2005 Maxwell, Matthew S
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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.