Title page for ETD etd-08102007-140000

Type of Document

Dissertation

Author

Dillard, Karen Edna Michele,

URN

etd-08102007-140000

Title

An Application of Implicit Filtering to Water Resources Management

Degree

PhD

Graduate Program

Applied Mathematics

Advisory Committee

Advisor Name	Title
C.T. Kelley	Committee Chair
E.L. Stitzinger	Committee Member
G.W. Characklis	Committee Member
P.A. Gremaud	Committee Member

Keywords

water resources
implicit filtering
stochastic simulation
variance reduction
noisy functions
optimization

Date of Defense

2007-08-24

Availability

unrestricted

Abstract

We introduce the concept of a water market, the buying and selling of water as prices fluctuate based on supply and demand, applied to a region in southern Texas. The water market provides different alternatives for a municipal to acquire water. The water resources problem is to determine the combination of alternatives that results in minimum cost. To accomplish this, we link a one-year stochastic simulation that randomly selects from historical data to an
optimizer called implicit filtering. We find that a municipal can lower expected costs while meeting the water demand by allowing a
portfolio with cost variability. The stochastics create low amplitude, high frequency perturbations, called noise, in the optimization landscape. We apply a variance reduction method to reduce the noise. We select the control variate method to reduce the variance. This method does reduce the variance and the
computational cost as well. Variance reduction also makes it possible to expand to a multi-year model. A multi-year model is more useful to the water resources manager since municipals will not
change the portfolio every year. Municipals look at longer time horizons that account for such factors as growth in demand. Now, we are able to simulate multiple years with the model since the
computational cost is not prohibitive. Last, we design a methodology in which the model adapts the number of realizations to control the estimated level of noise. The model uses information from the optimizer about the current location and increases the number of realizations in the noisier areas of the landscape. We
find that the benefit of applying the adaptive model is the reduction in the average realizations per function call.

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