Journal of Water Resources Planning and Management

Water systems planners have long recognized the need for robust solutions capable of withstanding deviations from the conditions for which they were designed. Robustness analyses have shifted from expected utility to exploratory bottom-up approaches which identify vulnerable scenarios prior to assigning likelihoods. Examples include Robust Decision Making (RDM), Decision Scaling, Info-Gap, and Many-Objective Robust Decision Making (MORDM). We propose a taxonomy of robustness frameworks to compare and contrast these approaches based on their methods of (1) alternative generation, (2) sampling of states of the world, (3) quantification of robustness measures, and (4) sensitivity analysis to identify important uncertainties. Building from the proposed taxonomy, we use a regional urban water supply case study in the Research Triangle region of North Carolina to illustrate the decision-relevant consequences that emerge from each of these choices. Results indicate that the methodological choices in the taxonomy lead to the selection of substantially different planning alternatives, underscoring the importance of an informed definition of robustness. Moreover, the results show that some commonly employed methodological choices and definitions of robustness can have undesired consequences when ranking decision alternatives. For the demonstrated test case, recommendations for overcoming these issues include: (1) decision alternatives should be searched rather than prespecified, (2) dominant uncertainties should be discovered through sensitivity analysis rather than assumed, and (3) a carefully elicited multivariate satisficing measure of robustness allows stakeholders to achieve their problem-specific performance requirements. This work emphasizes the importance of an informed problem formulation for systems facing challenging performance tradeoffs and provides a common vocabulary to link the robustness frameworks widely used in the field of water systems planning.

The impact of water quality conditions in source reservoirs on the optimal operation of a regional multiquality water-distribution system is analyzed. The optimization model concurrently minimizes three operational objectives being pump energy costs, turbidity, and salinity deviations at customer demand nodes from allowed values. The optimization problem is solved using the optimization tool GANetXL incorporating the NSGA-II, linked with the network analysis software EPANet. The example network adapted from the literature captures some of the unique features of the Wimmera Mallee Pipeline in Australia. Six scenarios representing different water quality conditions in source reservoirs are analyzed. It was discovered that two types of trade-offs, competing and noncompeting, exist between the objectives and that the type of trade-off is not unique between a particular pair of objectives for all scenarios. These and other findings may be of particular use to system operators in their long-term operational planning and decision making.

This paper evaluates the impacts of multiple water uses on the operation of a system of existing reservoirs that originally were designed for hydropower generation. The research reported in this paper utilizes a nonlinear optimization model, developed to optimize hydropower production for a system of interconnected reservoirs. This model was modified to include water withdrawals for consumptive uses. The formulated multiobjective optimization problem is solved by employing the weighting method. The formulation considers water allocation policy for consumptive uses and individual hydropower plants. By parametrically varying the weighting coefficients, the tradeoff relationship (Pareto front) between hydropower generation and water demand for consumptive uses was traced out. The modified model is applied to the São Francisco River Basin in Brazil, where there are several hydropower plants in operation with a total installed capacity of 10.7 GW. The river basin is an important agricultural land that requires water supply for crop irrigation. The power generation loss as a result of increased water demand due to consumptive uses was evaluated. Water demand scenarios range from current estimated consumptive uses to the amount expected to be granted by the federal government in the future. It is concluded that these demands cannot fully be met in critical drought periods, and the proposed methodology can be helpful in leading to more equitable solutions among competing water users.

This paper presents a coupled self-adaptive multiobjective differential evolution and network flow algorithm for the optimal operation of complex multipurpose reservoir systems. The developed algorithm (i.e., self-adaptive multiobjective differential evolution) is compared to nondominated sorting genetic algorithm II using a set of common test problems and a real-world case study. An out-of-kilter method for minimal-cost flow problems is used to optimize the water resource system from self-adaptive multiobjective differential evolution inputs driven by the evolutionary process. Self-adaptive multiobjective differential evolution is then used to evaluate objective functions based on the outputs from out-of-kilter algorithm and the process continues until the stop criterion is met. The advantages of the proposed approach include (1) flexible evolutionary algorithms for solving highly complex objective function, and (2) efficient network flow method for dealing with large and highly constrained problems. The case study includes one part of a complex water supply system located in southwestern Brazil that provides water for almost 20 million people in Sao Paulo metropolitan area. The objectives of the case study include minimization of demand shortage (the difference between demand for water and available water supply), maximization of water quality (or minimization of the deviation from the water quality standards), and minimization of pumping cost. The coupled model is applied to the case study using one inflow scenario representing a drought period with inflows below historical average. Multiobjective analyses are performed by comparing two pairs of objective functions, as follows: (1) minimization of demand shortage versus minimization of pumping cost, and (2) minimization of demand shortage versus minimization of the deviation from the water quality standards. The problem constraints include reservoir capacity, capacity of tunnels, channel flow limitations, and minimum downstream release for all reservoirs within the system. The proposed coupled model (self-adaptive multiobjective differential evolution and out-of-kilter) is outperforming both pure self-adaptive multiobjective differential evolution and nondominated sorting genetic algorithm II, as it requires significantly smaller number of generations to derive the Pareto front. In addition, the proposed approach is capable of handling larger problems without major computational burden. The coupled model and self-adaptive multiobjective differential evolution also converge closer to, and provide better coverage of the true Pareto front than, nondominated sorting genetic algorithm II.

Differential evolution (DE) algorithms have been successfully used to handle a wide range of water resource optimization problems in recent years. The relative performance of various DE variants has been typically assessed based on the quality of the final solutions for the selected problems within the given computational budget. Such a comparative analysis, however, provides limited understanding on how various operational mechanisms alter the DE algorithms’ searching behavior and what searching properties lead to improved performance. To improve research in this area, this study aims to characterize and compare the searching behavior of four DE variants using a range of measure metrics, mainly focusing on real-time statistics of the algorithm’s search quality, search progress, and convergence manner. The utility of the metrics is demonstrated using the four DE variants (SDE, dDE, MdDE, and SADE) applied to three water distribution network (WDN) design problems with significantly increased complexity (scales). The behavioral results offer an appreciably improved understanding of the searching characteristics associated with each DE variant, thereby providing guidance for choosing the most suitable DE algorithm to solve a particular WDN optimization problem as well as offering knowledge to develop new advanced algorithms. For real-world problems, the SDE algorithm is more suitable if a limited computational budget is allowed, whereas the SADE and MdDE variants are respectively more appealing when moderate and large computational budgets are available. A new solution with a cost of $12.62 million for the large-scale problem (1,278 decision variables) is presented.

One key alternative for removing, preventing, and effectively coping with the often vexing presence of air in water pipelines is the combination air-vacuum valve. Despite their often effective role, such valves can be highly problematic if not well designed and maintained. This paper critically reviews the current design, application, functionality, and simulation of air valves and the associated shortcomings, with a primary focus on air/vacuum valves (AVVs). It is argued that the efficient number of air valves along undulating pipelines is yet to be fully articulated. Air-valve simulations should expressively consider their dynamic behavior, the physical behavior of any air pockets that might form below an air valve, and the varying character of the water surface at the air valve location. There is a pressing need for a comprehensive and systematic study on the proper sizing and location of AVVs for the transient protection of systems. Overall, the efficient application of AVVs requires broad research and development theoretically (i.e., their physical behavior and improved numerical simulations) and experimentally, as well as field studies to document their in situ dynamic behavior and operational efficiency.

Reliability of a water-distribution system (WDS) can address mechanical, hydraulics, and water quality failure in the system. The research reported in this paper focused on mechanical reliability (subsequently referred to simply as reliability) assessment of a WDS. Existing techniques are restricted to lower states of reliability (one pipe failure at a time) and very little attention has been paid to higher states (simultaneous failure of several pipes). This is due to large computational workload associated with higher-states reliability assessment. Studying various reliability measures, the research reported in this paper revealed statistical flow entropy had stronger correlation with higher states of reliability and was a better surrogate measure. A multicriteria decision analysis (MCDA) was applied to rank a set of WDS layouts (alternatives) using various states of reliabilities (criteria). The MCDA considered the relative importance of each state of reliability in the process of finding the most reliable system (decision making). The MCDA revealed the higher-state reliabilities should have more contribution in the decision-making process.

Efficiency of hydraulic solvers for the simulation of flows and pressures in water distribution systems (WDSs) is very important, especially in the context of optimization and risk analysis problems, where the hydraulic simulation has to be repeated many times. Among the methods used for hydraulic solvers, the most prominent nowadays is the global gradient algorithm (GGA), based on a hybrid node-loop formulation. Previously, another method based just on loop flow equations was proposed, which presents the advantage that it leads to a system matrix that is in most cases much smaller than in the GGA method, but has also some disadvantages, mainly a less sparse system matrix and the fact that introducing some types of valves requires the redefinition of the set of network loops initially defined. The contribution of this paper is to present solutions for overcoming the mentioned disadvantages of the method based on loop flow equations. In particular, efficient procedures are shown for selecting the network loops so as to achieve a highly sparse matrix and methods are presented to incorporate check valves and automatic control valves while avoiding the need to redefine the loops initially selected.

Research in water distribution networks during recent decades has often focused on calibration. There is no unique solution for this problem as the methodologies are developed depending on which parameters have to be calibrated and the final use of the model. This work presents a demand calibration methodology that identifies a set of patterns that minimize the error in predicted measurements. The singular value decomposition (SVD) of the sensitivity matrix is a powerful tool for solving the optimization problem. Additionally, in this work, the deep understanding of the SVD allows the selection of an alternative to the classic patterns. Each individual demand is defined as a combination of geographically distributed patterns. The membership of each demand to every pattern is produced naturally through the analysis of the SVD of the sensitivity matrix. Three types of memberships are considered: binary, positive, and free. The SVD analysis is also used to define the location of sensors for the calibration. The performance of the methodology proposed is tested on a real water distribution network using synthetic data. Results show that the use of positive memberships to define individual demands is the best option to reduce the error in predicted pressures and flows.

The aim of this work is to analyze the extent to which the demand-related uncertainty and long-term effects impact the optimization of the operation of a small hydropower system (SHPS). To this end, a SHPS is assumed to be installed in a real Alpine water distribution system, and its settings are optimized in order to investigate the SHPS long time performance (10-year simulations with EPANET 2) under different future scenarios. Results show that neglecting demand uncertainty and the long-term sequence of demand patterns prevents obtaining a realistic assessment of the profits connected with the SHPS operation. Furthermore, the issue of setting optimization is marginal compared to that of uncertainty assessment and long-term effects.

This paper examines a case where a plan for aquifer management was constructed on the basis of a single criterion. Though the plan was constructed with stakeholder engagement, the criterion for planning success was predefined before any public input was solicited. The Texas state legislature had mandated all regions establish an aquifer plan but it also created the metric for planning success which it operationalized as the aquifer storage remaining after 50 years. The region of the research reported in this paper met the state’s requirement by setting a target for 50% of aquifer storage to remain after 50 years, a so-called 50/50 rule. As this aquifer is functionally nonrenewable, the 50-year storage target is only meaningful when defined in the context of a so-called terminal condition, or a time period for aquifer exhaustion. It is argued that the technical criterion and the policy target were introduced too early. This obviated important pathways of public discussion that could have addressed how to transition from irrigated to dryland agriculture. Discourse instead was filtered through the lens of this simple so-called future condition criterion, which virtually forced policy and policy discourse to center almost exclusively on irrigation restrictions as the way to extend the life of the aquifer. This narrowed focus had several unintended consequences. The final plan reduces agricultural producer profitability today but it also reduces profitability into the distant future, and the plan actually accelerates rather than slows the pace at which producers eventually exit irrigated agriculture. A more meaningful focus might have been discussion on what a transition to dryland might look like and when it might occur. The attempt to extend the life of the aquifer through irrigation restrictions not only fails to extend aquifer life but it defers any real discussion on dryland conversation. More open and more unconstrained conversation needs to occur before experts ever introduce technical planning criteria.