Comment on ‘‘Hockey sticks, principal components, and spurious

significance’’ by S. McIntyre and R. McKitrick

Hans von Storch and Eduardo Zorita

GKSS Research Centre, Geesthacht, Germany

Received 18 February 2005; revised 2 September 2005; accepted 2 September 2005; published 21 October 2005.

Citation: von Storch, H., and E. Zorita (2005), Comment on

‘‘Hockey sticks, principal components, and spurious significance’’ by S. McIntyre and R. McKitrick, Geophys. Res. Lett., 32,

L20701, doi:10.1029/2005GL022753.

[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

Figure 1. Time-filtered Northern Hemisphere annual nearsurface air temperature anomalies in the last millennium

(relative to the mean of the calibration period 1902 – 1980),

as simulated with the model ECHO-G [von Storch et al.,

2004] (black thick line), and resulting from the application

of the MBH98 algorithm to a network of pseudo-proxies

taken from the same simulation and degraded with

stochastic noise (thick colored lines: one noise realization

close to the mean of 100 realizations). The variance of the

pseudoproxies contains 50% reconstruction scatter (after

time filtering) estimated from 100 realizations of the noise.

The reconstruction with 1900 – 1980 centering is given in

red, the one with full centering in blue.

GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L20701, doi:10.1029/2005GL022753, 2005

Copyright 2005 by the American Geophysical Union.

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PCs, thus producing an artificial hockey-stick shape. The

MBH98 algorithm, however, involves several other steps

and it is not clear if the AHS-effect carries any relevance for

the final temperature reconstructions.

[4] We had previously used multicentennial climate

simulations with the coupled models ECHO-G and

HadCM3 to test the MBH98 reconstruction method [von

Storch et al., 2004]. The models were driven by estimations of past solar irradiance, radiative effects of volcanic

eruptions and concentrations of greenhouse gases for the

past 1000 years. In that test simulated grid-point temperatures, collocated with the frozen-in complete proxy network of MBH98 and degraded with statistical noise,

played the role of pseudo-proxies. In the von Storch et

al. [2004] test, the PCA of the pseudoproxies was not

included, as the resolution of the model is coarse enough to

prevent excessive clustering. Thus the AHS effect could

not play a role in that analysis.

[5] We have redone the test, this time including the

previous PCA of the pseudoproxies. The PCA was applied

to the pseudoproxies after AHS-centering or after centering

relative to the millennial mean. The PCA was carried out

with annual values in three areas separately (North America,

South America, and Australia). The numbers of PCs

retained for the subsequent steps was decided from the

eigenvalue spectrum following accepted rules [North et al.,

1982], but these (within a reasonable range) had only a very

minor influence on the results. Two types of noise were

tested: white noise and red-noise. A guideline for the amount

of added white noise is the local correlation r between real

proxies and nearby temperature observations, which usually

lies in the range r = 0.3– 0.7 [Jones and Mann, 2004]. This

corresponds to a noise variance between 85% and 50% of

the total variance [von Storch et al., 2004]. The level of

noise at centennial timescales, or alternatively the steepness

of the spectrum of an AR-1 noise, is very uncertain, so that

only rough guesses can be used.

[6] Figure 1 (top) shows the result of these pseudoreconstructions for one realization of the white noise (with

noise variance 50%) and (bottom) one realization of the red

noise (high-frequency noise variance 50% and with 1-year

lag autocorrelation of a = 0.8): in both cases PCA-centerings has a small relevance for the final result and the

differences are within the uncertainty range (Figure 1).

The conclusion is essentially the same for all realizations

and other constructions of noise. For instance, white noise

with r = 0.7 yields a standard deviation of the differences of

0.006K; r = 0.4 yields 0.007K; red noise with a = 0.5 and

r = 0.7 (r = 0.4) yields 0.01K (0.02K); red noise with a = 0.8

and r = 0.7 (r = 0.4) yields 0.02K(0.03K). Therefore, the

differences increase slightly with the amount and redness of

the noise, but they remain small, even in the case of high and

red noise with a steep red spectrum.

[7] Our results, derived in the artificial world of an

extended historical climate simulation, indicate therefore

that the AHS does not have a significant impact but leads

only to very minor deviations. We suggest, however, that

this biased centering should be in future avoided as it may

unnecessarily compromise the final result.

[8] Finally, we note that we have strictly addressed here

the question of the PCA-centering within the MBH98

algorithm. Other concerns raised by MM05 [see, e.g., Crok,

2005] about the MBH methodology have been not dealt

with.

[9] Acknowledgment. This work was accomplished within the EU

project SO&P.

References

Crok, M. (2005), Kyoto Protocol based on flawed statistics, Naturwetenskap

Techniek, 2, 20 – 31.

Intergovernmental Panel on Climate Change (IPCC) (2001), Climate

Change 2001: The Scientific Basis: Contribution of Working Group I

to the Third Assessment Report of the Intergovernmental Panel on Climate Change, edited by J. T. Houghton et al., 881 pp., Cambridge Univ.

Press, New York.

Jones, P. D., and M. E. Mann (2004), Climate over past millennia, Rev.

Geophys., 42(2), RG2002, doi:10.1029/2003RG000143.

Mann, M. E., R. S. Bradley, and M. K. Hughes (1998), Global-scale temperature patterns and climate forcing over the past 6 six centuries, Nature,

392, 779 – 787.

McIntyre, M., and R. McKitrick (2005), Hockey sticks, principal components and spurious significance, Geophys. Res. Lett., 32, L03710,

doi:10.1029/2004GL021750.

North, G. R., T. L. Bell, R. F. Cahalan, and F. J. Moeng (1982), Sampling

errors in the estimation of empirical orthogonal functions, Mon. Weather

Rev., 110, 699 – 706.

von Storch, H., E. Zorita, J. Jones, Y. Dimitriev, F. Gonza ́lez-Rouco, and

S. Tett (2004), Reconstructing past climate from noisy data, Science, 306,

679 – 682.



H. von Storch and E. Zorita, GKSS Research Centre, D-21502

Geesthacht, Germany. (storch@gkss.de)

L20701 VON STORCH AND ZORITA: COMMENTARY L20701

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