A game theoretic approach for interbasin water resources allocation considering the water quality issues

In this paper, a new game theoretic methodology is developed for interbasin water transfer management with regard to economic, equity, and environmental criteria. The main objective is to supply the competing users in a fair way, while the efficiency and environmental sustainability criteria are satisfied and the utilities of water users are incorporated. Firstly, an optimization model is developed to proportionally allocate water to the competing users in water donor and receiving basins based on their water demands. Secondly, for different coalitions of water users, the water shares of the coalitions are determined using an optimization model with economic objectives regarding the physical and environmental constraints of the system. In order to satisfy water-quality requirements, the impacts of decreasing the instream flow in donor basin are estimated using a water-quality simulation model, and the required treatment levels for effluents discharged into the river, downstream of the water transfer point are determined. Finally, to achieve equity and to provide sufficient incentives for water users to participate in the cooperation, some cooperative game theoretic approaches are utilized for reallocation of net benefits to water users. This model is applied to a large-scale interbasin water allocation problem including two different basins struggling with water scarcity in Iran. The results show that this model can be utilized as an effective tool for optimal interbasin water allocation management involving stakeholders with conflicting objectives subject to physical and environmental constraints.     

A fuzzy multi-stakeholder multi-criteria methodology for water allocation and reuse in metropolitan areas

In this paper, a fuzzy decision making methodology is proposed to find a socially optimal scenario for allocating effluent of wastewater treatment plants and urban and suburban runoffs to agricultural regions and recharging aquifers. The presented methodology named modified fuzzy social choice (MFSC) considers multi-stakeholder multi-criteria problems under uncertainties inherent in a decision making process utilizing a fuzzy ranking method and the fuzzy social choice (FSC) theory. A set of water and wastewater allocation scenarios are proposed for water quantity and quality management of the study area, while six main stakeholders with conflicting utilities and different negotiation powers are involved. The proposed methodology is applied to Tehran metropolitan area, the capital city of Iran with the population of about 8 million people, to examine its applicability and effectiveness. The results shows that using fuzzy multi-stakeholder multi-criteria decision making method considering equal and different negotiation powers can lead to different outcomes. Based on the results, the MFSC method, which considers a number of decision makers having different negotiation powers, degrees of importance of decision making criteria, and some important uncertainties, performs more promising in real water resources management problems.     

A stochastic conflict resolution model for trading pollutant discharge permits in river systems

This paper presents an efficient methodology for developing pollutant discharge permit trading in river systems considering the conflict of interests of involving decision-makers and the stakeholders. In this methodology, a trade-off curve between objectives is developed using a powerful and recently developed multi-objective genetic algorithm technique known as the Nondominated Sorting Genetic Algorithm-II (NSGA-II). The best non-dominated solution on the trade-off curve is defined using the Young conflict resolution theory, which considers the utility functions of decision makers and stakeholders of the system. These utility functions are related to the total treatment cost and a fuzzy risk of violating the water quality standards. The fuzzy risk is evaluated using the Monte Carlo analysis. Finally, an optimization model provides the trading discharge permit policies. The practical utility of the proposed methodology in decision-making is illustrated through a realistic example of the Zarjub River in the northern part of Iran.     

Critical Sampling Points Methodology: Case Studies of Geographically Diverse Watersheds

Only with a properly designed water quality monitoring network can data be collected that can lead to accurate information extraction. One of the main components of water quality monitoring network design is the allocation of sampling locations. For this purpose, a design methodology, called critical sampling points (CSP), has been developed for the determination of the critical sampling locations in small, rural watersheds with regard to total phosphorus (TP) load pollution. It considers hydrologic, topographic, soil, vegetative, and land use factors. The objective of the monitoring network design in this methodology is to identify the stream locations which receive the greatest TP loads from the upstream portions of a watershed. The CSP methodology has been translated into a model, called water quality monitoring station analysis (WQMSA), which integrates a geographic information system (GIS) for the handling of the spatial aspect of the data, a hydrologic/water quality simulation model for TP load estimation, and fuzzy logic for improved input data representation. In addition, the methodology was purposely designed to be useful in diverse rural watersheds, independent of geographic location. Three watershed case studies in Pennsylvania, Amazonian Ecuador, and central Chile were examined. Each case study offered a different degree of data availability. It was demonstrated that the developed methodology could be successfully used in all three case studies. The case studies suggest that the CSP methodology, in form of the WQMSA model, has potential in applications world-wide.     

Water and waste load allocation in rivers with emphasis on agricultural return flows: application of fractional factorial analysis

In this paper, a new methodology is developed to handle parameter and input uncertainties in water and waste load allocation (WWLA) in rivers by using factorial interval optimization and the Soil, Water, Atmosphere, and Plant (SWAP) simulation model. A fractional factorial analysis is utilized to provide detailed effects of uncertain parameters and their interaction on the optimization model outputs. The number of required optimizations in a fractional factorial analysis can be much less than a complete sensitivity analysis. The most important uncertain inputs and parameters can be also selected using a fractional factorial analysis. The uncertainty of the selected inputs and parameters should be incorporated real time water and waste load allocation. The proposed methodology utilizes the SWAP simulation model to estimate the quantity and quality of each agricultural return flow based on the allocated water quantity and quality. In order to control the pollution loads of agricultural dischargers, it is assumed that a part of their return flows can be diverted to evaporation ponds. Results of applying the methodology to the Dez River system in the southwestern part of Iran show its effectiveness and applicability for simultaneous water and waste load allocation in rivers. It is shown that in our case study, the number of required optimizations in the fractional factorial analysis can be reduced from 64 to 16. Analysis of the interactive effects of uncertainties indicates that in a low flow condition, the upstream water quality would have a significant effect on the total benefit of the system.     

Application of cooperative and non-cooperative games in large-scale water quantity and quality management: a case study

In this paper, two cooperative and non-cooperative methodologies are developed for a large-scale water allocation problem in Southern Iran. The water shares of the water users and their net benefits are determined using optimization models having economic objectives with respect to the physical and environmental constraints of the system. The results of the two methodologies are compared based on the total obtained economic benefit, and the role of cooperation in utilizing a shared water resource is demonstrated. In both cases, the water quality in rivers satisfies the standards. Comparing the results of the two mentioned approaches shows the importance of acting cooperatively to achieve maximum revenue in utilizing a surface water resource while the river water quantity and quality issues are addressed.     

Optimal redesign of groundwater quality monitoring networks: a case study

Assessment and redesign of water quality monitoring networks is an important task in water quality management. This paper presents a new methodology for optimal redesign of groundwater quality monitoring networks. The measure of transinformation in discrete entropy theory and the transinformation–distance (T–D) curves are used to quantify the efficiency of sampling locations and sampling frequencies in a monitoring network. The existing uncertainties in the T–D curves are taken in to account using the fuzzy set theory. The C-means clustering method is also used to classify the study area to some homogenous zones. The fuzzy T–D curve of the zones is then used in a multi-objective hybrid genetic algorithm-based optimization model. The proposed methodology is utilized for optimal redesign of monitoring network of the Tehran aquifer in the Tehran metropolitan area, Iran.     

Use of a GIS-based hybrid artificial neural network to prioritize the order of pipe replacement in a water distribution network

A methodology based on the integration of a seismic-based artificial neural network (ANN) model and a geographic information system (GIS) to assess water leakage and to prioritize pipeline replacement is developed in this work. Qualified pipeline break-event data derived from the Taiwan Water Corporation Pipeline Leakage Repair Management System were analyzed. “Pipe diameter,” “pipe material,” and “the number of magnitude-3^?+? earthquakes” were employed as the input factors of ANN, while “the number of monthly breaks” was used for the prediction output. This study is the first attempt to manipulate earthquake data in the break-event ANN prediction model. Spatial distribution of the pipeline break-event data was analyzed and visualized by GIS. Through this, the users can swiftly figure out the hotspots of the leakage areas. A northeastern township in Taiwan, frequently affected by earthquakes, is chosen as the case study. Compared to the traditional processes for determining the priorities of pipeline replacement, the methodology developed is more effective and efficient. Likewise, the methodology can overcome the difficulty of prioritizing pipeline replacement even in situations where the break-event records are unavailable.     

Spatial based compromise programming for multiple criteria decision making in land use planning

Today, competing land use is continuing to occur in many developed regions. In the Agricultural Development Zone of Western Sydney Region, which is characterised by complex landscape patterns, land use competition is widespread. From a land use planning perspective, identification of suitable locations for a given type of land use is necessary for decision makers to formulate land use alternatives in different locations, based on existing land potential and constraints. For such a region, use of a simple method that implements a categorical system and considers only inherent land characteristics in the analysis is often inadequate to arrive at an optimal spatial decision. The primary aim of this paper is to develop spatial modelling procedures for agricultural land suitability analysis using compromise programming (CoPr) and fuzzy set approach within a geographical information systems (GIS) environment. Five main sets of spatial data for use as decision criteria were developed by using fuzzy set methodology: a land suitability index (LSI) for maximising the land productivity objective; an erosion tolerance index (ETI) for minimising the erosion risk objective; a runoff curve number (CN) for maximising the water discharge regulation objective; an accessibility (RP) measure for maximising the land accessibility objective; and the proximity to water body (WP) for minimising the water pollution objective. An L _p -metric was used in the analysis utilising different strategies with representative indices ranging from a situation where full tradeoff among criteria occurs to a noncompensatory condition. Different weighting combinations were also applied, and decision analysis was carried out by using values ranging from 0 to 1.0, where 1.0 is considered as an ideal point. The CoPr model demonstrated in this paper yielded a promising result, as several different techniques of sensitivity analysis show reasonably good results. Likewise, an overlay of that result with the present land use/land cover indicates a good corresponding spatial matching between existing land use (orchard and cultivated land), and the cells (land parcels) classified as the best in CoPr. The results are amenable to various map display techniques, either using continuous values or by defining different cut off points in the data space within a raster GIS environment.     

Fuzzy Logic Model to Estimate Seasonal Pseudo Steady State Chlorophyll-A Concentrations in Reservoirs

A fuzzy logic model is developed to estimate pseudo steady state chlorophyll-a concentrations in a very large and deep dam reservoir, namely Keban Dam Reservoir, which is also highly spatial and temporal variable. The estimation power of the developed fuzzy logic model was tested by comparing its performance with that from the classical multiple regression model. The data include chlorophyll-a concentrations in Keban lake as a response variable, as well as several water quality variables such as PO₄ phosphorus, NO₃ nitrogen, alkalinity, suspended solids concentration, pH, water temperature, electrical conductivity, dissolved oxygen concentration and Secchi depth as independent environmental variables. Because of the complex nature of the studied water body, as well as non-significant functional relationships among the water quality variables to the chlorophyll-a concentration, an initial analysis is conducted to select the most important variables that can be used in estimating the chlorophyll-a concentrations within the studied water body. Following the outcomes from this initial analysis, the fuzzy logic model is developed to estimate the chlorophyll-a concentrations and the advantages of this new model is demonstrated in model fitting over the traditional multiple regression method.     

A simplified model for reservoir operation considering the water quality issues: Application of the Young conflict resolution theory

In this study, an algorithm combining a multi-objective genetic algorithm (GA)-based optimization model and a water quality simulation model is developed for determining a trade-off curve between objectives related to the allocated water quantity and quality. To reduce the run-time of the GA-based optimization model, the main problem is decomposed to long-term and annual optimization models. The reliability of water supply is considered to be the objective function in the long-term stochastic optimization model, but the objective functions of the annual models are related to both the allocated water quantity and quality. The operating policies obtained using this long-term model provide the time series of the optimum reservoir water storages at the beginning and the end of each water year. In the next step, these optimal reservoir storage values are considered as constraints for water storage in the annual reservoir operation optimization models. The epsilon-constraint method is then used to develop a trade-off curve between the reliability of water supply and the average allocated water quality. The Young conflict resolution theory, which incorporates the existing conflicts among decision-makers and stakeholders, is used for selecting the best solution on the trade-off curve. The monthly reservoir operating rules are then calculated using an Adaptive Neuro-Fuzzy Inference System, which is trained using the optimal operating policies. The proposed model is applied to the 15-Khordad Reservoir in the central part of Iran. The results show that this simplified procedure does not reduce the accuracy of the reservoir operating policies and it can effectively reduce the computational burden of the previously developed models.     

Wasteload Allocation Using Wastewater Treatment and Flow Augmentation

A Wasteload allocation model, named Cost-Flow-Augmentation Model involving wastewater treatment and flow augmentation as a method of pollution abatement has been developed. The cost functions for wastewater treatment were developed as power functions of biochemical oxygen demand (BOD) removal using the regression module of the SPSS10 software. The cost function for flow augmentation was also developed using a regression between cost of dam/barrage and corresponding flow released from upstream reservoir for downstream water quality improvement. The response of wasteloads and flow augmentation on the water quality was quantified in terms of transfer coefficient calculated using the QUAL2E water quality simulation model. The performance of these models is demonstrated on the 22-km-long Delhi stretch of river Yamuna, India. Optimal solutions of the formulated models were obtained using the Web-based interactive non-differentiable interactive multiobjective bundle-based optimization system software. The optimal solutions obtained reveal that flow augmentation is not an economically feasible pollution abatement option for the Delhi stretch of river Yamuna.     

Simulating Nitrate Leaching Profiles in a Highly Permeable Vadose Zone

An approach is developed to simulate leaching of a dissolved chemical constituent in the vadose zone of an aquifer. Specifically, nitrate loading at the water table for different water table depths, for a range of aquifer permeability values, and for different cases of heterogeneity of the aquifer, are considered. Models from the literature are first used to derive soil–water characteristic curves (water retention and hydraulic conductivity) from a grain size distribution curve for unsaturated conditions. Given infiltration from the surface, the initial conditions for the chemical concentration, and the water content profile, leaching of the chemical in the vadose zone is simulated as a function of both time and depth. The methodology is illustrated for a permeable aquifer. Simulations are undertaken using a finite element code for saturated and unsaturated flow. Different scenarios are simulated depending on the heterogeneity of the aquifer and the depth of the water table. Modeling results show that in the example case studied, nitrate concentration loading at the water table does not depend strongly on the position of the water table, but rather on the material properties of the aquifer. The contribution of this endeavor resides in the methodology which allows a prediction of nitrate leaching using only the grain size property of the aquifer. It allows practitioners to obtain a first assessment of leaching with limited data.     

Comprehensive River Water Quality Management by Simulation and Optimization Models

In this paper, the performance of water quality modeling is investigated in the analysis of the natural assimilative capacity (NAC) of a river system. The new data available, along with the appropriate integrated model, allow for the analysis of the NAC of the entire river. The integrated model developed here emphasized the implementation of the QUAL2E simulation model and the appropriate allocation of waste loads (optimization model) in a subtropical area. Simulations are calibrated and validated according to the data from the Water Quality and Flow Rate Monitoring Project using the QUAL2E model. On the basis of the optimal allocation model, the results of the NAC and allowable pollution loading in the Putzu River basin are discussed. The study provides a framework of the integrated model that can be used as a guideline to determine the NAC of subtropical rivers.     

改进的模糊综合评价法在太湖水质类别判定中的应用

水质判别是一个多参数多级别的模糊概念,基础的模糊综合评价法存在局限性,对基础模糊数学法中隶属度函数及最大隶属度原则进行改进,建立一种改进的模糊综合评价法。以太湖流域水质判别为实例验证了此方法比传统的方法更有效,且适合在太湖流域应用。     

A probabilistic water quality index for river water quality assessment: a case study

Available water quality indices have some limitations such as incorporating a limited number of water quality variables and providing deterministic outputs. This paper presents a hybrid probabilistic water quality index by utilizing fuzzy inference systems (FIS), Bayesian networks (BNs), and probabilistic neural networks (PNNs). The outputs of two traditional water quality indices, namely the indices proposed by the National Sanitation Foundation and the Canadian Council of Ministers of the Environment, are selected as inputs of the FIS. The FIS is trained based on the opinions of several water quality experts. Then the trained FIS is used in a Monte Carlo analysis to provide the required input-output data for training both the BN and PNN. The trained BN and PNN can be used for probabilistic water quality assessment using water quality monitoring data. The efficiency and applicability of the proposed methodology is evaluated using water quality data obtained from water quality monitoring system of the Jajrood River in Iran.     

Uncertainty based optimal monitoring network design for a chlorinated hydrocarbon contaminated site

An application of a newly developed optimal monitoring network for the delineation of contaminants in groundwater is demonstrated in this study. Designing a monitoring network in an optimal manner helps to delineate the contaminant plume with a minimum number of monitoring wells at optimal locations at a contaminated site. The basic principle used in this study is that the wells are installed where the measurement uncertainties are minimum at the potential monitoring locations. The development of the optimal monitoring network is based on the utilization of contaminant concentration data from an existing initial arbitrary monitoring network. The concentrations at the locations that were not sampled in the study area are estimated using geostatistical tools. The uncertainty in estimating the contaminant concentrations at such locations is used as design criteria for the optimal monitoring network. The uncertainty in the study area was quantified by using the concentration estimation variances at all the potential monitoring locations. The objective function for the monitoring network design minimizes the spatial concentration estimation variances at all potential monitoring well locations where a monitoring well is not to be installed as per the design criteria. In the proposed methodology, the optimal monitoring network is designed for the current management period and the contaminant concentration data estimated at the potential observation locations are then used as the input to the network design model. The optimal monitoring network is designed for the consideration of two different cases by assuming different initial arbitrary existing data. Three different scenarios depending on the limit of the maximum number of monitoring wells that can be allowed at any period are considered for each case. In order to estimate the efficiency of the developed optimal monitoring networks, mass estimation errors are compared for all the three different scenarios of the two different cases. The developed methodology is useful in coming up with an optimal number of monitoring wells within the budgetary limitations. The methodology also addresses the issue of redundancy, as it refines the existing monitoring network without losing much information of the network. The concept of uncertainty-based network design model is useful in various stages of a potentially contaminated site management such as delineation of contaminant plume and long-term monitoring of the remediation process.     

Interval-parameter Fuzzy-stochastic Semi-infinite Mixed-integer Linear Programming for Waste Management under Uncertainty

An interval-parameter fuzzy-stochastic semi-infinite mixed-integer linear programming (IFSSIP) method is developed for waste management under uncertainties. The IFSSIP method integrates the fuzzy programming, chance-constrained programming, integer programming and interval semi-infinite programming within a general optimization framework. The model is applied to a waste management system with three disposal facilities, three municipalities, and three periods. Compared with the previous methods, IFSSIP have two major advantages. One is that it can help generate solutions for the stable ranges of the decision variables and objective function value under fuzzy satisfaction degree and different levels of probability of violating constraints, which are informative and flexible for solution users to interpret/justify. The other is that IFSSIP can not only handle uncertainties through constructing fuzzy and random parameter, but also reflect dynamic features of the system conditions through interval function of time over the planning horizon. By comparing IFSSIP with interval-parameter mixed-integer linear semi-infinite programming and parametric programming, the IFSSIP method is more reasonable than others.     

Design of River Water Quality Monitoring Networks: A Case Study

Karoon River, from Gotvand Dam to Persian Gulf with more than 450 km in length and an annual discharge of 11,891 million cubic meters, is the largest river in Iran. Increasing water withdrawal from and wastewater discharge to the river has endangered the aquatic life of this important ecosystem. Furthermore, the drinking and in-stream water quality standards have been violated in many instances. In this paper, a river water quality monitoring network is designed, including determination of sampling frequencies as well as location of water quality monitoring stations. In this regard, two models are developed. The first model is a Genetic Algorithm-based optimization model and the second one is a combination of Kriging method and Analytical Hierarchy Process. The temporal variation of the concentration of water quality variables along Karoon and Dez Rivers are evaluated and the main water quality indicators are selected. Then, thirty five stations are selected and the application of Entropy Theory in calculating the sampling frequency is demonstrated. The results show the significant value of the proposed methodology in the design of monitoring network.     

Inexact Fuzzy-Stochastic Programming for Water Resources Management Under Multiple Uncertainties

In this study, an interval-parameter fuzzy-stochastic two-stage programming (IFSTP) approach is developed for irrigation planning within an agriculture system under multiple uncertainties. A concept of the distribution with fuzzy-interval probability (DFIP) is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets, and probability distributions. IFSTP integrates the interval programming, two-stage stochastic programming, and fuzzy-stochastic programming within a general optimization framework. IFSTP incorporates the pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised amounts are not delivered. IFSTP is applied to an irrigation planning in a water resources management system. Solutions from IFSTP provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable solutions are generated for objective function values and decision variables; thus, a number of decision alternatives can be generated under different levels of stream flows.