Www.siena.edu/booker Water Demand, Risk, and Optimal Reservoir Storage James F. Booker with contributions by John O’Neil Siena College Annual Conference.

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Presentation transcript:

Water Demand, Risk, and Optimal Reservoir Storage James F. Booker with contributions by John O’Neil Siena College Annual Conference of the University Council on Water Resources, Portland, Oregon, July 20-22, 2004

or, How dammed should the river be?

Previous approaches Meet predetermined (inelastic) demand, and find probability (and costs?) of failing to “meet” the demand. Burness and Quirk, 1978: “The Theory of the Dam: An Application to the Colorado River” - uses elastic demand.

Outline The basic scenario “Theory of the Dam” Fundamental intertemporal condition Optimal reservoir size Application: Colorado River

My starting point Think about getting the most out of a predetermined resource -- go beyond meeting a predetermined (inelastic) “demand” with a certain reliability.

“Optimal size” maximize diversions from a stochastic flow using storage

The Physical Problem Single stochastic inflow Reservoir storage upstream from use Loss (e.g. evaporation) is a function of storage Single use below reservoir

The Objective Maximize the beneficial use of water over time, where marginal benefits of use in each time are defined by a demand function: p(x) = x 1/ , where  is the price elasticity of demand.

Now do some math...

Solutions look like...

or...

or...

From here Generalize:An approach for an arbitrary basin Application: The Colorado River Basin

General solutions (numerical) evaporation loss = 0.05 * storage

The Colorado

442 year Lee Ferry Tree-Ring reconstruction; evaporation=3%

Conclusions Optimal reservoir storage is a function of the price elasticity of demand, evaporation losses, and variance of inflow. Existing capacities may be greater than optimal given evaporation losses.

Future work Add more realistic decisionmaking: Monte Carlo approach to future flows. Add more realistic inflow distributions, including autocorrelation. Define more precisely “maximum” reservoir size.