Comment on “Hockey sticks, principal components, and spurious significance” by S. McIntyre and R. McKitrick

Abstract

[1] We analyse a climate simulation of the last millennium to check whether the ‘‘artificial hockey stick’’ (AHS) effect introduced by biased centering has a significant bearing on the performance of historical climate reconstructions. The ‘‘hockey stick’’ shaped reconstructions of the northern hemisphere temperature has been a contested icon in climate science since a it was advanced by the IPCC as likely temperature history, against which the recent warming trends should be evaluated [Intergovernmental Panel on Climate Change, 2001]. This reconstruction has by now faced a number of challenges on different grounds. One of challenges was brought forward by McIntyre and McKitrick [2005] (hereinafter referred to as MM05), who had noted that the original code contained an uncommon mathematical procedure. In this study we examine whether this uncommon procedure, which under certain circumstances can result in ‘‘artificial hockey sticks’’, would affect the final result of the reconstruction. [2] The statistical method behind the ‘‘hockey stick’’ temperature reconstruction [Mann et al., 1998] (hereinafter referred to as MBH98) is based on an inverted regression method, which maps proxy data on the Northern Hemisphere temperature field. The proxy-data are irregularly distributed over the globe, and in some regions their spatial density (mainly for dendroclimatological data) is high. To avoid overweighting these regions, a Principal Component Analysis (PCA) was used to condense these spatially clustered proxy data into a few principal components. MM05 noted that MBH98 normalized their data unconventionally prior to the PCA, by centering the time series relative to the instrumental-period mean, 1902– 1980, instead of relative to the whole available period. Why this was done is unclear. It is, however, not entirely uncommon in climate sciences. [3] MM05 performed a Monte Carlo study with a series of independent red-noise series; they centered their 1000 year-series relative to the mean of the last 100 years, and calculated the PCs based on the correlation matrix. It turned out that very often the leading PCs show a hockey stick pattern, even if the data field was by construction free of such structures. This finding was recently confirmed by others (F. Zwiers, personal communication). The paradox in the AHS effect is that the true covariance matrix is a unity matrix, so that no real structures will steer the eventual selection of the eigenvectors. However, in the biased centering approach, those time series with largest differences between their 1000–1901 mean and 1902–1980 mean will tend to contribute more strongly to the leading