Bayesian WLS/GLS Regression for Regional Skewness Analysis for Regions with Large Cross-Correlations among Flood Flows

Abstract

This paper summarizes methodological advances in regional log-space skewness analyses to support flood frequency analysis with the LP3 distribution. Due to large cross-correlations among flood peaks in some areas of the United States, a new Bayesian Weighted Least Squares/ Generalized Least Squares (WLS/GLS) methodology is developed that relates observed skewness estimators to basin characteristics. It provides estimates of the precision of the models and of parameter estimators. Bayesian WLS/GLS is an extension of the quasi-analytic Bayesian analysis of the Generalized Least Squares (GLS) regional hydrologic regression framework introduced by Reis et al. [2005] and extended by Gruber et al. [2007] and Veilleux [2009]. Flood frequency analysis is performed with the Expected Moments Algorithm (EMA) when flood records contain low outliers and zero flows. This methodology is illustrated through the development of regional log-space skewness models for annual maximum 1-, 3-, 7-, 15-, and 30day rainfall flood volumes in the Central Valley and surrounding areas of California [Lamontagne et al., 2011]. For non-linear models relating skew to elevation, the average variance of prediction ranges from 0.048 to 0.056, while Pseudo R 2 values range from 60% to 85% corresponding to effective record lengths of 120 to 170 years, depending on rainfall-flood