Piecing together the past: Statistical insights into paleoclimatic reconstructions

Reconstructing the spatial pattern of a climate process through time from incomplete instrumental and climate proxy time series is a problem with clear societal relevance that poses both scientific and statistical challenges. The scope of these challenges, along with the interdisciplinary nature of the reconstruction problem, point to the need for greater cooperation between the earth science and statistics community – a sentiment echoed in recent parliamentary reports. As a step in this direction, it is prudent to formalize what is meant by one important aspect of the paleoclimate reconstruction problem using the language and tools of modern statistics. This article considers the challenge of inferring, with uncertainties, a climate process through space and time from overlapping instrumental and climate sensitive proxy time series that are assumed to be well dated – an assumption that is likely only reasonable for certain proxies over at most the last few millennia. Within a unifying, hierarchical space– time modeling framework for this problem, the modeling assumptions made by a number of published methods can be understood as special cases, and the distinction between modeling assumptions and analysis or inference choices becomes more transparent. Over the last two decades, the statistics community has made major advances in the modeling and analysis of space-time processes such as surface temperature anomalies. In addition, increases in available computational power, advances in statistical computation, and the development of data-reduction techniques now allow rich classes of space-time models to be fit to very large data sets. Many of these advances have not yet been applied to the paleoclimate reconstruction problem, and doing so has the potential to improve understanding of the climate of the past.