A Statistical Reconstruction of Bivariate Climate from Tree Ring Width Measurements Using Scientifically Motivated Process Models.

The ability to reconstruct historical climate is important to understanding how climate has changed in the past. The instrumental record of temperature and precipitation only spans the most recent centuries. Thus, reconstructions of the climate features are typically based on proxy archives. The proxy archives integrate climate information through biological, geological, physical, and chemical processes. Tree ring widths provide one of the most spatially and temporally rich sources of high quality climate proxy data. However, the statistical reconstruction of paleoclimate from tree ring widths is quite challenging because the climate signal is inherently multi-dimensional while tree ring widths are a one dimensional data source.

We propose a Bayesian Hierarchical model using a non-linear, scientifically motivated tree ring growth models to reconstruct multivariate climate (i.e., temperature and precipitation) in the Hudson Valley region of New York. Our proposed model extends and enhances former methods in a number of ways. We allow for species-specific responses to climate, which further constrains the many-to-one relationship between tree rings and climate. The resulting model allows for prediction of reasonable climate scenarios given tree ring widths. We explore a natural model selection framework that weighs the influence of multiple candidate growth models in terms of their predictive ability. To enable prediction backcasts, the climate variables are modeled with an underlying continuous time latent process. The continuous time process allows for added flexibility in the climate response through time at different temporal scales and enables investigation of differences in climate between the reconstruction period and the instrumental period. Validation of the model's predictive abilities is achieved through a pseudo-proxy simulation experiment where the quality of climate predictions are measured by out of sample performance based on a proper local scoring rule. By accounting for species specific repsonses to climate and adding flexibility in predictions through a continuous time process, we achieve a scientifically motivated reconstruction of paleoclimate from tree ring widths with associated uncertainties that furthers the understanding of historical climate change.