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Research group of Dr. Arturo S. Leon

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Quantification of Uncertainty in River Flow Dynamics Using Polynomial Chaos Stochastic Expansion Techniques

E-mail: cgiffordmiears@gmail.com

Phone: (530) 588-5771

Project: Quantification of Uncertainty in River Flow Dynamics Using Polynomial Chaos Stochastic Expansion Techniques (March 2012-June 2013)

Abstract: In this research we present a novel approach for propagation of uncertainty in river systems. Errors in data observations and predictions (e.g., stream inflows), in model parameters, and resulting from the discretization of continuous systems, all point to the need to accurately quantify the amount of uncertainty carried through the modeling process. However, it is not sufficient to merely understand the magnitude of these uncertainties. We also need to be able to quantify the sensitivity of the system to the uncertainties in individual model parameters and forcings.

In the proposed framework, stochastic processes are incorporated directly into the physical description of the system (e.g., river flow dynamics) with the goal of better modeling uncertainties (both aleatoric and epistemic) and hence, reducing the ranges of the confidence intervals on quantities of interest.  Only the stream inflows (external source) are assumed to be purely stochastic; other uncertain quantities (e.g., water stages) are correlated to the uncertainty of the stream inflows using the flow dynamics of the river as the physical description of the system. The flow dynamics are simulated efficiently using the performance graphs approach implemented in the OSU Rivers model. We represent uncertainty in stream inflows via an error term modeled as a stochastic process. Stochastic collocation is then used to discretize random space.  This non-intrusive approach is both more efficient than Monte-Carlo methods and is as flexible in its application.   Upon computation of the expansion coefficients for the quantities of interest, we have an analytical representation of a surrogate of the stochastic solution in polynomial form. This allows, among other things, various solution statistics to be easily obtained, such as expected value (or higher order modes), or parametric sensitivities. The application of this framework to a complex river network is described in the paper.

Funding Agency: Bonneville Power Administration (US Department of Energy)

Advisor: Dr. Arturo S. Leon

Collaborator: Dr. Nathan Gibson (Mathematics)

Polynomial Chaos Expansions (PCE) and Stochastic collocation uncertainty quantification performed using Sandia Laboratories DAKOTA software: http://dakota.sandia.gov/index.html










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