Tipping elements in the Earth���s climate system Timothy M. Lenton*���, Hermann Held���, Elmar Kriegler�����, Jim W. Hall��, Wolfgang Lucht���, Stefan Rahmstorf���, and Hans Joachim Schellnhuber������ ** *School of Environmental Sciences, University of East Anglia, and Tyndall Centre for Climate Change Research, Norwich NR4 7TJ, United Kingdom ���Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany ��Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213-3890 ��School of Civil Engineering and Geosciences, Newcastle University, and Tyndall Centre for Climate Change Research, Newcastle NE1 7RU, United Kingdom and Environmental Change Institute, Oxford University, and Tyndall Centre for Climate Change Research, Oxford OX1 3QY, United Kingdom **This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected on May 3, 2005. Edited by William C. Clark, Harvard University, Cambridge, MA, and approved November 21, 2007 (received for review June 8, 2007) The term ������tipping point������ commonly refers to a critical threshold at which a tiny perturbation can qualitatively alter the state or development of a system. Here we introduce the term ������tipping element������ to describe large-scale components of the Earth system that may pass a tipping point. We critically evaluate potential policy-relevant tipping elements in the climate system under anthropogenic forcing, drawing on the pertinent literature and a recent international workshop to compile a short list, and we assess where their tipping points lie. An expert elicitation is used to help rank their sensitivity to global warming and the uncertainty about the underlying physical mechanisms. Then we explain how, in principle, early warning systems could be established to detect the proximity of some tipping points. Earth system tipping points climate change large-scale impacts climate policy Hthat uman activities may have the potential to push com- ponents of the Earth system past critical states into qualitatively different modes of operation, implying large-scale impacts on human and ecological systems. Examples have received recent attention include the po- tential collapse of the Atlantic thermohaline circulation (THC) (1), dieback of the Amazon rainforest (2), and decay of the Greenland ice sheet (3). Such phenomena have been described as ������tipping points������ following the popular notion that, at a particular moment in time, a small change can have large, long-term consequences for a system, i.e., ������little things can make a big difference������ (4). In discussions of global change, the term tipping point has been used to describe a variety of phenomena, including the appearance of a positive feedback, reversible phase transitions, phase transitions with hysteresis effects, and bifurcations where the transition is smooth but the future path of the system depends on the noise at a critical point. We offer a formal definition, introducing the term ������tipping element������ to describe subsystems of the Earth system that are at least subcontinental in scale and can be switched���under certain circumstances��� into a qualitatively different state by small perturbations. The tipping point is the corresponding critical point���in forcing and a feature of the system���at which the future state of the system is qualitatively altered. Many of the systems we consider do not yet have convincingly established tipping points. Nevertheless, increasing political demand to define and justify binding temperature targets, as well as wider societal interest in nonlinear climate changes, makes it timely to review potential tipping elements in the climate system under anthropogenic forcing (5) (Fig. 1). To this end, we organized a workshop entitled ������Tipping Points in the Earth System������ at the British Embassy, Berlin, which brought together 36 leading experts, and we conducted an expert elicitation that involved 52 members of the international scientific community. Here we combine a critical review of the literature with the results of the workshop to compile a short list of potential policy-relevant future tipping elements in the climate system. Results from the expert elicitation are used to rank a subset of these tipping elements in terms of their sensitivity to global warming and the associated uncertainty. Then we consider the prospects for early warning of an approaching tipping point. Defining a Tipping Element and Its Tipping Point Previous reviews (6���10) have defined ������abrupt climate change������ as occurring ������when the climate system is forced to cross some threshold, triggering a transition to a new state at a rate determined by the climate system itself and faster than the cause������ (8), which is a case of bifurcation (i.e., one that focuses on equilibrium properties, implying some degree of irreversibil- ity). We have formulated a much broader definition of a tipping element, because (i) we wish to include nonclimatic variables (ii) there may be cases where the transition is slower than the anthropogenic forcing causing it (iii) there may be no abrupt- ness, but a slight change in control may have a qualitative impact in the future and (iv) for several important phase changes, state-of-the-art models differ as to whether the transition is reversible or irreversible (in principle). We consider ������components������ ( ) of the Earth system that are associated with a specific region (or collection of regions) of the globe and are at least subcontinental in scale (length scale of order 1,000 km). A full formal definition of a tipping element is given in supporting information (SI) Appendix 1. For the cases considered herein, a system is a tipping element if the following condition is met: 1. The parameters controlling the system can be transparently combined into a single control , and there exists a critical control value crit from which any significant variation by 0 leads to a qualitative change (F) �� in a crucial system feature F, after some observation time T 0, measured with respect to a reference feature at the critical value, i.e., F crit T F crit T F �� 0. [1] This inequality applies to forcing trajectories for which a slight deviation above a critical value that continues for some time inevitably induces a qualitative change. This change may oc- Author contributions: T.M.L., H.H., E.K., J.W.H., and H.J.S. designed research T.M.L., H.H., E.K., J.W.H., W.L., S.R., and H.J.S. performed research T.M.L., H.H., E.K., and J.W.H. analyzed data and T.M.L., H.H., E.K., and H.J.S. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. Freely available online through the PNAS open access option. ���To whom correspondence may be addressed. E-mail: t.lenton@uea.ac.uk or john@pik- potsdam.de. This article contains supporting information online at www.pnas.org/cgi/content/full/ 0705414105/DC1. �� 2008 by The National Academy of Sciences of the USA 1786���1793 PNAS February 12, 2008 vol. 105 no. 6 www.pnas.org cgi doi 10.1073 pnas.0705414105

cur immediately after the cause or much later. The definition encompasses equilibrium properties with threshold behavior as well as critical rates of forcing. In its equilibrium application, it includes all orders of phase transition and the most common bifurcations found in nature: saddle-node and Hopf bifurcations. The definition could in principle be applied at any time, e.g., in Earth���s history. The feature of the system and the parameter(s) that influence it need not be climate variables. Critical condi- tions may be reached autonomously (without human interfer- ence), and natural variability could trigger a qualitative change. Here we restrict ourselves to tipping elements that may be accessed by human activities and are potentially relevant to current policy. We define the subset of policy-relevant tipping elements by adding to condition 1 the following conditions: 2. Human activities are interfering with the system such that decisions taken within a ������political time horizon������ (TP 0) can determine whether the critical value for the control crit is reached. This occurs at a critical time (tcrit) that is usually within TP but may be later because of a commitment to further change made during TP. 3. The time to observe a qualitative change plus the time to trigger it lie within an ������ethical time horizon������ (TE) tcrit T TE. TE recognizes that events too far away in the future may not have the power of influencing today���s decisions. 4. A significant number of people care about the fate of the component , because it contributes significantly to the overall mode of operation of the Earth system (such that tipping it modifies the qualitative state of the whole system), it contributes significantly to human welfare (such that tipping it impacts on many people), or it has great value in itself as a unique feature of the biosphere. A qualitative change should correspondingly be defined in terms of impacts. Conditions 2���4 give our definition of a policy-relevant tipping element an ethical dimension, which is inevitable because a focus on policy requires the inclusion of normative judgements. These enter in the choices of the political time horizon (TP), the ethical time horizon (TE), and the qualitative change that fulfills con- dition 4. We suggest a maximum TP 100 years based on the human life span and our (limited) ability to consider the world we are leaving for our grandchildren, noting also the Intergov- ernmental Panel on Climate Change (IPCC) focus on this timescale. We suggest TE 1,000 years based on the lifetime of civilizations, noting that this is longer than the timescale of nation states and current political entities. Thus, we focus on the consequences of decisions enacted within this century that trigger a qualitative change within this millennium, and we exclude tipping elements whose fate is decided after 2100. In the limit 3 0, condition 1 would only include vanishing equilibria and first-order phase transitions. Instead we consider that a ������small������ perturbation should not exceed the magnitude of natural variability in . Considering global temperature, climate variability on interannual to millennial timescales is 0.1���0.2��C. Alternatively, a popular target is to limit anthropo- genic global mean temperature increase to 2��C, and we take a ������small������ perturbation to be 10% of this. Either way, 0.2��C seems reasonable. One useful way of classifying tipping elements is in terms of the time, T, over which a qualitative change is observed: (i) rapid, abrupt, or spasmodic tipping occurs if the observation time is very small compared with TP (but T 0) (ii) gradual or episodic tipping occurs if the observation time is intermediate (e.g., of order TP) and (iii) slow or asymptotic tipping occurs if the observation time is very long (in particular, T 3 TE). Several key questions arise. What are the potential policy- relevant tipping elements of the Earth system? And for each: What is the mechanism of tipping? What is the key feature F of interest? What are the parameter(s) projecting onto the control , and their value(s) near crit? How long is the transition time T? What are the associated uncertainties? Policy-Relevant Tipping Elements in the Climate System Earth���s history provides evidence of nonlinear switches in state or modes of variability of components of the climate system (6���10). Such past transitions may highlight potential tipping elements under anthropogenic forcing, but the boundary con- ditions under which they occurred were different from today, and anthropogenic forcing is generally more rapid and often different in pattern (11). Therefore, locating potential future tipping points requires some use of predictive models, in com- bination with paleodata and/or historical data. Here we focus on policy-relevant potential future tipping elements in the climate system. We considered a long list of candidates (Fig. 1, Table 1), and from literature review and the aforementioned workshop, we identified a short list of candi- dates that meet conditions 1���4 (top nine rows in Table 1). To meet condition 1, there needed to be some theoretical basis ( 1 model study) for expecting a system to exhibit a critical threshold Fig. 1. Map of potential policy-relevant tipping elements in the climate system, up- dated from ref. 5 and overlain on global population density. Subsystems indicated could exhibit threshold-type behavior in re- sponse to anthropogenic climate forcing, where a small perturbation at a critical point qualitatively alters the future fate of the system. They could be triggered this century and would undergo a qualitative change within this millennium. We exclude from the map systems in which any threshold appears inaccessible this century (e.g., East Antarctic Ice Sheet) or the qualitative change would appear beyond this millennium (e.g., marine methane hydrates). Question marks indicate systems whose status as tipping elements is particularly uncertain. Lenton et al. PNAS February 12, 2008 vol. 105 no. 6 1787 PERSPECTIVE