OPTIMAL GROUND WATER MANAGEMENT IN TWO-AQUIFER SYSTEMS1

ABSTRACT; This paper presents a numerical model for the prediction of optimal ground water withdrawal from a two-aquifer system by observing a set of constraints determined by the ecological conditions of the ground water basin. The aquifer system consists of an upper unconfined and a lower confined aquifer with a leaky stratum between them. It is assumed that water is withdrawn from the confined aquifer only, but the unconfined aquifer will also be affected due to the leakiness of the layer separating the upper and lower aquifers. Simulation and linear programming are employed for developing a computer model for the optimal management of such systems, with the objectives of determining withdrawal rates for predetermined ground water levels.     

OPTIMAL MANAGEMENT OF A REGIONAL AQUIFER IN EASTERN SAUDI ARABIA1

ABSTRACT: This paper describes the formulation and application of a ground-water hydraulic management model to determine the optimal development and operating policies of a regional aquifer in the Eastern Province of Saudi Arabia. The hydraulic response of the aquifer system is represented by a simulation model that is linked to an optimization management model using response functions. Yearly optimal ground-water extraction rates over a planning horizon of 15 years are determined for four scenarios, each reflecting alternative ground-water development policies. The results are presented in the form of tradeoff curves, relating drawdowns to optimal pumpage, which may enhance the decisionmaker's ability to select the best development policy from a set of alternatives. The results illustrate how various optimal management schemes can be devised to increase the total withdrawal from the aquifer while preventing excessive de-watering.     

THE OPTIMAL STEADY-STATE IN GROUNDWATER MANAGEMENT1

Groundwater use is likely to be inefficient in the absence of regulation and hence there is substantial interest in optimal groundwater withdrawals over time. Under an optimal regime withdrawals, pumping lifts, and profits converge to steady-state levels. In this paper we show that optimal steady-state lifts, withdrawals, and marginal user costs can be readily calculated for multi-cell models of confined aquifers. Applications to the design of economically efficient groundwater management policies are discussed, comparisons to previous work and to the safe yield concept are made, and an illustrative example is given.     

OPTIMAL CONTROL OF RESERVOIR RELEASES TO MINIMIZE SEDIMENTATION IN RIVERS AND RESERVOIRS1

ABSTRACT: An optimal control methodology and computational model are developed to evaluate multi‐reservoir release schedules that minimize sediment scour and deposition in rivers and reservoirs. The sedimentation problem is formulated within a discrete‐time optimal control framework in which reservoir releases represent control variables and reservoir bed elevations, storage levels, and river bed elevations represent state variables. Constraints imposed on reservoir storage levels and releases are accommodated using a penalty function method. The optimal control model consists of two interfaced components: a one‐dimensional finite‐difference simulation module used to evaluate flow hydraulics and sediment transport dynamics, and a successive approximation linear quadratic regulator (SALQR) optimization algorithm used to update reservoir release policies and solve the augmented control problem. Hypothetical two‐reservoir and five‐reservoir networks are used to demonstrate the methodology and its capabilities, which is a vital phase towards the development of a more robust optimal control model and application to an existing multiple‐reservoir river network.     

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.     

OPTIMAL RESERVOIR MANAGEMENT AND CROP PLANNING UNDER DETERMINISTIC AND STOCHASTIC INFLOWS1

ABSTRACT: This study analyzes planning under deterministic and stochastic inflows for the Mayurakshi project in India. Models are developed to indicate the optimal storage of reservoir water, the transfer of water to the producing regions, and the spillage of water from the reservoir, if needed. A deterministic programming model was first formulated to represent the existing situation. A chance-constrained model then was constructed to evaluate potential violations of the deterministic model. Both models were quantified for the command area. Data were collected from surveys of the area and from government agencies. Both the deterministic and change-constrained models suggest a more intensive cropping program in the region. Both emphasize more dependence on rabi and less on kharif crops. The chance-constrained especially suggests use of more water in the rabi season. Important chances in cropping programs and labor use take place under the chance-constrained model.     

OPTIMAL MANAGEMENT AND DESIGN OF HYDRAULIC SYSTEMS1

ABSTRACT: A possible methodology is developed to deal with the problem of designing complex pipeline systems, when they are subject to different rates of demand, and when a hypothesis of the flow distribution in different branches is not allowed. The mathematical algorithm used in linear programming. The problem, which is not linear, is dealt with by means of an iterative method; that is, by starting with a possible solution and inserting at each iteration the solution found in the preceding iteration. By taking as variables of the problem the piezometric heads of the ends for each branch of the network, the piezometric gradients and flows, and by thus considering the diameter as a derived variable, it is possible to isolate the nonlinearity in the cost function of the network. The latter is linearized each time close to the solution found in the preceding iteration.     

RESERVOIR MANAGEMENT RULES DERWED WITH THE AID OF MULTIPLE OBJECTIVE DECISION MAKING TECHNIQUES1

ABSTRACT: The determination of optimum reservoir operating rules for reservoirs with multiple conflicting objectives is still a difficult task - despite many publications in this field. In this paper a three-step Multi Objective Decision Making (MODM) method is presented, the emphasis of which is placed on the necessity to make the work easy for the decision maker, which many MODM techniques fail to achieve. The method is applied to the development of a compromise optimum operating rule for a multi-purpose reservoir. In the first step of the method stochastic DP is chosen which is combined with the “weighting method” allowing combination of various objectives into one objective function. By systematically varying the weights for the objectives a large number of pareto optimum reservoir operating rules is generated. In the second step of the method the performance of all these operating rules is tested with the aid of a model simulating reservoir operation. The results are statistically analyzed and the reliabilities for attaining the various objectives are computed. The third step of the model applies another MODM technique which allows the decision maker - in a computer dialog - to select his optimum reservoir operating rule from the large number of pareto optimum solutions generated in step 1. Here he can specify his preferences for the various objectives. For this purpose two alternative MODM techniques are offered: Compromise Programming and the SEMOPS method. Their performance is shown along with the generation and selection of operating rules for the multi-objective Wupper reservoir system in Germany.     

THE EFFECTS OF RISK AND RELIABILITY ON OPTIMAL RESERVOIR DESIGN1

A chance-constrained linear programming model, which utilizes multiple linear decision rules and is useful for river basin planning, is used to evaluate the effects of risk and reliability on optimal reservoir design. Streamflow forecasts or predictions can be explicitly included in the linear program. The risk associated with the predictions is included in the model through the use of cumulative distribution functions (CDF) of streamflows which are conditioned on the predictions. A multiple-purpose reservoir on the Gunpowder River in Maryland is used to illustrate the effectiveness of the model. In order to provide the decision makers with complete and useful information, trade-off curves relating minimum reservoir capacity (a surrogate for dam costs), water supply and flood control targets, and the reliability of achieving the targets are developed. The trade-off curves may enhance the decision maker's ability to select the best dam capacity, considering technological and financial constraints as well as the trade-offs between targets, risks, and costs.     

RECIRCULATING WELLS: GROUND WATER REMEDIATION AND PROTECTION OF SURFACE WATER RESOURCES1

ABSTRACT: Several chlorinated solvent plumes threaten the sole‐source aquifer underlying the Massachusetts Military Reservation at the western end of Cape Cod. Sensitive surface water features including ponds, cranberry bogs, and coastal wetlands are hydraulically connected to the aquifer. For one of the plumes (CS‐10 the original remedy of 120 extraction and reinjection wells has the potential for significant disruption of surface water hydrology, through the localized drawdown and mounding of the water table. Recirculating wells with in‐well air stripping offer a cost‐effective alternative to conventional pump‐and‐treat technology that does not adversely affect the configuration of the water table. Pilot testing of a two well system, pumping 300 gpm, showed a capture radius of > 200 feet per well, in‐well trichloroethylene (TCE) removal efficiencies of 92 to 98 percent per recirculation cycle, an average of three recirculation cycles within the capture zone, and no measurable effect on water table elevations at any point within the recirculation/treatment zone. During 120 days of operation, the mean concentration of TCE in the treatment zone was reduced by 83 percent, from 1,111 μg/l to 184 μg/l. Full‐scale design projections indicate that 60 wells at an average spacing of 160 feet, having an aggregate recirculation 11 MGD, can contain the CS‐b plume without ground water extraction or adverse hydraulic effects on surface water resources. The estimated capital costs for such a system are about $7 million, and annual operations‐and‐maintenance costs should be about $1.4 million, 40 percent of those associated with a pump and treat system over a 20‐year period.     

OPTIMAL LONG-TERM SCHEDULING OF STORMWATER DRAINAGE REHABILITATION1

ABSTRACT: A mathematical model is developed to optimally schedule long-term stormwater infrastructure rehabilitation activities. The model is capable of considering multiple rehabilitation projects and is driven by overall cost eensiderations. Rehabilitation activities are scheduled based on perceived reliabilities and future deterioration expected within the specified planning horizon. Future growth within the stormwater drainage basin is incorporated using chance constraints that limit the likelihood that a stormwater discharge exceeds system conveyance capacity. Model structure and development are discussed, and a hypothetical example using a drainage network is presented.     

ANALYSIS OF NITROGEN MANAGEMENT STRATEGIES USING EPIC1

ABSTRACT: This paper illustrates a method of using a hydrologic/water quality model to analyze alternative management practices and recommend best management practices (BMPs) to reduce nitrate-nitrogen (NO₃^--N) leaching losses. The study area for this research is Tipton, an agriculturally intensive area in southwest Oklahoma. We used Erosion Productivity Impact Calculator (EPIC), a field-scale hydrologic/water quality model, to analyze alternative agricultural management practices. The model was first validated using observed data from a cotton demonstration experiment conducted in the Tipton area. Following that, EPIC was used to simulate fertilizer response curves for cotton and wheat crops under irrigated and dryland conditions. From the fertilizer response functions (N-uptake and N-leaching), we established an optimum fertilizer application rate for each crop. Individual crop performances were then simulated at optimum fertilizer application rates and crop rotations for the Tipton area, which were selected based on three criteria: (a) minimum amount of NO₃^--N leached, (b) minimum concentration of NO₃^--N leached, and (c) maximum utilization of NO₃^--M. Further we illustrate that by considering residual N from alfalfa as a credit to the following crop and crediting NO₃^--N present in the irrigation water, it is possible to reduce further NO₃^--N loss without affecting crop yield.     

INTERPRETATION OF THE DUAL PROGRAM FOR OPTIMAL GROUNDWATER HYDRAULIC CONTROL1

ABSTRACT: Optimization formulations for hydraulic control that take the form of linear programs possess a corresponding dual linear program. The economic and physical interpretations of the dual linear program are examined for formulations in which hydraulic head in groundwater systems is constiained. In each case it is shown that the dual linear program has a physically meaningful interpretation. For a hydraulic gradient control formulation used for remedial analysis it is shown that the dual variable can be interpreted as the remedial benefit due to each gradient control constraint. The dual linear program maximizes the remedial benefit. The value of the dual variable can be used to compute such useful properties as the total remedial benefit of pumping at a specific location. For a formulation that optimizes aquifer yield while constraining drawdown the dual variable can be used to measure the total cost of drawdown capacity consumption per unit of pumping at a specific location. The dual program minimizes the cost of drawdown capacity consumption. By examining the meaning of the dual linear program an alternate statement of the problem under study is revealed. Quantities arising from the dual program add to the value of the optimization approach. Significant new information can be derived from existing linear optimization formulations with minimal additional computational effort.     

A LAW AND ECONOMICS APPROACH TO RESOLVING RESERVOIR SEDIMENT MANAGEMENT CONFLICTS1

The loss of the world's reservoir capacity to sedimentation can be mitigated by altering dam operations to release sediment downstream. However, legal uncertainty regarding whether dam owners are liable for damages to surrounding landowners due to altered operations provides a significant disincentive for sustainable sediment management. Past work recommends that courts apply a “rule of reasonableness” in assessing liability: dam owners should be held liable for damages only if they act unreasonably in altering operations, and surrounding landowners should take reasonable measures to mitigate foreseeable damage. Based on past cases, judicial determinations of reasonable reservoir management and reasonable precautionary measures by landowners are generally highly speculative, controversial, and based on limited information. Courts can ease the future burden of making these difficult determinations with rulings that create economic incentives for parties to act reasonably. For example, courts might entitle landowners to be free from sediment related damages, and protect the entitlement with a liability rule. This gives dam owners an economic incentive to release sediment only if the benefits of doing so outweigh court ordered damages to landowners. Past judicial decisions are largely consistent with this legal regime.     

INTEGRATED MANAGEMENT OF QUANTITY AND QUALITY OF URBAN WATER RESOURCES1

ABSTRACT. This paper will present a total water quality-quantity management approach which has incorporated the costs of water pollution control and water treatment, the benefits of water-based activities, and the trade-off between low flow augmentation and water quality improvement in its consideration. The analytical framework is based on the decomposition procedures provided by dynamic programming within which the optimal management plans are developed.     

RIVERWARE: A GENERALIZED TOOL FOR COMPLEX RESERVOIR SYSTEM MODELING1

ABSTRACT: Water management agencies seek the next generation of modeling tools for planning and operating river basins. Previous site‐specific models such as U.S. Bureau of Reclamation's (USBR) Colorado River Simulation System and Tennessee Valley Authority's (TVA) Daily Scheduling Model have become obsolete; however, new models are difficult and expensive to develop and maintain. Previous generalized river basin modeling tools are limited in their ability to represent diverse physical system and operating policy details for a wide range of applications. RiverWare(tm), a new generalized river basin modeling tool, provides a construction kit for developing and running detailed, site‐specific models without the need to develop or maintain the supporting software within the water management agency. It includes an extensible library of modeling algorithms, several solvers, and a rich “language” for the expression of operating policy. Its point‐and‐click graphical interface facilitates model construction and execution, and communication of policies, assumptions and results to others. Applications developed and used by the TVA and the USBR demonstrate that a wide range of operational and planning problems on widely varying basins can be solved using this tool.     

COMPARISON OF RESERVOIR LINEAR OPERATION RULES USING LINEAR AND DYNAMIC PROGRAMMING1

ABSTRACT: Mathematical optimization techniques are used to study the operation and design of a single, multi-purpose reservoir system. Optimal monthly release policies are derived for Hoover Reservoir, located in Central Ohio, using chance-constrained linear programming and dynamic programming-regression methodologies. Important characteristics of the former approach are derived, discussed, and graphically illustrated using Hoover Reservoir as a case example. Simulation procedures are used to examine and compare the overall performance of the optimal monthly reservoir release policies derived under the two approaches. Results indicate that, for the mean detention time and the corresponding safe yield target water supply release under existing design of Hoover Reservoir, the dynamic programming policies produce lower average annual losses (as defined by a two-sided quadratic loss function) while achieving at least as high reliability levels when compared to policies derived under the chance-constrained linear programming method. In making this comparison, the reservoir release policies, although not identical, are assumed to be linear. This restricted form of the release policy is necessary to make the chance-constrained programming method mathematically tractable.     

IDENTIFICATION OF AN OPTIMAL GROUNDWATER MANAGEMENT STRATEGY IN A CONTAMINATED AQUIFER1

A groundwater hydraulic management model is used to identify the optimal strategy for allocating limited fresh-water supplies and containing wastes in a hypothetical aquifer affected by brine contamination from surface disposal ponds. The present cost of pumping from a network of potential supply and interception wells is minimized over a five-year planning period, subject to a set of hydraulic, institutional, and legal constraints. Hydraulic constraints are formulated using linear systems theory to describe drawdown and velocity variables as linear functions of supply and interception well discharge decision variables. Successful validation of the optimal management strategy suggests that the model formulation can feasibly be applied to define management options for locally contaminated aquifer systems which are used to fulfill fresh-water demands.     

REGIONAL MANAGEMENT OF DEPLETED AQUIFERS1

ABSTRACT: Aquifers with pressure head seriously reduced by overdrafting are referred to as depleted. In coastal areas they may be invaded by saltwater. An obvious remedy is to reduce the rate of withdrawal to the permanently available dependable yield. This is being done now in two areas for New Jersey, under the authority of the State's Water Supply Management Act; but it has not previously been accomplished on a regional scale. The dependable yield was estimated by means of detailed hydrogeological modeling. “Water Supply Critical Areas” were delimited on the basis of piezometric pressure, drawn down 30 feet below sea level. Within the depleted area, water withdrawals must be reduced by a fixed ratio (35 to 50 percent) below the amount withdrawn during 1983. This reduction is effective as soon as al alternative source of water can be made available, usually from a surface source. Special arrangements are made whereby ground water users unconnected to the alternative source of supply can pay to withdrawn their full needs from the depleted aquifers, the money being used to purchase additional water from the new surface water source, in return for which some other user will reduce his ground water withdrawal below his reduced allocation.