An Inexact Two-stage Fuzzy-stochastic Programming Model for Water Resources Management

An inexact two-stage fuzzy-stochastic programming (ITFSP) method is developed for water resources management under uncertainty. Fuzzy sets theory is introduced to represent various punishment policies under different water availability conditions. As an extension of conventional two-stage stochastic programming (TSP) method, two special characteristics of the proposed approach make it unique compared with existing approaches. One is it could handle flexible penalty rates, which are much reasonable for both of the authorities and users, and have seldom been considered in the TSP framework. The other is uncertain information expressed as discrete intervals and probability distribution functions can be effectively reflected in the optimization processes and solutions. After formulating the model, a hypothetical case is employed for demonstrating its applicability under two scenarios, where the inflow is divided into four and eight intervals, respectively. The results indicate that reasonable solutions have been obtained. They provide desired allocation patterns with maximized system benefit under two feasibility levels. The solutions present as stable intervals with different risk levels in violating the water demands, and can be used for generating decision alternatives. Comparisons of the solution from the ITFSP with that from the ITSP (inexact two-stage stochastic programming) and TSP approach are also undertaken. It shows that the ITFSP could produce more system benefit than existing methods and deal with flexible penalty policies for better water management and utilization.     

IFTSQP: An Inexact Optimization Model for Water Resources Management under Uncertainty

Abstract

An interval-fuzzy two-stage quadratic programming (IFTSQP) method is developed for water resources management under uncertainty. The methodincorporates techniques of interval-parameter programming, two-stage stochastic programming, and fuzzy quadratic programming within a general optimization framework to tackle multiple uncertainties presented as intervals, fuzzy sets and probability distributions. In the model formulation, multiple control variables are adopted to handle independent uncertainties in the model's right-hand sides; fuzzy quadratic terms are used in the objective function to minimize the variation in satisfaction degrees among the constraints. Moreover, the method can support the analysis of policy scenarios that are associated with economic penalties when the promised targets are violated. The developed method is then applied to a case study of water resources management planning. The results indicate that reasonable solutions have been obtained. They can help provide bases for identifying desired water-allocation plans with a maximized system benefit and a minimized constraint-violation risk.     

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.     

Interval-parameter Two-stage Stochastic Nonlinear Programming for Water Resources Management under Uncertainty

Over the past decades, controversial and conflict-laden water allocation issues among competing interests have raised increasing concerns. In this research, an interval-parameter two-stage stochastic nonlinear programming (ITNP) method is developed for supporting decisions of water-resources allocation within a multi-reservoir system. The ITNP can handle uncertainties expressed as both probability distributions and discrete intervals. It can also be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised allocation targets are violated. Moreover, it can deal with nonlinearities in the objective function such that the economies-of-scale effects in the stochastic program can be quantified. The proposed method is applied to a case study of water-resources allocation within a multi-user, multi-region and multi-reservoir context for demonstrating its applicability. The results indicate that reasonable solutions have been generated, which present as combined interval and distributional information. They provide desired water allocation plans with a maximized economic benefit and a minimized system-disruption risk. The results also demonstrate that a proper policy for water allocation can help not only mitigate the penalty due to insufficient supply but also reduce the waste of water resources.     

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.     

Water Resources Management and Planning under Uncertainty: an Inexact Multistage Joint-Probabilistic Programming Method

In this study, an inexact multistage joint-probabilistic programming (IMJP) method is developed for tackling uncertainties presented as interval values and joint probabilities. IMJP improves upon the existing multistage programming and inexact optimization approaches, which can help examine the risk of violating joint-probabilistic constraints. Moreover, it can facilitate analyses of policy scenarios that are associated with economic penalties when the promised targets are violated within a multistage context. The developed method is applied to a case study of water-resources management within a multi-stream, multi-reservoir and multi-period context, where mixed integer linear programming (MILP) technique is introduced into the IMJP framework to facilitate dynamic analysis for decisions of surplus-flow diversion. The results indicate that reasonable solutions for continuous and binary variables have been generated. They can be used to help water resources managers to identify desired system designs against water shortage and for flood control, and to determine which of these designs can most efficiently accomplish optimizing the system objective under uncertainty.     

Optimal Land-Use Management for Surface Source Water Protection Under Uncertainty: A Case Study of Songhuaba Watershed (Southwestern China)

The water supply to Chinese cities is increasingly degrading from pollution due to watershed activities. Consequently, water source protection requires urgent action using optimal land-use management efforts. An inexact linear programming model for optimal land-use management of surface water source area was developed. The model was proposed to balance the economic benefits of land-use development and water source protection. The maximum net economic benefit (NEB) was chosen as the objective of land-use management. The total environmental capacity (TEC) of rivers and the minimum water supply (MWS) were considered key constraints. Other constraints included forest coverage, government requirements concerning the proportions of various land-use types, soil loss, slope lands, and technical constraints. A case study was conducted for the Songhuaba Watershed, a reservoir supplying water to Kunming City, the third largest city in southwestern China. A 15-year (2006 to 2020) optimal model for land-use management was developed to better protect this water source and to gain maximum benefits from development. Ten constraints were involved in the optimal model, and results indicated that NEB ranged between 893 and 1,459 million US$. The proposed model will allow local authorities to better understand and address complex land-use systems and to develop optimal land-use management strategies for balancing source water protection and local economic development.     

平面二维动态水质数学模型

本文根据工业环境影响评价的需要，提出了一个平面二维动态水质数学模型，该水质数学模型以ＮＨ３－Ｎ，ＤＯ，ＣＯＤ为评价参数，考虑了大气复氧，ＣＢＯＤ和ＮＢＯＤ的降解和沉淀，底泥耗氧，温度等影响因素。针对具体评价河流，本文进行了模型参数的选取及灵敏度分析，并对该模型进行了验证与应用，结果表明该水质模型具有较高的计算精度和较强的预测能力，为工程环境影响评价提供了一个有力的工具。     

An Inexact Two-Stage Water Resources Allocation Model for Sustainable Development and Management Under Uncertainty

In this study, an inexact two-stage water resources allocation (ITWR) model is put forward for supporting sustainable development and management of water resources in Sanjiang Plain, China, which is in such a situation, with multi-water source, multi-water supply subarea, multi-water user and multi-planning goal. The costs of net system, water supply and recourse are analyzed. The developed ITWR model, which shows a strong ability in tacking with various uncertain factors in probability distributions and discrete interval numbers, mixes the techniques of interval-parameter programming (IPP) and two-stage stochastic programming (TSP) within a general optimization framework. And it also has formed an effective link in such a conflict between the policy scenarios and the associated various levels of economic penalties, when the pre-allocation targets of water resources are violated. Based on this model, a series of scenarios under different levels of pre-allocation water is done and different degrees of water surplus and shortage are obtained correspondingly. The results indicate that the reasonable distribution plans with maximum system benefit and minimum system-failure risk have been generated. And these results are valuable for saving water resources to realize its sustainable development and mitigating the penalty to gain economic benefits maximum, and thus some desired results are provided for decision makers in tackling with a complex and uncertain water-resource system.     

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.     

瀑河渠道倒虹吸工程质量管理

为确保南水北调工程质量，必须建立健全质量保证体系，建立各项规章制度，落实质量管理责任，强化质量意识，搞好质量培训，提高质量管理人员的素质，严格工程施工过程控制，把工作做深、做细、做实，加强检查验收，做好事后控制。     

淮河流域水质管理模型

淮河流域水质管理模型作为分析研究淮河流域水污染规律的工具 ,以淮河入洪泽湖河口以上流域为研究区域。在深入分析研究区域内水文气象、自然地理、河道和水流特性以及水污染特点的基础上 ,利用Mike 11,MIKEBASIN和ArcView软件研制和开发水质管理模型 ,为有效实施水污染防治和水资源管理提供依据。简要介绍模型的结构 ,主要参数的确定 ,模型的结果和模型的应用情况     

Successive Approximation Linear Quadratic Regulator for Estuarine Management Problem

A successive approximation linear quadratic regulator (SALQR)method is applied to solve estuarine management problems to determine the optimal amount of freshwater inflows into baysand estuaries to maximize fishery harvests. Fishery harvests areexpressed in regression equations as functions of freshwaterinflows. The optimization problem is posed as a discrete-timeoptimal control problem in which salinity represents the statevariable and freshwater inflow represents the control variable. A two-dimensional hydrodynamic-salinity transport model, HYD-SAL,is used as the transition to simulate the flow circulation andtemporal and spatial salinity pattern in an estuary system. Thebound constraints for the control and state variables areincorporated into the objective function using a penalty functionmethod to convert the problem into an unconstrained formulation. The SALQR method is applied to the Lavaca-Tres Palacios Estuaryin Texas and the results are compared with those of usingregression equations as the transition equations.     

基于遗传程序的南水北调中线节制闸过闸流量模型研究*

南水北调中线线路长,沿线分水口门多,且无调蓄水库,输水技术难度大。输水调度通过调整总干渠沿线各节制闸过闸流量,实现用水户所需的供水目标。过闸流量计算是中线水量调度模型的重要组成,目前通过传统水力学经验公式进行计算,在输水运行过程中,需不断根据实测水情数据,定期人工修正公式中参数,并更改程序源代码中的参数,灵活性差。本文通过南水北调中线输水调度的实践,建立了基于遗传程序结合水力学方法的过闸流量模型,根据实测流量计算流量系数,并利用遗传程序自动拟合节制闸前、后水位、闸门开度与流量系数的非线性关系,进而实现过闸流量计算。经在南北调中线节制闸的试用表明,该模型具有很强的自适应能力,灵活性强,拟合精度高,而且较好地避免直接拟合流量时泛化能力较弱的不足,具有较强的实际应用和推广价值。     

确定排污水域的优化计算模型研究

如何根据接受水体如湖泊、河流、海岸水域等的水环境承载能力或水质保护目标区域（或敏感区域）的水质标准,选择污水源排放位置区域使得保护目标区域的水质标准得以维护,是一个非常值得研究的重要问题。该问题利用常规的水动力学模型加上污染物输移模拟技术通过试－错方法求解,存在一是耗时、二是受主观影响,三是只能对少数个排放点给出有限的解等缺点,有鉴于此,专门针对区域规则中污水排放位置优化控制问题,应用逆问题求解理论,提出了一种显示的共轭水质模型,该模型可应用于确定一、二维自由面水流系统中可行的污水排放位置或区域,以维持规则目标区域所期望的水质标准。     

Hydrodynamic Model of the Lower Hudson River Estuarine System and its Application for Water Quality Management

In this paper a hydrodynamic model and associated post-processing tools for the Lower Hudson River (LHR) are presented. The model computes the two-dimensional (2D), depth-averaged Eulerian time-dependent velocity field in response to various external signals. The paper documents the mathematical background of the model, describes modeling logistics and provides the comparison of model results with observed data. As an example of the potential application, the scenario of managing sewage releases from two New York City water pollution treatment plants was investigated using this numerical model. The study was undertaken as part of research on the chaotic nature of the LHR estuarine system and pollutant dispersion characteristics.     

Water Quality Programs In Developing Countries

Abstract

In many developing countries water quality has become the principal limiting factor to water availability. Estimates of future levels of water pollution in many parts of the world under “business as usual” scenarios will be catastrophic for public health, the environment, and national economies in many countries that have limited resources to deal with a contaminated resource. The reality in many developing countries is that political and institutional instability, combined with financial restraint, and poor domestic scientific capacity, means that “western” approaches to water quality management are often inappropriate and unsustainable. Traditional models of technical assistance and technology transfer, including foreign aid and international loans for water quality management, often leave little real change in domestic capacity while generating substantial cash flow for the foreign company. Without a major change in how water quality is managed, including adoption of new paradigms of policy effectiveness, institutional and technical modernization, new methods of knowledge and technology transfer, and innovative investment, the situation can only become more and more serious until the final collapse of major freshwater and coastal ecosystems, and associated economic and public health implications. This paper addresses these various technical, policy, institutional, and financing issues and proposes actions which can lead to sustainability and self-reliance     

Product Policy as an Instrument for Water Quality Management

A main reason for the persistence of current water pollution lies in the diffuse character of many of its sources. For a large part such diffuse pollution is related to the production, use and waste of various kinds of products. For the reduction of this pollution, a product-oriented policy strategy, based on interaction with stakeholders could be more successful than the traditional measures of direct regulation that were devised for point source reduction. In this article we identify different types of product policy, and explore the potential benefits and costs for water quality management. The methods that can be used in a product policy approach are illustrated with some examples. Although the specific advantages for water quality management have not been quantified yet, governments increasingly recognise the potential positive effects. In this context, the European Water Framework Directive, in stimulating product policy by enhancing public and stakeholders participation, can be considered to be part of a general development towards interactive water management.     

澳大利亚雪山工程水质安全与运营管理经验及思考

它山之石可以攻玉,成功的经验值得借鉴。我国的南水北调工程与澳大利亚雪山工程同是跨流域、跨省(州)界的特大型调水工程,无论在建设阶段还是在运营管理时期,均应有值得借鉴的成功经验和值得吸取的失败教训。在介绍澳大利亚雪山工程水质安全与运营管理等方面成功经验的基础上,对我国南水北调工程如何开展水源与调水水质安全和运营管理工作做了一点思考,以期能对南水北调工程的建设与运营管理有所裨益。     

大型潮汐河网水质模型的求解方法及其应用

用有限体积法对描述河流污染物运动规律的对流扩散方程积分，提出了一种处理潮汐河网汉道水质模拟的新方法；同时针对潮汐河网水质离散方程的特点建立了一种水质模型分级求解程式，实际应用表明：综合利用本文提出的汊道模拟方法及模型分级求解对于大型潮汐河网水质模拟不仅可以提高其模拟精度，而且具有极快的求解速度。