1. www.siena.edu/booker 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

2. www.siena.edu/booker or, How dammed should the river be?

3. www.siena.edu/booker 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.

4. www.siena.edu/booker Outline The basic scenario “Theory of the Dam” Fundamental intertemporal condition Optimal reservoir size Application: Colorado River

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

6. www.siena.edu/booker “Optimal size” maximize diversions from a stochastic flow using storage

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

8. www.siena.edu/booker 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.

9. www.siena.edu/booker

11. Now do some math...

12. www.siena.edu/booker Solutions look like...

13. www.siena.edu/booker or...

14. www.siena.edu/booker or...

15. www.siena.edu/booker From here Generalize:An approach for an arbitrary basin Application: The Colorado River Basin

16. www.siena.edu/booker General solutions (numerical) evaporation loss = 0.05 * storage

17. www.siena.edu/booker The Colorado

18. www.siena.edu/booker 442 year Lee Ferry Tree-Ring reconstruction; evaporation=3%

19. www.siena.edu/booker 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.

20. www.siena.edu/booker 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.

21. www.siena.edu/booker