An inexact optimization approach for river water-quality management

A previously developed fuzzy waste load allocation model (FWLAM) for a river system is extended to address uncertainty involved in fixing the membership functions for the fuzzy goals of the pollution control agency (PCA) and the dischargers using the concept of grey systems. The model provides flexibility for the PCA and the dischargers to specify their goals independently, as the parameters for membership functions are considered as interval grey numbers instead of deterministic real numbers. An inexact or a grey fuzzy optimization model is developed in a multiobjective framework, to maximize the width of the interval valued fractional removal levels for providing latitude in decision-making and to minimize the width of the goal fulfillment level for reducing the system uncertainty. The concept of an acceptability index for order relation between two partially or fully overlapping intervals is used to get a deterministic equivalent of the grey fuzzy optimization model developed. The improvement of the optimal solutions over a previously developed grey fuzzy waste load allocation model (GFWLAM) is shown through an application to a hypothetical river system. The fuzzy multiobjective optimization and fuzzy goal programming techniques are used to solve the deterministic equivalent of the GFWLAM.     

A COMPLEMENTARY TOOL TO WATER QUALITY INDEX: FUZZY CLUSTERING ANALYSIS1

ABSTRACT: A general methodology for fuzzy clustering analysis is developed and illustrated with a case study of water quality evaluation for Dianshan Lake, Shanghai, China. Fuzzy clustering analysis may be used whenever a composite classification of water quality incorporates multiple parameters. In such cases, the technique may be used as a complement or an alternative to comprehensive assessment. In fuzzy clustering analysis, the classification is determined by a fuzzy relation. After a fuzzy similarity matrix has been established and the fuzzy relation stabilized, a dynamic clustering chart can be developed. Given a suitable threshold, the appropriate classification is worked out. The methodology is relatively simple, and the results can be interpreted to provide valuable information to support decision making and to aid water quality management.     

Irrigation Water Allocation Using an Inexact Two‐Stage Quadratic Programming with Fuzzy Input under Climate Change

Agricultural irrigation accounts for nearly 70% of the total water use around the world. Uncertainties and climate change together exacerbate the complexity of optimal allocation of water resources for irrigation. An interval‐fuzzy two‐stage stochastic quadratic programming model is developed for determining the plans for water allocation for irrigation with maximum benefits. The model is shown to be applicable when inputs are expressed as discrete, fuzzy or random. In order to reflect the effect of marginal utility on benefit and cost, the model can also deal with nonlinearities in the objective function. Results from applying the model to a case study in the middle reaches of the Heihe River basin, China, show schemes for water allocation for irrigation of different crops in every month of the crop growth period under various flow levels are effective for achieving high economic benefits. Different climate change scenarios are used to analyze the impact of changing water requirement and water availability on irrigation water allocation. The proposed model can aid the decision maker in formulating desired irrigation water management policies in the wake of uncertainties and changing environment.     

Multi‐Criteria Decision Support Systems for Flood Hazard Mitigation and Emergency Response in Urban Watersheds1

Abstract: Flood management problems are inherently complex, time‐bound and multi‐faceted, involving many decision makers (with conflicting priorities and dynamic preferences), high decision stakes, limited technical information (both in terms of quality and quantity), and difficult tradeoffs. Multi‐Criteria Decision Support Systems (MCDSS) can help to manage this complexity and decision load by combining value judgments and technical information in a structured decision framework. A brief overview of MCDSS is presented, an original MCDSS architecture is put forth, and future research directions are discussed, including extensions to Multi‐Criteria Spatial Decision Support Systems and group MCDSS (as flood management involves shared resources and broad constituencies). With application to the September 11‐12, 2000 Tokai floods in Japan, the proposed multi‐criteria decision support instruments enhance communication among stakeholders and improve emergency management resource allocation. In summary, by making the links among flood knowledge, assumptions and choices more explicit, MCDSS increases stakeholder satisfaction, saves lives, and reduces flood management costs, thereby increasing decision‐making effectiveness, efficiency and transparency.     

Landfill space consumption dynamics in the Lower Rio Grande Valley by grey integer programming-based games

The Lower Rio Grande Valley (LRGV) region in South Texas emerges as a warehouse and transportation center between Central America and the US with positive growth impacts due to the North American Free Trade Agreement (NAFTA). In 10 years time, a 39.8% population increase has resulted in a 25% boost in solid waste per capita disposal rate in the region. A landfill space shortage drives a need for landfill operators to understand their optimal management strategies in this highly-competitive market. Initially, a strategic plan for optimal solid waste pattern distribution minimizes net costs for cities. This is accomplished through a grey integer programming algorithm that encapsulates all uncertainty present in the solid waste system. Secondly, a series of grey integer submodels construct payoff matrices for a zero-sum two-person game. The ensuing game theoretic analysis is critical for evaluating optimal pricing strategies for tipping fees available to the most significant regional landfills (e.g. Browning-Ferris Industries (BFI) and City of Edinburg) as they compete over disposal contracts. The BFI landfill intrinsically benefits from its competitive pricing policy and central location to solid waste generators. The City of Edinburg landfill, on the other hand, wishes to secure its lucrative solid waste management revenue. It desires a gaming strategy backed by optimality that integrates ambiguity in solid waste generation, design capacity boundaries, and unitary shipping costs. Results show that a two-tiered analysis via grey integer programming-based games may pave the way for 'grey Nash equilibria' pricing tactics that will help the Edinburg landfill maintain its waste contracts.     

Violation analysis for solid waste management systems: an interval fuzzy programming approach

This paper introduces a violation analysis approach for the planning of regional solid waste management systems under uncertainty, based on an interval-parameter fuzzy integer programming (IPFIP) model. In this approach, several given levels of tolerable violation for system constraints are permitted. This is realized through a relaxation of the critical constraints using violation variables, such that the model's decision space can be expanded. Thus, solutions from the violation analysis will not necessarily satisfy all of the model's original constraints. Application of the developed methodology to the planning of a waste management system indicates that reasonable solutions can be generated through this approach. Considerable information regarding decisions of facility expansion and waste flow allocation within the waste management system were generated. The modeling results help to generate a number of decision alternatives under various system conditions, allowing for more in-depth analyses of tradeoffs between environmental and economic objectives as well as those between system optimality and reliability.     

Sustainable Water Resources Management in a Conflict Resolution Framework1

Abstract: A decision support system for sustainable water resources management in a water conflict resolution framework is developed to identify and evaluate a range of acceptable alternatives for the Geum River Basin in Korea and to facilitate strategies that will result in sustainable water resource management. Working with stakeholders in a “shared vision modeling” framework, sustainable management strategies are created to illustrate system tradeoffs as well as long‐term system planning. A multi‐criterion decision‐making (MCDM) approach using subjective scales is utilized to evaluate the complex water resource allocation and management tradeoffs between stakeholders and system objectives. The procedures used in this study include the development of a “shared vision model,” a simulated decision‐making support system (as a tool for sustainable water management strategies associated with water conflicts, management options, and planning criteria), and the application of MCDM techniques for evaluating alternatives provided by the model. The research results demonstrate the utility of the sustainable water resource management model in aid of MCDM techniques in facilitating flexibility during initial stages of alternative identification and evaluation in a basin suffering from severe water conflicts.     

An Interval-Parameter Waste-Load-Allocation Model for River Water Quality Management Under Uncertainty

A simulation-based interval quadratic waste load allocation (IQWLA) model was developed for supporting river water quality management. A multi-segment simulation model was developed to generate water-quality transformation matrices and vectors under steady-state river flow conditions. The established matrices and vectors were then used to establish the water-quality constraints that were included in a water quality management model. Uncertainties associated with water quality parameters, cost functions, and environmental guidelines were described as intervals. The cost functions of wastewater treatment units were expressed in quadratic forms. A water-quality planning problem in the Changsha section of Xiangjiang River in China was used as a study case to demonstrate applicability of the proposed method. The study results demonstrated that IQWLA model could effectively communicate the interval-format uncertainties into optimization process, and generate inexact solutions that contain a spectrum of potential wastewater treatment options. Decision alternatives can be generated by adjusting different combinations of the decision variables within their solution intervals. The results are valuable for supporting local decision makers in generating cost-effective water quality management strategies.     

A Water Allocation Decision‐Support Model and Tool for Predictions in Ungauged Basins in Northeast British Columbia,Canada

Pressures on water resources due to changing climate, increasing demands, and enhanced recognition of environmental flow needs result in the need for hydrology information to support informed water allocation decisions. However, the absence of hydrometric measurements and limited access to hydrology information in many areas impairs water allocation decision‐making. This paper describes a water balance‐based modeling approach and an innovative web‐based decision‐support hydrology tool developed to address this need. Using high‐resolution climate, vegetation, and watershed data, a simple gridded water balance model, adjusted to account for locational variability, was developed and calibrated against gauged watersheds, to model mean annual runoff. Mean monthly runoff was modeled empirically, using multivariate regression. The modeled annual runoff results are within 20% of the observed mean annual discharge for 78% of the calibration watersheds, with a mean absolute error of 16%. Modeled monthly runoff corresponds well to observed monthly runoff, with a median Nash–Sutcliffe statistic of 0.92 and a median Spearman rank correlation statistic of 0.98. Monthly and annual flow estimates produced from the model are incorporated into a map‐ and watershed‐based decision‐support system referred to as the Northeast Water Tool, to provide critical information to decision makers and others on natural water supply, existing allocations, and the needs of the environment.     

Structured Decision Making to Meet a National Water Quality Mandate

Water quality criteria are necessary to ensure protection of ecological and human health conditions, but compliance can require complex decisions. We use structured decision making to consider multiple stakeholder objectives in a water quality management process, with a case study in the Three Bays watershed on Cape Cod, Massachusetts. We set a goal to meet or exceed a nitrogen load reduction target for the watershed and four key objectives: minimizing economic costs of implementing management actions, minimizing the complexity of permitting management actions, maximizing stakeholder acceptability of the management actions, and maximizing the provision of ecosystem services (recreational opportunity, erosion and flood control, socio‐cultural amenity). We used multi‐objective optimization and sensitivity analysis to generate many possible solutions that implement different combinations of nitrogen‐removing management actions and reflect tradeoffs between the objectives. Results show technological advances in controlling household nitrogen sources could provide lower cost solutions and positive impacts to ecosystem services. Although this approach is demonstrated with Cape Cod data, the decision‐making process is not specific to any watershed and could be easily applied elsewhere.     

Interactive two-stage stochastic fuzzy programming for water resources management

In this study, an interactive two-stage stochastic fuzzy programming (ITSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact two-stage stochastic programming (ITSP) framework. ITSFP can not only tackle dual uncertainties presented as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints, but also permit in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. A management problem in terms of water resources allocation has been studied to illustrate applicability of the proposed approach. The results indicate that a set of solutions under different feasibility degrees has been generated for planning the water resources allocation. They can help the decision makers (DMs) to conduct in-depth analyses of tradeoffs between economic efficiency and constraint-violation risk, as well as enable them to identify, in an interactive way, a desired compromise between satisfaction degree of the goal and feasibility of the constraints (i.e., risk of constraint violation).     

SUBJECTIVE DECISION-MAKING FOR URBAN WATER RESOURCES DEVELOPMENT1

ABSTRACT: Bayesian decision theory provides a procedure for the use of subjective data in a decision-making situation related to urban water resources development. This procedure is effectual in pursuing a set of goals and in transforming individual or group indecisiveness into satisfactory decisions. This approach is highlighted due to its capability to incorporate seemingly unquantifiable, abstract factors into the decision-making process. It is realized that the soliciting of expert and general public opinion is indispensable in making choices for the welfare of the general public from alternative courses of action under uncertainty. The analysis presented here considers engineering alternatives, quality, quantity, cost and the intangible public response in an integrated effort for the selection of optimum strategies in urban water resources development.     

A Web‐Based Decision Support System for Assessing Regional Water‐Quality Conditions and Management Actions1

Booth, Nathaniel L., Eric J. Everman, I‐Lin Kuo, Lori Sprague, and Lorraine Murphy, 2011. A Web‐Based Decision Support System for Assessing Regional Water‐Quality Conditions and Management Actions. Journal of the American Water Resources Association (JAWRA) 47(5):1136‐1150. DOI: 10.1111/j.1752‐1688.2011.00573.x Abstract: The U.S. Geological Survey National Water Quality Assessment Program has completed a number of water‐quality prediction models for nitrogen and phosphorus for the conterminous United States as well as for regional areas of the nation. In addition to estimating water‐quality conditions at unmonitored streams, the calibrated SPAtially Referenced Regressions On Watershed attributes (SPARROW) models can be used to produce estimates of yield, flow‐weighted concentration, or load of constituents in water under various land‐use condition, change, or resource management scenarios. A web‐based decision support infrastructure has been developed to provide access to SPARROW simulation results on stream water‐quality conditions and to offer sophisticated scenario testing capabilities for research and water‐quality planning via a graphical user interface with familiar controls. The SPARROW decision support system (DSS) is delivered through a web browser over an Internet connection, making it widely accessible to the public in a format that allows users to easily display water‐quality conditions and to describe, test, and share modeled scenarios of future conditions. SPARROW models currently supported by the DSS are based on the modified digital versions of the 1:500,000‐scale River Reach File (RF1) and 1:100,000‐scale National Hydrography Dataset (medium‐resolution, NHDPlus) stream networks.     

WATER FOR ENERGY: AN APPROACH TO COMPREHENSIVE IMPACT ASSESSMENT1

ABSTRACT: The effects of energy development on the water resources of the Colorado River and Great Basin regions is expected to be substantial. Complex physical, economic and institutional interactions may be expected. Most research on these impacts appears single purpose, fragmented, uncoordinated, and often inaccessible to potential users - particularly those with responsibility for energy/water policy and program decisions. A comprehensive, integrative framework for assessing alternative water allocation decisions is outlined, taking a heuristic decision making model for evaluating impacts on maximization of gross (or net) regional product, and regional social welfare, and for assessing the region's contribution to national objectives. The suggested model provides a structure for application and integration of data of various kinds to a range of situations arising from possible impacts from energy proposals. The focus is on water and energy relationships but the model may provide a framework for comprehensive analysis of a variety of environmental actions and resulting system perturbations and effects.     

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max–min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga–Bhadra river system in India.     

Watershed-based point sources permitting strategy and dynamic permit-trading analysis

Permit-trading policy in a total maximum daily load (TMDL) program may provide an additional avenue to produce environmental benefit, which closely approximates what would be achieved through a command and control approach, with relatively lower costs. One of the important considerations that might affect the effective trading mechanism is to determine the dynamic transaction prices and trading ratios in response to seasonal changes of assimilative capacity in the river. Advanced studies associated with multi-temporal spatially varied trading ratios among point sources to manage water pollution hold considerable potential for industries and policy makers alike. This paper aims to present an integrated simulation and optimization analysis for generating spatially varied trading ratios and evaluating seasonal transaction prices accordingly. It is designed to configure a permit-trading structure basin-wide and provide decision makers with a wealth of cost-effective, technology-oriented, risk-informed, and community-based management strategies. The case study, seamlessly integrating a QUAL2E simulation model with an optimal waste load allocation (WLA) scheme in a designated TMDL study area, helps understand the complexity of varying environmental resources values over space and time. The pollutants of concern in this region, which are eligible for trading, mainly include both biochemical oxygen demand (BOD) and ammonia-nitrogen (NH3-N). The problem solution, as a consequence, suggests an array of waste load reduction targets in a well-defined WLA scheme and exhibits a dynamic permit-trading framework among different sub-watersheds in the study area. Research findings gained in this paper may extend to any transferable dynamic-discharge permit (TDDP) program worldwide.     

An approach to tackling the environmental and health impacts of municipal solid waste disposal in developing countries

Indiscriminate disposal of municipal solid waste in developing countries poses severe environmental and health threats. The study proposes a new method for dealing with these problems. The hybrid structural interaction matrix (HSIM) was used to prioritise major identifiable environmental health factors arising from improper solid waste disposal. The simplistic resource allocation model was adopted to ensure optimality in the allocation of resources to prioritised factors. The study indicates that tackling environmental health impacts from the most prioritised negative disposal factors through optimal allocation of resources, will either reduce or eliminate the impacts associated with subsequent less prioritised factors that are direct consequences of the highly prioritised negative factors. The method proposed will aid decision makers in knowing which set of systemic factors are to be given preference and to what extent at given periods in time.     

EVALUATION OF THE WORTH OF ADDITIONAL DATA1

ABSTRACT .Inherent in every decision process is a certain amount of uncertainty, which is reduced with information. Perfect knowledge yields no uncertainty for a process, but perfect knowledge for hydrologic and water resource systems would require a highly excessive investment. Therefore, it is the aim of this paper to delineate a procedure that places a value on this uncertainty so that it may be compared to a cost of further investment, which would provide a basis for deciding the time at which the value of additional data does not exceed the cost of that data. A decision theory approach is employed on a hydrologic problem to formalize the steps in making a decision. Examples are given.     

Growth of the Decision Tree: Advances in Bottom‐Up Climate Change Risk Management

There has recently been a return in climate change risk management practice to bottom‐up, robustness‐based planning paradigms introduced 40 years ago. The World Bank's decision tree framework (DTF) for “confronting climate uncertainty” is one incarnation of those paradigms. In order to better represent the state of the art in climate change risk assessment and evaluation techniques, this paper proposes: (1) an update to the DTF, replacing its “climate change stress test” with a multidimensional stress test; and (2) the addition of a Bayesian network framework that represents joint probabilistic behavior of uncertain parameters as sensitivity factors to aid in the weighting of scenarios of concern (the combination of conditions under which a water system fails to meet its performance targets). Using the updated DTF, water system planners and project managers would be better able to understand the relative magnitudes of the varied risks they face, and target investments in adaptation measures to best reduce their vulnerabilities to change. Next steps for the DTF include enhancements in: modeling of extreme event risks; coupling of human‐hydrologic systems; integration of surface water and groundwater systems; the generation of tradeoffs between economic, social, and ecological factors; incorporation of water quality considerations; and interactive data visualization.     

IMPLEMENTATION OF ACUTE CRITERIA FOR CONSERVATIVE SUBSTANCES1

ABSTRACT: Acute criteria are assigned to the fish and wildlife propagation beneficial use in Oklahoma's water quality standards. Dye studies are analyzed to show that these criteria can be implemented through acute regulatory mixing zones. Acute regulatory mixing zones may be defined as areas in receiving streams where acute numerical criteria may be exceeded without causing acute toxicity. Acute regulatory mixing zones are used to obtain acute waste load allocations. If effluent loading does not exceed acute waste load allocation, acute criteria exceedance is confined to the acute regulatory mixing zone and there is no acute toxicity in the receiving stream. Waste load allocations for acute and chronic criteria are compared to determine which is appropriate to develop permit limits for the dye studies.