• Berliner, L. M., , C. K. Wikle, , and N. Cressie, 2000: Long-lead prediction of Pacific SSTs via Bayesian dynamic modeling. J. Climate, 13, 39533968.

    • Search Google Scholar
    • Export Citation
  • Buckley, B. M., and Coauthors, 2010: Climate as a contributing factor in the demise of Angkor, Cambodia. Proc. Natl. Acad. Sci. USA, 107, 67486752.

    • Search Google Scholar
    • Export Citation
  • Cook, E. R., 1985 : A time series analysis approach to tree-ring standardization. Ph.D. dissertation, University of Arizona, 342 pp.

  • Cook, E. R., , and G. Jacoby, 1977: Tree-ring drought relationships in the Hudson Valley, New York. Science, 198, 399401.

  • Cook, E. R., , and K. Peters, 1981: The smoothing spline: A new approach to standardizing forest interior ring-width series for dendroclimatic studies. Tree-Ring Bull., 41, 4553.

    • Search Google Scholar
    • Export Citation
  • Cook, E. R., , and G. Jacoby, 1983: Potomac River streamflow since 1730 as reconstructed by tree rings. J. Climate Appl. Meteor., 22, 16591672.

    • Search Google Scholar
    • Export Citation
  • Cook, E. R., , and L. A. Kairiukstis, 1990: Methods of Dendrochronology: Applications in the Environmental Sciences. Kluwer Academic, 304 pp.

  • Cook, E. R., , and N. Pederson, 2010: Uncertainty, emergence, and statistics in dendrochronology. Dendroclimatology: Progress and Prospects, M. K. Hughes, T. W. Swetnam, and H. F. Diaz, Eds., Vol. 11, Developments in Paleoenvironmental Research, Springer Verlag, 77–112.

  • Cook, E. R., , D. Meko, , D. Stahle, , and M. Cleaveland, 1999: Drought reconstructions for the continental United States. J. Climate, 12, 11451162.

    • Search Google Scholar
    • Export Citation
  • Cook, E. R., , R. Seager, , R. R. Heim Jr., , R. S. Vose, , C. Herweijer, , and C. Woodhouse, 2010: Megadroughts in North America: Placing IPCC projections of hydroclimatic change in a long-term palaeoclimate context. J. Quat. Sci., 25, 4861.

    • Search Google Scholar
    • Export Citation
  • Dempster, A. P., , N. M. Laird, , and D. B. Rubin, 1977: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc., 39, 138.

    • Search Google Scholar
    • Export Citation
  • DRBC, cited 2007: Flexible flow management program. [Available online at http://water.usgs.gov/osw/odrm/.]

  • Friedman, J. H., 1984: A variable span smoother. Stanford University SLAC PUB-3477 STAN-LCS 005, 30 pp. [Available online at http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-3477.pdf.]

  • Fritts, H. C., 1976: Tree Rings and Climate. Academic Press, 567 pp.

  • Gangopadhyay, S., , B. L. Harding, , B. Rajagopalan, , J. J. Lukas, , and T. J. Fulp, 2009: A nonparametric approach for paleohydrologic reconstruction of annual streamflow ensembles. Water Resour. Res., 45, W06417, doi:10.1029/2008WR007201.

    • Search Google Scholar
    • Export Citation
  • Gelman, A., 2005: Prior distribution for variance parameters in hierarchical models. Bayesian Anal., 1, 119.

  • Gelman, A., , and D. B. Rubin, 1992: Inference from iterative simulation using multiple sequences. Stat. Sci., 7, 457511.

  • Gelman, A., , and J. Hill, 2007: Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, 648 pp.

  • Gelman, A., , J. B. Carlin, , H. S. Stern, , and D. B. Rubin, 2004: Bayesian Data Analysis. Chapman & Hall, 668 pp.

  • Gilks, W. R., , and G. O. Roberts, 1995: Strategies for improving MCMC. Markov Chain Monte Carlo in Practice: Interdisciplinary Statistics, W. R. Gilks, S. Richardson, and D. Spiegelhalter, Eds., Chapman & Hall, 89–114.

  • Helsel, D. R., , and R. M. Hirsch, 1992: Statistical Methods in Water Resources. Studies in Environmental Science Series, Vol. 49, Elsevier Science, 522 pp.

  • Kagawa, A., , A. Sugimoto, , and T. C. Maximov, 2006: 13CO2 pulse-labelling of photoassimilates reveals carbon allocation within and between tree rings. Plant Cell Environ., 29, 15711584.

    • Search Google Scholar
    • Export Citation
  • Kauffman, G. J., , and K. J. Vonck, 2011: Frequency and intensity of extreme drought in the Delaware basin, 1600–2002. Water Resour. Res., 47, W05521, doi:10.1029/2009WR008821.

    • Search Google Scholar
    • Export Citation
  • Kolesar, P., , and J. Serio, 2011: Breaking the deadlock: Improving water-release policies on the Delaware River through operations research. INFORMS Interfaces, 41, 1834.

    • Search Google Scholar
    • Export Citation
  • Kwon, H.-H., , U. Lall, , and A. F. Khalil, 2007: Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: Applications to rainfall and temperature. Water Resour. Res., 43, W05407, doi:10.1029/2006WR005258.

    • Search Google Scholar
    • Export Citation
  • Kwon, H.-H., , C. Brown, , and U. Lall, 2008: Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modeling. Geophys. Res. Lett., 35, L05404, doi:10.1029/2007GL032220.

    • Search Google Scholar
    • Export Citation
  • Kwon, H.-H., , U. Lall, , and V. Engel, 2011: Predicting foraging wading bird populations in Everglades National Park from seasonal hydrologic statistics under different management scenarios. Water Resour. Res., 47, W09510, doi:10.1029/2010WR009552.

    • Search Google Scholar
    • Export Citation
  • Li, B., , D. W. Nychka, , and C. M. Ammann, 2010: The value of multi-proxy reconstruction of past climate. J. Amer. Stat. Assoc., 105, 883911.

    • Search Google Scholar
    • Export Citation
  • Lima, C. H. R., , and U. Lall, 2009: Hierarchical Bayesian modeling of multisite daily rainfall occurrence: Rainy season onset, peak and end. Water Resour. Res., 45, W07422, doi:10.1029/2008WR007485.

    • Search Google Scholar
    • Export Citation
  • Lima, C. H. R., , and U. Lall, 2010: Spatial scaling in a changing climate: A hierarchical Bayesian model for non-stationary multi-site annual maximum and monthly streamflow. J. Hydrol., 383, 307318, doi:10.1016/j.jhydrol.2009.12.045.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1956: Empirical orthogonal functions and statistical weather prediction. MIT Department of Meteorology Statistical Forecasting Scientific Rep. 1, 57 pp.

  • Lunn, D. J., , A. Thomas, , N. Best, , and D. Spiegelhalter, 2000: WinBUGS—A Bayesian modelling framework: Concepts, structure, and extensibility. Stat. Comput., 10, 325337.

    • Search Google Scholar
    • Export Citation
  • Mann, H. B., 1945: Nonparametric tests against trend. Econometrica, 13, 245259.

  • Maxwell, R. S., , A. E. Hessl, , E. R. Cook, , and N. Pederson, 2011: A multispecies tree ring reconstruction of Potomac River streamflow (950–2001). Water Resour. Res., 47, W05512, doi:10.1029/2010WR010019.

    • Search Google Scholar
    • Export Citation
  • Meko, D. M., , and D. A. Graybill, 1995: Tree-ring reconstruction of Upper Gila River discharge. Water Resour. Bull., 31, 605616.

  • Meko, D. M., , C. A. Woodhouse, , C. H. Baisan, , T. Knight, , J. J. Lukas, , M. K. Hughes, , and M. W. Salzer, 2007: Medieval drought in the Upper Colorado River basin. Geophys. Res. Lett.,34, L10705, doi:10.1029/2007GL029988.

    • Search Google Scholar
    • Export Citation
  • Namias, J., 1966: Nature and possible causes of the northeastern United States drought during 1962–1965. Mon. Wea. Rev., 94, 543557.

    • Search Google Scholar
    • Export Citation
  • Namias, J., 1967: Further studies of drought over northeastern United States. Mon. Wea. Rev., 95, 497508.

  • NYCDEP, cited 2011: History of drought and water consumption. [Available online at http://www.nyc.gov/html/dep/html/drinking_water/droughthist.shtml.]

  • Pederson, N., 2005: Climatic sensitivity and growth of southern temperate trees in the Eastern US: Implications for the carbon cycle. Ph.D. dissertation, Columbia University, 186 pp.

  • Pederson, N., , E. R. Cook, , G. C. Jacoby, , D. M. Peteet, , and K. L. Griffin, 2004: The influence of winter temperatures on the annual radial growth of six northern-range-margin tree species. Dendrochronologia, 22, 729.

    • Search Google Scholar
    • Export Citation
  • Pederson, N., , A. R. Bell, , E. R. Cook, , U. Lall, , N. Devineni, , R. Seager, , K. Eggelston, , and K. J. Vranes, 2013: Is an epic pluvial masking the water insecurity of the Greater New York City region? J. Climate, 26, 13391354.

    • Search Google Scholar
    • Export Citation
  • Raftery, A., 1995: Bayesian model selection in social research. Sociol. Methodol., 25, 111163.

  • Royston, P., 1995: Remark AS R94: A remark on algorithm AS 181: The W test for normality. Appl. Stat., 44, 547551.

  • Schneider, T., 2001: Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. J. Climate, 14, 853871.

    • Search Google Scholar
    • Export Citation
  • Spiegelhalter, D., , A. Thomas, , N. Best, , and W. Gilks, 1996: BUGS 0.5: Bayesian inference using Gibbs sampling manual (version ii). Medical Research Council Biostatistics Unit Manual, 59 pp.

  • Stockton, C. W., , and G. C. Jacoby, 1976: Long-term surface-water supply and streamflow trends in the Upper Colorado River basin based on tree-ring analyses. National Science Foundation Lake Powell Research Project Bull. 18, 70 pp.

  • Stokes, M. A., , and T. L. Smiley, 1968: An Introduction to Tree-Ring Dating. University of Arizona Press, 73 pp.

  • Tingley, M. P., , and P. Huybers, 2010a: A Bayesian algorithm for reconstructing climate anomalies in space and time. Part I: Development and applications to paleoclimate reconstruction problems. J. Climate, 23, 27592781.

    • Search Google Scholar
    • Export Citation
  • Tingley, M. P., , and P. Huybers, 2010b: A Bayesian algorithm for reconstructing climate anomalies in space and time. Part II: Comparison with the regularized expectation–maximization algorithm. J. Climate, 23, 27822800.

    • Search Google Scholar
    • Export Citation
  • Trumbore, S., , J. Gaudinski, , P. Hanson, , and J. Southon, 2002: Quantifying ecosystem–atmosphere carbon exchange with a 14C label. Eos, Trans. Amer. Geophys. Union, 83, 265268.

    • Search Google Scholar
    • Export Citation
  • Wikle, C. K., 2003: Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology, 84, 13821394.

  • Woodhouse, C. A., , and J. Lukas, 2006a: Drought, tree rings and water resource management in Colorado. Can. Water Resour. J., 31, 114, doi:10.4296/cwrj3104297.

    • Search Google Scholar
    • Export Citation
  • Woodhouse, C. A., , and J. Lukas, 2006b: Multi-century tree-ring reconstructions of Colorado streamflow for water resource planning. Climatic Change, 78, 293315, doi:10.1007/s10584-006-9055-0.

    • Search Google Scholar
    • Export Citation
  • Woodhouse, C. A., , S. T. Gray, , and D. M. Meko, 2006: Updated streamflow reconstructions for the Upper Colorado River basin. Water Resour. Res., 42, W05415, doi:10.1029/2005WR004455.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 93 93 18
PDF Downloads 76 76 13

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

View More View Less
  • 1 Columbia Water Center, The Earth Institute, Columbia University, New York, New York
  • | 2 Department of Earth and Environmental Engineering, and Columbia Water Center, Columbia University, New York, New York
  • | 3 Tree Ring Laboratory, Lamont-Doherty Earth Observatory, Palisades, New York
© Get Permissions
Restricted access

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 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.

Corresponding author address: Naresh Devineni, Columbia Water Center, The Earth Institute, Columbia University, New York, NY 10027. E-mail: nd2339@columbia.edu

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 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.

Corresponding author address: Naresh Devineni, Columbia Water Center, The Earth Institute, Columbia University, New York, NY 10027. E-mail: nd2339@columbia.edu
Save