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Earth System Dynamics An interactive open-access journal of the European Geosciences Union
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Volume 7, issue 2
Earth Syst. Dynam., 7, 313-326, 2016
https://doi.org/10.5194/esd-7-313-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Earth Syst. Dynam., 7, 313-326, 2016
https://doi.org/10.5194/esd-7-313-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 13 Apr 2016

Research article | 13 Apr 2016

Early warning signals of tipping points in periodically forced systems

Mark S. Williamson1, Sebastian Bathiany2, and Timothy M. Lenton1 Mark S. Williamson et al.
  • 1Earth System Science group, College of Life and Environmental Sciences, University of Exeter, Laver Building, North Park Road, Exeter EX4 4QE, UK
  • 2Aquatic Ecology and Water Quality Management, Wageningen University, PO Box 47, Wageningen, the Netherlands

Abstract. 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.

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We find early warnings of abrupt changes in complex dynamical systems such as the climate where the usual early warning indicators do not work. In particular, these are systems that are periodically forced, for example by the annual cycle of solar insolation. We show these indicators are good theoretically in a general setting then apply them to a specific system, that of the Arctic sea ice, which has been conjectured to be close to such a tipping point. We do not find evidence of it.
We find early warnings of abrupt changes in complex dynamical systems such as the climate where...
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