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

Abstract

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 nopooling 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.

China’s socioeconomic risk from extreme events in a changing climate: a hierarchical Bayesian model

“…At the second level of the model, we assess the spread of covariate effects across provinces. A multivariate Normal distribution is considered for the regression coefficients β s and b s , respectively (Chen et al 2014;Devineni et al 2013;Kwon et al 2011). The corresponding equations are expressed as…”

“…A hierarchical Bayesian approach can help quantify model and parameter uncertainties, and provides an opportunity for uncertainty reduction through partial pooling of the common information from different regions while considering heterogeneity (Gelman and Hill 2007). Such methods have been employed to flexibly construct statistical relationships in some fields (Chen et al 2014;Devineni et al 2013;Sun et al 2015). For climate change impact analysis, a hierarchical Bayesian model could help provide reasonable ranges of potential damages.…”

Climate information based streamflow and rainfall forecasts for Huai River basin using hierarchical Bayesian modeling

“…In this paper, we follow an approach similar to that used by Devineni et al (2013) for tree-ring-based streamflow reconstruction, but for multi-variate seasonal forecasts for regional Table 2. The correlation between streamflow/area rainfall and climate predictors chosen in this study * .…”

“…This allows a better representation of model and parameter uncertainties. Recently, Devineni et al (2013) presented a hierarchical Bayesian regression strategy for estimating streamflow at multiple locations using various model structures to pool information across multiple sites to an appropriate degree such that the features that are common to the site regression and those that vary across sites can be identified for an overall reduction in parameter uncertainty while preserving the structure in errors across the stations. Here, a similar Hierarchical Bayesian approach is developed for regional rainfall and streamflow forecasts using appropriate climate indicators that could be derived from GCMs or observed climate fields.…”

Annual Precipitation Reconstruction Based on Tree-ring Data at Seorak

“…기존의 연구에서 Treering 자료가 가지는 비선형 추계학적 특징이 제시되었으므 로 (Grassberger, 1986;Kim, 1997) 자료의 비선형성･추계학 적 특성을 반영하는 재생성이 필요하다. 그에 따라서, 최근 에는 추계학적 특성을 반영할 수 있는 Tree-ring 연구가 이 루어지기도 하였으나 (Devineni et al, 2013;Gray et al, 2004;Raffalli-Delerce et al, 2004;Stoffel and Bollschweiler, 2009), 최근까지도 선형적인 가정에 기반을 둔 재생성 기법 이 많이 사용되었다 (Akkemik et al, 2005;Brázdil et al, 2002;Salzer and Kipfmueller, 2005;Woodhouse, 2001;Wilson and Luckman, 2002;Xuemei and Xiangding, 1997 (Battiti, 1989, Giill et al, 1981. Brock et al, 1991;Brock et al, 1996;Kim et al, 2003).…”