Comments on "Reconstructing the NH mean temperature: Can underestimation of trends and variability be avoided?"

In a recent paper, Bo Christiansen presents and discusses 'LOC,' a methodology for reconstructing past climate that is based on local regressions between climate proxy time series and instrumental time series (Christiansen 2010, hereafter C2010). LOC respects two important scientific facts about proxy data which are often overlooked: 1) many proxies are likely influenced by strictly local temperature, and 2) to reflect causality, the proxies must be written as functions of climate, not vice versa. There are, however, several shortcomings to the LOC method: uncertainty is not propagated through the multiple stages of the analysis, the effects of observational errors in the instrumental observations are not considered, and as the proxies become uninformative of climate, the variance of a reconstruction produced by LOC becomes unbounded - a result which is clearly unphysical. This comment interprets the LOC method in the context of recently proposed Bayesian Hierarchical reconstruction methods, and describes how LOC can be derived as a frequentist implementation of a special case of two previously published methods: that described in Li et al. (2010) and the BARCAST approach of Tingley and Huybers (2010a). Recasting LOC within a Bayesian hierarchical framework allows for an inference scheme that propagates uncertainty through the multiple stages of the model. In addition, prior information about the target temperature process can be included in the hierarchical model, and doing so insures that the variance of the reconstruction remains bounded in the limit as the proxies become uninformative of the target process.