Can we reliably provide early warnings for tipping points? Brian Huang Claudie Beaulieu 1

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 Transition Critical Slowing Down (Autocorrelation/Variance) Skewness and Flickering Before Transitions “Early-warning signals for critical transitions” (Scheffer et al., 2009) 3 Interpolated

Methodology/Objectives Compare 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)/Variance Apply to data sets that haven’t been studied in the literature Apply to vegetation-grazing model to judge risk of false alarms and power of technique 4

Estimations of Autocorrelation 5

Vostok Ice Core Data (Glaciation 1)Petit et al. (1999) Trends significant for the 99% confidence level The Three Indicators (Successful AR(1)/Variance) 6

The Three Indicators (Successful Skewness) Trends significant at the 99% confidence level Global Methane Conc. Data (Glaciation 1)Spahni et al. (2005) 7

The Three Indicators (Miss) Global Benthic O 18 Data (Glaciation 1) Lisiecki and Raymo (2005) Trends significant at the 99% confidence level 8

Summary of Results (Paleoclimate) EventHit (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) 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) 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 Model) Rising Grazing 78.4/86.6 Halting Grazing 95.3/ % Significant AR(1)/Variance % Significant Skewness Rising Grazing Noise 100/99.6 Rising Veg. Noise 77.8/81.6 Constant Grazing 20.7/86.5

Discussion/Further Progress Different data sets lead to different conclusions about the same events. Indicators may also be fallible to false positives More 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 11

Acknowledgements Jorge Sarmiento Vishwesha Guttal PEI 12