Noise induced jumping prior to a fold applied to climate tipping predictions
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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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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

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.


Paleo tippings

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

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

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

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

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

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

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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