NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS
description
Transcript of NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS
![Page 1: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/1.jpg)
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)
![Page 2: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/2.jpg)
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.
![Page 3: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/3.jpg)
![Page 4: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/4.jpg)
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.
![Page 5: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/5.jpg)
![Page 6: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/6.jpg)
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).
![Page 7: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/7.jpg)
![Page 8: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/8.jpg)
![Page 9: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/9.jpg)
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.
![Page 10: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/10.jpg)
![Page 11: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/11.jpg)
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
![Page 12: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/12.jpg)
![Page 13: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/13.jpg)
![Page 14: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/14.jpg)
![Page 15: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/15.jpg)
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.
![Page 16: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/16.jpg)
![Page 17: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/17.jpg)
![Page 18: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/18.jpg)
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).
![Page 19: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/19.jpg)
![Page 20: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/20.jpg)
![Page 21: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/21.jpg)
![Page 22: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/22.jpg)
![Page 23: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/23.jpg)
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.
![Page 24: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/24.jpg)
![Page 25: NOISE-INDUCED JUMPING PRIOR TO A FOLD: APPLIED TO CLIMATE TIPPING PREDICTIONS](https://reader036.fdocuments.us/reader036/viewer/2022062519/56815188550346895dbfc017/html5/thumbnails/25.jpg)