Development Of Regional Skew Models For Rainfall Floods In California Using Baseyian Least Squares Regression

Abstract

The thesis here reports on and expands the results published in Lamontagne et al. [2012]. A hybrid Bayesian weighted/generalized least squares regression procedure is used to generate regional skew models for annual maximum rainfall floods of various durations in California. The procedure uses weighted least squares to estimate the model coefficients, and generalized least squares to estimate model precision. This procedure is necessitated by the unusually high cross-correlation exhibited between concurrent rainfall floods at different sites, which caused the regression weights to become unjustifiably erratic. New diagnostic statistics are developed for this special case and applied to real data. Overall model precision is excellent, which is important in the context of Bulletin 17B flood frequency analysis. Chapter 1 of the thesis provides an introductory background to flood frequency analysis, and the scope and area of the study. Chapter 1 also describes the procedure used by the United States Army Corps of Engineers to develop the rainfall flood time series. Chapter 2 discusses the characteristics of the log-Pearson Type III distribution, the Bulletin 17B flood frequency procedure, the Expected Moments Algorithm, and the effect of outliers on frequency estimation and tests for their identification and removal. Chapter 3 describes the development of weighted least squares and generalized least squares for regionalization of hydrologic variables. Chapter 3 then derives the new hybrid weighted/generalized least squares regression procedure and its accompanying diagnostic statistics. Finally, Chapter 3 discusses recent research which uses an alternative generalized least squares framework. Chapter 4 details the application of the procedure from Chapter 3 to rainfall flood of various durations from California to create a regional skew model for California. Finally, Chapter 5 examines various aspects of the analysis in Chapter 4 which were noticeably different from previous regional skew studies. In particular, Chapter 4 reexamines the Pseudo ANOVA table and proposes a new, alternative table. ii