Andrea G. Veilleux

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

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

Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho

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Bayesian WLS/GLS Regression for Regional Skewness Analysis for Regions with Large Crest Stage Gage Networks

This paper summarizes methodological advances in regional log-space skewness analyses that support flood-frequency analysis with the log Pearson Type III (LP3) distribution. A Bayesian Weighted Least Squares/Generalized Least Squares (B-WLS/B-GLS) methodology that relates observed skewness coefficient estimators to basin characteristics in conjunction with diagnostic statistics represents an extension of the previously developed B-GLS methodology. B-WLS/B-GLS has been shown to be effective in two California studies. B-WLS/B-GLS uses B-WLS to generate stable estimators of model parameters and B-GLS to estimate the precision of those B-WLS regression parameters, as well as the precision of the model. The study described here employs this methodology to develop a regional skewness model for the State of Iowa. To provide cost effective peak-flow data for smaller drainage basins in Iowa, the U.S. Geological Survey operates a large network of crest stage gages (CSGs) that only record flow values above an identified recording threshold (thus producing a censored data record). CSGs are different from continuous-record gages, which record almost all flow values and have been used in previous B-GLS and B-WLS/B-GLS regional skewness studies. The complexity of analyzing a large CSG network is addressed by using the B-WLS/B-GLS framework along with the Expected Moments Algorithm (EMA). Because EMA allows for the censoring of low outliers, as well as the use of estimated interval discharges for missing, censored, and historic data, it complicates the calculations of effective record length (and effective concurrent record length) used to describe the precision of sample estimators because the peak discharges are no longer solely represented by single values. Thus new record length calculations were developed. The regional skewness analysis for the State of Iowa illustrates the value of the new B-LS/B-GLS methodology with these new extensions.