Reply to comment by Huybers on “Hockey sticks, principal components, and spurious significance”

Abstract

[1] McIntyre and McKitrick [2005a] (hereinafter referred to as MM05) showed that the actual Mann et al. [1998] (hereinafter referred to as MBH98) PC method used an unreported short-centering method, which was biased towards producing a hockey stick shaped PC1 with an inflated eigenvalue. Huybers [2005] concurs with these particular findings, but argues that we ‘‘exaggerated’’ the MBH98 bias by comparing the MBH98 PC1 for the North American tree ring network to a covariance PC1 rather than a correlation PC1 by MM05 (Figure 3). [2] Tree ring chronologies (both density and ring width) are already standardized to common dimensionless units with a mean of 1. Huybers’ [2005] two statistical authorities either do not recommend standardizing variance for PC analysis on series with common units [Preisendorfer, 1988] or recommend the opposite (i.e., a covariance PC calculation) [Rencher, 1995, p. 430; see also Overland and Preisendorfer, 1982; Rencher, 1992]. Only Rencher [1995] even mentions the possibility of standardizing variance of networks in common units in exceptional circumstances that do not apply here. [3] One of Huybers’ [2005] principal justifications for proposing a correlation PC1 is his observation that the covariance PC1 underweights density series, which have lower variances. But in the MBH98 network, only 2 of 70 series are density series, and both are from sites also represented in the same network with a ring width series. Indeed, the Spruce Canyon site (density series co509x and ring width series co509w) also occurs in 4 series in the MBH98 Stahle/SWM network. Accommodating these 2 density series should not be at the expense of the most appropriate treatment for the other 68. [4] Relative to the MBH98 PC1, the differences between the covariance PC1 and correlation PC1 are trifling and both confirm the bias reported in MM05. The MBH98 method applied to North American tree rings had the distinctive hockey stick shape (Figure 1a) and a very large first eigenvalue (38%), which they interpreted as evidence of a ‘‘dominant component of variance’’. Neither the covariance PC1 (Figure 1c) nor the correlation PC1 (Figure 1e) have a hockey stick shape and their first eigenvalue is much reduced (19%, 17% respectively). The correlation PC1 is a little higher in the 20th century than the covariance PC1, but the differences are trifling. [5] Huybers’ [2005] approach also ignores fundamental properties of the data and introduces new and unconsidered biases: [6] a) Tree ring chronologies are typically autocorrelated, especially the controversial bristlecones. For autocorrelated series, the ordinary least squares sample variance (used by Huybers) is a biased (under-) estimate of the long-run variance, so the bristlecones will tend to be over-weighted this way. An ‘‘unbiased fully normalized’’ PC1 can be obtained using an autocorrelation-consistent variance estimator [e.g., Andrews, 1991]. This bias correction yields a result (Figure 1g) very similar to the covariance PC1. [7] b) Huybers argues that the correlation PC1 captured a ‘‘robust feature of the NOAMER dataset’’ based on its similarity to the mean of the 70 series in the AD1400 network scaled by their standard deviation (Figure 1f). If the purpose of PC analysis is merely to predict the mean, then there is no reason not to simply use the mean. As for the robustness of the feature, only 70 of 212 series in the NOAMER network extend back to AD1400. Using all 212 NOAMER series scaled by their standard deviation (Figure 1d) yields a network mean closer to the covariance PC1 than the correlation PC1—by this criterion ‘‘full normalization’’ adds bias to the PC1. [8] The differences among these PC series can be traced to differing weights for bristlecones. Bristlecone sites are well-known examples of CO2 fertilization and their nonclimatic biases have been extensively assessed already—see the caveat by Intergovernmental Penal on Climate Change [1996] and the review by McIntyre and McKitrick [2005b]. Huybers [2005] is correct to acknowledge the need to assess their validity and possibly to exclude or down-weight them, but having said so it is inadequate to defer this to ‘‘future studies.’’ We see no sense deferring to the future a remedy for what is already a well-understood source of bias. [9] Bristlecone impact can be seen directly by comparing the MBH98 PC1 (Figure 1a), which is weighted almost entirely from bristlecones, with an unreported PC1 from Mann’s FTP site (Figure 1b), which Mann obtained by GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L20713, doi:10.1029/2005GL023586, 2005