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NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS

NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS. by Michael Thompson and Jan Sieber ------------------------- Background in Geo-Engineering Climate Change ed. Launder & Thompson, CUP 2010. J. Bifn & Chaos ( http://arxiv.org/abs/1007.1376 ). Paleoclimate.

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NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS

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  1. NOISE-INDUCED JUMPING PRIOR TO A FOLD:APPLIED TO CLIMATE TIPPING PREDICTIONS by Michael Thompson and Jan Sieber ------------------------- Background in Geo-Engineering Climate Change ed. Launder & Thompson, CUP 2010. J. Bifn & Chaos (http://arxiv.org/abs/1007.1376)

  2. Paleoclimate Geologists have many time-series relating to the Earth's paleo-climate. Data derives from ice-cores, sediments, isotope concentrations, etc. It gives a comprehensive picture of climatic changes over millions of years. Four latest ice ages are covered by proxies for both temperature and carbon dioxide.

  3. Paleo Tippings • Records show many sudden jumps, called climate tipping points. • There is a sudden warming of the Earth at the end of each of the four ice ages. • Earlier (34 million years ago) there was a sudden cooling in what is called the green-house to ice-house tipping.

  4. Prediction of Paleo Tips • Recent work tries to predict past tippings using the preceding geological data: • Livina & Lenton, Geophysical Research Letters 34, 2007. • Dakos, Scheffer, et al, Proc Nat Acad Sci 105, 2008. • Thompson & Sieber, IMA Journal of Applied Maths, accepted (available on http://arxiv.org/abs/1007.1376).

  5. Tipping Elements • Tim Lenton et al : PNAS, 105, 1786–1793 (2008) • Many tipping points are strongly associated with just one well defined sub-system of the climate, called a tipping element. • Interactions between an element and the rest of the system can be expressed as a control parameter varying (slowly) with time. • Lenton listed 9 elements that may tip due to human activities, relevant to political decision making in the follow-up to Copenhagen.

  6. Thermohaline Circulation • THC is a global oceanic flow which aids burial of carbon in the deep ocean • Salty surface waters sink near the poles • Extra fresh–water melt due to warming can disrupt the sinking • Such disruption has in the past shutdown the THC, giving less burial and reinforced warming

  7. Auto-regression Analysis • A precursor of many bifurcational instabilities is a slowing of transients. • The prediction studies use auto-regressive techniques to estimate this slowing. • They can do this using the internal ‘transients’ that are generated intrinsically within a complex dynamical system.

  8. Fold for Incipient Tipping (FIT) • Suppose we have reason to believe (as in the THC) that we are looking for an incipient fold. • We can use its normal form to sharpen the ARC analysis, and assess the actual noise level and actual rate of loading (control drift rate). • This work with Jan Sieber is to be published in the IMA Journal of Applied Mathematics (available on http://arxiv.org/abs/1007.1376).

  9. Fold for Incipient Tipping (FIT): Results • We have made two studies with this new approach using: • (1) Time series from a COMPUTER MODEL for the greenhouse to icehouse transition • (2) Time series from real ICE-CORE DATA for the end of the last ice age.

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