How fast to turn around: preventing tipping after a system has crossed a climate tipping threshold

2020 ◽  
Author(s):  
Paul Ritchie ◽  
Peter Cox ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Climate System ◽  
Tipping Points ◽  
Simple Criterion ◽  
Inverse Square Law ◽  
Parameter Drift ◽  
Simple Models

<p>A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive<br>feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. We demonstrate the inverse-square law relationship using simple models of recognised potential future tipping points in the climate system. </p>

scholarly journals Inverse-square law between time and amplitude for crossing tipping thresholds

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180504 ◽  
Author(s):  
Paul Ritchie ◽  
Özkan Karabacak ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Dimensional System ◽  
Stochastic Forcing ◽  
Inverse Square Law ◽  
System A ◽  
Asymptotic Expressions ◽  
Higher Dimensional ◽  
Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

scholarly journals Dansgaard-Oeschger events: tipping points in the climate system

2012 ◽  
Vol 8 (5) ◽  
pp. 4269-4294 ◽  
Author(s):  
A. A. Cimatoribus ◽  
S. S. Drijfhout ◽  
V. Livina ◽  
G. van der Schrier
Keyword(s):  
High Resolution ◽  
Abrupt Change ◽  
Ice Core ◽  
Tipping Point ◽  
Statistical Properties ◽  
Climate System ◽  
Tipping Points ◽  
External Forcing ◽  
Observational Constraint ◽  
Climate Fluctuations

Abstract. The largest variability in temperature over the last sixty thousand years is connected with Dansgaard-Oeschger events. Various prototype models have been proposed to explain these rapid climate fluctuations, but until now no observational constraint has been forwarded to choose between different theories. We assess the bimodality of the system reconstructing the topology of the multi-dimensional attractor over which the climate system evolves. Furthermore, we show that Dansgaard-Oeschger events are compatible with the crossing of a tipping point in the climate system. We use high-resolution ice core isotope data to investigate the statistical properties of the climate fluctuations in the period before the onset of the abrupt change. We find that the statistics are consistent with the switches between two different climate equilibrium states in response to a changing external forcing.

scholarly journals Extreme sensitivity and climate tipping points

2020 ◽  
Author(s):  
Anna von der Heydt ◽  
Peter Ashwin
Keyword(s):  
Climate Sensitivity ◽  
Climate Models ◽  
Tipping Point ◽  
Climate System ◽  
Tipping Points ◽  
Equilibrium Climate Sensitivity ◽  
Future Global Warming ◽  
Wide Range ◽  
Extreme Sensitivity ◽  
Global Mean

<p>The equilibrium climate sensitivity (ECS) is widely used as a measure for possible future global warming. It has been determined from a wide range of climate models, observations and palaeoclimate records, however, it still remains relatively unconstrained. In particular, large values of warming as a consequence of atmospheric greenhouse gas increase cannot be excluded, with some of the most recent state-of-the-art climate models (CMIP6) supporting (much) more warming than previous generations of climate models. Moreover, a number of tipping elements have been identified within the climate system, some of which may affect the global mean temperature. Therefore, it is interesting to explore how the climate systems response (e.g. ECS) behaves when the system is close to a tipping point. <br>A climate state close to a tipping point will have a degenerate linear response to perturbations, which can be associated with extreme values of the equilibrium climate sensitivity (ECS). In this talk we contrast linearized ('instantaneous') with fully nonlinear geometric ('two-point') notions of ECS, in both presence and absence of tipping points. For a stochastic energy balance model of the global mean surface temperature with two stable regimes, we confirm that tipping events cause the appearance of extremes in both notions of ECS. Moreover, multiple regimes with different mean sensitivities are visible in the two-point ECS. We confirm some of our findings in a physics-based multi-box model of the climate system.</p><p><strong>Reference</strong><br>P. Ashwin and A. S. von der Heydt (2019), Extreme Sensitivity and Climate Tipping Points, J. Stat. Phys.  <strong>370</strong>, 1166–24. http://doi.org/10.1007/s10955-019-02425-x.</p>

scholarly journals Tipping points in the climate system

Weather ◽  
2021 ◽  
Author(s):  
Timothy M. Lenton
Keyword(s):  
Climate System ◽  
Tipping Points

scholarly journals Harnessing tipping points in complex ecological networks

2019 ◽  
Vol 16 (158) ◽  
pp. 20190345 ◽  
Author(s):  
Junjie Jiang ◽  
Alan Hastings ◽  
Ying-Cheng Lai
Keyword(s):  
Real World ◽  
Management Strategy ◽  
Ecological Networks ◽  
Tipping Point ◽  
Active Management ◽  
Reduced Model ◽  
Tipping Points ◽  
Two Dimensional ◽  
Pollinator Species ◽  
Global Extinction

Complex and nonlinear ecological networks can exhibit a tipping point at which a transition to a global extinction state occurs. Using real-world mutualistic networks of pollinators and plants as prototypical systems and taking into account biological constraints, we develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with a tipping point. If conditions are changing so as to approach a tipping point, the management strategy we describe can prevent sudden drastic changes. Additionally, if the system has already moved past a tipping point, we show that a full recovery can occur for reasonable parameter changes only if there is active management of abundance, again due essentially to removal of the hysteresis. This recovery point in the aftermath of a tipping point can be predicted by a universal, two-dimensional reduced model.

Tipping Points in the Anthropocene: Crafting a Just and Sustainable Earth

2017 ◽  
Vol 04 (01) ◽  
pp. 1750004 ◽  
Author(s):  
David C. Eisenhauer
Keyword(s):  
Political Theory ◽  
Political Science ◽  
Science And Technology Studies ◽  
Sustainability Science ◽  
Modern Science ◽  
Tipping Point ◽  
Tipping Points ◽  
Earth System ◽  
Critical Thresholds ◽  
The Earth

The arrival of the Anthropocene entails an evolutionary tipping point that challenges basic precepts of political theory and modern science. Within this paper, emerging scholarship in political science, science and technology studies, and sustainability science are brought together to sketch out an approach for crafting more just and sustainable pathways in response to the crossing of critical thresholds in the Earth system. Accomplishing this task requires responding to the emerging reality of possibility, irreversibility, entanglement, and novelty that the Anthropocene and tipping points entail. I argue that grounding political projects in recognition of the unfolding and unpredictable terrain tipping points present allows for the opening of novel pathways toward a still possible just and sustainable planet.

Composer's Notebook: Star Networks at the Singing Point

2004 ◽  
Vol 14 ◽  
pp. 81-82
Author(s):  
Ralph Jones
Keyword(s):  
Chaos Theory ◽  
Analog Circuits ◽  
Feedback Loop ◽  
Tipping Point ◽  
Feedback Circuit ◽  
Star Network ◽  
Star Networks ◽  
Gain Stage

Star Networks at the Singing Point, poetic though it sounds, is merely a description in engineering terminology of the sound-producing method that forms the basis for the piece. A “star network” is a circuit node having three or more connections. The “singing point” is the particular tuning at which the gain in a feedback circuit produces oscillation. In Star Networks at the Singing Point, the performer creates analog circuits composed of multiple nodes, each of which has three or more connections—in essence, “mazes” having a number of paths through which current can flow. Connecting such a circuit in a feedback loop around a gain stage produces an oscillator that is inherently unstable. Tuned to what is called in chaos theory a “tipping point,” the circuit sings unpredictably of its own accord.

scholarly journals Reduced carbon cycle resilience across the Palaeocene–Eocene Thermal Maximum

2018 ◽  
Vol 14 (10) ◽  
pp. 1515-1527 ◽  
Author(s):  
David I. Armstrong McKay ◽  
Timothy M. Lenton
Keyword(s):  
Organic Carbon ◽  
Carbon Cycle ◽  
Deep Ocean ◽  
Tipping Point ◽  
Tipping Points ◽  
Carbon Burial ◽  
Thermal Maximum ◽  
Organic Carbon Burial ◽  
Carbon Release ◽  
Hyperthermal Events

Abstract. Several past episodes of rapid carbon cycle and climate change are hypothesised to be the result of the Earth system reaching a tipping point beyond which an abrupt transition to a new state occurs. At the Palaeocene–Eocene Thermal Maximum (PETM) at ∼56 Ma and at subsequent hyperthermal events, hypothesised tipping points involve the abrupt transfer of carbon from surface reservoirs to the atmosphere. Theory suggests that tipping points in complex dynamical systems should be preceded by critical slowing down of their dynamics, including increasing temporal autocorrelation and variability. However, reliably detecting these indicators in palaeorecords is challenging, with issues of data quality, false positives, and parameter selection potentially affecting reliability. Here we show that in a sufficiently long, high-resolution palaeorecord there is consistent evidence of destabilisation of the carbon cycle in the ∼1.5 Myr prior to the PETM, elevated carbon cycle and climate instability following both the PETM and Eocene Thermal Maximum 2 (ETM2), and different drivers of carbon cycle dynamics preceding the PETM and ETM2 events. Our results indicate a loss of “resilience” (weakened stabilising negative feedbacks and greater sensitivity to small shocks) in the carbon cycle before the PETM and in the carbon–climate system following it. This pre-PETM carbon cycle destabilisation may reflect gradual forcing by the contemporaneous North Atlantic Volcanic Province eruptions, with volcanism-driven warming potentially weakening the organic carbon burial feedback. Our results are consistent with but cannot prove the existence of a tipping point for abrupt carbon release, e.g. from methane hydrate or terrestrial organic carbon reservoirs, whereas we find no support for a tipping point in deep ocean temperature.

scholarly journals Effects of Resource Limitations and Cost Influences on Computer Virus Epidemic Dynamics and Tipping Points

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Chung-Yuan Huang ◽  
Chuen-Tsai Sun
Keyword(s):  
Computer Virus ◽  
Tipping Point ◽  
Tipping Points ◽  
Scale Free Network ◽  
Virus Infections ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Resource Limitations ◽  
Free Network ◽  
Network Power

One of the most important assessment indicators of computer virus infections is epidemic tipping point. Although many researchers have focused on the effects of scale-free network power-law connectivity distributions on computer virus epidemic dynamics and tipping points, few have comprehensively considered resource limitations and costs. Our goals for this paper are to show that (a) opposed to the current consensus, a significant epidemic tipping point does exist when resource limitations and costs are considered and (b) it is possible to control the spread of a computer virus in a scale-free network if resources are restricted and if costs associated with infection events are significantly increased.

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