Can we reliably provide Can we reliably provide early warnings for tipping early warnings for tipping points?points?

Brian HuangClaudie Beaulieu

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Tipping Point:Tipping Point:A “critical threshold at which a tiny

perturbation can qualitatively alter the state or development of a system” (Lenton et al., 2008)

“Early-warning signals for critical transitions” (Scheffer et al., 2009) 2

Before a Critical TransitionBefore a Critical TransitionCritical Slowing Down Critical Slowing Down (Autocorrelation/Variance)(Autocorrelation/Variance)Skewness and Flickering Before Skewness and Flickering Before TransitionsTransitions

“Early-warning signals for critical transitions” (Scheffer et al., 2009)

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Interpolated

Methodology/ObjectivesMethodology/ObjectivesCompare ways to calculate AR(1) on

unevenly spaced data:◦ Take the mean of evenly spaced buckets of

data (e.g. Lenton et al., 2011)◦ Linearly interpolate evenly spaced data (Dakos

et al., 2008)◦ Fit AR(1) to raw data (unevenly spaced)

(Mudelsee, 2002)Examine all three indicators together

◦ Couple AR(1)/VarianceApply to data sets that haven’t been

studied in the literatureApply to vegetation-grazing model to judge

risk of false alarms and power of technique

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Estimations of Estimations of AutocorrelationAutocorrelation

5

Vost

ok Ic

e Co

re D

ata

(Gla

ciatio

n 1) Pe

tit e

t al.

(199

9)

Trends significant for the 99% confidence level

The Three IndicatorsThe Three Indicators(Successful AR(1)/Variance)(Successful AR(1)/Variance)

6

The Three IndicatorsThe Three Indicators(Successful Skewness)(Successful Skewness)

Trends significant at the 99% confidence level

Glob

al M

etha

ne C

onc.

Dat

a (G

lacia

tion

1)Sp

ahni

et a

l. (2

005)

7

The Three IndicatorsThe Three Indicators(Miss)(Miss)

Glob

al B

enth

ic O1

8 D

ata

(Gla

ciatio

n 1)

Lisie

cki a

nd R

aym

o (2

005)

Trends significant at the 99% confidence level

8

Summary of Results Summary of Results (Paleoclimate)(Paleoclimate)Event Hit (AR(1)/Variance)

Hit (Skewness) Miss

End of Glaciation 1

Petit et al. (1999) Spahni et al. (2005)EPICA Community Members (2004)

Kawamura et al. (2007)Lisiecki and Raymo (2005)

End of Glaciation 2

Petit et al. (1999) Petit et al. (1999)Lisiecki and Raymo (2005)Kawamura et al. (2007)

Spahni et al. (2005)EPICA Community Members (2004)

End of Glaciation 3

Lisiecki and Raymo (2005)Petit et al. (1999)Kawamura et al. (2007)

Kawamura et al. (2007)

End of Glaciation 4

Lisiecki and Raymo (2005)

Petit et al. (1999)

End of Glaciation 5

Siegenthaler et al. (2005)

End of Glaciation 6

Siegenthaler et al. (2005)

End of Younger Dryas

Hughen et al. (2000) Hughen et al. (2000) Lea et al (2003)EPICA Community Members (2004)

Post-Glacial Cooling (~8.2 ka)

Hughen et al. (2000)Von Grafenstein et al. (1998)Lachniet et al. (2004)

Note: only tipping points that are far enough apart are analyzed. 9

Summary of Results (Grazing Summary of Results (Grazing Model) Model)

Rising Grazing78.4/86.6

Halting Grazing 95.3/88.2

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% Significant AR(1)/Variance

% Significant Skewness

Rising Grazing Noise 100/99.6

Rising Veg. Noise77.8/81.6

Constant Grazing 20.7/86.5

Discussion/Further Discussion/Further ProgressProgressDifferent data sets lead to different

conclusions about the same events.Indicators may also be fallible to false

positivesMore research necessary before we

can use these indicators to provide early warning signals

Needs extension to predict the timing of impending critical transitions

Automating the selection of parameters

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AcknowledgementsAcknowledgementsJorge SarmientoVishwesha GuttalPEI

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