Piecing together the past: Statistical insights into paleoclimatic reconstructions

Reconstructing a climate process in both space and time from incomplete instrumental and climate proxy time series is a problem with clear societal relevance that poses both scientific and statistical challenges. These challenges, along with the interdisciplinary nature of the reconstruction problem, point to the need for greater cooperation between the earth science and statistics communities - a sentiment echoed in recent parliamentary reports. As a step in this direction, it is prudent to formalize what is meant by 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. The key aims of this article are to 1) establish a unifying modeling and notational framework for the paleoclimate reconstruction problem that is transparent to both the climate science and statistics communities; 2) describe how currently favored methods fit within this framework; 3) outline and distinguish between scientific and statistical challenges; 4) indicate how recent advances in the statistical modeling of large space-time data sets, as well as advances in statistical computation, can be brought to bear upon the problem; 5) offer, in broad strokes, some suggestions for model construction and how to perform the required statistical inference; and 6) identify issues that are important to both the climate science and applied statistics communities, and encourage greater collaboration between the two.