Title: A Bayesian approach to reconstructing space-time climate fields from proxy and instrumental time series, applied to 600 years of northern hemisphere surface temperature data
Description: Human kind's activities over the last few centuries have increased the levels of greenhouse gasses in the atmosphere to levels not seen in at least 800 thousand years. While it is of the utmost importance to understand how the climate system will respond to these changes, an exigent precursor is to understand the natural variability of the climate system on a wide range of spatial and temporal scales. As instrumental data sets are of limited length, it is necessary to analyze elements of the natural world sensitive to the local climate to explore the time evolution of the climate system prior to about 1850. Reconstructing the spatial pattern of a climate field through time from a data set of overlapping instrumental and climate proxy time series is a non-trivial statistical problem. The need to convert the proxy time series into the correct units, and the fact that the data time series are incomplete and heterogeneously distributed in space and time, further complicate the analysis. A new approach to this problem is formulated by specifying simple parametric forms for the spatial covariance and temporal evolution of the climate field, as well as 'observation equations' that describe the relationships between the data types and the corresponding true values of the climate field.

A Bayesian model assimilates both the proxy and instrumental records to estimate the probability distribution of the climate field through time, as well as the scalar parameters that define the model. The main output from this approach is an ensemble of draws of the spatially and temporally complete climate field, each of which is consistent with the data and the model assumptions. The analysis of instrumental temperature records and a multiproxy data set that extends back to 1400 demonstrates the novel features of this approach, provides insight into the variability of the climate system over the last 600 years, and quantifies the extent to which the 20th Century is anomalous with respect to the previous five hundred years in terms of the magnitudes and rates of changes of observed temperatures.