Stephen McIntyre

Corrections to the Mann et. al. (1998) Proxy Data Base and Northern Hemispheric Average Temperature Series

The data set of proxies of past climate used in Mann, Bradley and Hughes (1998, “MBH98” hereafter) for the estimation of temperatures from 1400 to 1980 contains collation errors, unjustifiable truncation or extrapolation of source data, obsolete data, geographical location errors, incorrect calculation of principal components and other quality control defects. We detail these errors and defects. We then apply MBH98 methodology to the construction of a Northern Hemisphere average temperature index for the 1400–1980 period, using corrected and updated source data. The major finding is that the values in the early 15th century exceed any values in the 20th century. The particular “hockey stick” shape derived in the MBH98 proxy construction – a temperature index that decreases slightly between the early 15th century and early 20th century and then increases dramatically up to 1980 — is primarily an artefact of poor data handling, obsolete data and incorrect calculation of principal components.

The M&M Critique of the MBH98 Northern Hemisphere Climate Index: Update and Implications

The differences between the results of McIntyre and McKitrick [2003] and Mann et al. [1998] can be reconciled by only two series: The Gaspé cedar ring width series and the first principal component (PC1) from the North American tree ring network. We show that in each case MBH98 methodology differed from what was stated in print and the differences resulted in lower early 15th century index values. In the case of the North American PC1, MBH98 modified the PC algorithm so that the calculation was no longer centered, but claimed that the calculation was “conventional”. The modification caused the PC1 to be dominated by a subset of bristlecone pine ring width series which are widely doubted to be reliable temperature proxies. In the case of the Gaspé cedars, MBH98 did not use archived data, but made an extrapolation, unique within the corpus of over 350 series, and misrepresented the start date of the series. The recent Corrigendum by Mann et al. denied that these differences between the stated methods and actual methods have any effect, a claim we show is false. We also refute the various arguments by Mann et al. purporting to salvage their reconstruction, including their claims of robustness and statistical skill. Finally, we comment on several policy issues arising from this controversy: the lack of consistent requirements for disclosure of data and methods in paleoclimate journals, and the need to recognize the limitations of journal peer review as a quality control standard when scientific studies are used for public policy.

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

[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

Proxy inconsistency and other problems in millennial paleoclimate reconstructions

Mann et al. (1) present two paleoclimate reconstruction methods [“error-in-variables” (EIV) and “composite plus scale” (CPS)], claiming statistically significant skill for both. Their figure 3 reveals that from approximately 750 to 1100, the CPS 95% confidence interval excludes the EIV 95% confidence interval and vice versa. This is evidence not of skill, but of inconsistency.

Reply to comment by von Storch and Zorita on “Hockey sticks, principal components, and spurious significance”

[1] Von Storch and Zorita [2005] (hereinafter referred to as VZ) concur that the Mann et al. [1998] (hereinafter referred to as MBH98) principal component (PC) method ‘‘very often shows a hockey stick shaped pattern even if the data was by construction free of such structures’’ the Artificial Hockey Stick (AHS) effect. We did not claim that the AHS effect applied to all situations. We did claim that it affected MBH98 [McIntyre and McKitrick, 2005a, 2005b] (hereinafter referred to as MM05a and MM05b, respectively), where the AHS effect interacted with flawed bristlecone proxies. [2] VZ provided a simulated example where the AHS effect does not ‘‘matter’’. Unfortunately, VZ pseudoproxies dramatically overestimate the correlations of MBH98 proxies to gridcell temperature. This results in both the construction of a much stronger ‘‘temperature signal’’ in VZ simulations than is justified for MBH98 15th century proxies and the exclusion of proxies with strong nonclimatic trends, like bristlecones, which was a focus of our articles, making their example irrelevant. We discuss what is necessary to create a relevant simulation.