Ground surface paleotemperature reconstruction using information measures and empirical Bayes

We outline an empirical Bayesian approach to ground‐surface temperature (GST) reconstruction that utilizes Akaike's Bayesian information criterion (ABIC). Typical unknown statistical quantities, such as the noise variance and so on, are automatically determined through the analysis. We compare the ABIC inversion to the singular value decomposition on a synthetic downhole temperature data set. In comparing the root mean square errors between the synthetic climatic signal and each of the reconstructions (singular value and ABIC) from 1900 to 2002, we see that the ABIC solution produced the ‘best’ reconstruction in a mean square sense. We also carry out an analysis of the Canadian borehole data set in which we use 221 temperature profiles. The reconstructed GST record shows warming between 1800 and 1949 of approximately 1.0 K, with the maximum rate of warming occurring between 1900 and 1949.