Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Martin, James L

Committee Member

McAnally, William H.

Committee Member

Diaz-Ramirez, Jairo N.

Committee Member

Zhang, Song

Committee Member

Rodriguez, Hugo N.

Other Advisors or Committee Members

Sucsy, Peter V.

Date of Degree

1-1-2013

Document Type

Dissertation - Open Access

Abstract

Uncertainty analysis in hydrodynamic modeling is useful to identify and report the limitations of a model caused by different sources of error. In the practice, the main sources of errors are divided into model structure errors, errors in the input data due to measurement imprecision among other, and parametric errors resulting from the difficulty of identifying physically representative parameter values valid at the temporal and spatial scale of the models. This investigation identifies, implements, evaluates, and recommends a set of methods for the evaluation of model structure uncertainty, parametric uncertainty, and input data uncertainty in hydrodynamic modeling studies. A comprehensive review of uncertainty analysis methods is provided and a set of widely applied methods is selected and implemented in real case studies identifying the main limitations and benefits of their use in hydrodynamic studies. In particular, the following methods are investigated: the First Order Variance Analysis (FOVA) method, the Monte Carlo Uncertainty Analysis (MCUA) method, the Bayesian Monte Carlo (BMC) method, the Markov Chain Monte Carlo (MCMC) method and the Generalized Likelihood Uncertainty Estimation (GLUE) method. The results of this investigation indicate that the uncertainty estimates computed with FOVA are consistent with the results obtained by MCUA. In addition, the comparison of BMC, MCMC and GLUE indicates that BMC and MCMC provide similar estimations of the posterior parameter probability distributions, single-point parameter values, and uncertainty bounds mainly due to the use of the same likelihood function, and the low number of parameters involved in the inference process. However, the implementation of MCMC is substantially more complex than the implementation of BMC given that its sampling algorithm requires a careful definition of auxiliary proposal probability distributions along with their variances to obtain parameter samples that effectively belong to the posterior parameter distribution. The analysis also suggest that the results of GLUE are inconsistent with the results of BMC and MCMC. It is concluded that BMC is a powerful and parsimonious strategy for evaluation of all the sources of uncertainty in hydrodynamic modeling. Despites of the computational requirements of BMC, the method can be easily implemented in most practical applications.

URI

https://hdl.handle.net/11668/20240

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