LowFrequency Ranges in Multiproxy Climate Reconstructions

1
Low-Frequency Ranges in Multiproxy Climate
Reconstructions

• AGU December 2005 Meeting
• Stephen McIntyre
• Toronto Ontario
• www.climateaudit.org/pdf/agu05.ppt

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.

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.

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)

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.

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(i) Differing Geographical Coverage

• But MBH99 uses no proxies in 0-30N either

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

8
(ii) Inverse Regression Hypothesis

• But the criticized authors rescale variance
• Esper et al. (2002)
• Jones et al (1998)
• MBH99

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(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

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

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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

12
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 SDs, the greater the
  low-frequency range,

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General Issue Short-segment Sample Variance
underestimates Long-Run (Population) Variance in
autocorrelated series

• EXAMPLE (PERCIVAL (1993)
• s2 1/(1-r2) 166.9
• s2 in sample shown 0.7
• For all 991 possible samples of 10 observations,
  s2 averages lt2

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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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A bigger problem most reconstructions have
heavily autocorrelated residuals

• DW lt 1.5 implies autocorrelated residuals model
  not usable
• Implies estimated variance lt true variance
• Size of under-estimate is unknown
• Expect much worse out-of-sample performance

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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
  (MM05)

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.

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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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Conclusions

• Existing explanations for differing low-frequency
  reconstruction variability dont 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

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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, doi10.1029/2004GL021750. M
oberg, A., Sonechkin, D.M., Holmgren, K.,
Datsenko, N.M. and Karlén, W., 2005. Nature, 433,
613-617.
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Low-Frequency Ranges in Multiproxy Climate
Reconstructions

• AGU December 2005 Meeting
• Stephen McIntyre
• Toronto Ontario
• www.climateaudit.org/pdf/agu05.ppt