Journal of Water Resources Planning and Management

This is the first of two papers dealing with schematic models for water distribution systems. Schematic models for use in preliminary design of water distribution systems are developed by two approaches: (1) A step‐wise combination of elements; and (b) a nonlinear continuum representation of the system as a whole. The objective is to create models that are equivalent to a detailed network model in terms of the computed distributions of heads and flows over the area, yet are much more efficient, and therefore enhance the engineering‐economic analysis. The step‐wise combination method is developed beyond existing procedures to consider more complex arrangements of pipes as well as water withdrawals, which vary along the pipes and with time.

This is the second of two papers dealing with the development and use of schematic models for water distribution systems. The first paper covered methods for step‐wise combination of elements into equivalent ones. Herein, a different and novel approach, which views the system as a nonlinear horizontal continuum, is proposed. An areally distributed conductance, a function of pipe properties and areal density, is the link between a potential function, which is related to the heads and the flow field. The model can be used to obtain the flow field of an existing system for a prescribed potential, or to optimize the conductance of a planned system for a given distribution of demands and specified boundary conditions. The method is demonstrated by a case study, for the city of Jerusalem, Israel.

A planning model is presented for the control of seawater intrusion in regional groundwater systems. The management model is structured as a problem in optimal control. The hydraulic response equations, which are developed from continuity principles, relate the movement of the interface to the magnitude and location of groundwater pumping and recharge. Finite difference methods are used to approximate the solution of the aquifer's response to management strategies. The control problem is solved using: (1) The influence‐coefficient method allied with quadratic programming; and (2) reduced‐gradient methods in conjunction with a quasi‐Newton algorithm. The planning model is applied to the Yun Lin groundwater basin in southwestern Taiwan where excessive pumping has produced declining water levels, localized land subsidence, and saltwater intrusion. The optimal groundwater pumping and recharge schedules for the Peikang area of the basin are presented. The computational efficiency of the algorithms is also discussed.

Numerical quadrature methods are used to solve the integral equations for steady‐state reservoir‐storage density functions. The resulting approximations are used in a variety of problems with particular emphasis on the joint optimization of the design and operation of reservoirs and water delivery systems. Basic examples, to illustrate the use of the methods, expose several interesting economic tradeoffs present in reservoir operation, and factors affecting these tradeoffs are characterized and categorized. More involved examples show the interdependence of target deliveries, delivery capacities, and the probabilistic nature of the water supplies in joint optimization problems. The continuous approximations from the quadrature methods are used in nonlinear optimization programs, jointly with a probabilistic delivery system model, to determine the partition of storage between interyearly and intrayearly uses to maximize the expected benefits from the corresponding optimally designed and operated delivery system.

Water quality although acceptable when it leaves the treatment plant may deteriorate before it reaches the user. Changes in quality may be caused by chemical or biological transformations, by a loss of system integrity, or by blending of waters from different sources. Until recently, little attention has been paid to the problem of changes in water quality in the distribution system. This paper applies a sequential steady‐state approach to modeling water quality in distribution systems and compares the results to field data. The field data showed significant spatial and temporal water quality variation in the distribution system. The sequential steady‐state solutions provided a reasonable representation of changes in water quality with time. A major conclusion of the research is that an understanding of the hydraulic flow patterns and directions that create gradients of concentration is extremely important in interpreting quality modeling results. Field quality data is important in developing, verifying, and understanding predictive models. Such quality data should be at time intervals sufficient to reflect changes in system dynamics.

A procedure for estimating benefits associated with the cleanup of groundwater contamination is proposed. The first step in this procedure is development of a joint probability distribution of contaminant concentration and duration of exposure at a specified location X. A computer model using the turning bands method to generate spatiallyvarying, but correlated hydraulic conductivity fields and a groundwater flow/mass transport computer program to move the contaminant downstream is used to construct the probability distribution. The second step is involved with the formation of a joint incidence fraction distribution of test organism response to various contaminant concentration and duration of exposure levels at the specific location. The sum of the products of the joint probability and incidence fraction distribution values for various contaminant concentration and duration of exposure levels are multiplied by the number of organisms exposed at the specified location in order to estimate benefits resulting from a groundwater cleanup effort.

In many metropolitan areas it is common for a large central city to sell water to many of its surrounding suburban communities. In the Seattle, Washington metropolitan region, the city (population 494,000) provides water to 34 suburban cities and water districts with a total population of roughly 596,000. The development of this water market has its origins in the geographic pattern of metropolitan population and institutional development, water law, the economies of scale of water production, and the economic scarcity of clean, inexpensive water sources. Management and long‐range planning for such a system are reviewed and the advantages and disadvantages of this market system for Seattle and its customers are discussed. The de facto regionalization of the metropolitan water supply is contrasted with the de jure regionalization of metropolitan Seattle's wastewater system, which is managed jointly by the region's governments.