Elementary Reconstruction of the Hockey Stick Curve: Discussion of Paper by Li, Nychka and Ammann

The paper by Li, Nychka and Ammann (2010) has exemplified the power of Bayesian Hierarchical Models to solve fundamental problems in paleoclimatology. However, much can also be learned by more elementary statistical methods. In this discussion, we use principal components analysis, regression, and time series analysis, to reconstruct the temperature signal since 1400 based on tree rings data. Although the “hockey stick” shape is less clear cut than in the original analysis of Mann, Bradley and Hughes (1998, 1999), there is still substantial evidence that recent decades are among the warmest of the past 600 years. The problem of paleoclimate reconstruction is a natural one for the use of Bayesian hierarchical models (BHMs). As in most BHMs, there is an unobserved “process” which is the true object of interest — in this case, the true series of temperatures. There are also various sources of “data” which are dependent on the “process” with different levels of accuracy — observational data, tree rings, boreholes, ice cores etc. The problem of paleoclimate reconstruction may be characterized as how to combine the different data series to obtain the best reconstruction of the unobserved process, with suitable measures of uncertainty. The BHM technique is especially valuable for answering non-standard uncertainty questions, for instance, “what is the probability that the 1990s were the warmest decade of the [1000–2000] millennium?” In an earlier paper, Li, Nychka and Ammann (henceforth LNA, 2007) used an ensemble reconstruction, obtained via a combination of linear regression, bootstrapping and cross-validation, to reconstruct Northern Hemisphere average temperatures back to 1000, using 14 proxy series first discussed in Mann, Bradley and Hughes (MBH, 1999). Their results showed that there is indeed ∗Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, N.C. and Department of Statistics and Operations Research, University of North Carolina, Chapel Hill. Email: [email protected]