Journal of Water Resources Planning and Management

Diminishing marginal utility is an important characteristic of water resources systems. With the assumption of diminishing marginal utility (i.e., concavity) of reservoir utility functions, this paper derives a monotonic relationship between reservoir storage and optimal release decision under both deterministic and stochastic conditions, and proposes an algorithm to improve the computational efficiency of both deterministic dynamic programming (DP) and stochastic dynamic programming (SDP) for reservoir operation with concave objective functions. The results from a real-world case study show that the improved DP and SDP exhibit higher computational efficiency than conventional DP and SDP. The computation complexity of the improved DP and SDP is $O(n)$ (order of $n$, the number of state discretization) compared to $O(n^2)$ with conventional DP and SDP.

The water rights analysis package (WRAP) is a generalized river/reservoir system simulation model that is routinely applied in Texas in regional and statewide planning studies and administration of the water right permit system. The WRAP modeling system was recently expanded by adding short-term storage frequency and supply reliability analysis capabilities. Individual reservoirs and multiple-reservoir systems can be analyzed considering numerous water users and complex water management practices. The new modeling features are based on dividing the hydrologic period-of-analysis into many short-simulation sequences with each starting with the same storage conditions. Two alternative frequency/reliability analysis methodologies, called the equal-weight and probability-array options, are compared in this paper with a case-study application. The probability array option is designed to improve the accuracy of storage frequency estimates by modeling hydrologic persistence as reflected in the preceding reservoir storage contents on the basis of a regression of natural streamflow versus preceding storage from a long-term simulation.

Representing peak and off-peak energy prices is often difficult in hydropower modeling because the time scale of price variability (hours or less) is much shorter than that needed for many operations planning models (days to months). This work extends and examines the reliability of an existing approximate method to incorporate hourly energy price information into revenue functions used in hydropower reservoir optimization models with larger time steps (weekly or monthly). The method assumes constant head, an exogenously known frequency distribution for hourly prices during each modeled time period (day, week, or month), and a revenue-maximizing operational strategy that allocates hydropower releases in order of decreasing hourly price. The method is extended to the case with minimum instream flow requirements. The reliability of the method was tested for the cases with and without minimum instream flow requirements. Revenue estimates for a hypothetical hydropower site were compared with the exact optimal revenue from solving the hourly optimization problem within one week, and showed less than 1% error by using a finely discretized price-frequency curve.

During a model calibration process, errors in field measurements propagate to uncertainties in model parameter estimates and model predictions. This paper presents a means to quantify that effect in a water distribution water quality model and provides guidance on data collection experiment design. Water quality in the distribution systems is dominated by advective transport that is hydraulically driven. The hydraulic model, including the nodal demand, is assumed well calibrated and provides no uncertainty. Thus, only the wall decay coefficients are to be estimated and evaluated. The uncertainty assessment procedure consists of a parameter estimation model, parameter estimation uncertainty analysis, and model prediction uncertainty analysis. The shuffled frog leaping algorithm (SFLA), an optimization algorithm, is used to estimate the parameters in the water quality model in a least-squares regression given a set of field data. The parameter uncertainty is calculated using a first-order approximation and is further propagated to model prediction uncertainty. The model prediction uncertainty is calculated using a similar first-order analysis. The methodology is applied to two networks. Alternative conditions are analyzed in terms of data collection and model prediction conditions to examine the benefits of performing pulse injection test and data collection design. The results showed that pulse injection provides more information and better parameter estimates. As a result, parameters estimated from a data set with pulse injection produced lower model prediction uncertainty. For a given simulation time, earlier pulses remained in the system for a longer duration, providing more calibration information and, hence, improving parameter estimation accuracy.

This paper presents the findings of an investigation into predicted/modeled water age and the associated quality characteristics within a UK drinking water distribution network to determine if there is a discernable link. The hydraulic and water quality software Aquis was used to identify water volumes of different ages, generated by localized demand patterns in pipes that are in close proximity to one another. The pipe network studied was small spatially, of a single material, and had a consistent demand attributable to serving predominately light industry, but with interesting hydraulic patterns involving loops and mixing of water volumes, and some long retention times. Field work was undertaken to obtain water quality samples from five network locations identified as containing a broad range of calculated water age. The samples were analyzed for standard regulated parameters by a UK Accreditation Service (UKAS) [formerly known as the National Measurement Accreditation Service (NAMAS)] accredited water laboratory in line with UK water industry standard quality assurance practice. The water sample analytical results were examined to test how a number of physical, chemical, and bacteriological parameters related to the calculated water age at each sample point. Heterotrophic plate counts were used as the indicator of general bacteriological water quality. A limited association between the calculated water mean age and quality parameters was observed. Further investigations, taking into account mixing of different aged water volumes and the maximum age contributions to the mean age at each sample location, produced some association. The work demonstrated that mean age is not a sufficient guide to general water quality in this small network area. Mixing effects, and maximum age volume contributions, need to be taken into account if a more comprehensive understanding of water quality is to be obtained.

The Newton-based global gradient algorithm (GGA) (also known as the Todini and Pilati method) is a widely used method for computing the steady-state solution of the hydraulic variables within a water distribution system (WDS). The Newton-based computation involves solving a linear system of equations arising from the Jacobian of the WDS equations. This step is the most computationally expensive process within the GGA, particularly for large networks involving up to $O({10}^5)$ variables. An increasingly popular solver for large linear systems of the M-matrix class is the algebraic multigrid (AMG) method, a hierarchical-based method that uses a sequence of smaller dimensional systems to approximate the original system. This paper studies the application of AMG to the steady-state solution of WDSs through its incorporation as the linear solver within the GGA. The form of the Jacobian within the GGA is proved to be an M-matrix (under specific criteria on the pipe resistance functions), and thus able to be solved using AMG. A new interpretation of the Jacobian from the GGA is derived, enabling physically based interpretations of the AMG’s automatically created hierarchy. Finally, extensive numerical studies are undertaken where it is seen that AMG outperforms the sparse Cholesky method with node reordering (the solver used in EPANET2), incomplete LU factorization (ILU), and PARDISO, which are standard iterative and direct sparse linear solvers.

This study introduces a new search method for box-constrained optimization problems called the search method for box optimization (SMBO). SMBO is a population heuristic-based search methodology that solves global optimization problems. SMBO represents the population as a probability density function (PDF) inside the problem bounds. The PDF shape is dynamically adapted during the process to guide to a “good” search domain. The applicability and the efficiency of the method are demonstrated using two benchmark sets, which include unimodal, multimodal, expanded, and hybrid composition functions. The performance of SMBO is compared with several genetic algorithms (GAs); the first benchmark compares it with nine codes of traditional/classic GAs, and the second compares SMBO with two recent variants of genetic algorithms. The results show that SMBO performs as well as or better than the GAs in both comparisons. The method is demonstrated on a nonlinear model for management of a water supply system (WSS), and the results are compared with the commercial GA toolbox of matrix laboratory (MATLAB).

The course of settlement, development, and economies within nations has long been deeply affected by the availability of water. In a New Zealand context, Maori (the indigenous people) cannot divorce themselves from the challenges associated with setting environmental flows and allocating water. In the last two decades, Maori have become more vocal in seeking greater recognition of their cultural beliefs, values, and practices. Maori, however, face the challenge of conveying to decision makers how environmental flows affect their cultural interests. This paper introduces a cultural flow preference study, which is a tool that has been developed for Maori to assess their opportunities to engage in a range of cultural experiences in a catchment under differing stream flows. The process was applied in the Kakaunui River and enabled Maori to identify their flow preferences, together with the dependencies of a number of cultural values and uses on specific flows at a particular time of year. The results suggested that the current flow regime, which only prescribes a minimum flow, is unsatisfactory. A number of flow-related issues that can only be investigated as part of a collaborative investigation involving biophysical scientists and Maori were identified.

Sustainable development in river basins depends on sound management of land use and water allocation policies. Integrated water resources management (IWRM) is considered a path to bring many elements within the development schemes together toward a unified land-water planning and management process. In this study, an integrated water resources management model is developed to connect three groups of decision makers in pollution control, agricultural planning, and water resources allocation with economic, environmental, and social objectives. A genetic algorithm–based optimization model is developed for providing desirable water quality and quantity while maximizing agricultural production in the upstream region, mitigating the unemployment (social) impacts of land use changes, and providing reliable water supply to the downstream region. The upstream region is divided into subbasins, and a fuzzy-based multiobjective optimization model is used to determine the optimal land uses in each subbasin and water allocation to agricultural lands in the watershed. To illustrate the practical application of the model, a case study at the Aharchay watershed in Iran has been used. Land use planning as an alternative strategy of nonpoint source pollution control is evaluated in this watershed. The study represents a novel and practical mean of integrating water quality and quantity management and land use planning on a watershed scale.

This paper presents a simple and straightforward technique to solve the problem of least-cost reservoir filling with the help of a variable speed pump in the case of a highly simplified hydraulic system. Although artificial performance curves are used, the presented technique is directly applicable for real-life hydraulic systems of the same topology. The technique is based on keeping the specific energy consumption of the pump as low as possible and uses easy-to-implement control policy. Because of the simplicity of the model, it is believed that it can serve as a tutorial or benchmark problem for pump-schedule optimization problems. The near optimality of the results is demonstrated numerically by comparing them to the solution of a general-purpose global optimization software.