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 research presented in this thesis develops new statistical techniques for estimating regional skewness coefficients to improve flood frequency analysis in the United States. Flood frequency guidelines for the United States, specified in Bulletin 17B, recommend fitting the log-Pearson Type III (LP3) distribution to the series of annual flood maxima, in which the third moment of the distribution, the skewness coefficient , is combined with a regional skewness coefficient to improve its precision. The research presented here extends the quasi-analytic Bayesian analysis of the Generalized Least Squares (GLS) regional hydrologic regression framework introduced by Reis et al. [2005] to more accurately and precisely estimate regional skewness coefficients. Specifically, formulas derived within a Bayesian regression framework for the computation of estimators, standard errors, and diagnostic statistics are provided by Reis [2005] and Reis et al. [2005]. Diagnostic statistics further developed here include a Bayesian plausibility value, pseudo adjusted R-squared, pseudo-Analysis of Variance table, two diagnostic error variance ratios, as well as leverage and influence metrics. In addition, this research also develops a new influence diagnostic statistic which, in conjunction with the Bayesian extension of GLS leverage and influence metrics, can be used to better identify rogue observations and to effectively address lack-of-fit when estimating skewness coefficients. Currently, Bulletin 17B allows for regional skew values to be obtained from the skew map included with the Bulletin. As it is over 30 years old, the regional skew values from the Bulletin 17B skew map do not reflect annual maximum data acquired since 1976. This increase in available data, along with advances in computing power to support the Bayesian GLS regional hydrologic regression framework, allow for a much more precise estimate of the regional skewness coefficient for use in flood frequency analysis. This research employs the Bayesian GLS regression framework to estimate regional log-space skewness coefficients for three data sets: the Illinois River basin, the state of South Carolina, and the Southeastern United States. Bulletin 17B allows for the generation of skew prediction equations as an alternative method for determining regional skew coefficients when the mean squared error of the equations is smaller than reported from the Bulletin's skew map. These skew prediction equations can be generated using Ordinary Least Squares analysis, Weighted Least Squares analysis, Generalized Least Squares analysis employing the method of moment model-error-variance estimator introduced by Stedinger and Tasker [1985, 1986ab], or the new Bayesian GLS estimator. The advantages of using the Bayesian GLS estimation technique to determine a skew prediction equation are demonstrated here in the Illinois River basin and the state of South Carolina studies. To correctly analyze the Southeastern United States data set, methods are developed for identifying and screening redundant sites corresponding to nested watersheds with similar drainage areas. Special attention is devoted to developing an improved cross-correlation model of annual peak flows. The Bayesian GLS analysis using 342 stations from the Southeastern U.S. results in a highly accurate, constant regional skew model, with an average variance of prediction equal to 0.14. More complex models which include regional information and basin characteristics as additional regression parameters result in very little improvement. The application of the Bayesian estimator in the Southeastern study generates improved results over the mean square error of 0.30 reported for the Bulletin 17B regional map skew.

Proceedings of the International Symposium on Flood Frequency and Risk Analyses, May 14-17, 1986, Louisiana State University, Baton Rouge, U.S.A.

After five decades, the field of Statistical Hydrology continues to evolve and remains a very active area of investigation. Researchers continue to examine various distributions, methods of estimation of parameters, and problems related to regionalization. However, much of this research appears in journals and reports and usually in a form not easi

Sacramento, California, has grown literally at the edge of the Sacramento and American Rivers and for 150 years has struggled to protect itself from periodic floods by employing structural and land management measures. Much of the population lives behind levees, and most of the city's downtown business and government area is vulnerable to flooding. A major flood in 1986 served as impetus for efforts by federal, state, and local entities to identify an acceptable and feasible set of measures to increase Sacramento's level of safety from American River floods. Numerous options were identified in 1991 by the U.S. Army Corps of Engineers (USACE) in a report known as the American River Watershed Investigation. Due to the controversial nature of many of the alternatives identified in that report, study participants were not able to reach consensus on any of the flood control options. In response, the Congress directed the USACE to reevaluate available flood control options and, at the same time, asked the USACE to engage the National Research Council (NRC) as an independent advisor on these difficult studies. In 1995 NRC's Committee on Flood Control Alternatives in the American River Basin issued Flood Risk Management and the American River Basin: An Evaluation. This report outlined an approach for improving the selection of a flood risk reduction strategy from the many available.