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

Abstract

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.