NOISE-INDUCED JUMPING PRIOR TO A FOLD:

APPLIED TO CLIMATE TIPPING PREDICTIONS

 by

Michael Thompson and Jan Sieber

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Background in Geo-Engineering Climate Change

ed. Launder & Thompson, CUP 2010.

J. Bifn & Chaos (http://arxiv.org/abs/1007.1376)

PaleoclimateGeologists 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.

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.

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).

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.

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

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.

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).

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.