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

[1] McIntyre and McKitrick [2005] (hereinafter referred to as MM05) point out a bias in the Mann et al. [1998] (hereinafter referred to as MBH98) Northern Hemisphere temperature reconstruction, one tending to enhance trends during the last century. Having reproduced the statistical results of MM05, this comment is prompted by further questions regarding appropriate implementation of principal component analysis (PCA) and the presence of discrepancies in their estimate of significance levels. [2] MBH98 use principal component analysis (PCA) to distill the large number of tree ring records (90% of the total 415 proxy records) into a smaller number of principal components (PCs). MM05 focus on a subset of the data, the seventy North American tree ring records (NOAMER) extending back to AD1400, and show that the MBH98 normalization leads to biases in the leading principal component (PC1). It is in this same step that MM05 use a questionable normalization procedure, making it useful to describe the various normalization conventions in detail. [3] The MBH98 normalization convention for a record, x, is xMBH = (x ! x1902)/s1902, where x1902 and s1902 are the mean and standard deviation computed between 1902 and 1980. MBH98 compute the standard deviation after detrending x, indicated as s0, an additional step that seems questionable but turns out not to influence the results. Because proxy records span different intervals, it is impossible to both normalize records over a fixed interval and ensure that records are zero-mean over their entire duration. MBH98 presumably chose the 1902 to 1980 normalization period because almost all records span this interval, but which MM05 point out leads to a bias in the results. [4] The reason for the bias in the MBH98 PC1 can be understood by considering that PCA maximizes the variance described by each principal component where variance is measured as the sum of the squared record, s = X