资源环境科技发展态势分析平台

This paper develops the quasi‐analytic Bayesian analysis of the Generalized Least Squares (B‐GLS) model introduced by Reis et al. (2005) into an operational and statistically comprehensive GLS regional hydrologic regression methodology to estimate flood quantiles, regional shape parameters, low flows, and other statistics with spatially correlated flow. New GLS regression diagnostic statistics include a Bayesian plausiblity value, pseudo adjusted R‐squared, pseudo‐Analysis of Variance table, and two diagnostic error variance ratios. Traditional leverage and influence are extended to identify rogue observations, address lack‐of‐fit, and to support gauge network design and region‐of‐influence regression. Formulas are derived for the Bayesian computation of estimators, standard errors, and diagnostic statistics. The use of B‐GLS and the new diagnostic statistics is illustrated with regional log‐space skew regression analysis for the State of South Carolina. A comparison of ordinary, weighted, and generalized least squares (GLS) analyses documents the advantages of the Bayesian estimator over the method‐of‐moment estimator of model‐error variance introduced by Stedinger and Tasker (1985). Of the 3, only GLS considers the covariance among concurrent flows. The example demonstrates that GLS regional skewness models can be highly accurate when correctly analyzed: the Bayesian‐GLS average variance of prediction is 0.090 for South Carolina (92 stations), whereas a traditional OLS analysis published by the USGS yielded 0.24. B‐GLS provides a statistical valid framework for the rigorous analysis of spatially‐correlated hydrologic data allowing for the estimation of parameters and their actual precision, and computation of several diagnostic statistics, as well as correctly attributing variability to the 3 key sources.