# Probabilistic reconstructions of local temperature and soil moisture from tree-ring data with potentially time-varying climatic response

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## Abstract

We explore a probabilistic, hierarchical Bayesian approach to the simultaneous reconstruction of local temperature and soil moisture from tree-ring width observations. The model explicitly allows for differing calibration and reconstruction interval responses of the ring-width series to climate due to slow changes in climatology coupled with the biological climate thresholds underlying tree-ring growth. A numerical experiment performed using synthetically generated data demonstrates that bimodality can occur in posterior estimates of past climate when the data do not contain enough information to determine whether temperature or moisture limitation controlled reconstruction-interval tree-ring variability. This manifestation of nonidentifiability is a result of the many-to-one mapping from bivariate climate to time series of tree-ring widths. The methodology is applied to reconstruct temperature and soil moisture conditions over the 1080–1129 C.E. interval at Methusalah Walk in the White Mountains of California, where co-located isotopic dendrochronologies suggest that observed moisture limitations on tree growth may have been alleviated. Our model allows for assimilation of both data sources, and computation of the probability of a change in the climatic controls on ring-width relative to those observed in the calibration period. While the probability of a change in control is sensitive to the choice of prior distribution, the inference that conditions were moist and cool at Methuselah Walk during the 1080–1129 C.E. interval is robust. Results also illustrate the power of combining multiple proxy data sets to reduce uncertainty in reconstructions of paleoclimate.

## Keywords

Bayesian hierarchical modeling Biological–statistical modeling Multiproxy paleoclimate reconstruction Tree-ring width Time-varying climate-paleodata relationship## Notes

### Acknowledgments

This work was supported in part by Grants NSF ATM-0724802, NSF ATM-0902715, NSF DMS-1204892, NSF AGS 1304309, and NOAA NA060OAR4310115. We thank Steve Leavitt for lending his isotope data as well as insights on their interpretation, Chris Daly and the PRISM project for making their work freely available, and Benno Blumenthal for making the PRISM data easily accessible on the IRI Data Library. We are also grateful for insightful comments from Chris Paciorek and one other anonymous reviewer, which substantially improved the final version of this paper.

## Supplementary material

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