2005 Maxwell, Matthew S

							                             Maxwell, Matthew
                            Demand Forecast Modeling
                          A Water Resources Application
                       Faculty Mentor: Sean Warnick, Computer Science

The Sevier River Basin is located in rural south-central Utah. It
covers approximately 12.5 percent of the state of Utah and is
managed by the Sevier River Water Users Association (SRWUA).
The majority of water in the basin is used for irrigation purposes.
The basin is divided into five regions as represented in Figure 1:
Upper, Central, Gunnison, Lower, and San Pitch. Piute Reservoir is
located in the Upper region. Valuable run-off collects in Piute
Reservoir each spring. Releases from this reservoir flow north into
diversions located along the river in the Central region. Excess
water runs over Vermillion Dam (located on the Central/Gunnison
border) and is lost to water users in the Central and Upper regions.    Figure 1 – Sevier River Basin


Because the Sevier River Basin is located in an arid climate and generally uses all possible water
resources each year, effective management of Piute Reservoir is a high priority. To facilitate a
more efficient water management system, the Sevier River Basin has been heavily instrumented
and has many diversions and release structures that can be controlled remotely via radio. Piute
Dam is one of these remotely automated structures. This automated gate forms the framework
from which the Piute Dam model-driven automation project is based.

The goal of water management for Piute Reservoir is to release the least amount of water from
the reservoir as possible while ensuring that all downstream demands are met. If the proper
amount of water is released from Piute Dam all demands will be met and very little excess water
will be lost at the end of the river stretch; however, if an incorrect amount of water is released
from the dam there will be either too little water to meet the demands of farmers or too much
excess water lost at the end of the river. This water management process is complicated by the
fact that the delay from reservoir to the lowest downstream point is over 24 hours long and that
river flow is subject to disturbances such as evaporation, seepage, unmeasured inflow, and
precipitation. Both the delays and disturbances complicate the task of estimating how much
water will be flowing at the end of the river given known inflows and diversions.

The current model used by the SRWUA to estimate downstream flow is a lagged mass balance
model. The model simply estimates the downstream flow by taking the sum of the outflows
from the sum of the inflows. As such, this model does not account for any unmeasured
disturbances. Additionally, lags for this model were determined entirely by guesses based on
experience.

As part of my project I researched current models used in river system estimation models and
adapted those results to the Sevier River. Through my research I discovered that there were two
main processes used to model river system flow: a physics-based and a data-driven modeling
procedure1. Since the Sevier River has been instrumented since the beginning 2000, we have a
large amount of data to develop models from; however, the physical data required to model a
river adequately was neither widely-available nor reliable. Consequently, the model we
developed for the Sevier River used a data-driven approach to fit a parameterized model. The
decision to use a data-driven model is further justified by research showing that data-driven
models and physical-based models often have comparable results2.

The parameterized model developed for the Sevier River was based upon a number of
observations we made during the research process. The first observation was that about 6%
more water was flowing out of the river than was flowing into the river. This means that
contrary to our initial beliefs the Sevier River actually gains more water from unmeasured
inflows along the course of the river than is lost to seepage and evaporation. This also indicates
that a mass balance model (which assumes the same amount of water that flows into a river will
be the same amount that flows out) would consistently be off by at least 6% due to this
phenomenon. Another observation we made that aided in the modeling procedure was that all of
the outflow measurements were at locations very near to the actual river diversions. Thus we
were able to assume that there were no significant disturbances in the outflow.

From these observations we were able to develop a model appropriate for the Sevier River. We
used a weighted mass balance model where the weights of the outflows were fixed at unity and
the weights of the two measured inflows were parameterized through linear regression.
Additionally we used statistical correlation tests to empirically decide on lag estimates for each
stretch of the river. We used roughly three years of historical data to fit our parametric model
and two years of data to validate the model.

The results of the validation show that the model we developed for the Sevier River was at least
comparable to the mass balance model used by the SRWUA. Additionally, the model we
developed consistently outperformed the original model during times of high flow. From a water
management perspective, periods of high flow are the most important time to estimate water
flows well. Consequently, the model we developed for the Sevier River was very successful and
improved upon the methods the SRWUA already used.

The model developed from this research we be used as the basis for the design and
implementation of a robust controller for the Sevier River. The resulting controller will be tested
on the actual river system in the spring of 2006. After the initial tests are completed, the results
will be analyzed and further developments will be made. If the results from this experiment are
favorable, this system will become the foundation of a fully-automated Sevier River Basin.




1
  P.O. Malaterre and B.P. Baume, ”Modeling and regulation of irrigation canals: existing applications and ongoing
researches”, in Proceedings of IEEE Conference on System, Man, and Cybernetics”, San Diego, CA, USA, 1998,
pp. 3850-3855.
2
  S.K. Ooi, M.P.M. Krutzen, and E. Weyer, ”On physical and data driven modelling of irrigation channels”, in
Control Engineering Practice, vol. 13, issue 4, April 2005, pp. 461-471.