Low-Frequency Ranges in Multiproxy Climate Reconstructions AGU December 2005 Meeting Stephen McIntyre Toronto Ontario www.climateaudit.org/pdf/agu05.ppt

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

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 May 6, 2019

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 May 6, 2019

(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 May 6, 2019

(i) Differing Geographical Coverage But MBH99 uses no proxies in 0-30N either AGU Dec. 2005 May 6, 2019

(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 May 6, 2019

(ii) Inverse Regression Hypothesis But the criticized authors rescale variance: Esper et al. (2002) Jones et al (1998) MBH99 AGU Dec. 2005 May 6, 2019

(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

(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

Variance Estimation Problems Proxies and temperature variances calibrated over short interval (e.g. 1902-1980) 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 May 6, 2019

SD estimated on short interval differs from full series SD Left: 1902-1980 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, AGU Dec. 2005 May 6, 2019

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 AGU Dec. 2005 May 6, 2019

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 AGU Dec. 2005 May 6, 2019

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 AGU Dec. 2005 May 6, 2019

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) AGU Dec. 2005 May 6, 2019

“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 May 6, 2019

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) AGU Dec. 2005 May 6, 2019

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 May 6, 2019

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., 2001. JGR 106 D3, 2929-2941 Crowley, T.J. and Lowery, T.S., 2000. Ambio 29, 51-54. Esper, J., Cook, E.R. and Schweingruber, F.H., 2002. Science 295: 2250-2253. 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., 1998. The Holocene, 8, 455-471. Mann, M.E. and Hughes, M.K., 2002. Science, 296, 848. Mann, M.E., Bradley, R.S. and Hughes, M.K., 1998. Nature, 392, 779-787. Mann, M.E., Bradley, R.S. and Hughes, M.K., 1999. GRL, 26, 759-762. McIntyre, S. and McKitrick, R., 2005. GRL, 32, L03710, doi:10.1029/2004GL021750. Moberg, A., Sonechkin, D.M., Holmgren, K., Datsenko, N.M. and Karlén, W., 2005. Nature, 433, 613-617. AGU Dec. 2005 May 6, 2019

Low-Frequency Ranges in Multiproxy Climate Reconstructions AGU December 2005 Meeting Stephen McIntyre Toronto Ontario www.climateaudit.org/pdf/agu05.ppt