Download or read book Bayesian GLS Regression for Regionalization of Hydrologic Statistics Floods and Bulletin 17 Skew written by Andrea Gruber Veilleux and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
