Date of Award

2011

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Mevin Hooten

Second Advisor

David Stevens

Third Advisor

Jürgen Symanzik

Abstract

Recent studies in the field of fluvial sediment transport underscore the difficulty in reliably estimating transport model parameters, collecting accurate observations, and making predictions due to measurement error and conceptual model uncertainty. There is a pressing need to develop models that can account for measurement error, conceptual model uncertainty, and natural variability while providing probability-based predictions as well as a means for conceptual model discrimination. The model presented in this research employs an excess shear sediment transport equation for a uni-size sediment bed developed in a Bayesian statistical framework. This statistical model provides a means to rigorously estimate distributions of model parameters, such as critical shear, given observations of sediment transport. The model provides transport predictions in the form of a posterior predictive distribution from which credible intervals of sediment transport can be designated. The proposed framework utilizes the Deviance Information Criterion to quantify model fit with model parsimony. This approach relies upon the incorporation of expert judgment in the form of prior distribution s for model parameters of interest. The uni-size sediment transport model developed in this research was tested against simulated observations for which the 'true' model parameters were known. Results of the simulation studies indicate that such a modeling approach is valid and presents opportunities for expert judgment to bolster parameter inference through the incorporation of prior knowledge. The proposed model was also tested against laboratory flume data for validity; results indicate that this framework is promising as it allows modelers to evaluate competing conceptual models; provides credible intervals of parameters and predictions; and weighs prior expert knowledge with information contained in new observations.

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