A Tree-Ring-Based Reconstruction of Delaware River Basin Streamflow Using Hierarchical Bayesian Regression

A hierarchical Bayesian regression model is presented for reconstructing the average summer streamflow at five gauges in the Delaware River basin using eight regional tree-ring chronologies. The model provides estimates of the posterior probability distribution of each reconstructed streamflow series considering parameter uncertainty. The vectors of regression coefficients are modeled as draws from a common multivariate normal distribution with unknown parameters estimated as part of the analysis. This leads to a multilevel structure. The covariance structure of the streamflow residuals across sites is explicitly modeled. The resulting partial pooling of information across multiple stations leads to a reduction in parameter uncertainty. The effect of no pooling and full pooling of station information, as end points of the method, is explored. The no-pooling model considers independent estimation of the regression coefficients for each streamflow gauge with respect to each tree-ring chronology. The full-pooling model considers that the same regression coefficients apply across all streamflow sites for a particular tree-ring chronology. The cross-site correlation of residuals is modeled in all cases. Performance on metrics typically used by tree-ring reconstruction experts, such as reduction of error, coefficient of efficiency, and coverage rates under credible intervals is comparable to, or better, for the partial-pooling model relative to the no-pooling model, and streamflow estimation uncertainty is reduced. Long record simulations from reconstructions are used to develop estimates of the probability of duration and severity of droughts in the region. Analysis of monotonic trends in the reconstructed drought events do not reject the null hypothesis of no trend at the 90% significance over 1754-2000.