A Fuzzy Stochastic Dynamic Nash Game Analysis of Policies for Managing Water Allocation in a Reservoir System

In this paper a fuzzy dynamic Nash game model of interactions between water users in a reservoir system is presented. The model represents a fuzzy stochastic non-cooperative game in which water users are grouped into four players, where each player in game chooses its individual policies to maximize expected utility. The model is used to present empirical results about a real case water allocation from a reservoir, considering player (water user) non-cooperative behavior and also same level of information availability for individual players. According to the results an optimal allocation policy for each water user can be developed in addition to the optimal policy of the reservoir system. Also the proposed model is compared with two alternative dynamic models of reservoir optimization, namely Stochastic Dynamic Programming (SDP) and Fuzzy-State Stochastic Dynamic programming (FSDP). The proposed modeling procedures can be applied as an appropriate tool for reservoir operation, considering the interaction among the water users as well as the water users and reservoir operator.     

Optimization of Nebhana Reservoir Water Allocation by Stochastic Dynamic Programming

This study is devoted to the identification of an optimal rule that would permit to improve the water resources management of dam in arid condition. The Nebhana dam is considered in this study as a representative of a set dams situated in such condition. The water storage is used for irrigation purpose. The identification of an optimal rule is based on two opposite objectives: the satisfaction of the irrigation water demand and the safeguard of a minimal water storage in the dam. By considering different weights for these objectives, the stochastic dynamic programming technique was lead to various optimal rules for the water resources management of the Nebhana dam. This technique takes into account the variability of the volume of water inflow to the dam on the basis of their occurrence probability; the water losses by means of forecasting models and the water resources goals using weight coefficients. The identified optimal rule would permit to estimate the necessary water release volume for irrigation by considering the water storage and the decision period.     

Inventory Theory-Based Stochastic Optimization for Reservoir Water Allocation

Water Resources Management - This study aims to develop an effective model for reservoir water allocation under conditions of uncertainty. To identify a practical method that increases the benefits...     

Water Costs Allocation in Complex Systems Using a Cooperative Game Theory Approach

The management of complex water resource systems that address water service recovery costs and consider adequate contributions and priorities require methods that integrate technical, economic, environmental, social and legal aspects into a comprehensive framework. In Europe, the Water Framework Directive (WFD) 2000/60/EC recommends that the pricing politics in a river basin take into account the cost recovery and the economic sustainability of the water use. However, the current cost allocation methods do not consider the user’s willingness to pay and often do not permit a total cost recovery. Thus, a new approach is required that includes these requirements when defining water rates. This article presents a methodology to allocate water service costs in a water resource system among different users that attempts to fulfil the WFD requirements. The methodology is based on Cooperative Game Theory (CGT) techniques and on the definition of the related characteristic function using a mathematical optimisation approach. The CGT provides the instruments that are necessary to analyse situations that require a cost-sharing rule. The CGT approach can define efficient and fair solutions that provide the appropriate incentives among the parties involved. Therefore, the water system cost allocation has been valued as a game in which it is necessary to determine the right payoff for each player that is, in this case, a water user. To apply the CGT principles in a water resources system, the characteristic function needs to be defined and evaluated using an adequate modelling approach; in this study, it is evaluated using the optimisation model WARGI. (Sechi and Zuddas 2000). The so-called “core” represents the game-solution set. It represents the area of the admissible cost allocation values from which the boundaries on the cost values for each player can be supplied. Within the core lie all of the allocations that satisfy the principles of equity, fairness, justice, efficiency and that guarantee cost recovery. The core of a cooperative game can represent a useful instrument to define the water cost rates. Furthermore, it can be used as a valid support in water resource management to achieve the economic analysis required by the WFD. The methodology was applied to a multi-reservoir and multi-demand water system in Sardinia, Italy.     

A New Inverse Solution Assessment for the Recovery Test Using Radial Basis Function Collocation Method

Recovery pumping tests are still one of the most commonly preferred preliminary design steps in the assessment of aquifer hydraulics. The use of the existing methods would be insufficient under non-ideal aquifer conditions (i.e. heterogeneity, measurement errors, and boundary effect, etc.) which violate the Theis model assumptions developed for recovery test analysis. In this study, a new parameter estimation methodology based on the Radial Basis Collocation Method (RBFCM) was formulated to access the hydraulic parameters in a reliable, robust and accurate manner using recovery pump test. The suggested approach was established on the idea that the dimensionless time value at the pump-cessation which serves as a matching value is obtained by means of RFBCM. The proposed approach is straightforward to implement; which requires no data refinement, additional parameter, and visual match. The performance of the proposed method was tested with several aquifer conditions including homogeneous synthetic data, heterogeneous aquifer simulation and real field applications. The results confirm that the proposed method has a parameter estimation capacity as high as the available techniques in the literature and provides the practitioners to understand a more accurate portrayal of the effects of heterogeneity on the hydraulic parameters during the test process. In addition, the suggested methodology for the interpretation of aquifer recovery test can be evaluated to be employed as a diagnostic tool to identify non-ideal conditions. The potential use of RBFCM in this study was also presented as the supplement of aquifer test interpretation assessment.     

Water Resources Allocation Using a Cooperative Game with Fuzzy Payoffs and Fuzzy Coalitions

In this paper, two fuzzy cooperative games are utilized for modeling equitable and efficient water allocation among water users in both inter-basin and intra-basin water allocation problems. The proposed all-inclusive water allocation approach consists of three main steps, following Sadegh et al. (Water Resour Manage 24(12):2991?C2310, 2010). In the first step, an initial water allocation is carried out using an optimization model taking into account an equity criterion. In the second step, the water users form crisp coalitions with fuzzy characteristic functions to increase the total net benefit of the system and also their own benefits. In the methodology used in this step, the water users do not need to have exact information about their payoffs and they can evaluate their payoffs as fuzzy numbers. In the second step, based on the Hukuhara difference of fuzzy numbers, optimum water allocation strategies are determined using a game with fuzzy characteristic function. In the third step, we applied another methodology which considers a class of fuzzy games with fuzzy characteristic functions and also fuzzy coalitions for water allocation. The methodology of this step is on the basis of the Hukuhara difference and the Choquet integral. The usefulness of the mentioned methodologies is studied by applying them to three defined real life scenarios in a case study of water allocation in Iran. The results showed that the proposed methodologies are professionally appropriate to real-world uncertain problems of equitable and economic inter-basin and intra-basin water resources allocations.     

三维地下水流随机分析的配点法

本文提出了三维地下水不确定分析的随机配点法，比较了张量积配点法（Tensor Product Collocation Method, TPCM），Smolyak配点法 (Smolyak Collocation Method, SmCM)，Stroud-2配点法 (Stroud-2 Collocation Method, StCM)，以及概率配点法 (Probability Collocation Method, PCM)等四种配点法的基本原理；渗透系数场和水头场分别被表示为Karhunen-Loeve展开和多项式展开的形式；初始随机偏微分方程被转化为在相应配点上的确定性方程；建立了基于Modflow-2000的随机模型；讨论了不同算法的计算精度及计算成本。分析结果表明，配点法可充分继承现有模拟软件或代码的求解功能，配点的选取方法决定了其计算成本，SmCM具有最高的计算精度，但StCM具有最好的性价比。     

Construction of Storage-Performance-Yield Relationships for a Reservoir Using Stochastic Simulation

In the past, many researchers have used stochastic streamflow models along with sequent peak algorithm or sim ulation to obtain storage-reliability-yield (S-R-Y) relationships for a reservoir. These S-R-Y relationships con sider only the probability of failure, but not the likely consequences of the failure (vulnerability). In this paper, separate contours of reservoir performance, n amely reliability and vulnerability (eventbased), have been developed on the storage-yield plane, using stochastic reservoir sim ulation. These contours of performance, when superposed, give rise to the storageperformance-yield (S-P-Y) relationships, the construction of which is illustrated in this paper through a case example. These relationships provide more com prehensive information to the reservoir planner regarding perform ance than the S-R-Y relationships.     

Optimal Reservoir Operation Using Bat and Particle Swarm Algorithm and Game Theory Based on Optimal Water Allocation among Consumers

Water Resources Management - Water resources scarcity and competition among stakeholders in water allocation always highlights the optimal operation of water resources. This research examines the...     

A Stochastic Non-linear Programming Model for a Multi-period Water Resource Allocation with Multiple Objectives

A rapid increase in demand and severe droughts in recent years has increased the pressure on water supplies throughout most parts of Australia. This has resulted in the need for tools to allocate limited water across users in different regions, and explore scenarios so as to achieve economic, social and environmental benefits. A major challenge in water resource allocation is dealing with the uncertainty in the system, particularly with respect to reservoir inflow. Stochastic non-linear programming is applied to water resource allocation to accommodate this uncertainty across the time periods of the planning horizon. A large range of solutions is produced representing the distributions of uncertainty in reservoir inflow. These solutions are used in a Monte Carlo simulation to estimate the trade-off in amounts of water allocated versus risk of not achieving minimal reservoir levels. The methodology is applied to a case study in South East Queensland in Australia, a region which is currently facing a severe water shortage over the next 3 years. A new water supply initiative that the Queensland State Government is considering to overcome the water crisis is assessed using the methodology.     

灌区整体效益模型在水库水量分配中的应用研究

水资源短缺及其水生态环境问题,已成为严重制约中国经济发展的重要因素。因此,如何对有限的水资源进行优化配置研究,已成为水资源规划与管理中的热点问题。文章运用多目标规划理论,建立了以经济、社会、财务等综合效益目标化最大的冯家山水库水量优化配置模型。通过确定模型各参数,调用Matlab优化工具箱中的函数进行编程求解,得到冯家山水库不同规划水平年(2015年、2020年)的水资源优化配置方案,为库区水资源规划与管理提供科学依据。     

面向总量控制的流域水量动态优化分配方法

为了根据来水情形确定年度用水总量控制指标并对水量分配过程进行合理控制,提出了面向总量控制的水量动态优化分配方法。以抚河流域为研究对象,构建了以流域余留期缺水量最小为目标,综合考虑用水区水量需求、控制断面流量要求等约束的水量优化模型,通过“预报-决策-执行-更新”的动态运行方式实现了用水总量控制指标的实时调整。结果表明:在年内水资源由丰转枯时,各用水区的缺水率较传统调度下降了3.8%~25.3%;当年内水资源由枯转丰时,各分区余留期用水量始终控制在余留期总量控制指标之内。本方法得到的年度用水总量控制指标能有效地适应年内不同来水情况,并能根据不同来水条件对供水行为进行激励或约束。     

A Modified Constrained State Formulation of Stochastic Soil Moisture for Crop Water Allocation

In response to uncertainty in crop water allocation, several methodologies have been proposed in the literature, most of them considering rainfall as a stochastic variable affecting soil moisture. A methodology considering uncertainties both in irrigation depth and soil moisture is more realistic for irrigated crops as developed here using an explicit stochastic optimization model. This new work is based on an earlier constrained state formulation which did not consider the irrigation depth as stochastic. In constrained state formulation methods, the first and second moments of state variables are developed considering the uncertainties which are then used as constraints in an optimization model. In contrast to alternative methods that are dynamic programming-based, the proposed optimization method can be solved using standard nonlinear optimization tools. Performance of the proposed model is evaluated for the case of two different crops, winter wheat and barley. Model verification is performed by comparing the results with simulation results. The model is quite acceptable and shows considerable improvement over analogous models.     

Reliability Improved Stochastic Dynamic Programming for Reservoir Operation Optimization

Stochastic Dynamic Programming (SDP) is widely used in reservoir operation problems. Besides its advantages, a few drawbacks have leaded many studies to improve its structure. Handling the infeasible conditions and curse of dimensionality are two major challenges in this method. The main goal of this paper is proposing a new method to avoid infeasible conditions and enhance the solution efficiency with new discretization procedure. For this purpose, an optimization module is incorporated into regular SDP structure, so that, near optimal values of state variables are determined based on the available constraints. The new method (RISDP) employs reliability concept to maximize the reservoir releases to satisfy the downstream demands. Applying the proposed technique improves the reservoir operating policies compared to regular SDP policies with the same assumptions of discretization. Simulation of reservoir operation in a real case study indicates about 15% improvement in objective function value and elimination of infeasible conditions by using RISDP operating policies.     

Long-Term Stochastic Reservoir Operation Using a Noisy Genetic Algorithm

To deal with stochastic characteristics of inflow in reservoir operation, a noisy genetic algorithm (NGA), based on simple genetic algorithms (GAs), is proposed. Using operation of a single reservoir as an example, the results of NGA and Monte Carlo method which is another way to optimize stochastic reservoir operation were compared. It was found that the noisy GA was a better alternative than Monte Carlo method for stochastic reservoir operation.     

A Fuzzy Variable Least Core Game for Inter-basin Water Resources Allocation Under Uncertainty

In this paper, a new solution concept, called Fuzzy Variable Least Core (FVLC), is developed for fuzzy cooperative games. The FVLC is able to incorporate fuzzy input variables and result in fuzzy benefit shares of players participating in a coalition. This solution concept is used for water and benefit allocation to water users in inter-basin water transfer systems considering the uncertainties associated with their benefit coefficients. In the proposed water allocation methodology, an Integrated Stochastic Dynamic Programming (ISDP) model is developed to obtain the water rights of players and economic water allocation policies. In the next step, the total net fuzzy benefit of the system is reallocated to water users in an equitable and rational way using a FVLC-based model. In this model, a new algorithm is proposed for converting a multilateral cooperative game with fuzzy variables to some fuzzy bilateral cooperative games, which are solved using the FLVC solution concept. The applicability and efficiency of the proposed methodology is examined by applying it to a large scale inter-basin water transfer project in Iran.     

Feasibility Improved Stochastic Dynamic Programming for Optimization of Reservoir Operation

Water Resources Management - Stochastic Dynamic Programming (SDP) is a major method for optimizing reservoir operation. Handling non-linear, non-convex and non-differentiable objective functions...     

新型含砷水样前处理技术开发研究

砷是一种对人体健康造成严重伤害的污染物,受管理规定和检测手段的限制,由砷诱发癌症的风险仍然较高。选取离子液体作为萃取溶剂,开发出一种基于离子交换机理的分散液液微萃取方法,应用于含砷水样的前处理。通过研究水样体积、pH值、离子液体用量等6项关键因素对该方法萃取效率的影响,以及对该方法的表现效果进行了优化和评价。本方法可在数分钟内完成对砷的萃取,富集因子可达到210,在0.05～10 μg/L范围内均有较好线性关系,相对标准偏差仅为1.5%;当本方法与石墨炉原子吸收光谱仪联用时,对砷的检出限可达到10 ng/L。另外,避免了传统样品前处理方法中使用的大量有机溶剂,因此更加绿色、环保。研究结果为水环境分析监测技术领域的开拓和发展提供了新思路。     

基于区间拟shannon小波配点法的供水系统水锤计算技术方法研究

文中将区间拟shannon小波配点法应用于水锤方程求解,通过将水锤方程中的待求函数用一系列拟shannon小波基函数逼近,对空间域进行离散,从而建立起关于时间的常微分方程组,构造出了水锤方程在小波空间的计算方法,并推演了管道中水锤波的传播。最后通过仿真实例计算出水锤方程的数值解,说明该方法对水锤计算具有较好的数值模拟性,从而为确保供水系统的安全和稳定运行提供技术支持。     

Development of a Dynamic Long-Term Water Allocation Model for Agriculture and Industry Water Demands

Demands growth and water resources limitation, enforce water sector policy makers to integrate water supply–demand interactions in a coherent framework for efficient water allocation. Water supply–demand interaction, changes long-term trend of water demands, which in turn has a substantial influence on water allocation. Researches on water allocation modeling lack adequate projection of relationship between water supply and demand. Socio-economic factors representing water allocation stakeholders’ benefits, account for the main share of water supply–demand interaction. Identification, representation and consideration of these factors in a water allocation model, is the main limitation of researches on this issue. In this paper a new long-term water allocation model at basin level is developed and introduced. This model considers water supply–demand interaction in agriculture and industry sectors, by use of socio-economic parameters; such as, production, cultivated land area, revenue and employment. The model main advantage is its ability to reflect the interrelationship between essential hydro-system and supply–demand components. It can explore both socio-economic and water allocation consequences of various policy choices. The model is used to assess two different development policies at basin level. The first one is fourth 5-year development plan of Iran, which fixes predefined growth rate for different sectors. The second one assumes the present state continues up to the end of planning horizon. A typical multi-reservoir water basin is modeled and analyzed for two policies. Indices that summarize long-term state of hydro-system and stakeholders are defined and used in policies assessment and decision making. Results of these assessments show fourth 5-year development policy provides opportunities for substantial improvement in water allocation and stakeholders’ benefits.