HR: 1340h
AN: PP13B-1271    [Abstracts]
TI: A Bayesian Algorithm for Reconstructing Spatially Averaged Temperature
AU: * Tingley, M P
EM: tingley@fas.harvard.edu
AF: Harvard University, 20 Oxford Street, Cambridge, MA 02138, United States
AU: Huybers, P
EM: phuybers@fas.harvard.edu
AF: Harvard University, 20 Oxford Street, Cambridge, MA 02138, United States
AB: The determination of spatially averaged temperature from point estimates is a non-trivial statistical problem. In the paleo-climate context, the additional need to convert proxy time-series into temperature estimates presents a serious challenge. Most estimates of spatially averaged temperature at paleo-climate time-scales address these two issues sequentially: the proxy values are first averaged through space, and these estimates are then transformed onto the temperature scale via some form of regression. This two step approach distances the final estimate of temperature from the underlying data, complicating estimates of the associated uncertainty. Our approach is to model the relationship between the true temperature field and the noisy, localized measurements of it using a hidden Markov model. We use a fully Bayesian algorithm to simultaneously estimate the coefficients linking the proxy values to temperature units, the parameters associated with both the temporal and spatial covariance structures, the observational error variances, the temperature values at a large number of uniformly distributed spatial locations, and the average of these estimated temperature values. We assume proper but weakly informative priors for all unknowns. We have, when possible, used conjugate priors - many of them not normal. A major benefit of this Bayesian approach is that, by drawing repeatedly from the full conditional posterior distributions, we obtain an estimate of the uncertainty covariance structure. This allows us to make quantitative statements about both the relative contributions of the different proxies to the spatial average, and the extent to which the model can constrain the various parameters. In particular, the model outputs the uncertainty in the coefficients of the transformation linking the proxy values to temperature units. The model can easily be generalized to accommodate different categories of proxy data assumed to have different uncertainty properties. We first apply the model to surrogate data to test the method and develop intuition about the convergence properties of the Monte-Carlo sampling procedure. We then apply the model to instrumental data, before extending the reconstruction back in time using proxy data.
DE: 1616 Climate variability (1635, 3305, 3309, 4215, 4513)
DE: 1637 Regional climate change
DE: 3252 Spatial analysis (0500)
DE: 3270 Time series analysis (1872, 4277, 4475)
DE: 4914 Continental climate records
SC: Paleoceanography and Paleoclimatology [PP]
MN: 2007 Fall Meeting