The instrumental temperature record covers at most 150 years. Because a longer record is needed to characterize the natural variability of the climate system, it is necessary to call upon climate proxy data, which are noisy and sparsely distributed in space. Information about pre-historic temperatures can be derived from elements of the natural world sensitive to local temperature variations, such as tree rings, ice cores, and lake-floor sediment cores.
Reconstructing the spatial pattern of a climate field through time from incomplete instrumental and climate proxy time series poses both scientific and statistical challenges. Over the last two decades, the statistics community has made major advances in the modeling and analysis of space-time processes. 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.
I begin by outlining both the scientific and statistical challenges involved in reconstructing past climate, and then discuss popular approaches that have been used to overcome them. I then outline a unifying, hierarchical space–time modeling framework for the paleoclimate reconstruction problem, and indicate how modern statistical expertise can be brought to bear upon the problem. Within this framework, 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.
As a demonstration of the power of hierarchical space-time models in this context, I present an analysis of a 600-year high-northern-latitude temperature proxy data set based on simple data-level and process-level assumptions.