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 It is assumed that water is withdrawn from the confined aquifer only, but the unconfined aquifer will also be affected due to the leakiness of the layer separating the upper and lower aquifers.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 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.     

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.     

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.     

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.     

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.     

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.     

MULTIOBJECTWE OPTIMIZATION OF RESERVOIR SYSTEMS OPERATION1

ABSTRACT: Development of optimal operational policies for large-scale reservoir systems is often complicated by a multiplicity of conflicting project uses and purposes. A wide range of multiobjective optimization methods are available for appraising tradeoffs between conificting objectives. The purpose of this study is to provide guidance as to those methods which are best suited to dealing with the challenging large-scale, nonlinear, dynamic, and stochastic characteristics of multireservoir system operations. As a case study, the selected methodologies are applied to the Han River Reservoir System in Korea for four principal project objectives: water supply and low flow augmentation; annual hydropower production, reliable energy generation, and minimization of risk of violating firm water supply requirements. Additional objectives such as flood control are also considered, but are imposed as fixed constraints.     

PLANNING OF URBAN BEST MANAGEMENT PRACTICES1

ABSTRACT: A “user-friendly” computer program has been developed for application in personal computers for preliminary design, evaluation, and cost effectiveness analysis of various best management practice (BMP) measures to control stormwater quantity and quality. The algorithms utilize the SCS TR-55 method for calculating runoff hydrographs for a single storm event and a first order pollutant washoff equation to generate pollutographs. Sensitivity analyses based on different policy scenarios is performed on a hypothetical watershed for the purpose of illustration. Three types of BMP measures, namely detention ponds (dry, wet, and extended wet ponds), infiltration trenches, and porous pavements are considered. It is found that the extended wet ponds have the best cost effective performance of the measures evaluated.     

A GAMING EVALUATION OF COLORADO RWER DROUGHT MANAGEMENT INSTITUTIONAL OPTIONS1

ABSTRACT: Researchers representing each of the Colorado River Basin states as well as the Secretary of the Interior were presented with an interactive computer simulation of a progressively increasing drought and were given the collective opportunity to change the ways in which basin-wide and within-state water management were conducted. The purpose of this “gaming” exercise was to identify rules for managing the Colorado River which are effective in preventing drought-caused damages to basin water users. This water management game was conducted three times, varying the collective choice roles for management of the river yet staying substantially within the current institution for management of the Colorado River known as the “Law of the River.” The Law of the River was quite effective in minimizing drought impacts upon consumptive water uses. Additional effective drought-coping measures to protect consumptive uses consisted mostly of intrastate water management improvements which states were able to implement independently. The Law of the River did not protect non-consumptive water uses, such as hydroelectric power generation, water-based recreation, endangered species, and water quality from drought, as well as it protected consumptive water uses. Players reached collective choice decisions to cope with rising salinity, equalize storage between the upper and lower basins, and protect endangered species. While these measures had some success, only reductions in withdrawals for consumptive uses, particularly in the upper basin, could have substantially lessened adverse impacts.     

MANAGEMENT OF BASEFLOW AUGMENTATION: A REVIEW1

ABSTRACT: Baseflow augmentation refers to the temporary storage of subsurface water in floodplains, streambanks, and/or stream bottoms during the wet season, either by natural or artificial means, for later release during the dry season to increase the magnitude and permanence of low flows. Management strategies for baseflow augmentation fall into the following categories: (1) range management, (2) upland vegetation management, (3) riparian vegetation management, (4) upland runoff detention and retention, and (5) the use of instream structures. The benefits of a management strategy focused on baseflow augmentation are many, including: (1) increased summer flows, (2) healthier riparian areas, (3) increased channel and bank stability, (4) decreased erosion and sediment transport, (5) improved water quality, (6) enhanced fish and wildlife habitat, (7) lower stream temperatures, and (8) improved stream aesthetics. This review has shown that baseflow augmentation has been successfully accomplished in a few documented cases. Given its clear impact on soil and water conservation, particularly in the semiarid western U.S., it appears that baseflow augmentation is a concept whose time has come. Research is needed on how to successfully integrate baseflow augmentation within comprehensive resource management strategies.     

OPTIMAL OPERATION OF SHELBYVILLE AND CARLYLE LAKES1

ABSTRACT: Dams were built by the U. S. Army Corps of Engineers on the Kaskaskia River at Shelbyville and Carlyle in Illinois, in 1969 and 1967, respectively. The operation of the Shelbyville and Carlyle Lakes has changed over the years because of considerably lower bankfull channel capacities downstream of the dams than were adopted in the project designs. This study was conducted to review the present operation policy. Intent was to derive a policy for maximizing the overall benefits (or minimizing the overall damages) and to compare these benefits or damages with those with the present policy. The operating rules were optimized through a simulation model which was structured considering the physical nature of the system and the desirable operation in the best interest of various beneficial uses. The expected annual value of overall benefits from recreation and agriculture is shown to increase by $0.2 million with the optimal policy. With the optimal operation, the overall damages are reduced by 76 percent on the average over the 24 years of flow record at Shelbyville and Carlyle.     

AQUIFER MANAGEMENT UNDER TRANSIENT AND STEADY-STATE CONDITIONS1

ABSTRACT: The equations of transient and steady-state flow in two-dimensional artesian aquifers are approximated using finite differences. The resulting linear difference equations, combined with other linear physical and management constraints and a linear objective function, comprise a linear programming (LP) formulation. Solutions of such LP models are used to determine optimal well distributions and pumping rates to meet given management objectives for a hypothetical transient problem and for a steady-state field problem.