Climate of the Past Discussions www.clim-past-discuss.net 1814-9340 1814-9359 5 2 2009 10.5194/cpd-5-797-2009 http://www.clim-past-discuss.net/5/797/2009/ http://www.clim-past-discuss.net/5/797/2009/cpd-5-797-2009.html http://www.clim-past-discuss.net/5/797/2009/cpd-5-797-2009.pdf 797 816 2009-03-04 Extracting a common high frequency signal from northern Quebec black spruce tree-rings with a Bayesian hierarchical model J.-J. Boreux jj.boreux@ulg.ac.be P. Naveau O. Guin L. Perreault J. Bernier The University of Liège, Arlon, Belgium Laboratoire des Sciences du Climat et de l'Environnement, IPSL-CNRS, France Institut de Recherche d'Hydro-Quebec, Montréal, Canada Dendrochronology, the scientific dating method based on the analysis of tree-ring growth patterns, has been frequently applied in climatology. The basic premise of dendroclimatology is that tree rings can be viewed as climate proxies, i.e. rings are assumed to contain some hidden information about past climate. From a statistical perspective, this extraction problem can be understood as the search of a hidden variable which represents the common signal within a collection of tree-ring width series. Classical average-based techniques used in dendrochronology have been, with different degrees of success (depending on tree species, regional factors and statistical methods), applied to estimate the mean behavior of this latent variable. Still, a precise quantification of uncertainties associated to the hidden variable distribution is difficult to assess. To model the error propagation throughout the extraction procedure, we propose and study a Bayesian hierarchical model that focuses on extracting an inter-annual high frequency signal. Our method is applied to black spruce <i>(Picea mariana)</i> tree-rings recorded in northern Quebec and compared to a classical average-based techniques used by dendrochronologists. %REFERENCE 1 Berliner L., Wikle, C., and Cressie, N.: Long-lead prediction of Pacific SSTs via Bayesian Dynamic Modeling, J. Climate, 13, 3953–3968, 2000. Cooley, D., Naveau, P., Jomelli, V., Rababtel, A., and Grancher, D.: A bayesian hierarchical extreme value model for lichenometry, Environmetrics, 16, 1–20, 2005. Cooley, D., Nychka, D., and Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels, J. Am. Stat. Assoc., 102(479), 824–840, 2007. Cook, E. R. and Kairiukstis, A.: Methods of dendrochronology, Kluwer Academic Publishers, 1992. Douglass, A. E.: Climatic cycles and tree-growth, Carnegie Institution of Washington publication, 289, vol 3, 1936. Esper J., Cook, E. R., and Schweingruber, F. H.: Low-Frequency Signals in Long Tree-Ring Chronologies for Reconstructing Past Temperature Variability, Science, 295, 2250–2254, 2002. Gencay, R., Selcuk, F., and Whitcher, B.: An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press, San Diego, 2002. Gelman, A., Carlin, J., Stern, H., and Rubin, D.: Bayesian Data Analysis, 2nd ed. Chapman andHall, 2003. George, S., Meko, D. M., and Evans M. E.: Regional tree growth and inferred summer climate in the Winnipeg River basin, Canada, since AD 1783, Quat. Res., 70, 158–172, 2008. Gelman, A.: Inference and monitoring convergence, in: Gilks, W. R., Richarson, S., and Spiegelhalter, D. J., Markov Chain Monte Carlo in Practice, Chapman and Hall, 1996. % %Guin, O., Naveau P., Boreux J.J., Yiou P., Franck D. and Bernier J. (2009). %\newblock %Bayesian hierarchical modeling of regional tree growths in the Alps. %\newblock \em Unpublished manuscript. Hooten, M. B. and Wikle, C. K.: Shifts in the spatio-temporal growth dynamics of shortleaf pine, Environmental and Ecological Statistics, 14, 3, 2007. \newblock Nicault, A., Guiot, J., Edouard, J.-L., and Brewer, S.: Preserving long-term fluctuations in standardisation of tree-ring series by Adaptive Regional Growth Curve (ARGC) Dendrochronologia, submitted, 2008. Melvin, T. M., Briffa, K. R., Nicolussi, K., and Grabner, M.: Time-varying-response smoothing, Dendrochronologia, 25, 65–69, 2007.