[1] This study contributes a many-objective analysis of the tradeoffs associated with using the portfolio planning approach for managing the urban water supply risks posed by growing population demands and droughts. The analysis focuses on four supply portfolio strategies: (1) portfolios with permanent rights to reservoir inflows, (2) adaptive options contracts added to the permanent rights, (3) rights, options, and leases, and (4) rights, options, and leases subject to a critical reliability constraint used to represent a maximally risk averse case. The portfolio planning strategies were evaluated using a 10 year Monte Carlo simulation of a city in the Lower Rio Grande Valley (LRGV) within Texas. Our solution sets provide the tradeoff surfaces between portfolios' expected values for cost, cost variability, reliability, surplus water, frequency of using leases, and dropped (or unused) transfers of water. Using an additional severe drought scenario, this work shows that leases and options can reduce the potential for critical supply failures when urban supply systems must contend with unexpected and severe extremes in both demand and water scarcity. In summary, this paper contributes a framework that couples interactive visualization and many-objective optimization to innovate urban water portfolio planning under uncertainty. The many-objective analysis of the LRGV case study shows that effective water portfolio planning can simultaneously improve the costs, efficiency, and reliability of urban water supply while ensuring adaptability and resiliency to future changes.Citation: Kasprzyk, J. R., P. M. Reed, B. R. Kirsch, and G. W. Characklis (2009), Managing population and drought risks using many-objective water portfolio planning under uncertainty, Water Resour. Res., 45, W12401,

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[1] Most cities rely on firm water supply capacity to meet demand, but increasing scarcity and supply costs are encouraging greater use of temporary transfers (e.g., spot leases, options). This raises questions regarding how best to coordinate the use of these transfers in meeting cost and reliability objectives. This paper combines a hydrologic-water market simulation with an optimization approach to identify portfolios of permanent rights, options, and leases that minimize the expected costs of meeting a city's annual demand with a specified reliability. Spot market prices are linked to hydrologic conditions and described by monthly lease price distributions which are used to price options via a riskneutral approach. Monthly choices regarding when and how much water to acquire through temporary transfers are made on the basis of anticipatory decision rules related to the ratio of expected supply to expected demand. The simulation is linked with an algorithm that uses an implicit filtering search method designed for solution surfaces that exhibit high-frequency, low-amplitude noise. This simulation-optimization approach is applied to a region that currently supports an active water market, with results suggesting that temporary transfers can reduce expected water supply costs substantially, while still maintaining high reliability. Also evaluated are trade-offs between expected costs and cost variability that occur with variation in a portfolio's distribution of rights, options, and leases.

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[1] The use of temporary transfers, such as options and leases, has grown as utilities attempt to meet increases in demand while reducing dependence on the expansion of costly infrastructure capacity (e.g., reservoirs). Earlier work has been done to construct optimal portfolios comprising firm capacity and transfers, using decision rules that determine the timing and volume of transfers. However, such work has only focused on the short-term (e.g., 1-year scenarios), which limits the utility of these planning efforts. Developing multiyear portfolios can lead to the exploration of a wider range of alternatives but also increases the computational burden. This work utilizes a coupled hydrologic-economic model to simulate the long-term performance of a city's water supply portfolio. This stochastic model is linked with an optimization search algorithm that is designed to handle the high-frequency, low-amplitude noise inherent in many simulations, particularly those involving expected values. This noise is detrimental to the accuracy and precision of the optimized solution and has traditionally been controlled by investing greater computational effort in the simulation. However, the increased computational effort can be substantial. This work describes the integration of a variance reduction technique (control variate method) within the simulation/optimization as a means of more efficiently identifying minimum cost portfolios. Random variation in model output (i.e., noise) is moderated using knowledge of random variations in stochastic input variables (e.g., reservoir inflows, demand), thereby reducing the computing time by 50% or more. Using these efficiency gains, water supply portfolios are evaluated over a 10-year period in order to assess their ability to reduce costs and adapt to demand growth, while still meeting reliability goals. As a part of the evaluation, several multiyear option contract structures are explored and compared.