Tipping Points In Earth System, Not Always Smooth
University of East Anglia - The Intergovernmental Panel on Climate Change in its many excellent reports tends to portray climate change as a smooth transition. Although the projections are rarely straight lines the underlying system and its responses appear ”linear’ in mathematical terms.
There are, of course, exceptions to this, notable ones being the possible collapse of the Atlantic thermohaline circulation or irreversible melt of the Greenland ice sheet, which both get significant attention in the latest IPCC report. These represent large scale ”non-linear’ components of the Earth system.
The apparent smoothness of typical IPCC projections presented arises for (at least) three reasons: (i) they tend to focus on global mean quantities (e.g. temperature, sea-level) that aggregate and average over regional scale spatial variability, (ii) these global average projections often come from a simple box model that has been ”trained’ to emulate large scale features of state-of-the-art general circulation models but not their non-linear and stochastic features, (iii) where GCM output is shown it is typically averaged over relatively long time windows, and sometimes over ensembles of runs, in order to iron out short-term temporal variability. This is not to say that the overall response of the Earth system, full of non-linearity though it is, could not be smooth and quasi-linear. However, there are many components (or sub-systems) of the Earth system that could display non-linear behaviour and transitions under human (anthropogenic) climate forcing.
Such non-linear transitions where “a small change can make a big difference” have been described as ”tipping points’ ” a term popularized in a sociological context by Malcolm Gladwell in his book ”The Tipping Point’. For clarity, we have recently introduced the term ”tipping element’ to describe the components of the Earth system that can be switched ” under particular conditions ” into a qualitatively different state by small perturbations (Lenton et al, submitted). The term ”tipping point’ is then used to refer to the critical point (in forcing and a feature of the system) at which such a transition is triggered. This article will expand on the tipping elements in the Earth system that may be triggered by anthropogenic climate change, and where their tipping points may lie. It is based on research that began when a group of us (H. Held, H. J. Schellnhuber and I) organised a UK-German workshop on ”Tipping points in the Earth system’ at the British Embassy, Berlin, 5”6 October 2005. An international expert elicitation exercise (led by E. Kriegler and J. Hall) was initiated at the workshop and continued through 2006 into 2007. Meanwhile I undertook a comprehensive review of the literature related to tipping points. The results of the workshop, review and expert elicitation are currently under review with scientific journals (Lenton et al., submitted; Kriegler et al., submitted). Here I will give a summary and personal perspective. For reasons of journal embargo's, ”collective’ results of the workshop and expert elicitation cannot be included. The reader should bear in mind that as with any group of scientific experts there was considerable difference of opinion. A different expert would no doubt give a different slant on the importance of various mechanisms. I will try to reflect this in the use of error ranges and qualitative statements about uncertainties.
Definition and historical examples
For components of the Earth system that are at least sub-continental in scale (~1000km), they are a tipping element if: The parameters controlling the system can be transparently combined into a single control, and there exists a critical value of this control from which a small perturbation leads to a qualitative change in a crucial feature of the system, after some observation time (a full formalization of this is given in Lenton et al., submitted). This definition is deliberately broad and inclusive. It includes ”abrupt climate change’ defined 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. However, it goes beyond this because we wish to include: (i) non-climatic variables, (ii) cases where the transition is slower than the forcing causing it, (iii) cases where there is no abruptness, but a slight change in control still makes a qualitative impact in the future (which can be thought of as analogous to passing the points on a railway track). The definition encompasses equilibrium properties with threshold behavior, including all orders of phase transition and the most common bifurcations found in nature (saddle-node and Hopf bifurcations). Qualitative change may occur immediately after the cause or much later, and the transition may be reversible or irreversible. Thus far there is nothing specific to human activities in the definition. Critical conditions may be reached without human interference and a qualitative change may be triggered by natural variability. Thus in its general form the definition may be applied to any time in Earth history (or future).
Before focusing on anthropogenic changes to the Earth system, let us briefly consider some events in Earth history that indicate the existence of tipping elements and tipping points.
Step back 2.4 billion years to the Great Oxidation ” the first significant rise in atmospheric oxygen, from less than one hundred-thousandth of its present level to over one hundredth of its present level. This event can be most parsimoniously explained as a transition between two pre-existing stable states for atmospheric oxygen, separated by the formation of an ozone layer. If this model is correct then at the time the entire atmosphere and surface system was a tipping element that passed a tipping point.
Jump forward to the postulated ”snowball Earth’ events around 700 million years ago. Extreme glaciations are thought to have occurred when the coverage of sea-ice and land snow reached a critical threshold in latitude beyond which the system ”ran away’ into an alternative state, either completely snow and ice covered (the hard ”snowball’) or with some open water remaining around the equator (the soft ”slushball’). Once again the global system appears to have passed a tipping point.
Step forward again to the warm Cretaceous world of 100 million years ago. Whilst dinosaurs thrived on the land surface the deep sea suffered a series of ”Oceanic Anoxic Events’ (OAEs) where large volumes were rid of oxygen causing mass extinctions. The onset of these events may have involved a strong positive feedback whereby as anoxia builds up, more nutrient phosphorus is recycled from the ocean sediments, fueling more productivity in the surface and more anoxia at depth.
Fifty-five million years ago, there is a striking warm spike in the global temperature record at what is now called the Paleocene-Eocene Thermal Maximum (PETM). This provides probably the closest available analogue to human impact on the climate system. Around 1500”4500 PgC of ”fossil’ carbon was released ” a similar amount to known fossil fuel reserves today. This carbon may have come from frozen methane hydrates under the ocean sediments or from a volcanic intrusion into a huge fossil fuel reservoir where the North Atlantic was opening up ” we don’t know for sure. We do know that within the resolution of the rock record (thousands of years), temperature at the equator rose 4”5 Â°C and at the poles 8”10 Â°C. The ocean acidified dissolving carbonate sediments and the system took the order of a hundred thousand years to recover. If, as many think, much of the carbon released came from frozen methane hydrates after they received a small initial perturbation, then they were a tipping element at the time.
In the glacial-interglacial cycles that have characterized the last few million years of Earth history, there have been a number of striking transitions. In particular, during the last ice age there are a series of Dansgaard-Oeschger events, initially recognized in the North Atlantic sediment and Greenland ice core records but now known to have reached further afield. Each event begins with a rapid warming, which at the Greenland ice core sites can exceed 10 Â°C. There is no clear trigger for such events; orbital forcing and greenhouse gas changes are relatively smooth. One favored explanation is that they involve coupled transitions of the Atlantic thermohaline circulation and Arctic sea-ice to a quasi-stable state with less ice and more northerly deep water formation, triggered occasionally in a ”stochastic resonance’ phenomenon. Arguably the last such event was the BÃ¶lling-AllerÃ¸d warming during the last deglaciation.
In our present interglacial, the Holocene, the climate system appears more stable than during the last ice age. However, there was a non-linear transition when much of the Sahara switched from being vegetated to the present desert around 5000 years ago. Again there is no sharp change in forcing at this time; orbital forcing is smooth. One of the consequences was to force people to settle around rivers and their deltas, ultimately giving rise to the first city states, the “hydraulic societies” in Egypt and Mesopotamia. This may be the best historical example of a tipping point in human systems linked to a tipping point in the climate system.
Have we already tipped some elements?
A cursory reading of the popular press (in the UK at least) would suggest that various elements of the Earth system have already passed a tipping point. A favorite example that has graced the front page of ”The Independent’ newspaper is the melt of Arctic permafrost and corresponding release of methane. There are indeed rapid rates of permafrost melt in various parts of the Arctic, particularly Siberia ” which has been a ”hotspot’ of warming in recent decades. We should be rightly concerned about this, but not on the grounds that it is a tipping element, because probably it is not. Clearly melting is a threshold phenomenon ” put a small amount of energy in at a certain temperature and a phase transition will ensue. However, to achieve tipping element status (i.e. meet our definition) a large (sub-continental) area of the permafrost would have to reach the melting threshold simultaneously, and there is no clear mechanism for this to occur. Furthermore, although methane released from under the permafrost (including melting methane clathrates) is a potent greenhouse gas, it is globally well-mixed, and consequently the strength of the resulting positive feedback is much weaker than has been portrayed in some articles and parts of the popular press.
Probably the clearest example of a tipping element that has already been triggered by human activities is one that is not primarily related to climate change; the Antarctic ozone hole. The process of ozone destruction, including reactions catalyzed on the surface of polar stratospheric clouds (PSC), is non-linear such that beyond a critical threshold of ozone depleting substances (CFCs) the formation of an ozone hole rapidly ensues. This happened coherently over a sub-continental scale because a large mass of air was trapped in the Antarctic polar vortex where cool conditions promoted PSC formation and ozone destruction.
More directly related to what we think of as climate variables, but more controversial is the suggestion that the Sahel drought of recent decades may be linked to removal of 90% of West Africa’s coastal rain forest in the interval 1920”1980. The onset of Sahel drought has been characterized as a switch between bi-stable states, and coastal deforestation has been predicted to generate a complete collapse of the West African Monsoon (WAM). However, GCM simulations tell a different story in which Sahel drying is due to past aerosol loading cooling the Northern Hemisphere. Furthermore, the WAM has not collapsed, and if it did it is not clear that the consequence would be to dry the Sahel (more on that below)
Another controversial candidate for a human-induced tipping point is the observed regime shift of the El NiÃ±o Southern Oscillation (ENSO) and a corresponding change in Pacific temperatures centered around 1976. Prior to 1976 there were low amplitude El NiÃ±o events with 2”3 year frequency, subsequently there have been large amplitude events with 4”5 year frequency. Some attribute this shift (in part at least) to anthropogenic greenhouse warming. However, there is by no means a consensus on this, not least because the nature of ENSO is still under debate, with some arguing that it is a damped oscillation sustained by external disturbances, and therefore its behavior will depend probabilistically on noise.
A more convincing case can be made that climate warming may have caused the Arctic sea-ice to pass a tipping point. Certainly the area coverage of both summer and winter Arctic sea-ice are declining at present, summer sea-ice more markedly, and the ice has thinned significantly over a large area. Elegant analysis has shown that positive ice-albedo feedback (the warming due to changing from reflective ice to dark ocean surface) dominates over external forcing (the global warming signal) in causing the thinning and shrinkage since around 1988. This suggests the system may already be undergoing a non-linear transition toward a different state with less Arctic sea-ice (perhaps none in summer).
Potential future tipping elements
If any of the above inferences are correct and these systems have already passed a tipping point then there is little we can do about it except try and adapt. Climate policy, especially mitigation policy, should be more concerned with what tipping elements might be triggered by human activities in the future, and whether their tipping points can be avoided. To try and focus on the subset of the most important potential tipping elements relevant to policy makers we extended our definition of a tipping element to include the following conditions:
1. Human activities are interfering with the system such that decisions taken within a “political time horizon” can determine whether the critical control value is reached.
2. The time to observe a qualitative change in the system plus the time to trigger it lie within an “ethical time horizon”.
3. A significant number of people care about the fate of the system, either because it is integral to the overall functioning of the Earth system, and/or tipping it will impact a large number of people, and/or it has intrinsic value as a feature of the biosphere.
We chose 100 years for the political time horizon (recall that most IPCC projections go to year 2100) and 1000 years for the ethical time horizon (based on the lifetime of human cultures). These are probably upper limits. Many people (including policy makers) struggle to consider the world beyond their own lifetime.
We have already made a ”commitment’ to ~0.6 Â°C of further warming even if we could stabilize greenhouse gas concentrations tomorrow (which we can’t). Hence, conceivably, there could be tipping elements that haven’t been triggered yet, but which we are already committed to triggering. However, our research thus far does not clearly indicate any tipping elements that fall into this category. Warming on the century timescale is projected to be in the range 1.1”6.4 Â°C above present (IPCC, 2007). This represents the ”accessible neighborhood’ of global temperatures. A number of potential tipping elements are excluded because their tipping point is estimated to be inaccessible on the century timescale (although they may become a concern for future policy makers). This leaves the subset summarized in Figure 1 and its caption.
even smaller version
Figure 1. Potential future policy-relevant tipping elements in the climate system and estimates of the global warming (above present) that could cause their control to reach a critical threshold. There is one more tipping element not shown ” the Indian Summer Monsoon ” because its critical threshold cannot be meaningfully related to global warming. The temperature ranges given here are from reviewing studies in the literature and conversations with individual experts. A similar (but not identical) ranking emerges from a formal expert elicitation exercise (Kriegler et al., submitted).
The tipping element that consistently emerges as having the closest threshold (in terms of global warming) and the least uncertainty in this is (irreversible) melt of the Greenland Ice Sheet (GIS). Paleo-data reveal that the GIS shrunk considerably during the last interglacial. Models also indicate that above a local warming of ~3 Â°C above present the Greenland ice sheet will go into net mass loss and shrink to a much smaller size (perhaps disappearing altogether). The corresponding global warming (accounting for polar amplification) is estimated at 1”2 Â°C. The IPCC (2007) give a more conservative range of 1”4 Â°C. Others have estimated <1 Â°C. Their case may be bolstered by observations indicating that the ice sheet is already in net mass loss and the rate of mass loss has accelerated in the last decade. The timescale for the ice sheet to melt is at least 300 years and often given as roughly 1000 years. However, given that it contains 7m of global sea-level rise the corresponding contribution to sea-level can dwarf other contributors.
The West Antarctic Ice Sheet (WAIS) is thought to be less vulnerable to warming than the Greenland Ice Sheet but a threshold could still be accessed this century. The setting is quite different, with most of the WAIS grounded below sea-level. The WAIS has the potential to collapse if grounding line retreat causes ocean water to undercut the ice sheet and trigger further separation from the bedrock (a strong positive feedback). This suggests that it is warming ocean water rather than a warming atmosphere that may pass a critical threshold, a point bolstered by the fact that for surface melting to occur, there would need to be ~8 Â°C warming of the surface atmosphere at 75”80 Â°S to reach the freezing point in summer. The corresponding global warming depends on the Antarctic polar amplification factor (which varies a lot between models for the 21st century but is likely much smaller than that for the Arctic). The threshold for ocean warming is estimated at 3”5 Â°C. A worst case scenario is for collapse to occur within 300 years, with a total of 4”6m of global sea-level rise.
The archetypal example of a tipping element is a reorganization of the Atlantic thermohaline circulation (THC) when sufficient freshwater enters the North Atlantic to halt density driven North Atlantic Deep Water (NADW) formation. All models exhibit a collapse of convection under sufficient freshwater forcing, but the additional North Atlantic freshwater input required ranges over 0.1”0.5 Sv (1 Sv = 106 m3s-1). The sensitivity of freshwater input to warming also varies between models, as does whether the transition is reversible or irreversible. Observed freshening of the North Atlantic has contributions from melting sea-ice, Greenland ice sheet melt and increased Eurasian river input, totaling ~0.025 Sv. If this is due to the observed ~0.8 Â°C global warming it could increase several-fold this century. However, best estimates are that reaching the threshold for THC collapse still requires at least 3”5 Â°C warming within the century. The IPCC (2007) view the threshold as more distant. The transition would probably take of order another 100 years. A THC collapse would tend to cool the North Atlantic and warm the Southern Ocean, it would raise sea-level in some regions by ~1m and cause a Southward shift of the Inter-Tropical Convergence Zone (ITCZ). Despite widespread misconceptions that the Gulf Stream will switch off it will instead be redirected Southward past Spain as part of the North Atlantic Gyre circulation.
Changes in the El NiÃ±o Southern Oscillation (ENSO) have already occurred (as discussed above) but it is unclear what they can be attributed to. In future projections, the first coupled model studies predicted a shift from current ENSO variability to more persistent or frequent El NiÃ±o conditions. Now that numerous models have been inter-compared, there is no consistent trend. However, in response to a stabilized 3”6 Â°C warmer climate, the most realistic models simulate increased El NiÃ±o amplitude (with no change in frequency). Although the transition may be smooth this could still represent a tipping element. Certainly paleo-data indicate different ENSO regimes under different climates of the past. The mechanisms and timescale of transition are unclear. The impacts of higher amplitude El NiÃ±o events would include droughts in South East Asia and elsewhere.
One region that would suffer drying is the Amazon, and more persistent El NiÃ±o conditions have been predicted to cause die back of the Amazon rain forest under 3”4 Â°C global warming in the Hadley Centre model. A recent study nesting a regional climate model within a different GCM also predicts Amazon die back due to reductions in precipitation and lengthening of the dry season. When different vegetation models are driven with similar climate projections they also show Amazon die back. However, other climate models predict different precipitation trends and therefore do not produce dieback. Rainforest loss itself leads to reductions in precipitation, so land-use change could be a trigger, as well as climate change. The transition time is of the order of decades and the impacts include widespread loss of biodiversity.
On the other side of the Atlantic, a rare example of a potential beneficial tipping element is a greening of the Sahara/Sahel region back toward conditions last seen around 6000 years ago. This suggestion may seem a little odd given recent Sahel drought, and indeed some models project further drought in the 21st century. However, a scenario is conceivable where the West African Monsoon (WAM) effectively collapses, adversely affecting some regions but this leads to increased inflow of moist air from the West to the Sahel, wetting it and promoting vegetation growth. Such a scenario plays out in one of the few GCMs that manage a realistic representation of today’s WAM. However, WAM collapse is triggered by a rather rapid ~3 Â°C warming of sea surface temperatures (SSTs) in the Gulf of Guinea. The fate of vegetation in the region will depend not only on the fate of the WAM but also on the degree of land-use change activity (which is currently very high in West Africa). In the best-case scenario the number of people the region can support would increase.
The Indian summer monsoon (ISM) system could also be in for a rocky ride this century. Paleo-records indicate its volatility, with Dansgaard-Oeschger events accompanied by flips on and off of monsoonal rainfall. Recent data also display strongly non-linear characteristics on different timescales. Although greenhouse warming, which is stronger over land and in the Northern Hemisphere, would be expected to strengthen the monsoon system, increases in planetary albedo over the continent due to aerosol emissions and/or land use change are expected to weaken it. In a simple model, if regional planetary albedo exceeds ~0.5, the ISM collapses. Thus global warming should protect the ISM but other anthropogenic climate changes may trigger it to switch off and then the greenhouse warming may trigger it to switch back on, producing a ”roller coaster ride’ for many millions of people. If switches occur they could happen from one year to the next.
Moving away from the tropics, to a less populated region, the boreal forest system has been predicted to experience widespread dieback in at least one model, when regional temperatures reach around 7 Â°C above present, corresponding to around 3 Â°C global warming. The causes are complex with increased water stress and increased peak summer heat stress causing increased mortality, vulnerability to disease, and fires, along with decreased reproduction rates. The forest would be replaced over large areas by open woodlands or grasslands that support increased fire frequency.
North from the boreal forest lies the tundra, but as already discussed, melt of the permafrost and associated methane release ” and on longer timescales, replacement of the tundra by boreal forest ” are expected to be quasi-linear responses and therefore not tipping elements.
Current Arctic sea-ice loss has also been discussed above and in most future projections there is a decline of summer sea-ice cover which can disappear within a century at a polar temperature of around 9 Â°C above present. However, in most of the models, the transition is quasi-linear, not exhibiting a critical threshold. In two of the models used in IPCC (2007) there is a complete loss of annual sea-ice and in one the transition is non-linear, happening within 10 years, however it requires polar warming of 13 Â°C above present which is probably not accessible this century.
Under the ocean sediments resides a large reservoir of frozen methane hydrates, perhaps of order ~10,000 PgC. As mentioned above, in the PETM warm event 55 Myr ago, a large amount of carbon may have been lost from this reservoir (and subsequently replenished). However, existing models and understanding suggest that such loss takes the form of lots of small release events rather than one big one. Hence it’s not clear it is a tipping element. Furthermore the release is estimated to occur over many thousands of years and therefore it may fall outside of the ”ethical time horizon’ considered in present policies, even thought it could be started within the ”political time horizon’ of this century.
Interactions between tipping elements
There are many potential interactions between tipping elements, which can be divided into those where tipping one element increases the probability of tipping another (”positive’ ” in a mathematical sense), and those where it reduces it (”negative’ ” although a better thing from a human point of view). For example, melt of the Greenland ice sheet (GIS) will add freshwater to the North Atlantic tending to increase the probability of a shut-off in North Atlantic Deep Water formation and a reorganization of the thermohaline circulation (THC) ” a positive causal connection. However, a reorganization of the THC would itself tend to cool the region around Greenland and thus reduce the probability of melt of the GIS (or potentially slow it, if it is already underway) ” a negative interaction.
Current mechanistic understanding suggests that there are more positive causal connections between tipping elements than negative ones. In the worst case scenario, this raises the alarming possibility of ”domino dynamics’ in the climate system where tipping one element encourages tipping the next and so on. However, lest the reader be panicking, there are also notable negative interactions between tipping elements that could produce ”self-regulation’ scenarios. Furthermore, Earth history indicates that transitions of the whole Earth system are rare.
Continuing our example above, if the GIS starts to melt the ensuing sea level rise will encourage grounding line retreat of the West Antarctic Ice Sheet (WAIS). Furthermore, if there is a collapse of the THC promoted by GIS melt this would tend to warm the Southern Ocean also encouraging disintegration of the WAIS. Hence there is the possibility of domino dynamics between the Greenland and West Antarctic ice sheets. If the WAIS tips before the Atlantic THC then the rapid advection of additional freshwater up the Atlantic would increase the probability of a THC reorganization. However, on a longer timescale, the establishment of a stronger density contrast between the South and North Atlantic would tend to stabilize the THC. An increase in ENSO amplitude would also have a stabilizing effect on the Atlantic THC, as El NiÃ±o events are observed to cause more water vapour transport from the Atlantic (Gulf of Mexico) to the Pacific, thus creating saltier Gulf Stream waters that are more prone to sinking.
What can we do about tipping points?
The existence of tipping elements in the climate system that could pass a tipping point this century gives an added impetus to mitigation efforts. Crossing any of the tipping points identified (with the possible exception of the Sahara/Sahel system) would represent “dangerous anthropogenic interference in the climate system”. Given their large scale impacts and uncertainty as to exactly where their thresholds lie, an important question for policy makers is: Can we anticipate a tipping point before it is reached?
In principle, time series data could reveal that a system is approaching a tipping point. As a bifurcation point is approached, the rate of recovery of a system from perturbations caused by internal variability in the climate system gets more and more sluggish (the present state of the system becomes ”degenerate’). At the bifurcation point all memory in the system is lost as it switches to a different state, i.e. it never returns from the fatal perturbation. The decay rate of perturbations can be extracted by careful analysis of time series data once any systematic trends in the data have been removed (Held and Kleinen, 2004).
This method of anticipating a tipping point has been shown to work in principle using the output of a model forced to cross a tipping point in the Atlantic thermohaline circulation (THC). However, it requires a timeseries that is an order of magnitude longer than the transition time of the system in question and has an order of magnitude higher resolution than the transition time. In reality, these are tough requirements to meet. For the Atlantic we don’t have a sufficiently long, high resolution record indicating the underlying THC strength. We have considered a number of the other tipping elements identified above, but in all cases there are shortcomings in the data that make the scope for anticipating a tipping point seem remote. That is not to say that a better monitoring system could not be set up for many systems, but the common problem will tend to be getting a regular, accurate measure of its past state and behaviour (i.e. a better paleo record).
Whatever we do to try and anticipate future tipping elements it will rely on some use of computer models in concert with available data, and will always carry uncertainty associated with both the model and the data. However, from our review, workshop and expert elicitation it appears that useful information is already available regarding the likely proximity of various tipping points. The existence of positive causal interactions between some of them sharpens the impetus to mitigate against tipping them in the first place.
Our present warming commitment alone seems insufficient to tip any of the elements we have identified. However, it could get us close to the threshold for irreversible melt of the Greenland ice sheet. If that threshold is at the nearest end of its estimated error range (1 Â°C further global warming) then it will be nearly impossible to avoid by mitigation unless we are lucky and the climate sensitivity is at the bottom end of its uncertainty range (circa 1.6 Â°C warming for a doubling of pre-industrial CO2). If the threshold is further away (we estimate an upper limit of 2 Â°C global warming) then mitigation would still need to be extremely aggressive to avoid it. Given this, it seems prudent to design long-term adaptation strategies in anticipation of a progressive melt of the Greenland ice sheet. Critically there remains an argument for mitigation even when the threshold is passed because the rate of GIS melt and the corresponding contribution to sea level rise depends on how far the threshold is exceeded.
Based on current information all the other potential tipping elements might be avoided by limiting global warming to 2 Â°C above pre-industrial (although we cannot be sure). This is the EU target and the canonical value assumed in the international policy arena when discussing “avoiding dangerous climate change”. Continuing business as usual could threaten all of the tipping elements discussed above. This is, needless to say, an unwise path to follow. The socio-economic consequences would be huge and include step increases in damage costs that fundamentally alter the nature and outcome of any cost-benefit analysis aimed at deciding on a temperature stabilization target. Perhaps it is better instead to think about the socio-economic system as one that also possesses tipping points. One of these would be a non-linear transition to an economic regime where fossil fuels are replaced by low carbon energy sources as the backstop technology. In at least one macro-economic model such a transition can be triggered as the price of emitting carbon is gradually increased (Edenhofer et al., 2006). A policy to avoid tipping points in the climate system might best be one that encourages such a tipping point in the socio-economic system.
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