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This paper develops the quasi‐analytic Bayesian analysis of the generalized least squares (GLS) (B‐GLS) model introduced by Reis et al. (2005, https://doi.org/10.1029/2004WR003445) 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 records. New GLS regression diagnostic statistics include a Bayesian plausibility value, pseudo adjusted R2, 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 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 are illustrated with a regional log‐space skew regression analysis for the Piedmont region in the Southeastern U.S. A comparison of ordinary, weighted, and 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, https://doi.org/10.1029/WR021i009p01421). Of the three types of analyses, only GLS considers the covariance among concurrent flows. The example demonstrates that GLS regional skewness models can be highly accurate when correctly analyzed: The B‐GLS average variance of prediction is 0.090 for South Carolina (92 stations), whereas a traditional ordinary least squares analysis published by the U.S. Geological Survey yielded 0.193 (Feaster & Tasker, 2002, https://doi.org/10.3133/wri024140). 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 three key sources: time sampling error, model error, and signal. Key Points: A comprehensive statistical framework for regional hydrologic regression is presented with spatially correlated flow data and varying record lengthsFramework correctly attributes variability to sampling errors in computed statistic, variability explained by the model, and model errorNew diagnostics includes Bayesian plausibility value, pseudo adjusted R2, pseudo ANOVA, and Bayesian metrics for leverage and influence [ABSTRACT FROM AUTHOR]

Seasonal streamflow forecasts based on climate information can guide water managers toward superior reservoir operations, leading to improved water resources management efficiency. Uncertainty, however, is always present in seasonal streamflow forecasts, affecting the forecast value. Thus, a forecast should not be considered complete without a description of its uncertainty, which is critical for climate risk and water resources management. This study investigates the uncertainties of a seasonal streamflow forecast system for Northeastern Brazil based on climate precipitation forecasts and hydrologic modeling. These two sources of uncertainty are treated independently and then compared in order to guide future investments in the forecast system. Sea surface temperature is considered to be the primary source of uncertainty for the seasonal precipitation forecasts, based upon a 10-member climate model ensemble. Parameter uncertainty is considered to be the only source of uncertainty for the hydrologic model. Estimation of parameter uncertainty is estimated by the Shuffled Complex Evolution Metropolis algorithm, which employs a Markov Chain Monte Carlo scheme to provide the posterior distribution of the parameters and form uncertainty bounds on streamflow forecasts. Results indicate that uncertainties associated with the climate forecast are much larger than those from parameter estimation in the hydrologic model. Although model structure has not been considered in the evaluation of hydrologic uncertainties, this study indicates that future efforts to address the predominant source of uncertainty should focus on the climate prediction models. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]