The first point concerns the bias in the Atlantic freshwater budget of the GCMs. Because of this bias, there is only one stable equilibrium AMOC state, as the AMOC exports salt out of the Atlantic basin and hence no transition to a collapsed state can occur Drijfhout et al.
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However, from observations and also reanalysis results , the present-day AMOC appears to export freshwater and hence a stable off state may also exist Bryden et al. The second argument is that ocean—atmosphere feedbacks are too weak to remove the multiple equilibrium regime den Toom et al. The third argument is that when ocean vortices on smaller scales so-called eddies are taken into account, the response of the AMOC to freshwater anomalies turns out to be stronger than in the lower resolution non-eddying ocean models, such as those used in CMIP5 Weijer et al.
There are many indications that there have been large-scale reorganizations of both the atmosphere and ocean associated with Dansgaard—Oeschger events. These events consist in large, abrupt shifts identified in ice core records from Greenland and are a prominent feature of the millennial climate variability during the last glacial period. As discussed in Clement and Peterson and Crucifix , several different views have been proposed to explain Dansgaard—Oeschger events, but all leading theories involve changes in the Atlantic Ocean circulation.
Plausible explanations interpret Dansgaard—Oeschger events as transitions between different AMOC states, and the mathematical phenomena behind these transitions are known as stochastic resonance Ganopolski and Rahmstorf, , coherence resonance Timmermann et al. The observed loss of Arctic sea ice in recent years, and the fact that this loss was faster than models predicted Stroeve et al. Essentially, two bifurcation scenarios can be distinguished.
The first scenario is an abrupt summer ice loss, a transition from a perennial ice cover directly to an ice-free ocean.
The second scenario is a gradual loss of summer sea ice to a seasonally ice-covered Arctic, with an abrupt loss of the remaining winter sea ice thereafter. In both cases, an essential positive feedback is the ice-albedo feedback, i. In some models, a feedback involving changes in cloud cover is also essential to the existence of bifurcations Abbot et al.
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This is because the physics behind the growth and melt of sea ice are relatively simple, and hence a variety of models of different complexity has been established. In principle, two types of reduced complexity models can be distinguished: energy balance models, resolving latitudinal but no seasonal differences e. Budyko, ; North, ; Sellers, and single-column models, often resolving a seasonal cycle but no spatial differences e.
Eisenman and Wettlaufer, ; Thorndike, Interestingly, Lindzen and Farrell argued early on that this result was a model artefact arising from the oversimplified nature of heat transport. Later on, a number of single-column models suggested the scenario of an abrupt summer sea ice loss Abbot et al. However, this behaviour can be attributed to the limited resolution of space and time in the models. For example, it is important to resolve the annual cycle sufficiently because the balance of feedbacks depends on the season.
Hence, the bifurcation in summer sea ice disappears in a model when the annual cycle is better resolved Moon and Wettlaufer, Consequently, the transition to a summer without any sea ice is gradual in comprehensive models Overland and Wang, ; Wang and Overland, Initializing such a comprehensive climate model from an ice-free summer results in a fast recovery due to stabilizing feedbacks in winter Tietsche et al.
The second bifurcation scenario, the abrupt loss of winter sea ice, still appeared in a column model with a well-resolved annual cycle Eisenman and Wettlaufer, However, in a spatially explicit model version, the diffusive heat transport between different latitudes tends to stabilize sea ice cover and removes the bifurcation Wagner and Eisenman, b. Wagner and Eisenman b also showed that the model is much more stable if both seasonal and latitudinal variations are considered, even if one of these variations is unrealistically small.
Again, comprehensive climate models are in agreement with these results. In several of these complex models it was explicitly shown that the total loss of Arctic sea ice is reversible Armour et al. There is thus an emerging consensus that no bifurcation-induced abrupt loss of Arctic sea ice is to be expected in the future. However, the absence of multiple sea ice states in CMIP5 models does not necessarily rule out abrupt sea ice loss. In two of these models, a winter ice area of several million square kilometres disappears within only a few years.
In the rest of the models, Arctic winter sea ice area decreases more gradually, but it is still more sensitive to warming than summer ice area Bathiany et al. The reason is that the freezing point introduces a threshold behaviour that can result in a rapid loss of Arctic sea ice. In contrast to the feedback-induced abrupt loss in simple models, the threshold-induced loss is reversible. While complex models agree on the existence of this mechanism, they disagree on how fast Arctic winter sea ice area can disappear.
Moreover, multiple sea ice states do not only occur in oversimplified models. For example, Marotzke and Botzet found a stable, globally ice-covered state in a comprehensive GCM with the current continental distribution. These states are associated with the meridional pattern of the ocean heat transport, which may suggest the possibility of an interplay between multiple sea ice states and multiple AMOC states. The case of Arctic sea ice in the previous section already indicated the importance of external drivers that change over time and question the concept of equilibrium.
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The great ice ages may be viewed as the manifestation of a particularly dramatic mode of variability of the climate system. The deep sea record analysed by Broecker and van Donk has revealed the sawtooth character of the latest four ice ages. Each of them followed a cycle of about years, with a gradual ice accumulation phase, followed by a catastrophic deglaciation. Spectral analysis of additional records Hays et al. More specifically, effects of precession and obliquity on the ice ages dynamics were identified above a continuous background of variability see also Berger, Longer deep sea records also highlighted changes in the regime of these oscillations, with a transition around 1 million years ago towards longer, higher amplitude and more non-linear ice age cycles Lisiecki and Raymo, ; Ruddiman et al.
Finally, Antarctic ice core records have revealed that greenhouse gas concentrations varied in concert with temperature, amplifying the cooling during ice ages Genthon et al. These six elements high amplitude glacial variations, asymmetric cycles with abrupt termination, orbital signature, background spectrum, regime change and synchronous greenhouse gas variations constitute the empirical basis to be addressed by ice age models.
Multistability has been presented as a consequence of the ice-albedo feedback: Extensive ice sheets reflecting sunlight become resilient to small increases in incoming solar radiation Budyko, ; Sellers, This framework featuring the two coexisting stable states has remained in use for interpreting experiments with more sophisticated models Abe-Ouchi et al.
This kind of non-linearity can easily be captured with continuous dynamical systems Saltzman and Maasch, and hybrid dynamical systems Paillard, The framework may even be extended to explain regime changes such as the Mid-Pleistocene transition, where the typical frequency of ice age cycles changed Ashwin and Ditlevsen, There is a spread of views about the physical nature of the potential action.
Several authors have pointed out various effects associated with ice sheet dynamics, their interactions with the bedrock and ice sheet margins that may be responsible for a runaway deglaciation Abe-Ouchi et al. Accumulation of dust on ice sheets may also constitute a significant destabilizing effect Ganopolski and Calov, Another thread of literature gives a more prominent role to CO 2 dynamics and their coupling with ocean circulation dynamics and sea level Paillard and Parrenin, ; Saltzman and Maasch, High-resolution ice core records also revealed abrupt changes in atmospheric CO 2 on decadal timescales during deglaciation Marcott et al.
Although human intervention may prevent the occurrence of the next glacial inception Ganopolski et al. In particular, multiple equilibria have been found in ice sheet models under present-day conditions Ridley et al. In addition to the complexity associated with out-of-equilibrium conditions and multiple forcings highlighted in the previous cases, the history of the Sahara is a prime example of the challenge of temporal variability and spatial heterogeneity. The explanation for the Holocene Green Sahara is based on changes in the Earth orbital parameters. In the early to middle Holocene, the Northern Hemisphere received considerably more solar irradiation in summer.
The Holocene greening of the Sahara was likely amplified by a positive feedback between vegetation and rainfall. Charney pointed out that the heat loss due to the high albedo maintains the sinking motion of dry atmospheric masses and suppresses rainfall over the region. An increase in rainfall leads to more vegetation, and since this vegetation is darker than sand, a lower albedo.
Consequently, more radiation can be absorbed over land, which amplifies the monsoon circulation and convection over the continent. In experiments with the comprehensive atmosphere—vegetation ECHAM3-BIOME model, Claussen found multiple stable states in the Sahara for present-day conditions: the desert state, if the surface was initialized with a high albedo, and the green state, if the surface initially had a low albedo. Several other models also revealed multiple stable states for certain orbital forcings Irizarry-Ortiz, ; Kiang and Eltahir, ; Wang and Eltahir, ; Zeng and Neelin, Brovkin et al.
Experiments with an intermediate complexity model, CLIMBER-2, showed that a combination of orbital forcing changes and the positive climate—vegetation feedback in the model leads to an abrupt decrease in vegetation cover in the Sahara between and years ago Claussen et al. Since then, however, the story has become more complicated. Stability landscape of the Green Sahara and desert. The larger the atmosphere—vegetation feedback i. Current Earth system models do not show alternative vegetation states Boucher et al. It was also observed that considering small-scale heterogeneity in the form of subgrid-scale processes also tends to make the transition smoother in model simulations Claussen et al.
Moreover, spatial heterogeneity tends to desynchronize changes at different locations and makes a transition gradual on a larger scale van Nes and Scheffer, A further complication is imposed by natural climate variability which sometimes obliterates multiple states Guttal and Jayaprakash, and makes a transition more gradual. On the other hand, climate variability can even enhance an abrupt change. An illustrative example is a simulation of the end of the Green Sahara by Liu et al. As soil moisture fluctuates on longer timescales than rainfall, vegetation can still persist after the start of a drying trend.
When the soil water is finally exploited, climate can have changed substantially already, making the collapse into the desert state more dramatic than the gradual decrease in rainfall. As no strong positive feedback is required, Liu et al. Another important aspect is that the fast fluctuations are usually not independent of the long-term state of the system. This will affect the stability of the system. For example, rainfall fluctuations become small towards the desert state.
Once the Sahara becomes too dry, the chances for green spells are very low because the natural variability is also reduced Bathiany et al.
Such considerations may be crucial when subgrid-scale variability is introduced in the model by means of stochastic parameterizations. Such parameterizations can be one approach to account for the effects of unresolved temporal variability as well as spatial heterogeneity Franzke et al. It is clear, however, that a singular, large-scale vegetation dieback at a tipping point is not an adequate description.
The West African monsoon is not the only monsoon system that has been discussed in the context of tipping points. Observations from several monsoon systems on the planet show a markedly abrupt onset of the monsoonal rainfall in spring Ananthakrishnan and Soman, ; Sultan and Janicot, ; Ueda et al. Many potential reasons for these abrupt monsoon onsets have been discussed, most of which involve non-linear processes like hydrodynamic instabilities Hagos and Cook, ; Plumb and Hou, , air—sea interactions and moisture advection Minoura et al.
This raises the interesting question whether the same processes can cause tipping points on longer timescales, e. It is still under debate as to which mechanism may have caused these abrupt responses to the gradual change in forcing Boos and Storelvmo, a , b ; Levermann et al.
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