Defining spatial comparison metrics for evaluation of paleoclimatic field reconstructions of the Common Era

Climate field reconstructions (CFR) of the Common Era (the last two millennia) provide important insights into the dynamics of past climate change that, in turn, have implications for the future. Multiple CFR methods have emerged in the literature, and comparisons between these methods using pseudoproxy experiments have been performed. These experiments, however, have not fully quantified the spatial skill of the CFRs, particularly with regard to the relative performance of each. Toward such ends, a formal statistical hypothesis test is proposed as a means of evaluating the differences between two random fields that integrate the differences in both the mean and the dependence structure. This involves a careful selection of the statistical model for the CFR residual process and systematic comparisons over different spatial scales. Application of this method yields a systematic assessment of the spatial character of five widely applied CFRs in a pseudoproxy experiment context. The analyses indicate that spatial differences among the five CFRs are not statistically significant. Further rigorous statistical assessments will help elucidate the strength and weakness of each CFR method, while quantifying the degree to which their spatial dissimilarities can be ascribed to methodological choices.