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

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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