Early warning signals of tipping points in periodically forced systems
This is the final version of the article. Available from the European Geosciences Union via the DOI in this record. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a sep...
| Published in: | Earth System Dynamics |
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| Main Authors: | , , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
European Geosciences Union (EGU) / Copernicus Publications
2016
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10871/23492 https://doi.org/10.5194/esd-7-313-2016 |
| Summary: | This is the final version of the article. Available from the European Geosciences Union via the DOI in this record. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation. The research leading to these results has received funding from the European Union Seventh Framework Programme FP7/2007-2013 under grant agreement no. 603864 (HELIX). We are grateful to Peter Ashwin, Peter Cox, Michel Crucifix, Vasilis Dakos, Henk Dijkstra, Jan Sieber, Marten Scheffer and Appy Sluijs for the fruitful discussions over beers and balls. |
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