Journal of Water Resources Planning and Management

This paper addresses the problem of determining the optimal daily operating policy of a small reservoir subject to yearly probabilistic constraints on floods and shortages. The problem is difficult to solve because the reservoir inflows on day $k$ are stochastic and correlated with those on days $k-1,k-2,\dots ,k-n$ . The problem is broken down into two subproblems that are solved with a set of inflow scenarios and not with the conditional probability distributions of the inflows. The first subproblem determines the conditions to be respected each day for the yearly probabilistic constraints to be satisfied. The second finds the reservoir’s optimal feedback operating policy for each day of the year that respects those conditions. This method is applied to the Kenogami reservoir located in Quebec, Canada, and the results are presented. The method is robust, fast to execute, and easy to program. Furthermore, it does not require that the problem be linear or differentiable.

One of the first steps in developing an optimal water resources design model is creating appropriate objective functions that represent the primary goals of the design. In many cases, one major objective is minimizing cost. A more realistic cost function, with detailed cost terms, may yield more accurate results but will require more development effort. This research examines the benefits of developing a realistic cost function using two multiobjective groundwater remediation case studies. The results show that realistic cost functions find better solutions than the simplified cost functions, as well as identifying more optimal solutions on the Pareto frontier than the other functions. The realistic cost functions achieved up to 14% improvement in total cost, although the degree of loss in accuracy varies substantially for the two case studies considered in this work and for different parameter settings within each case study. Given the difficulties of predicting which case studies or parameter settings would have significant loss of performance from using simplified cost functions, investments in developing accurate site-specific cost functions appear to be worthwhile.

In urban storm water management planning, a common problem associated with the widespread implementation of storage/treatment facilities, is the determination of the relative magnitudes of the storage capacity and the controlled outflow capacity in conjunction with the desired levels of system performance. For this purpose, cost-effective designs in the configuration of storage/treatment facilities can benefit from analytical tools that are able to provide explicit analytical solutions to system control measures in terms of the catchment meteorological characteristics and the drainage system control elements (e.g., storage capacity and controlled release rate). This paper presents methodologies and necessary procedures for the development of system performance measures (such as average annual volume of spills and number of spills from storage facilities) for storm water runoff quantity control based on derived probability distribution theory. Essentially, these runoff control measures with closed-form mathematical expressions are derived from transformations of the probability density functions (PDFs) of the rainfall characteristics into the PDF of runoff volume in terms of a modified version of the rainfall–runoff transformation, which explicitly considers the infiltration process. Results from a case study indicate that these analytical models can be employed as effective tools for storm water runoff quantity control analysis. In contrast to continuous simulation, these analytical tools (models) are especially useful at the planning stage in the evaluation of a wide range of alternative designs.

Due to inherent variability in instantaneous water consumption levels, values of demands at nodes in a water distribution system remain one of the major sources of uncertainty in the network design process. Uncertainty in demand leads to uncertainty in head at the nodes, which, in turn, affects the system performance and has to be taken into account when designing new water distribution systems or extending/rehabilitating existing ones. One approach to dealing with this difficulty is to formulate and solve the stochastic optimization problem providing a robust, cost-effective solution. However, stochastic formulation usually requires Monte Carlo simulation, which involves calculation of a large number of state estimates, even for relatively simple networks. This renders the approach intractable when combined with heuristic adaptive search techniques, such as genetic algorithms (GAs) or simulated annealing. These methodologies require the fitness function to be evaluated for thousands of possible network configurations in the course of the search process. In this paper a new approach to quantifying the influence of demand uncertainty on nodal heads is proposed. The original stochastic model is reformulated as a deterministic one, which uses standard deviation as a natural measure of variability. Such an approach allows the use of effective numerical methods to quantify the influence of uncertainty on the robustness of water distribution system solutions. The deterministic equivalent is then coupled with an efficient GA solver to find robust and economic solutions. The proposed methodology was tested on the New York tunnels and Anytown problems. A number of low cost network solutions were found for different levels of reliability and different forms of probability distribution function for demands. The robustness of the solutions found was compared to known solutions for deterministic formulations, whose results were postprocessed using full Monte Carlo simulation.

The implementation of water use restrictions in a given district is very much related to the severity of an evolving drought; thus, water management agencies such as City Water Departments often face the question of how critical or severe a particular drought event is. While this question has typically been examined using drought indices (e.g., the Palmer Drought Severity Index), unfortunately they do not provide any information on the frequency or recurrence time of the drought or on the risk that specific drought events may occur in a given time horizon. In this paper, the severity of alternative drought events are determined following a similar concept as for the severity of floods, i.e., the return period of a flood event, e.g., the $500\text{-}\text{year}$ flood. We develop procedures for determining drought severity based on historical data, generated data, and mathematical algorithms. In particular, we focus on the drought that has been occurring in the Western United States and take the Poudre River, Colo., as an example. The analysis was based on $119\text{years}$ of records of naturalized flows of the Poudre River. A stochastic model was used for generating long-term synthetic flows, from which the return period and risk of drought events were determined. In addition, we used a mathematical algorithm for determining the distribution of drought events and their return periods. Assuming the sample mean as the water demand threshold, drought severity, frequency, and risk statistics were obtained; e.g., the severity of the $3\text{-}\text{year}$ (2000–2002) drought (i.e., $3\text{-}\text{year}$ drought with $D>\mathrm{404,011}\text{acre}\text{-}\mathrm{ft}$ ) is of the order of a $\mathrm{1,000}\text{-}\text{year}$ return period and the risk that such a $3\text{-}\text{year}$ drought will occur in a $25\text{-}\text{year}$ period is about 2.4%.

This paper presents a comparative evaluation of methods for climate-based estimation of the net inflow rate into Lake Okeechobee, Fla. The estimated net inflow rate is used by the South Florida Water Management District (SFWMD) to support the management and operations of the Lake Okeechobee hydrologic system. The first method evaluated in this paper (Croley) uses rainfall outlooks provided by the National Oceanic and Atmospheric Administration’s Climate Prediction Center (CPC) to calculate a weighed average of historical inflow values for each month. The second method evaluated in this paper (SFWMD Empirical) uses a linear regression on statistics of historical data to predict the net inflow rate. These two methods were developed and have been used operationally by the SFWMD since 2000. Three new methods are presented and comparatively evaluated to gauge their ability in estimating net inflow rates. The first two of these methods are based on CPC issued forecasts in decile probability density format. The remaining method is based on a subsampling technique for “peer” wet∕dry years in the historical record and is found to yield better results in a retrospective analysis. For extreme climatic events on the historical record, CPC rainfall outlooks are found not to yield a large enough shift in probabilities for forecasts to match observed net inflow rates; this is especially noticeable during El Niño Southern Oscillation events. Recommendations are made for potential improvements to climate-based net inflow rate estimation methods, particularly in regard to their ability to reproduce observed results for net inflow into Lake Okeechobee in the presence of an extreme climatic event, as well as over an extended climatological period.

The events of September 11, 2001 in the United States have brought to the fore the problem of drinking water distribution systems security. As a water distribution system is spatially diverse, limiting physical access to all components is practically impossible. Deliberate intrusions of contaminants directly into tanks, treatment plants, or through connecting devices is considered one of the most serious terrorist threats. An effective means of reducing this threat is online contamination monitoring. This paper extends previous work of the writers for optimal allocation of monitoring stations to secure drinking water distribution systems against deliberate contamination intrusions. The current methodology takes explicitly into account the randomness of the flow rate of the injected pollutants, the randomness in consumer’s demands, and the detection sensitivity and response time of the monitoring stations. The objective is to determine the optimal location of a set of monitoring stations aimed at detecting deliberate external terrorist hazard intrusions through water distribution system nodes: sources, tanks, treatment plant intakes, consumers—subject to extended period hydraulic demands and water quality conditions, and a maximum volume of polluted water exposure to the public at a concentration higher than a minimum hazard level. The methodology is implemented in a noncommercial program entitled optiMQ-S and demonstrated on EPANET Example 3.