1. Low-Frequency Ranges in Multiproxy Climate Reconstructions
AGU December 2005 Meeting
Stephen McIntyre
Toronto Ontario

2. The Issue
Multiproxy climate reconstructions have very different low-frequency variability, with differing hypotheses from:
von Storch et al., 2004;
Mann and Hughes, 2002,
Esper et al., 2004
I critique the proposed explanations and offer a new one:
The varying low-frequency ranges are directly linked to biases in calculating variances of highly autocorrelated series on short segments
I argue that these estimation problems are a symptom of more fundamental modeling problems in the reconstructions, which are typically marked by adverse calibration period Durbin-Watson statistics and very poor out-of-sample R2 statistics.
AGU Dec. 2005
May 6, 2019

3. Low Frequency Variability
21-year gaussian smooth
Varies from 0.42 to 1.2 deg C.
Esper et al [2002] and Moberg et al [2005] are at the high end.
AGU Dec. 2005
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4. Proposed Explanations
(i) Differing geographical coverage of proxies (Mann and Hughes, 2002)
(ii) Inverse regression (von Storch et al, 2004)
(iii) “Non-conservative” tree ring standard-ization in some MBH series (Esper et al, 2004)
AGU Dec. 2005
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5. (i) Differing Geographical Coverage
Mann and Hughes (2002) argue Esper et al. rely on entirely extratropical tree ring set.
In contrast, they claim that the Mann et al. reconstruction estimates temperature trends over the full NH and that “Half of the NH surface area estimated by Mann et al lies below 30N.”
AGU Dec. 2005
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6. (i) Differing Geographical Coverage
But MBH99 uses no proxies in 0-30N either
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7. (ii) Inverse Regression Hypothesis
Von Storch et al. (2004) state that:
a regression model yields
predicted values must have diminished variance:
and hypothesized this affected variance of MBH, Jones et al [1998] and other reconstructions
AGU Dec. 2005
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8. (ii) Inverse Regression Hypothesis
But the criticized authors rescale variance:
Esper et al. (2002)
Jones et al (1998)
MBH99
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9. (iii) Tree Ring Standardization
Esper et al. (2004) argue that millennial scale information lost in standardization of tree-ring chronologies used in MBH, citing 2 records (France, Morocco);
They compare this to Esper et al. (2002), who used tree-ring methods intended to preserve low-frequency variation;
Mann and Hughes (2002) counter-criticized that MWP sample sizes used in Esper were too small
AGU Dec. 2005
May 6, 2019

10. (iii) Tree Ring Standardization
In fact, nearly all tree ring series used in MWP portion of MBH were “conservatively standardized” to retain low-frequency variability.
While the France and Morocco series were not, their weighting is very low and they make a negligible contribution to final MBH results
AGU Dec. 2005
May 6, 2019

11. Variance Estimation Problems
Proxies and temperature variances calibrated over short interval (e.g )
Series heavily autocorrelated
Sample variance is a very inaccurate estimate of true variance
Matching two such sample variances is very imprecise, especially if autocorrelations do not match
AGU Dec. 2005
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12. SD estimated on short interval differs from full series SD
Left: SD; Right: Full series SD
Biggest differences associated with largest low frequency ranges
the larger the gap between SD’s, the greater the low-frequency range,
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13. General Issue: Short-segment Sample Variance underestimates Long-Run (Population) Variance in autocorrelated series
EXAMPLE (PERCIVAL (1993)
σ2 = 1/(1-r2) = 166.9;
s2 in sample shown = 0.7
For all 991 possible samples of 10 observations, s2 averages <2
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14. An alternative explanation: the low-frequency range is likely to be larger when short-run variance is an underestimate of long-run variance
Almost linear
relationship for canonical studies
Outlier: CL00
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15. A bigger problem: most reconstructions have heavily autocorrelated residuals
DW < 1.5 implies autocorrelated residuals – model not usable
Implies estimated variance < true variance
Size of under-estimate is unknown
Expect much worse out-of-sample performance
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16. Poor out-of-sample results
Left: calibration R2, Right: verification R2
Cross-validation R2 results are uniformly insignificant
Note RE stat will not identify this problem (M&M05)
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17. “Honest” Confidence Intervals
standard errors should be calculated on verification period, NOT the calibration period. Because cross-validation R2 are so low, intervals are very wide;
This is additional to the very wide confidence intervals for variance matching. Actual confidence intervals are MUCH wider than reported to date.
AGU Dec. 2005
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18. Another symptom: results lack robustness
E.g. sensitivity version of Crowley and Lowery [2000] without stereotypes (problematic bristlecones, Dunde) in yellow versus base case (black)
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19. Conclusions
Existing explanations for differing low-frequency reconstruction variability don’t work;
Differences between short-segment proxy variance and long-run proxy variance in autocorrelated series appears to provide a better explanation;
The estimating problems are a symptom of bigger modeling problems, marked by adverse calibration period Durbin-Watson statistics and very poor out- of-sample R2 statistics. Sharing of stereotyped proxies may give false security.
A pressing need to confirm that the classic proxies (e.g. bristlecones, Urals, Dunde) have satisfactory out-of-sample performance in warm 1990s
AGU Dec. 2005
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20. References Briffa, K.R., 2000. Quat . Sci. Rev. 19, 87-105.
Briffa, K.R, Osborn, T.J., Schweingruber, F.H., Harris, I.C., Jones, P.D., Shiyatov, S.G. and Vaganov, E.A., JGR 106 D3,
Crowley, T.J. and Lowery, T.S., Ambio 29,
Esper, J., Cook, E.R. and Schweingruber, F.H., Science 295:
Esper, J., Frank, D.C. and R.J.S. Wilson, 2004, EOS 85, 113.
Jones, P. D., Briffa, K. R., Barnett, T. P. and Tett, S. F. B., The Holocene, 8,
Mann, M.E. and Hughes, M.K., Science, 296, 848.
Mann, M.E., Bradley, R.S. and Hughes, M.K., Nature, 392,
Mann, M.E., Bradley, R.S. and Hughes, M.K., GRL, 26,
McIntyre, S. and McKitrick, R., GRL, 32, L03710, doi: /2004GL
Moberg, A., Sonechkin, D.M., Holmgren, K., Datsenko, N.M. and Karlén, W., Nature, 433,
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21. Low-Frequency Ranges in Multiproxy Climate Reconstructions
AGU December 2005 Meeting
Stephen McIntyre
Toronto Ontario