Extracting a Common Signal in Tree Ring Widths with a Semi-parametric Bayesian Hierarchical Model

International audience; There are numerous statistical challenges involved in the general field of climate reconstructions, including the preprocessing of raw data, often called standardization. This paper focuses on this essential but often overlooked preprocessing stage for one of the most used climate proxy, tree ring widths. One basic premise of dendroclimatology (dendron = tree) is that tree ring widths are assumed to contain relevant information about past climate. By going back to the data source, we focus on improving uncertainty assessments and more accurately identifying a climatic signal. Tree ring width logarithms measured on a given tree are classically decomposed into an individual age effect and a common signal shared by all trees from the same site. Through informative priors, we assume that the individual age effect component lives on a narrow frequency band. This corresponds to the a priori knowledge that individual trees have a smooth aging process. In contrast, the environmental signal shared by all trees is not assumed to belong to a specific frequency range. From a statistical perspective, the search of this common signal shared by a series of tree ring width logarithms can be viewed at inferring the different components of a specific additive model. Compared to past dendroclimatology studies, we propose a semi-parametric Bayesian hierarchical model that offers the possibility to capture low and high frequencies in tree ring widths. Our new model is tested on simulated data and applied to Pinus halepensis Mill. ring widths recorded in French Mediterranean.