MULTIOBJECTIVE DECISION MAKING TECHNIQUES FOR RESERVOIR OPERATION1

ABSTRACT: Six applications of multiobjective decision making techniques for finding optimal or satisfying operating rules for reservoir systems are presented. The examples include situations with hydropower vs. water supply (for irrigation), flood control vs. low flow augmentation, selection of an operating rule, low-flow vs. reliability, and low flow and recreation vs. water quality. The techniques applied include the constraint method, compromise programming, goal programming, Tchebycheff approach (max-mm), Consensus, and ELECTRE I and II.     

COMPARISON OF STOCHASTIC AND DETERMINISTIC DYNAMIC PROGRAMMING FOR RESERVOIR OPERATING RULE GENERATION1

ABSTRACT: Two dynamic programming models — one deterministic and one stochastic — that may be used to generate reservoir operating rules are compared. The deterministic model (DPR) consists of an algorithm that cycles through three components: a dynamic program, a regression analysis, and a simulation. In this model, the correlation between the general operating rules, defined by the regression analysis and evaluated in the simulation, and the optimal deterministic operation defined by the dynamic program is increased through an iterative process. The stochastic dynamic program (SDP) describes streamflows with a discrete lag-one Markov process. To test the usefulness of both models in generating reservoir operating rules, real-time reservoir operation simulation models are constructed for three hydrologically different sites. The rules generated by DPR and SDP are then applied in the operation simulation model and their performance is evaluated. For the test cases, the DPR generated rules are more effective in the operation of medium to very large reservoirs and the SDP generated rules are more effective for the operation of small reservoirs.     

RESERVOIR OPERATION THROUGH OBJECTIVE TRADE-OFFS1

ABSTRACT: Water resource development has progressed to the stage where various human factors are now being considered in reservoir design and operation. The introduction of human factor objectives complicates the problem since they are noncommensurate with other objectives and they are difficult to identify quantitatively. Some of the problems that now arise concern the proper methods for consideration of several different, sometimes subjectively identified, objectives in reservoir planning. The classical systems analysis approach to decision making for multiple objective problems is outlined and the inherent difficulties associated with multiple objectives and subjective estimates are identified. Techniques being used in reservoir design and operation are reviewed and discussed. An alternate technique for considering noncommensurate, subjectively identified, objectives, which relates the objectives in terms of real trade-off costs and eliminates the need for a priori estimates of objective worth is then presented. The method is illustrated with three examples, including a reservoir operation problem and a cooling tower design problem.     

A DECISION SUPPORT TOOL FOR THE MANAGEMENT OF MULTI‐RESERVOIR SYSTEMS1

ABSTRACT: A decision support tool is developed for the management of water resources, focusing on multipurpose reservoir systems. This software tool has been designed in such a way that it can be suitable to hydrosystems with multiple water uses and operating goals, calculating complex multi‐reservoir systems as a whole. The mathematical framework is based on the parameterization‐simulation‐optimization scheme. The main idea consists of a parametric formulation of the operating rules for reservoirs and other projects (i.e., hydropower plants). This methodology enables the radical decrease of the number of decision variables, making feasible the location of the optimal management policy, which maximizes the system yield and the overall operational benefit and minimizes the risk for the management decisions. The program was developed using advanced software engineering techniques. It is adaptable in a wide range of water resources systems, and its purpose is to support water and power supply companies and related authorities. It already has been applied to two of the most complicated hydrosystems of Greece, the first time as a planning tool and the second time as a management tool.     

A COMPUTER SIMULATION PROGRAM FOR OPTIMIZING CONJUNCTIVE OPERATION OF DESALTING PLANTS1

ABSTRACT .Desalting plants can provide a means of firming up erratic natural supplies when properly operated in conjunction with existing water supply reservoir systems. Since the natural inflow is variable, the choice of when to run the desalting plant is difficult. If the plant is turned on too late, a shortage may result; or if the plant runs too long, costly water may be wasted. A computer program is described that can help water planners find an optimal operating rule, i.e., a policy that tells when to turn the plant on and off to meet a given demand. Criteria for defining the firm water yield of the system (with and without desalting) are first defined. The logic of the program is then described. The program, written in FORTRAN IV, successively simulates operation of the given size reservoir-desalting plant system under control of various operating rules and selects the optimal rule as the one which produces the required firm water yield at the least unit cost. The optimal plant size and the staging of construction can also be studied by making a series of computations. Applications of the Operating Rule Program to water systems in California, Utah and New York are described. The studies show that, compared with base load operation, substantial savings are possible if optimum intermittent conjunctive operation of the desalting plant is followed.     

REAL CODED GENETIC ALGORITHM OPTIMIZATION OF LONG TERM RESERVOIR OPERATION1

ABSTRACT: An optimization and simulation model holds promise as an efficient and robust method for long term reservoir operation, an increasingly important facet of managing water resources. Recently, genetic algorithms have been demonstrated to be highly effective optimization methods. According to previous studies, a real coded genetic algorithm (RGA) has many advantages over a binary coded genetic algorithm. Accordingly, this work applies an RGA to obtain the 10‐day (the traditional period of reservoir operation in Taiwan) operating rule curves for the proposed reservoir system. The RGA is combined with an effective and flexible scheme for coding the reservoir rule curves and applied to an important reservoir in Taiwan, considering a water reservoir development scenario to the year 2021. Each rule curve is evaluated using a complex simulation model to determine a performance index for a given flow series. The process of generating and evaluating decision parameters is repeated until no further improvement in performance is obtained. Many experiments were performed to determine the suitable RGA components, including macro evolutionary (ME) selection and blend‐α crossover. Macro evolution (ME) can be applied to prevent the premature problem of the conventional selection scheme of genetic algorithm. The purpose of adjusting a of a crossover scheme is to determine the exploratory or exploitative degree of various subpopulations. The appropriate rule curve searched by an RGA can minimize the water deficit and maintain the high water level of the reservoir. The results also show that the most promising RGA for this problem consists of these revised operators significantly improves the performance of a system. It is also very efficient for optimizing other highly nonlinear systems.     

A COMPARISON OF TWO METHODS FOR MULTIOBJECTIVE OPTIMIZATION FOR RESERVOIR OPERATION1

ABSTRACT: Two major objectives in operating the multireservoir system of the Upper Colorado River basin are maximization of hydroelectric power production and maximization of the reliability of annual water supply. These two objectives conflict. Optimal operation of the reservoir system to achieve both is unattainable. This paper seeks the best compromise solution for an aggregated reservoir as a surrogate of the multireservoir system by using two methods: the constraint method and the method of combined stochastic and deterministic modeling. Both methods are used to derive the stationary optimal operating policy for the aggregated reservoir by using stochastic dynamic programming but with different objective functions and minimum monthly release constraints. The resulting operating policies are then used in simulated operation of the reservoir with historical inflow records to evaluate their relative effectiveness. The results show that the policy obtained from the combination method would yield more hydropower production and higher reliability of annual water supply than that from the constraint-method policy.     

Empirical study on voting power in participatory forest planning

Multicriteria decision support systems are applied in natural resource management in order to clarify the planning process for the stakeholders, to make all available information usable and all objectives manageable. Especially when the public is involved in planning, the decision support system should be easy to comprehend, transparent and fair. Social choice theory has recently been applied to group decision-making in natural resources management to accomplish these objectives. Although voting forms the basis of democracy, and is usually taken as a fair method, the influence of voters over the outcome may vary. It is also possible to vote strategically to improve the results from each stakeholder's point of view. This study examines the use of social choice theory in revealing stakeholders' preferences in participatory forest planning, and the influence of different voters on the outcome. The positional voting rules examined were approval voting and Borda count, but both rules were slightly modified for the purposes of this study. The third rule examined, cumulative rule, resembles utilitarian voting rules. The voting rules were tested in a real participatory forest planning situation in eastern Lapland, Finland. All voting rules resulted in a different joint order of importance of the criteria. Yet, the preference orders produced had also a lot in common and the criteria could be divided into three quite distinct groups according to their importance. The influence of individual voters varied between the voting rules, and in each case different voter was the most influential.     

A Simple Framework for Incorporating Seasonal Streamflow Forecasts into Existing Water Resource Management Practices1

Gong, Gavin, Lucien Wang, Laura Condon, Alastair Shearman, and Upmanu Lall, 2010. A Simple Framework for Incorporating Seasonal Streamflow Forecasts Into Existing Water Resource Management Practices. Journal of the American Water Resources Association (JAWRA) 46(3):574-585. DOI: 10.1111/j.1752-1688.2010.00435.x Abstract: Climate-based streamflow forecasting, coupled with an adaptive reservoir operation policy, can potentially improve decisions by water suppliers and watershed stakeholders. However, water suppliers are often wary of straying too far from their current management practices, and prefer forecasts that can be incorporated into existing system modeling tools. This paper presents a simple framework for utilizing streamflow forecasts that works within an existing management structure. Climate predictors are used to develop seasonal inflow forecasts. These are used to specify operating rules that connect to the probability of future (end of season) reservoir states, rather than to the current storage, as is done now. By considering both current storage and anticipated inflow, the likelihood of meeting management goals can be improved. The upper Delaware River Basin in the northeastern United States is used to demonstrate the basic idea. Physically plausible climate-based forecasts of March-April reservoir inflow are developed. Existing simulation tools and rule curves for the system are used to convert the inflow forecasts to reservoir level forecasts. Operating policies are revised during the forecast period to release less water during forecasts of low reservoir level. Hindcast simulations demonstrate reductions of 1.6% in the number of drought emergency days, which is a key performance measure. Forecasts with different levels of skill are examined to explore their utility.     

DERIVING THE NONLINEAR RISK-BENEFIT ALGORITHM FOR RESERVOIRS1

ABSTRACT: The Nonlinear Risk-Benefit (NRB) Algorithm includes risk as one of the objectives in a multiple-objective optimization problem. The NRB Algorithm is derived by extending the Surrogate Worth Trade-Off method to quadratic programming. This category of problem is common in water resources planning and design, especially multipurpose reservoir systems. Consequently, an example is given using the algorithm for optimally operating a multipurpose reservoir.     

THE DEVELOPMENT OF A MODEL TO EVALUATE HYDROLOGIC RISK IN WATER RESOURCE SYSTEM DESIGN1

In this paper, a procedure for analyzing a water resource system with special emphasis on evaluation of acceptable economic risk due to occasional failures to deliver water is proposed. The basic methodology includes the development of a simple mathematical model which describes the physical hydrologic and economic characteristics of a single reservoir irrigation and city water supply system and an evaluation of economic benefits of the system with full and partial deliveries of water. The system is simulated for various combinations of decision variables (system magnitudes) and an optimum design is obtained by response surface technology. Emphasis is placed on the basic model and methodology although, in order to introduce some realism, the procedure is applied to data based on the existing reservoir system on the South Concho River in West Central Texas.     

The development and application of a multilevel decision analysis model for the remediation of contaminated groundwater under uncertainty

A study was initiated which combined elements of stochastic hydrology, risk assessment, simulation modeling, cost analysis and decision making to define the optimum remediation choice(s) for a Superfund site in the southern United States. The effort focused upon the premise that groundwater remediation is inherently complex due to uncertainties in the geological matrix as well as in contaminant concentrations at points of compliance and/or exposure. The technical analyst should supply the decision maker with estimates of these uncertainties as well as the cost penalties required to reduce them to manageable levels. Monte Carlo transport modeling was employed to define the probability of contaminant excursions from the site, while geostatistical simulation identified a joint plume configuration and its attendant probability. Bayesian modeling was used to define the worth of additional data. These individual components were combined within a Decision Model to identify optimum remediation configurations for a given levels of risk tolerance which could be supplied by the decision maker or affected community. Sensitivity analyses were conducted to define ranges over which the decision would not be affected by variation in the respective decision parameter.     

COMPUTATIONAL IMPROVEMENT FOR STOCHASTIC DYNAMIC PROGRAMMING MODELS OF URBAN WATER SUPPLY RESERVOIRS1

ABSTRACT: This paper describes two methods that are introduced to improve the computational effort of stochastic dynamic programming (SDP) as applicable to the operation of multiple urban water supply reservoir systems. The stochastic nature of streamflow is incorporated explicitly by considering it in the form of a multivariate probability distribution. The computationally efficient Gaussian Legendre quadrature method is employed to compute the conditional probabilities of streamflow, which accounts for the serial correlation of streamflow into each storage and the cross correlation between the streamflow into various storages. A realistic assumption of cross correlation of streamflow is introduced to eliminate the need to consider the streamflow combinations which are unlikely to occur in the SDP formulation. A “corridor” approach is devised to eliminate the need to consider the infeasible and/or inferior storage volume combinations in the preceding stage in computing the objective function in the recursive relation. These methods are verified in terms of computational efficiency and accuracy by using a hypothetical example of three interconnected urban water supply reservoirs. Therefore, it can be concluded that these methods allow SDP to be more attractive for deriving optimal operating rules for multiple urban water supply reservoir systems.     

APPLICATION OF CROP YIELD FUNCTIONS IN RESERVOIR OPERATION1

ABSTRACT: A model is developed for real-time operation of an irrigation reservoir with the objective of maximizing the value of multiple crop yields during a growing season. The model employs monthly additive and product forms of crop yield functions for dry matter and grain crops, respectively. The resulting nonlinear optimization model uses a log transform to reduce nonlinearities in the model. An application of the proposed model is compared to a common operating rule used in simulation models. The proposed model results were better in terms of net benefits from crop yields. The model uses GAMS (General Algebraic Modeling System) language. It requires an IBM-compatible microcomputer and is suitable for use by a reservoir manager.     

Quantifying Tradeoffs Associated with Hydrologic Environmental Flow Methods

Freshwater management requires balancing and tradingoff multiple objectives, many of which may be competing. Ecological needs for freshwater are often described in terms of environmental flow recommendations (e.g., minimum flows), and there are many techniques for developing these recommendations, which range from hydrologic rules to multidisciplinary analyses supported by large teams of subject matter experts. Although hydrologic rules are well acknowledged as overly simplified, these techniques remain the state‐of‐the‐practice in many locations. This article seeks to add complexity to the application of these techniques by studying the emergent properties of hydrologic environmental flow methodologies. Two hydrologic rules are applied: minimum flow criteria and sustainability boundaries. Objectives and metrics associated with withdrawal rate and similarity to natural flow regimes are used to tradeoff economic and environmental needs, respectively, over a range of flow thresholds and value judgments. A case study of hypothetical water withdrawals on the Middle Oconee River near Athens, Georgia is applied to demonstrate these techniques. For this case study, sustainability boundaries emerge as preferable relative to both environmental and economic outcomes. Methods applied here provide a mechanism for examining the role of stakeholder values and tradeoffs in application of hydrologic rules for environmental flows.     

STOCHASTIC DYNAMIC PROGRAMMING FOR OPTIMUM RESERVOIR OPERATION1

ABSTRACT. For a multipurpose single reservoir a deterministic optimal operating policy can be readily devised by the dynamic programming method. However, this method can only be applied to sets of deterministic stream flows as might be used repetitively in a Monte Carlo study or possibly in a historical study. This paper reports a study in which an optimal operating policy for a multipurpose reservoir was determined, where the optimal operating policy is stated in terms of the state of the reservoir indicated by the storage volume and the river flow in the preceding month and uses a stochastic dynamic programming approach. Such a policy could be implemented in real time operation on a monthly basis or it could be used in a design study. As contrasted with deterministic dynamic programming, this method avoids the artificiality of using a single set of stream flows. The data for this study are the conditional probabilities of the stream flow in successive months, the physical features of the reservoir in question, and the return functions and constraints under which the system operates.     

INTERACTIVE MULTIOBJECTIVE ANALYSIS EMBEDDING THE DECISION MAKER'S IMPLICIT PREFERENCE FUNCTION1

ABSTRACT: Two simple interactive techniques are developed and illustrated by means of two different real-life examples in Thailand. The first technique, Evolutionary Sequential Multiobjective Problem Solving (ESEMOPS), is an open-ended algorithm designed for planning problems with discrete alternatives. ESEMOPS helps the decision making group (DMG) develop progressively a preference function over the alternatives. The algorithm follows an evolutionary “breeding” strategy to generate a small set of good alternative solutions. This heuristic search, which does not guarantee that the adopted ‘satisfactum’ is an efficient solution leads to plausible results when applied to the planning of the Mae Khlong-Chao Phraya interbasin water transfer and irrigation system. The second algorithm, Search Beam Method (SBM) is essentially a series of one-dimensional searches for an efficient point along a “beam” passing through a goal point. Repeated search towards displayed goal points is leading to a set of quasi non-dominated solutions. SBM is illustrated by the Ubol Ratana reservoir control problem with the two conflicting objectives of energy generation and irrigation water supply. Neither ESEMOPS nor SBM require that weights, utilities, or pairwise tradeoffs be assessed. These features have been very much appreciated by a real DMG presented with the two techniques.     

Models,Assumptions, and Stakeholders: Planning for Water Supply Variability in the Colorado River Basin1

Abstract: Declining reservoir storage has raised the specter of the first water shortage on the Lower Colorado River since the completion of Glen Canyon and Hoover Dams. This focusing event spurred modeling efforts to frame alternatives for managing the reservoir system during prolonged droughts. This paper addresses the management challenges that arise when using modeling tools to manage water scarcity under variable hydroclimatology, shifting use patterns, and institutional complexity. Assumptions specified in modeling simulations are an integral feature of public processes. The policymaking and management implications of assumptions are examined by analyzing four interacting sources of physical and institutional uncertainty: inflow (runoff), depletion (water use), operating rules, and initial reservoir conditions. A review of planning documents and model reports generated during two recent processes to plan for surplus and shortage in the Colorado River demonstrates that modeling tools become useful to stakeholders by clarifying the impacts of modeling assumptions at several temporal and spatial scales. A high reservoir storage‐to‐runoff ratio elevates the importance of assumptions regarding initial reservoir conditions over the three‐year outlook used to assess the likelihood of reaching surplus and shortage triggers. An ensemble of initial condition predictions can provide more robust initial conditions estimates. This paper concludes that water managers require model outputs that encompass a full range of future potential outcomes, including best and worst cases. Further research into methods of representing and communicating about hydrologic and institutional uncertainty in model outputs will help water managers and other stakeholders to assess tradeoffs when planning for water supply variability.