The Azimuth Project
Tipping point

Contents

Idea

A tipping point occurs when adjusting some parameter of a system causes it to transition abruptly to a new state. The term refers to a well-known example: as you push more and more on a glass of water, it gradually leans over further until you reach the point where it suddenly falls over. Another familiar example is pushing on a light switch until it ‘flips’ and the light turns on.

Details

In the Earth’s climate, tipping points could cause abrupt climate change. A number of possible tipping points have been analyzed in this paper:

They are shown here:

They are:

Thompson and Sieber have made a summary and classification:

Tipping points of sufficient magnitude, perhaps interacting with each other, could cause an overall ‘state shift’ in the Earth’s biosphere:

Abstract: Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds. Here we review evidence that the global ecosystem as a whole can react in the same way and is approaching a planetary-scale critical transition as a result of human influence. The plausibility of a planetary-scale ‘tipping point’ highlights the need to improve biological forecasting by detecting early warning signs of critical transitions on global as well as local scales, and by detecting feedbacks that promote such transitions. It is also necessary to address root causes of how humans are forcing biological changes.

Costs of tipping points

Nonlinear events could cost 3 times more than other climate events according to Checking the price tag on catastrophe - The social cost of carbon under non-linear climate response, at least for methane clathrate releases, oceanic thermohaline circulation and higher climate sensitivity. Usual estimates for best guess social costs for climate change is USD 72 / ton C, so a nonlinear change would be USD 216 / ton C.

Abstract. Research into the social cost of carbon emissions — the marginal social damage from a tonne of emitted carbon — has tended to focus on “best guess” scenarios. Such scenarios generally ignore the potential for low-probability, high-damage events, which are critically important to determining optimal climate policy. This paper uses the FUND integrated assessment model to investigate the influence of three types of low-probability, high-impact climate responses on the social cost of carbon: the collapse of the Atlantic Ocean Meridional Overturning Circulation; large scale dissociation of oceanic methane hydrates; and climate sensitivities above “best guess” levels. We find that incorporating these events can increase the social cost of carbon by a factor of over 3.

Planetary boundaries

  • Jonathan Foley, Gretchen C. Daily, Robert Howarth, David A. Vaccari, Adele C. Morris, Eric F. Lambin, Scott C. Doney, Peter H. Gleick and David W. Fahey, Boundaries for a healthy planet, Scientific American, April 2010.

is a popularization of these more detailed reports:

For more details, see:

  • Stockholm Resilience Centre, video.

which contains, among other things, a link to this Nature special page:

References

As always, it’s good to start here:

This book is a good overview:

Review. Marten Scheffer accessibly describes the dynamical systems theory behind critical transitions, covering catastrophe theory, bifurcations, chaos, and more. He gives examples of critical transitions in lakes, oceans, terrestrial ecosystems, climate, evolution, and human societies. And he demonstrates how to deal with these transitions, offering practical guidance on how to predict tipping points, how to prevent “bad” transitions, and how to promote critical transitions that work for us and not against us. Scheffer shows the time is ripe for understanding and managing critical transitions in the vast and complex systems in which we live. This book can also serve as a textbook and includes a detailed appendix with equations.

Abstract: Major restructuring of the Atlantic meridional overturning circulation, the Greenland and West Antarctic ice sheets?, the Amazon rainforest and ENSO, are a source of concern for climate policy. We have elicited subjective probability intervals for the occurrence of such major changes under global warming from 43 scientists. Although the expert estimates highlight large uncertainty, they allocate significant probability to some of the events listed above. We deduce conservative lower bounds for the probability of triggering at least 1 of those events of 0.16 for medium (2–4 °C), and 0.56 for high global mean temperature change (above 4 °C) relative to year 2000 levels.

The above paper was presented in a special issue if PNAS 2009 on tipping points:

James Hansen believes that we are near several tipping points:

NOAA’s Arctic Report Card provides recent data for changes in arctic atmosphere, sea ice, ocean, land, Greeenland, temperature and biology.

Methane from melting permafrost

Detecting tipping points

Abstract: A climate ‘tipping point’ occurs when a small change in forcing triggers a strongly nonlinear response in the internal dynamics of part of the climate system, qualitatively changing its future state. Human-induced climate change could push several large-scale ‘tipping elements’ past a tipping point. Candidates include irreversible melt of the Greenland ice sheet, dieback of the Amazon rainforest and shift of the West African monsoon. Recent assessments give an increased probability of future tipping events, and the corresponding impacts are estimated to be large, making them significant risks. Recent work shows that early warning of an approaching climate tipping point is possible in principle, and could have considerable value in reducing the risk that they pose.

Abstract: There is currently much interest in examining climatic tipping points, to see if it is feasible to predict them in advance. Using techniques from bifurcation theory, recent work looks for a slowing down of the intrinsic transient responses, which is predicted to occur before an instability is encountered. This is done, for example, by determining the short-term auto-correlation coefficient ARC in a sliding window of the time series: this stability coefficient should increase to unity at tipping. Such studies have been made both on climatic computer models and on real paleoclimate data preceding ancient tipping events. The latter employ re-constituted time-series provided by ice cores, sediments, etc, and seek to establish whether the actual tipping could have been accurately predicted in advance. One such example is the end of the Younger Dryas event, about 11,500 years ago, when the Arctic warmed by 7 C in 50 years. A second gives an excellent prediction for the end of ’greenhouse’ Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state, using data from tropical Pacific sediment cores. This prediction science is very young, but some encouraging results are already being obtained. Future analyses will clearly need to embrace both real data from improved monitoring instruments, and simulation data generated from increasingly sophisticated predictive models.

Some quotes:

In the last few years, the idea of “tipping points” has caught the imagination in climate science with the possibility, also indicated by both palaeoclimate data and global climate models, that the climate system may abruptly “tip” from one regime to another in a comparatively short time.

This recent interest in tipping points is related to a long-standing question in climate science: to understand whether climate fluctuations and transitions between different “states” are due to external causes (such as variations in the insolation or orbital parameters of the Earth) or to internal mechanisms (such as oceanic and atmospheric feedbacks acting on different timescales). A famous example is Milankovich theory, according to which these transitions are forced by an external cause, namely the periodic variations in the Earth’s orbital parameters. Remarkably, the evidence in favour of Milankovich theory still remains controversial.

Hasselmann was one of the first to tackle this question through simple climate models obtained as stochastically perturbed dynamical systems. He argued that the climate system can be conceptually divided into a fast component (the “weather”, essentially corresponding to the evolution of the atmosphere) and a slow component (the “climate”, that is the ocean, cryosphere, land vegetation, etc.). The “weather” would act as an essentially random forcing exciting the response of the slow “climate”. In this way, short-time scale phenomena, modelled as stochastic perturbations, can be thought of as driving long-term climate variations. This is what we refer to as noise-induced tipping.

Sutera studies noise-induced tipping in a simple global energy balance model previously derived by Fraedrich. Sutera’s results indicate a characteristic time of 105yr for the the random transitions between the “warm” and the “cold” climate states, which matches well with the observed average value. One shortcoming is that this analysis leaves open the question as to the periodicity of such transitions indicated by the power spectral analysis. There is a considerable literature on noise-induced escape from attractors in stochastic models. These have successfully been used for modelling changes in climate phenomena, although authors do not always use the word “tipping” and other aspects have been examined. For example, Kondepudi et al consider the combined effect of noise and parameter changes on the related problem of “attractor selection” in a noisy system.

More recently, bifurcation-driven tipping points or dynamic bifurcations have been suggested as an important mechanism by which sudden changes in the behaviour of a system may come about.

Abstract. Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

Stephen Carpenter works on detecting tipping points in lakes. See for example this free online book:

or this paper:

Abstract. Catastrophic ecological regime shifts may be announced in advance by statistical early-warning signals such as slowing return rates from perturbation and rising variance. The theoretical background for these indicators is rich but real-world tests are rare, especially for whole ecosystems. We tested the hypothesis that these statistics would be early-warning signals for an experimentally induced regime shift in an aquatic food web. We gradually added top predators to a lake over three years to destabilize its food web. An adjacent lake was monitored simultaneously as a reference ecosystem. Warning signals of a regime shift were evident in the manipulated lake during reorganization of the food web more than a year before the food web transition was complete, corroborating theory for leading indicators of ecological regime shifts.