A kernel-based Bayesian approach to climatic reconstruction

Abstract

To understand recent climatic trends and possible future climatic change, it is necessary to examine the nature of past climatic variability. Proxy measures of past climatic fluctuations can be used to extend this record beyond the limited period of instrumental measurements. Regression-based techniques are generally used to define transfer functions, which describe the statistical relationship between these proxy estimates of past climate and measured climatic parameters. Although these regression-based techniques have been extremely successful, they can engender bias in the estimates if not used with care. More significantly, we show that if regression errors are explicitly calculated they are often similar in magnitude to the total range of the parameter being estimated, implying that such reconstructions of past climate cannot be regarded as truly precise. A novel approach based upon Bayes' theorem is introduced which appears to increase the statisti cal veracity of such climatic reconstructions.