Journal of Water Resources Planning and Management

This paper introduces a framework for incorporating uncertainty in water supply system models that uses Bayesian statistics and mixed-integer programming. The output of the framework includes the most probable least cost solution, the probability of feasibility for a given solution, component probabilities for each decision, and a distribution of the optimal objective function value. The method is applied to the problem of developing a water supply system design for Israel, Jordan, and the Palestinian territories. The method allows decision makers to evaluate various alternatives for a water supply plan that incorporates uncertainties in future demand and costs. The design of a water supply plan is a concern with properties that are distinct from traditional approaches to the design of water distribution systems; namely, local engineering decisions concerning pipe diameters and water pressure are not explicitly modeled, but large-scale decisions concerning the construction of water conveyances (pipes, canals, and tunnels) and sources (desalination plants) are the focus in the model.

This paper investigates issue linkage of water and energy in transboundary water sharing agreements and evaluates how such issue linkages can enhance the scope of cooperation between upstream and downstream countries. In a case study on transboundary water sharing between Burkina Faso and Ghana, the main upstream and downstream riparians in the Volta Basin, the paper evaluates both the scope and sustainability of such cooperation based on issue linkage. In the framework of a static Stackelberg game with numerical analysis, it is found that the interdependency of countries can lead to efficient and effective solutions regarding water sharing. In the cooperation phase, Ghana has the opportunity to increase its water consumption for agriculture, which is currently restricted, while Burkina Faso benefits from discounted hydropower as a compensation for restricting its water consumption. In such a case, the cooperation is mutually beneficial and stable. However, such interdependency may not be sustainable in the very long term, i.e., when population increase induces Burkina Faso to increase its water consumption and destabilizes the cooperation based on the water and energy issue linkage. Overall, the results show that issue linkages within the water sector might present additional strategies to generate benefits from cooperation on transboundary rivers by taking into account more than water use alone. The collective benefits of hydropower can lead to an overall improvement in welfare.

The allocation of water resources has long been recognized as a critical optimization problem. In this study, a bilevel programming model with fuzzy random variables is developed for tackling a regional water resources allocation problem on the basis of water rights distribution in a river basin. The bilevel programming model takes the optimal total benefit of the society and the optimal economic benefit of each subarea as the upper and lower targets, respectively. In contrast to previous studies, the balance of the satisfactory degree between the upper and lower decision makers is considered in the bilevel optimization for ensuring the equity of the water resource allocation. To deal with inherent uncertainties, the fuzzy random variables are first transformed into trapezoidal fuzzy numbers, and by taking advantage of the expected value operation, the trapezoidal fuzzy numbers are subsequently defuzzified. For solving the complex and nonlinear bilevel programming model, an interactive fuzzy programming technique and an entropy-Boltzmann selection-based genetic algorithm are designed as a combined solution method. Finally, the results and comparisons analysis of a case study are presented to demonstrate the practicality and efficiency of the optimization method.

A hierarchical optimization method is presented for an assessment of the potential maximum energy output of the Three Gorges Project and Gezhouba cascade hydropower stations in China. The optimization incorporates a detailed description of daily load dispatching among different types of hydropower units. The optimization method is divided into three levels to render feasible the computation of the global optimization problem. In levels 1 and 2, a genetic algorithm is applied to optimize discharge and water head distribution between the upstream and downstream reservoirs. Level 1 selects the water levels at the beginning of each month in a year. Level 2 selects the water levels at the beginning of each day in a month. Level 3 solves a linear programming problem for allocation of water among the heterogeneous types of hydropower generation. Hydrological data of the years 2004 and 2005 are used to perform an optimized power generation process within the operating rules. The maximal annual energy production could be approximately 61 and 87 MWh higher than the actual recorded energy production in 2004 and 2005, respectively.

River bed materials are commonly removed and conveyed downstream. In this process, some sediments are deposited in reservoirs, causing a decrease in reservoir active storage capacity and thus its ability to meet water demand. Flushing is a sediment-release method operated from the bottom outlet gates that releases stored water to flush sediments. As a result, water shortages may occur after the flushing operation. Thus, it is important to develop a reservoir operation policy for time and volume release of sediment that meets water demand. Uncertainties in water and sediment inflows to the reservoir are also important issues that add to the complexity of such policies. This paper presents a stochastic dynamic programming (SDP) model with two uncertainties to determine the simultaneous optimal operation policies for meeting water demand and sediment flushing. To evaluate the capability of the SDP model with two uncertainties, four other operation policies are developed, and all five scenarios are evaluated by using various performance indices in the Sefidroud reservoir of northern Iran. All scenarios are designed with different rules and priorities of water and sediment release. The best performance indices are those resulting from the optimization scenario that considers both inflow and sediment uncertainties.

The process of urbanization transforms natural landscape into impervious land cover, affecting the ecosystem health of receiving water bodies and downstream communities by changing the timing and volumes of the natural flow regime. Best management practices (BMP) and low impact development (LID) are a set of mitigating measures that can be considered for watershed management to mitigate the hydrologic consequences of urbanization. This research develops a methodology to select sites for placing LID technologies, namely rainwater harvesting and permeable pavements, to reduce hydrologic impacts, measured as alterations to the peak flow while meeting a prespecified budget. A simulation-optimization methodology couples a genetic algorithm with a hydrologic model, a hydraulic model, and curve number-based models of LID technologies. The trade-off between costs and peak flow alteration is explored by optimizing LID placement under varying budget constraints. Strategies that combine a detention pond and LID are explored and optimized for a spectrum of design storms, including 2-, 10-, and 100-year events. Trade-offs among management strategies that are designed to control storms of different sizes are analyzed. The simulation-optimization framework and methodology is applied for a small watershed on the Texas A&M University campus.

Convex equations exist in different fields of research. As an example are the Hazen-Williams or Darcy-Weisbach head-loss formulas and chlorine decay in water supply systems. Pure linear programming (LP) cannot be directly applied to these equations and heuristic techniques must be used. This study presents a methodology for linearization of increasing or decreasing convex nonlinear equations and their incorporation into LP optimization models. The algorithm is demonstrated on the Hazen-Williams head-loss equation combined with a LP optimal operation water supply model. The Hazen-Williams equation is linearized between two points along the nonlinear flow curve. The first point is a fixed point optimally located in the expected flow domain according to maximum flow rate expected in the pipe (estimated through maximum flow velocities and pipe diameter). The second point is the calculated flow rate in the pipe resulting from the previous iteration step solution. In each iteration step, the linear coefficients are altered according to the previous step’s flow rate result and the fixed point. The solution gradually converges closer to the nonlinear head-loss equation results. The iterative process stops once both an optimal solution is attained and a satisfactory approximation is received. The methodology is demonstrated using simple and complex example applications.

Reclaimed wastewater is increasingly important to satisfaction of water-sustainability objectives in water-short municipalities throughout the United States and particularly in the Southwest. Water reclamation and reuse present new challenges for urban planners, who now tend to consider renewable freshwater and reclaimed wastewater as unique parts of a single water resources portfolio. Efficiency objectives in geographically dispersed communities lead planners to explore the relative merits of centralized versus decentralized wastewater-treatment capacity when new construction is required. However, the complexity of the planning landscape—in which existing water distribution and sewerage capacities; geographic factors; and uncertainty in growth projections, energy cost, and even the sustainability of existing freshwater supplies contribute to plan selection—suggests that decision support methods can usefully supplement engineering judgment to find a near-optimal level of decentralization in facilities planning. In this study, an existing decision support system (DSS) was modified to include costs attributable to infrastructure construction, operation, and maintenance for wastewater collection and transmission of both potable and reclaimed water at the regional (city or city subsection) level to aid water supply planning. The modified DSS was then applied to a study area in southeast Tucson, Arizona. Several scenarios are developed and compared on the basis of cost and energy consumption. A sensitivity analysis is provided. In general, increased peripheral demand, limited existing capacity, greater elevation differences, and lower discount rates favor decentralized design and construction.

Uncertainties facing water planners and designers include changes in demand resulting from community growth (temporal and spatial), per capita water use, public perceptions, and regulations. One of the most powerful and intuitive ways to represent these uncertainties in the planning stage is to use scenarios. A scenario represents a realization of the system’s random parameters. Scenario-based analysis provides organizational flexibility by planning for multiple potential future scenarios, each of which may be, although is not necessarily, associated with a probability of occurrence. In this study, a scenario-based multiobjective optimization model for robust optimal design of regional-scale water and wastewater infrastructure is presented. The proposed methodology is demonstrated with an application to the planning of a decentralized water supply and reuse system for a new development area in metropolitan Tucson, where sustainable water supply is a significant issue.

Waste-load allocation (WLA) is a difficult problem with multiobjective features, which requires models that consider a full range of competing goals to identify good and practical solutions. In this study, a general and multiobjective optimization model was proposed. This model integrates different decision variables related to multiple waste-removal efficiencies and outflow discharges into water bodies. This model also considered an equity measure and limits for the concentration of dissolved oxygen and biochemical oxygen demand. A simulated annealing (SA) algorithm and the enhanced stream water quality simulation model (QUAL2E) were used to solve the WLA problem. This approach was applied to the Santa Maria da Vitória River watershed in the state of Espírito Santo, Brazil. Computational results have demonstrated that the proposed optimization model with the SA metaheuristic and QUAL2E could effectively incorporate the expectations and conflicting objectives, providing various good solutions to support decision makers.