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...     

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 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.     

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...     

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。     

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.     

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.     

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.     

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.     

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...     

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.     

牛头山水库水资源优化配置研究

牛头山水库灌区内河网水系发达,有一定的调蓄能力,灌区内还有溪口水库和童燎水库两座中型水库,因此牛头山水库灌区内各用户的用水并非都需要牛头山水库来供给。为了达到牛头山水资源的优化配置,对灌区各个用水单元进行长系列水量平衡计算。优化配置的计算结果是合理的,为牛头山水库灌区水资源可持续利用规划与管理提供了决策依据。     

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.     

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。     

水库汛限水位动态控制方法研究及其应用

在对水库汛限水位动态控制管理运用中涉及到的几个关键问题进行研究分析的基础上,提出在不降低水库原防洪标准的前提下,考虑短时气象降雨和洪水实时预报信息的汛限水位动态控制方法。该方法考虑了预报误差的规律,能在降雨和洪水发生、发展及消退的演进过程中,按预报信息种类和精度分阶段、分层次地判断洪水量级,并及时作出合理调度决策,既利用了不同预报信息,又考虑了各自的误差风险率,具有可操作性强、洪水资源利用率高的特点,可用于汛期全过程实时调度,运用于隔河岩水库,每年平均增加发电量3900万kW·h。     

A Hybrid Dynamic Dual Interval Programming for Irrigation Water Allocation under Uncertainty

Along with the economic development in Canada, the shortage of irrigation water has become a serious concern (Bouwer 1993; Hennessy 1993). In this study, a model of Dynamic Dual Interval Programming (DDIP) is developed and applied to the irrigation water allocation systems with uncertainty. DDIP method improves the existing dynamics interval programming by explicitly addressing the system uncertainties with a dual interval that had higher system reliability. The solution of DDIP is computationally effective, and its decision variables are incorporated into the solutions for final decision. In order to obtain the optimal allocation schemes in a dynamic process, the developed DDIP was applied to an irrigation water system. The results from this case study revealed that optimal solution can be obtained through the DDIP approach from the agriculture water management activities for feasible decisions. These decisions reflect the high uncertainty of the information in the boundaries of dual intervals. The solution presents a maximum benefit under limited yearly uncertain natural resources. Furthermore, the information obtained though this model may help the authority to make optimal decisions and to reduce the risk for uncertain situations.     

A Factorial-based Dynamic Analysis Method for Reservoir Operation Under Fuzzy-stochastic Uncertainties

In this study, a factorial-based fuzzy-stochastic dynamic programming (FFS-DP) method is developed for tackling multiple uncertainties including fuzziness, randomness and their interaction in reservoir operation management (ROM). FFS-DP is framed on the integration of stochastic dynamic programming, fuzzy-Markov chain, vertex analysis and factorial analysis techniques. It can not only deal with the conventional optimization problem for reflecting dynamic and uncertain features in ROM, but also obtain detailed effects of uncertain parameters and their interactions on the system performance. The developed method is applied to a case study of a reservoir operation system, where the local authority is in charge of allocating relative scant water to the downstream municipality. The results obtained can help the local authority identify desired water release policies under uncertain system conditions. Besides, the results simultaneously indicate that significant factors and their interactions can be identified in ROM. Moreover, the results can be further analyzed for generating optimal parameter inputs to obtain maximized system benefits.