他县域的水资源优化配置提供技术参...     

Flavia Rocha Loures and Alistair Rieu-Clarke (eds), The UN Watercourses Convention in force: strengthening international law for transboundary water management

Abstract

The MODSIM 8.0 decision support system (DSS) for integrated river basin management (IRBM) has been adapted from a prior appropriation rights-based system to one found in Korea and in much of Asia where water deficits are shared among water use sectors, taking into account priorities established by water policy and institutional frameworks. The Korean version called KModSim is applied to the Geum River basin for evaluation of long-term sustainability of existing and new water infrastructure and facilities under integrated, basin-wide water resources management. KModSim is calibrated to the physical and hydrologic characteristics of the basin, as well as to operational and administrative water allocation policies for municipal and industrial water supply, irrigation, hydropower, transbasin diversions, and low-flow augmentation for environmental purposes. Conditional reservoir operational rules that adapt to changing river basin hydrologic conditions are developed from an implicit stochastic optimization algorithm and incorporated using the extensive user-customization capabilities of KModSim. Results demonstrate that decision guidance under KModSim enhances beneficial water uses in the Geum River system through fully integrated, basin-wide management.