Flood frequency analysis employing Bayesian regional regression and imperfect historical information

This thesis focuses on development of a Bayesian methodology for analysis of regional Generalized Least Squares (GLS) regression models, and the use of regional regression models and imperfect historical and palaeoflood information to reduce the uncertainty in flood quantile estimators.; The first part of this thesis develops a Bayesian approach to flood frequency analysis with imperfect historical information. A Markov Chain Monte Carlo algorithm provides the posterior distributions of the parameters of lognormal and log Pearson Type 3 distributions, flood quantiles, and flood damage estimators. An example shows that the Bayesian approach provides a better description of the actual uncertainty in some flood quantiles and other functions of the parameters than asymptotic approximations that use the Fisher Information matrix. In addition, the Bayesian MCMC algorithm avoids the numerical problems the Maximum Likelihood procedure faces when fitting the LP3 distribution. The proposed MCMC algorithm provides a computationally and conceptually simple way of appropriately incorporating into flood frequency analysis the joint distribution of possible errors in rating curves and individual observations, which is clearly important when dealing with historical and paleoflood information.; The second part of the thesis, develops an operational Bayesian methodology for the Generalized Least Squares (GLS) model for regionalization of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model-error variance using a convenient quasi-analytic approach. It provides both a measure of the precision of the model error variance that the traditional GLS lacks, and a more reasonable description of the possible values of the model error variance in cases where the model error variance is small compared to the sampling errors, which is often the case for regionalization of shape parameters. Examples illustrate the differences among Ordinary, Weighted, and GLS models, and the method-of-moments, maximum likelihood, and Bayesian estimators of the model error variance. A flood frequency analysis for three sites in the Illinois River basin illustrates the ability of regional information on the shape parameter to increase the precision of flood quantile estimators.