Journal of Water Resources Planning and Management

Six ground-water management models were developed and compared to identify the best management alternative for the containment of a ground-water pollution plume in a hypothetical aquifer that is used for freshwater supply. The proposed models are formulated as quadratic programming, linear programming, and mixed-integer programming models. Management models are grouped into two on the basis of treatment cost consideration. The optimal solutions of the models are compared and evaluated on the basis of total costs associated with the remediation system design. Sensitivity of the model solutions to variations in unit pumping and treatment costs are analyzed. The results of the models are quite different in regard to the number of potential interception wells completed, their pumping rates, resulting operation, and capital investment costs. Results show that considerable amounts of savings may be achieved through application of the mixed-integer programming models explicitly considering each of the cost components. Therefore, in remediation system designs that require installation of interception wells, ground-water managers should take into account the fixed charges incurred for each well that is introduced in the mathematical model.

The paper describes a network flow programming (NFP) model for sizing of reservoirs in a multiple reservoir design problem. It is a multiperiod model, where all single period networks, representing reservoirs, rivers, canals, and demand points, are interconnected in adjacent periods by reservoir carryover arcs. Flows in carryover arcs represent reservoir storage and the maximum flow in an arc for a reservoir indicates storage capacity requirement for that reservoir. The carryover arcs are split into multiple arcs representing multiple zones in the storage capacity. Reservoir capacities are obtained by optimizing the flow in carryover arcs. The model enables to plan reservoirs for a desirable reliability in fulfillment of demands. The concept of preference matrix (PM) has been introduced to reflect the interreservoir and interzonal competitiveness based on the objective function. Applicability of the model is demonstrated by estimating the capacities of seven reservoirs in a water transfer scheme in India using the criterion of minimization of forest submergence.

A dynamic optimal control algorithm for ground-water remediation was extended to incorporate treatment facility capital costs, as a function of the peak operating rate. Our approach to including the capital costs of treatment required no additional control variables and only a single additional state variable. Incorporation of the capital costs of the treatment facility had the greatest impact on design when the pumping policies were changed at intervals of six months or fewer. For longer management periods, inclusion of treatment facility capital costs had little effect on the selected optimal policies. This work demonstrates that capital treatment costs may significantly impact a dynamic management policy and that these capital costs should be explicitly incorporated into a dynamic management model.

A hydropower scheduling model that aims at minimizing thermal station-operation costs subject to various waterand power-demand constraints is described. The cost structure of the thermal power system is represented through incremental power-generation cost (or lambda) curves, which can be determined by running load-dispatching models. The model includes two control modules: one for the most efficient load allocation among the hydroplant turbines and another for the determination of the best hourly sequence of hydroplant power loads over the control horizon. These two modules are able to represent hydropower facilities and reservoir-management features in good detail, and the lambda curves effectively incorporate the essential elements of the thermal power system. The model is tested in the Lanier-Allatoona-Carters system in the southeastern United States and is shown to be computationally efficient even for very long control horizons.

Optimal seasonal multicrop irrigation water allocation and optimal stochastic intraseasonal (daily) irrigation scheduling are carried out using a two-stage decomposition approach based on a stochastic dynamic programming methodology. In the first stage the optimal seasonal water and acreage allocation among several crops or fields is defined using deterministic dynamic programming with the objective of maximizing total benefits from all the crops. The optimization is based on seasonal crop production functions. Seasonal crop production functions are obtained using single-crop stochastic dynamic programming, which incorporates the physics of soil moisture depletion and the stochastic properties of precipitation. In the second stage optimal intraseasonal irrigation scheduling is performed using a single-crop stochastic dynamic programming algorithm, conditional on the optimal seasonal water allocation of stage one. Optimal daily irrigation decision functions are obtained as a function of root-zone soil moisture content and the currently available irrigation water. The methodology is applied to a case study characterized by four crops in which both the optimal irrigation applications and the optimal acreage for each crop are determined.

Water resources planners and managers are continually faced with decisions to be made under uncertainty. In planning problems such as water supply, flood control, and ground-water remediation, the trade-offs among expected cost, cost variability, and system performance and reliability must be assessed amidst inherent variability and imperfect information. Robust optimization (RO) is introduced as a framework for evaluating these trade-offs and controlling the effects of uncertainty in water resources screening models. Upon the introduction of scenarios, which represent realizations of the random parameters in the model, two types of robustness are defined: a policy is optimality-robust if it remains optimal or nearly optimal for all scenarios, and feasibility-robust if it remains feasible or nearly feasible for all scenarios. Applications to urban water transfer planning and ground-water quality management are presented, with optimality robustness related to cost variability and feasibility robustness related to system reliability. Results show that RO can be a useful framework for evaluating the intrinsic trade-offs involving risk and finding solutions that hedge against inherent and parameter uncertainty.

In anticipation of a second consecutive critically dry year, the California Department of Water Resources (DWR) organized the 1995 Drought Water Bank Program. For the first time, DWR purchased water supply options from willing sellers as insurance against a possible water-short year. These options could be used by Water Bank members if needed to meet critical needs. If the options were not needed, sellers kept the option payment. This paper provides a program manager's view of the planning, management, operations, and financing of the 1995 Drought Water Bank Program and shares the writer's experiences in securing options to provide water supply certainty to California water agencies.