Tipping Elements in the Earth's Climate System

Abstract

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

Full text

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
†‡储
**
*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
储
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 兩 tipping points 兩 climate change 兩 large-scale impacts 兩 climate policy
H
uman activities may have the potential to push com-
ponents of the Earth system past critical states into
qualit atively different modes of operation, implying
large-scale impacts on human and ecological systems.
Examples that 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-ter m 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 variet y of phenomena, including the
appearance of a positive feedback, reversible phase transitions,
phase transitions with hysteresis ef fects, 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 for mal
defin ition, 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
organ ized 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 commun ity.
Here we combine a critical review of the literature with the
results of the workshop to c ompile a short list of potential
polic y-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
war ming 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
deter mined 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-
it y). We have formulated a much broader defin ition of a tipping
element, because (i) we wish to include nonclimatic variables; (ii)
there may be cases where the transition is slower than the
anthropogen ic forcing causing it; (iii) there may be no abrupt-
ness, but a slight change in control may have a qualit ative impact
in the future; and (iv) for several important phase changes,
st ate-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 for mal definition of a tipping element
is given in supporting information (SI) Appendix 1. For the cases
c onsidered herein, a system ⌺ is a tipping element if the
following condition is met:
1. The parameters c ontrolling the system can be transparently
c ombined into a single control
␳
, and there exists a critical
c ontrol value
␳
crit
f rom which any significant variation by
␦␳
⬎
0 leads to a qualitative change (F
ˆ
) 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.,
兩F共
␳
ⱖ
␳
crit
⫹
␦␳
兩T兲 ⫺ F共
␳
crit
兩T兲兩 ⱖ F
ˆ
⬎ 0. [1]
This inequalit y 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
兩
PNAS
兩
February 12, 2008
兩
vol. 105
兩
no. 6 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0705414105

cur immediately after the cause or much later. The definition
enc ompasses 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 variabilit y could trigger a qualit ative change.
Here we restrict ourselves to tipping elements that may be
ac cessed by human activities and are potentially relevant to
current polic y. We define the subset of policy-relevant tipping
elements by adding to condition 1 the following conditions:
2. Human activities are interfering w ith the system ⌺ such that
decisions taken w ithin a ‘‘political time horizon’’ (T
P
⬎ 0) can
deter mine whether the critical value for the control
␳
crit
is
reached. This occurs at a critical time (t
crit
) that is usually
within T
P
but may be later because of a commitment to further
change made during T
P
.
3. The time to observe a qualitative change plus the time to
trigger it lie within an ‘‘ethical time horizon’’ (T
E
); t
crit
⫹ T ⱕ
T
E
. T
E
rec ognizes 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
c omponent ⌺, 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 sign ificantly 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 inevit able because a focus
on policy requires the inclusion of normative judgements. These
enter in the choices of the political time horizon (T
P
), the ethical
time horizon (T
E
), and the qualitative change that fulfills con-
dition 4. We suggest a maximum T
P
⬃ 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-
ernment al Panel on Climate Change (IPCC) focus on this
timescale. We suggest T
E
⬃ 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
c onsequences 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, c ondition 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-
gen ic 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,
abr upt, or spasmodic tipping occurs if the observation time is
very small compared with T
P
(but T ⫽ 0); (ii) gradual or episodic
tipping occurs if the observation time is intermediate (e.g., of
order T
P
); and (iii) slow or asymptotic tipping oc curs if the
observation time is very long (in particular, T 3 T
E
).
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 uncert ainties?
Policy-Relevant Tipping Elements in the Climate System
Earth’s history provides evidence of nonlinear sw itches 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
dif ferent in pattern (11). Therefore, locating potential future
tipping points requires some use of predictive models, in com-
bination with paleodat a 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
兩
February 12, 2008
兩
vol. 105
兩
no. 6
兩
1787
PERSPECTIVE

(
␳
crit
) at a subcontinental scale, and/or past evidence of threshold
behavior. Where the proposed
␳
crit
c ould be meaningfully related
to temperature, condition 2 was evaluated based on an ‘‘acces-
sible neighborhood’’ of global temperatures from the IPCC (12)
of 1.1–6.4°C above 1980–1999 that c ould be committed to over
the next T
P
⬃ 100 years, and on recogn ition that transient
war ming is generally greater toward the poles and greater on
land than in the ocean. Condition 3 was evaluated on the basis
of model projections, known shortc omings of the models,
and paleodat a. Our collective judgement was used to evaluate
c ondition 4.
Our short list differs from that of the IPCC (ref. 12, chapter
10, especially p. 775 ff, p. 818 ff) because our definition and
criteria differ f rom, and are more explicit than, the IPCC notion
of abrupt climate change. The evidence base we use is also
slightly dif ferent because it enc ompasses some more recent
studies. The authors of this paper and the workshop participants
are a smaller group of scientists than the IPCC members, the
groups are only partially overlapping, and our analysis was
undert aken largely in parallel. We seek to add value to the IPCC
overview by injecting a more precise definition and undertaking
a complementary, in-depth evaluation.
We now discuss the entries that made our short list and seek
to ex plain significant discrepancies from the IPCC where they
arise. Those candidates that did not make the short list (and why)
are discussed in SI Appendix 2.
Arctic Sea-Ice. As sea-ice melts, it exposes a much darker ocean
surface, which absorbs more radiation–amplifying the warming.
Energy-balance models suggest that this ice-albedo positive
feedback can give rise to multiple stable states of sea-ice (and
land snow) cover, including finite ice cap and ice-free states, with
ice caps smaller than a certain size being unstable (13). This
small ice-cap instability is also found in some atmospheric
general circulation models (AGCMs), but it can be largely
eliminated by noise due to natural variability (14). The inst ability
is not expected to be relevant to Southern Ocean sea-ice because
the Ant arctic continent covers the region over which it would be
ex pected to arise (15). Different stable states for the flow rate
through the narrow outlets that drain parts of the Arctic basin
have also been found in a recent model (16). For both summer
and winter Arctic sea-ice, the area coverage is declining at
present (with summer sea-ice declining more markedly; ref. 17),
and the ice has thinned significantly over a large area. Positive
ice-albedo feedback dominates external forcing in causing the
thinn ing and shrink age since 1988, indicating strong nonlinearity
and leading some to suggest that this system may already have
passed a tipping point (18), although others disagree (19). In
IPCC projections with ocean-atmosphere general circulation
Table 1. Policy-relevant potential future tipping elements in the climate system and (below the empty line) candidates that we
considered but failed to make the short list*
Tipping element
Feature of
system, F
(direction of
change)
Control
parameter(s),
␳
Critical
value(s),
†
␳
crit
Global
warming
†‡
Transition
timescale,
†
T Key impacts
Arctic summer sea-ice Areal extent (⫺) Local ⌬T
air
, ocean heat
transport
Unidentified
§
⫹0.5–2°C ⬇10 yr (rapid) Amplified warming,
ecosystem change
Greenland ice sheet (GIS) Ice volume (⫺) Local ⌬T
air
⫹⬇3°C ⫹1–2°C ⬎300 yr (slow) Sea level ⫹2–7 m
West Antarctic ice sheet
(WAIS)
Ice volume (⫺) Local ⌬T
air
, or less
⌬T
ocean
⫹⬇5–8°C ⫹3–5°C ⬎300 yr (slow) Sea level ⫹5m
Atlantic thermohaline
circulation (THC)
Overturning (⫺) Freshwater input to N
Atlantic
⫹0.1–0.5 Sv ⫹3–5°C ⬇100 yr (gradual) Regional cooling, sea level,
ITCZ shift
El Nin˜ o–Southern
Oscillation (ENSO)
Amplitude (⫹) Thermocline depth,
sharpness in EEP
Unidentified
§
⫹3–6°C ⬇100 yr (gradual) Drought in SE Asia and
elsewhere
Indian summer monsoon
(ISM)
Rainfall (⫺) Planetary albedo over
India
0.5 N/A ⬇1 yr (rapid) Drought, decreased carrying
capacity
Sahara/Sahel and West
African monsoon (WAM)
Vegetation fraction
(⫹)
Precipitation 100 mm/yr ⫹3–5°C ⬇10 yr (rapid) Increased carrying capacity
Amazon rainforest Tree fraction (⫺) Precipitation, dry
season length
1,100 mm/yr ⫹3–4°C ⬇50 yr (gradual) Biodiversity loss, decreased
rainfall
Boreal forest Tree fraction (⫺) Local ⌬T
air
⫹⬇7°C ⫹3–5°C ⬇50 yr (gradual) Biome switch
Antarctic Bottom Water
(AABW)*
Formation (⫺) Precipitation–
Evaporation
⫹100 mm/yr Unclear
¶
⬇100 yr (gradual) Ocean circulation, carbon
storage
Tundra* Tree fraction (⫹) Growing degree days
above zero
Missing
储
— ⬇100 yr (gradual) Amplified warming, biome
switch
Permafrost* Volume (⫺) ⌬T
permafrost
Missing
储
— ⬍100 yr (gradual) CH
4
and CO
2
release
Marine methane
hydrates*
Hydrate volume (⫺) ⌬T
sediment
Unidentified
§
Unclear
¶
10
3
to 10
5
yr (⬎T
E
) Amplified global warming
Ocean anoxia* Ocean anoxia (⫹) Phosphorus input to
ocean
⫹⬇20% Unclear
¶
⬇10
4
yr (⬎T
E
) Marine mass extinction
Arctic ozone* Column depth (⫺) Polar stratospheric
cloud formation
195 K Unclear
¶
⬍1 yr (rapid) Increased UV at surface
N, North; ITCZ, Inter-tropical Convergence Zone; EEP, East Equatorial Pacific; SE, Southeast.
*See SI Appendix 2 for more details about the tipping elements that failed to make the short list.
†
Numbers given are preliminary and derive from assessments by the experts at the workshop, aggregation of their opinions at the workshop, and review of the
literature.
‡
Global mean temperature change above present (1980 –1999) that corresponds to critical value of control, where this can be meaningfully related to global
temperature.
§
Meaning theory, model results, or paleo-data suggest the existence of a critical threshold but a numerical value is lacking in the literature.
¶
Meaning either a corresponding global warming range is not established or global warming is not the only or the dominant forcing.
储
Meaning no subcontinental scale critical threshold could be identified, even though a local geographical threshold may exist.
1788
兩
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0705414105 Lenton et al.

models (OAGCMs) (12), half of the models become ice-free in
September during this century (19), at a polar temperature of
⫺9°C (9°C above present) (20). The transition has nonlinear
steps in many of the models, but a common critical threshold has
yet to be identified (19). Thinning of the winter sea-ice increases
the efficiency of formation of open water in summer, and abrupt
retreat occurs when ocean heat transport to the Arctic increases
rapidly (19). Only t wo IPCC models (12) exhibit a complete loss
of annual sea-ice cover under extreme forcing (20). One shows
a nonlinear transition to a new stable state in ⬍10 years when
polar temperature rises above ⫺5°C (13°C above present),
whereas the other shows a more linear transition. We conclude
that a critical threshold for summer Arctic sea-ice loss may exist,
whereas a further threshold for year-round ice loss is more
uncert ain and less accessible this century. Given that the IPCC
models significantly underestimate the observed rate of Arctic
sea-ice decline (17), a summer ice-loss threshold, if not already
passed, may be very close and a transition could occur well within
this century.
Greenland Ice Sheet (GIS). Ice-sheet models typically exhibit mul-
tiple stable states and nonlinear transitions between them (21).
In some simulations with the GIS removed, summer melting
prevents its reestablishment (22), indicating bistability, although
others disagree (23). Regardless of whether there is bistability,
in deglaciation, warming at the periphery lowers ice altitude,
increasing surface temperature and causing a positive feedback
that is expected to exhibit a critical threshold beyond which there
is ongoing net mass loss and the GIS shrinks radically or
eventually disappears. During the last interglacial (the Eemian),
there was a 4- to 6-m higher sea level that must have come from
Greenland and/or Antarctica. Increased Arctic summer insola-
tion caused an estimated ⬍3.5°C summertime warming of
Greenland, and shrinkage of the GIS contributed an estimated
1.9–3.0 m to sea level, although a widespread ice cap remained
(24). Broadly consistent with this, future projections suggest a
GIS threshold for negative surface mass balance resides at
ⱖ⬇3°C local war ming (above preindustrial) (3, 25). Uncertain-
ties are such that IPCC (12) put the threshold at ⬇1.9–4.6°C
global warming (above preindustrial), which is clearly accessible
this century. We give a closer and narrower range (above
present) because amplification of warming over Greenland may
be greater (26) than assumed (12, 25) because of more rapid
sea-ice decline than modeled (17). Also, recent observations
show the surface mass balance is declining (12) and contributing
to net mass loss from the GIS (27, 28) that is accelerating (28,
29). Finally, existing ice-sheet models are unable to explain the
speed of recent changes. These changes include melting and
thinn ing of the coastal margins (30) and surging of outlet gla-
ciers (29, 31), which may be contributed to by the intrusion of
war ming ocean waters (32). This is partly compensated by
some mass gain in the interior (33). There is a lack of knowl-
edge of natural GIS variability, and Greenland temperature
changes have differed from the global trend (26), so interpre-
t ation of recent observations remains uncertain. If a threshold
is passed, the IPCC (12) gives a ⬎1,000-year timescale for
GIS collapse. However, given the ack nowledged (12) lack of
processes that could accelerate collapse in current models,
and their inability to simulate the rapid disappearance of con-
tinent al ice at the end of the last ice age, a lower limit of 300
years is conceivable (34).
West Antarctic Ice Sheet (WAIS). Most of the WAIS is grounded
below sea level and has the potential to collapse if grounding-line
retreat triggers a strong positive feedback whereby ocean water
undercuts the ice sheet and triggers further separation from the
bedrock (35–37). The WAIS has retreated at least once during the
Pleistocene (38), but the full extent of retreat is not known, nor is
whether it occurred in the Eemian or the long, warm interglacial
MIS-11 ⬇400 ka. Approximately 1–4 m of the Eemian sea-level rise
may have come from Antarctica, but some could have been from
parts of the East Antarctic Ice Sheet grounded below sea level (and
currently thinning at a rapid rate). WAIS collapse may be preceded
by the disintegration of ice shelves and the acceleration of ice
streams. Ice shelf collapse could be triggered by the intrusion of
warming ocean water beneath them or by surface melting. It
requires ⬇5°C of local warming for surface atmospheric tempera-
tures to exceed the melting point in summer on the major (Ross and
Fischner-Ronne) ice shelves (12, 37). The threshold for ocean
warming is estimated to be lower (37). The WAIS itself requires
⬇8°C of local warming of the surface atmosphere at 75–80°S to
reach the melting point in summer (37). Although the IPCC (12)
declines to give a threshold, we estimate a range that is clearly
acce ssible this century. Concern is raised by recent inferences from
gravity measurements that the WAIS is losing mass (39), and
observations that glaciers draining into the Amundsen Sea are
losing 60% more ice than they are gaining and hence contributing
to sea-level rise (40). They drain a region containing ⬇1.3mofa
total ⬇5 m of global sea-level rise contained in the WAIS. Although
the timescale is highly uncertain, a qualitative WAIS change could
occur within this millennium, with collapse within 300 years being
a worst-case scenario. Rapid sea-level rise (⬎1 m per century) is
more likely to come from the WAIS than from the GIS.
Atlantic Thermohaline Circulation (THC). A shutoff in North Atlantic
Deep Water formation and the associated Atlantic THC can
oc cur if sufficient freshwater (and/or heat) enters the North
Atlantic to halt density-driven North Atlantic Deep Water
for mation (41). Such THC reorganizations play an important
part in rapid climate changes recorded in Greenland during the
last glacial cycle (42, 43). Hysteresis of the THC has been found
in all models that have been systematically tested thus far (44),
f rom conceptual ‘‘box’’ representations of the ocean (45) to
OAGCMs (46). The most complex models have yet to be
systematically tested because of excessive computational cost.
Under sufficient North Atlantic freshwater forcing, all models
exhibit a collapse of convection. In some experiments, this
c ollapse is reversible (47) (after the forcing is removed, convec-
tion resumes), whereas in others, it is irreversible (48)—
indicating bistability. In either case, a tipping point has been
passed ac cording to condition 1. The proximity of the present
climate to this tipping point varies considerably between models,
c orresponding to an additional North Atlantic freshwater input
of 0.1–0.5 Sv (44). The sensitivity of North Atlantic freshwater
input to anthropogenic forcing is also poorly known, but regional
precipit ation is predicted to increase (12) and the GIS c ould
c ontribute significantly (e.g., GIS melt over 1,000 years is
equivalent to 0.1 Sv). The North Atlantic is observed to be
f reshening (49), and estimates of recent increases in freshwater
input yield 0.014 Sv from melting sea ice (18), 0.007 Sv from
Greenland (29), and 0.005 Sv from Eurasian rivers (50), totaling
0.026 Sv, without considering precipitation over the oceans or
Canadian river runoff. The IPCC (12) argues that an abrupt
transition of the THC is ‘‘very unlikely’’ (probability ⬍10%) to
oc cur before 2100 and that any transition is likely to take a
century or more. Our definition encompasses gradual transitions
that appear c ontinuous across the tipping point; hence, some
of the IPCC runs (ref. 12, p. 773 ff) may yet meet our criteria
(but would need to be run for longer to see if they reach a
qualit atively different state). Furthermore, the IPCC does not
include f reshwater runoff from GIS melt. Subsequent
OAGCM simulations clearly pass a THC tipping point this
century and undergo a qualitative change before the next mil-
lenn ium (48). Both the timescale and the magnitude of forc-
ing are important (51), because a more rapid forcing to a
given level can more readily overwhelm the negative feedback
Lenton et al. PNAS
兩
February 12, 2008
兩
vol. 105
兩
no. 6
兩
1789

that redistributes salt in a manner that maintains whatever is
the current circulation state.
El Nin˜ o–Southern Oscillation (ENSO). Gradual anthropogenic forc-
ing is expected, on theoretical grounds, to interact with natural
modes of climate variability by altering the relative amount of
time that the climate system spends in different states (52).
ENSO is the most significant ocean-atmosphere mode, and its
variabilit y is controlled by (at least) three factors: zonal mean
ther mocline depth, thermocline sharpness in the EEP, and the
strength of the annual cycle and hence the meridional temper-
ature g radient across the equator (53, 54). Increased ocean heat
upt ake could cause a permanent deepening of the thermocline
in the EEP and a consequent shift from present day ENSO
variabilit y to greater amplitude and/or more frequent El Nin˜os
(55). However, a contradictory theory postulates sustained La
Nin˜a c onditions due to stronger warming of the West Equatorial
Pacific than the East, causing enhanced easterly winds and
reinforcing the up-welling of cold water in the EEP (56). The
mid-Holocene had a reduction in ENSO amplitude related to a
stronger zonal temperature gradient (57, 58). The globally ⬇3°C
war mer early Pliocene is characterized by some as having
persistent El Nin˜ o conditions (59), whereas others disagree (60).
Under future forcing, the first OAGCM studies showed a shift
f rom the current ENSO variability to more persistent or f requent
El Nin˜o-like conditions. Now that numerous OAGCMs have
been intercompared, there is no c onsistent trend in their tran-
sient response and only a small collective probabilit y of a shift
toward more persistent or f requent El Nin˜ o conditions (61, 62).
However, in response to a warmer stabilized climate, the most
realistic models simulate increased El Nin˜ o amplitude (with no
clear change in frequency) (54). This would have large-scale
impacts, and even if the transition is smooth and g radual, a
tipping point may exist by condition 1. Given also that past
climate changes have been acc ompanied by changes in ENSO,
we differ f rom IPCC (12) and consider there to be a significant
probabilit y of a future increase in ENSO amplitude. The re-
quired warming can be accessed this century (54) w ith the
transition happen ing within a millennium, but the existence and
location of any threshold is particularly uncertain.
Indian Summer Monsoon (ISM). The land-to-ocean pressure gradi-
ent, which drives the monsoon circulation is reinforced by the
moisture the monsoon itself carries from the adjacent Indian
Ocean (moisture-advection feedback) (63). Consequently, any
perturbation that tends to weaken the driving pressure gradient
has the potential to dest abilize the monsoon circulation. Green-
house war ming that is stronger over land and in the Northern
Hemisphere tends to strengthen the monsoon, but increases in
planet ary albedo over the continent due to aerosol forcing
and/or land-use change tend to weaken it. The ISM exhibited
rapid changes in variability during the last ice age (64) and the
Holocene (65), with an increased strength during recent centu-
ries consistent with Northern Hemisphere war ming (66). Recent
time series display strongly nonlinear characteristics, from the
intraseasonal via the interannual and the decadal to the centen-
n ial timescale (67), with the interannual variations lag correlated
with the phases of ENSO, although this may be increasingly
masked by anthropogenic forcing (68). A simple model (63)
predicts collapse of the ISM if regional planetary albedo exceeds
⬇0.5, whereas increasing CO
2
st abilizes the monsoon. IPCC
projections do not show obvious threshold behavior this century
(12), but they do agree that sulfate aerosols would dampen the
strength of ISM precipitation, whereas increased g reenhouse
gases increase the interannual variability of daily precipit ation
(69). We differ from IPCC (12) on the basis of past apparent
threshold behavior of the ISM and because brown haze and
land-use-change forcing are poorly captured in the models.
Further more, conceptual work on the potentially chaotic nature
of the ISM (70) has been developed (V. Petoukhov, K. Zickfeld,
and H.J.S., unpublished work) to suggest that under some
plausible decadal-scale scenarios of land use and greenhouse gas
and aerosol forcing, switches occur between two highly nonlinear
met astable regimes of the chaotic oscillations corresponding to
the ‘‘active’’ and ‘‘weak’’ monsoon phases, on the intraseasonal
and interannual timescales. Sporadic bifurcation transitions may
also happen f rom regimes of chaotic oscillations to regimes with
highly deterministic oscillations, or to regimes with very weak
oscillations.
Sahara/Sahel and West African Monsoon (WAM). Past greening of the
Sahara occurred in the mid-Holocene (71–73) and may have
happened rapidly in the earlier Bo¨lling-Allerod warming. Col-
lapse of veget ation in the Sahara ⬇5,000 years ago occurred
more rapidly than orbit al forcing (71, 72). The system has been
modeled and conceptualized in terms of bistable states that are
maint ained by veget ation–climate feedback (71, 74). However,
it is intimately tied to the WAM circulation, which in turn is
af fected by sea sur face temperatures (SSTs), particularly anti-
sy mmetric patterns between the Hemispheres. Greenhouse gas
forcing is expected to increase the interhemispheric SST gradi-
ent and thereby increase Sahel rainfall; hence, the recent Sahel
drought has been attributed to increased aerosol loading c ooling
the Northern Hemisphere (75). Future 21st centur y projections
dif fer (75, 76); in two AOGCMs, the WAM collapses, but in one
this leads to further drying of the Sahel, whereas in the other it
causes wetting due to increased inflow from the West. The latter
response is more mechanistically reasonable, but it requires a
⬇3°C warming of SSTs in the Gulf of Guinea (76). A third
AOGCM with the most realistic present-day WAM predicts no
large trend in mean rainfall but a doubling of the number of
anomalously dry years by the end of the century (76). If the
WAM is disrupted such that there is increased inflow from the
West (76), the resulting moisture will wet the Sahel and support
greening of the Sahara, as is seen in mid-Holocene simulations
(73). Indeed, in an inter mediate complexity model, increasing
atmospheric CO
2
has been predicted to cause future expansion
of grasslands into up to 45% of the Sahara, at a rate of up to 10%
of Saharan area per decade (11). In the Sahel, shrub vegetation
may also increase due to increased water use ef ficiency (stomatal
closure) under higher atmospheric CO
2
(77). Such greening of
the Sahara/Sahel is a rare example of a beneficial potential
tipping element.
Amazon Rainforest. A large fraction of precipitation in the Am-
azon basin is recycled, and, therefore, simulations of Amazon
deforestation typically generate ⬇20–30% reductions in precip-
it ation (78), lengthening of the dry season, and increases in
summer temperatures (79) that would make it difficult for the
forest to reestablish, and suggest the system may exhibit bist-
abilit y. Dieback of the Amazon rainforest has been predicted (2,
80) to oc cur under ⬇3–4°C global warming because of a more
persistent El Nin˜o state that leads to drying over much of the
Amazon basin (81). Different vegetation models driven with
similar climate projections also show Amazon dieback (82), but
other global climate models (83) project smaller reductions (or
increases) of precipit ation and, therefore, do not produce die-
back (84). A regional climate model (85) predicts Amazon
dieback due to widespread reductions in precipitation and
lengthen ing of the dry season. Changes in fire f requency prob-
ably contribute to bist ability and will be amplified by forest
f ragmentation due to human activity. Indeed land-use change
alone could potentially bring forest cover to a critical threshold.
Thus, the fate of the Amazon may be determined by a complex
interplay between direct land-use change and the response of
regional precipitation and ENSO to global forcing.
1790
兩
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0705414105 Lenton et al.

Boreal Forest. The boreal system exhibits a c omplex interplay
bet ween tree physiology, permaf rost, and fire. Under climate
change, increased water stress, increased peak summer heat
stress causing increased mortality, vulnerability to disease and
subsequent fire, as well as decreased reproduction rates c ould
lead to large-scale dieback of the boreal forests (77, 86), with
transitions to open woodlands or grasslands. In interior boreal
regions, temperate tree species will remain excluded from
suc cession due to frost damage in still very cold winters.
Continent al steppe g rasslands will ex pand at the expense of
boreal forest where soil moisture along the arid timberline
ec otone declines further (87), amplified through concurrent
increases in the frequency of fires. Newly unfrozen soils that
regionally drain well, and reductions in the amount of snow, also
support drying, more fire and hence less biomass. In contrast,
increased thaw depth and increased water-use ef ficiency under
elevated CO
2
will tend to increase available soil moisture,
decreasing fire frequency and increasing woody biomass. Studies
suggest a threshold for boreal forest dieback of ⬇3°C global
war ming (77, 86), but limit ations in existing models and physi-
ological understanding make this highly uncertain.
Others. We remind the reader that we considered other candidate
tipping elements, which are not listed here because they did not
meet conditions 2–4 for policy relevance. Some are listed in
Table 1 and discussed in SI Appendix 2.
Ranking the Threat
Given our identification of policy-relevant tipping elements in
the climate system, how do we decide which pose the greatest
threat to society and, therefore, need the greatest attention? The
first step is to asses the sensitivity of each tipping element to
global warming and the associated uncertainties, including the
c onfidence of the community in the argument for tipping
element status. Our workshop and systematic review of the
literature addressed this. In addition, formal elicitations of
ex pert beliefs have f requently been used to bring current un-
derst anding of model studies, empirical evidence, and theoret-
ical c onsiderations to bear on polic y-relevant variables (88).
From a natural science perspective, a general criticism is that
ex pert beliefs carry subjective biases and, moreover, do not add
to the body of scientific knowledge unless verified by dat a or
theory. Nonetheless, expert elicitations, based on rigorous pro-
toc ols from statistics (89–91) and risk analysis (91, 92), have
proved to be a very valuable source of information in public
polic ymaking (93). It is increasingly recognized that they can also
play a valuable role for informing climate policy decisions (94).
In the field of climate change, formal expert elicitations have
been conducted, e.g., on climate sensitivity (95), forest ecosys-
tems (96), the WAIS (97), radiative forcing of aerosols (98), and
the THC (99).
On the basis of previous experience (99), we used the afore-
mentioned workshop to in itiate an elicitation of expert opinions
on, among other things, six potential tipping elements listed in
Table 1: reorganization of the Atlantic THC, melt of the GIS,
disintegration of the WAIS, Amazon rainforest dieback, dieback
of boreal forests, and shift of the ENSO regime to an El
Nin˜o-like mean state. The elicitation was based on a computer-
based interactive questionnaire that was completed individually
by participating ex perts. Following a pilot phase at the workshop,
the questionnaire was distributed to 193 international scientists
in October and November 2005; 52 experts returned a completed
questionnaire (among them 16 workshop participants and 22
c ontributors to the IPCC Fourth Assessment Report). Although
participation inevitably involved a self-selection process, we
assembled a heterogeneous g roup covering a wide range of
ex pertise (see SI Appendix 3). The full results will be presented
separately (E.K., J.W.H., H.H., R. Dawson, and H.J.S., unpub-
lished work). Here we report a subset that reflect the range of
scientific perspectives to supplement our own assessment of the
tipping elements.
In the questionnaire, experts were asked for a pairwise
c omparison of tipping elements in terms of (i) their sensitivity to
global mean temperature increase and (ii) the uncertaint y about
the underlying physical mechanisms. The exact questions posed
to participants and the breakdown of their responses are de-
scribed in SI Appendix 3. We have identified partial rank ings of
tipping elements from the collection of expert responses. Be-
cause the number of experts commenting on individual pairs
of tipping elements varied widely, those rankings c ould not be
established with equal credibility. We highlight the difference
in expert consensus by using the symbols ⬎⬎ and ⬎ for strong
and weak consensus upon the ordering, respectively, and by
providing the number x that agreed with the direction of the or-
dering compared with the number y of experts who commented
on the pair [given as x(y)]. For sensitivity to global mean warm-
ing, we find
8(10) to WAIS 2(3)
GIS WAIS >
7(7) to THC
Amazon rainforest >
2(2)
THC,
>>
where the more sensitive tipping element is to the lef t. Owing to
the close link bet ween ENSO and the Amazon rainforest, both
were judged of similar sensitivit y to war ming, but experts were
divided as to whether ENSO would be more sensitive than the
THC. Boreal forests were only compared with the Amazon
rainforest, and three out of five experts judged the for mer to be
more sensitive to global mean warming. Concern ing the uncer-
t ainty about the physical mechanisms that may give rise to
tipping points, we find
3(4) to THC
WAIS >>
>>
6(9) to GIS
2(2) to THC 6(8)
Amazon rainforest > THC
1(1) to GIS
3+2(6) to THC
ENSO ≥
2(2) to GIS
GIS,
where the more uncertain tipping element is to the left. We
display a greater or equal uncertainty about the ENSO c om-
pared with the THC, because three and two out of six experts
believed the ENSO to be more and similarly uncertain, respec-
tively. In addition, five out of six experts judged the uncertainty
about the response of boreal forests to be larger than for the
Amazon rainforest.
Tak ing into account our own analysis of the literature (sum-
marized in the previous section and Table 1) and the expert
elicit ation (summarized above), the potential tipping elements in
the climate system may be grouped into three clusters: (i) high
sensitivity with smallest uncertainty: GIS and Arctic sea-ice; (ii)
inter mediate sensitivity with largest uncertainty: WAIS, Boreal
forest, Amazon rainforest, ENSO, and WAM; (iii) low sensitivity
with intermediate uncertaint y: THC. ISM is not included in the
clustering because its forcing differs, but it clearly has large
uncert ainty. We conclude that the greatest (and clearest) threat
Lenton et al. PNAS
兩
February 12, 2008
兩
vol. 105
兩
no. 6
兩
1791

is to the Arctic with summer sea-ice loss likely to occur long
before (and potentially contribute to) GIS melt. Tipping ele-
ments in the tropics, the boreal zone, and West A ntarctica are
surrounded by large uncertainty and, given their potential
sensitivity, constitute candidates for surprising society. The
archet ypal example of a tipping element, the THC appears to be
a less immediate threat, but the long-term fate of the THC under
sign ificant war ming remains a source of concern (99).
The Prospects for Early Warning
Est ablishing early warn ing systems for various tipping elements
would clearly be desirable, but can
␳
crit
be anticipated before we
reach it? In principle, an incipient bifurcation in a dynamical
system could be anticipated (100), by looking at the spectral
properties of time series data (101), in particular, extracting the
longest system-immanent timescale (
␶
) from the response of the
system to natural variability (102). Systems theory reveals (Fig.
2A)(i) that those tipping points that represent a bifurcation are
un iversally characterized by
␶
3 ⬁ at the threshold, and (ii) that
in principle
␶
c ould be reconstructed through methods of time
series analysis. Hence a ‘‘degenerate fingerprinting’’ method has
been developed for anticipating a threshold in a spatially ex-
tended system and applied to the detection of a threshold in the
Atlantic THC, by using time series output from a model of
inter mediate c omplexity (102) (Fig. 2B).
These studies reveal that if a system is forced slowly (keeping
it in quasi-equilibrium), proximity to a threshold may be inferred
in a model-independent way. However, if the system is forced
faster (as is probably the case for the THC today), a dynamical
model will also be needed. Even if there is no bifurcation,
deter mining
␶
is still worthwhile because it determines the
system’s linear response characteristics to external forcing, and
transitions that are not strictly bifurcations are expected to
resemble bifurcation-t ype behavior to a cert ain deg ree. For
strongly resource-limited ecosystems that show self-organized
patchiness, their observable macrostructure may also provide an
indication of their proximity to state changes (103).
If a forewarning system for approaching thresholds is to
bec ome work able, then real-time observation systems need to
be improved (e.g., building on the Atlantic THC mon itoring at
26.5°N). For slow transition systems, not ably ocean and ice
sheets, observation rec ords also need to be extended further
back in time (e.g., for the Atlantic beyond the ⬇150-year SST
rec ord). A nalysis of extended time series dat a c ould then be
used to improve models (104), e.g., an ef fort to deter mine the
Atlantic’s
␶
and assimilate it into ocean models c ould reduce
the vast intra- and inter model (44) spread regarding the
proximit y to a tipping point (102).
Conclusion
Societ y may be lulled into a false sense of security by smooth
projections of global change. Our synthesis of present knowledge
suggests that a variety of tipping elements could reach their
critical point within this century under anthropogenic climate
change. The greatest threats are tipping the Arctic sea-ice and
the Greenland ice sheet, and at least five other elements could
surprise us by exhibiting a nearby tipping point. This knowledge
should influence climate policy, but a full assessment of policy
relevance would require that, for each potential tipping element,
we answer the following questions: Mitigation: Can we stay clear
of
␳
crit
? Adaptation: Can F
ˆ
be tolerated?
The IPCC provides a thorough overv iew of mitigation (105)
and adaptation (106) work upon which such a policy assess-
ment of tipping elements could be built. Given the scale of
potential impacts f rom tipping elements, we anticipate that
they will shift the balance toward stronger mitigation and
demand adaptation c oncepts beyond incremental approaches
(107, 108). Policy analysis and implementation w ill be ex-
tremely challenging given the nonc onvexities in the human-
env ironment system (109) that will be enhanced by tipping
elements, as well as the need to handle intergenerational
justice and interpersonal equit y over long periods and under
c onditions of uncert ainty (110). A rigorous study of potential
tipping elements in human socioec onomic systems would also
be welc ome, especially to address whether and how a rapid
societ al transition toward sust ainabilit y c ould be triggered,
given that some models suggest there exists a tipping point for
the transition to a low-carbon-energy system (111).
It seems wise to assume that we have not yet identified all
potential policy-relevant tipping elements. Hence, a systematic
search for further tipping elements should be undertaken,
draw ing on both paleodata and multimodel ensemble studies.
Given the large uncertaint y that remains about tipping ele-
0 0.2 0.4 0.6 0.8 1
0
5
10
15
20
25
)vS( gninrutrevO
0 0.2 0.4 0.6 0.8 1
0.6
0.8
1
t (50,000 yrs)
erutavruC rof yxorP
A
B
Fig. 2. Method for estimating the proximity to a tipping point. (A) Schematic
approach: The potential wells represent stable attractors, and the ball, the
state of the system. Under gradual anthropogenic forcing (progressing from
dark to light blue potential), the right potential well becomes shallower and
finally vanishes (threshold), causing the ball to abruptly roll to the left. The
curvature of the well is inversely proportional to the system’s response time
␶
to small perturbations. ‘‘Degenerate fingerprinting’’ (102) extracts
␶
from the
system’s noisy, multivariate time series and forecasts the vanishing of local
curvature. (B) Degenerate fingerprinting ‘‘in action’’: Shown is an example for
the Atlantic meridional overturning circulation. (Upper) Overturning strength
under a 4-fold linear increase of atmospheric CO
2
over 50,000 years in the
CLIMBER-2 model with weak, stochastic freshwater forcing. Eventually, the
circulation collapses without early warning. (Lower) Overturning replaced by
a proxy of the shape of the potential (as in A). Although the signal is noisier
in Lower than it is in Upper, it allows forecasting of the location of the
threshold (data taken from ref. 102). The solid green line is a linear fit, and the
dashed green lines are 95% error bars.
1792
兩
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0705414105 Lenton et al.

ments, there is an urgent need to improve our understanding
of the underlying physical mechan isms deter mining their
behav ior, so that polic y makers are able ‘‘to avoid the unman-
ageable, and to manage the unavoidable’’ (112).
ACKNOWLEDGMENTS. We thank the British Embassy in Berlin for hosting the
workshop ‘‘Tipping Points in the Earth System’’ on October 5–6, 2005, and all
of the participants of the workshop and the expert elicitation. M. Wodinski
prepared Fig. 1. We thank O. Edenhofer, V. Petoukhov, the editor W. C. Clark,
and four anonymous referees for their suggestions that improved the paper.
T.M.L.’s work is part of the Natural Environment Research Council GENIEfy
(NE/C515904), Quaternary QUEST (NE/D001706), and Feedbacks QUEST (NE/
F001657) projects. H.H. was supported by the Volkswagen Foundation under
Grant II/78470. E.K. is supported by a Marie Curie International Fellowship
(MOIF-CT-2005–008758) within the 6th European Community Framework
Program, with research infrastructure partly provided by the Climate Decision
Making Center (National Science Foundation Grant SES-0345798). W.L.’s work
is a contribution to the Leibniz Association’s project on the Biosphere, Society
and Global Change. H.J.S. is a Senior James Martin Fellow at Oxford University.
1. Rahmstorf S, Ganopolski A (1999) Clim Change 43:353–367.
2. Cox PM, Betts RA, Jones CD, Spall SA, Totterdell IJ (2000) Nature 408:184–187.
3. Huybrechts P, De Wolde J (1999) J Clim 12:2169 –2188.
4. Gladwell M (2000) The Tipping Point: How Little Things Can Make a Big Difference
(Little Brown, New York).
5. Schellnhuber H-J, Held H (2002) in Managing the Earth: The Eleventh Linacre
Lectures, eds Briden J, Downing T (Oxford Univ Press, Oxford), pp 5–34.
6. Rahmstorf S (2001) in Encyclopedia of Ocean Sciences, eds Steele J, Thorpe S, Turekian
K (Academic, London), pp 1–6.
7. Lockwood JG (2001) Int J Climatol 21:1153–1179.
8. National Research Council (2002) Abrupt Climate Change: Inevitable Surprises (Natl
Acad Press, Washington, DC).
9. Alley RB, Marotzke J, Nordhaus WD, Overpeck JT, Peteet DM, Pielke RA, Pierrehum-
bert RT, Rhines PB, Stocker TF, Talley LD, Wallace JM (2003) Science 299:2005–2010.
10. Rial JA, Pielke RA, Beniston M, Claussen M, Canadel J, Cox P, Held H, De Noblet-
Ducoudre N, Prinn R, Reynolds JF, Salas JD (2004) Clim Change 65:11–38.
11. Claussen M, Brovkin V, Ganopolski A, Kubatzki C, Petoukhov V (2003) Clim Change
57:99–118.
12. IPCC (2007) Climate Change 2007: The Physical Science Basis. Contribution of Work-
ing Group I to the Fourth Assessment Report of the Intergovernmental Panel on
Climate Change, eds Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB,
Tignor M, Miller HL (Cambridge Univ Press, Cambridge, UK).
13. North GR (1984) J Atmos Sci 41:3390 –3395.
14. Lee W-H, North GR (1995) Clim Dyn 11:242–246.
15. Morales Maqueda MA, Willmott AJ, Bamber JL, Darby MS (1998) Clim Dyn 14:329–
352.
16. Hibler WD, Hutchings JK, Ip CF (2006) Ann Glaciol 44:339 –344.
17. Stroeve J, Holland MM, Meier W, Scambos T, Serreze M (2007) Geophys Res Lett
34:L09501.
18. Lindsay RW, Zhang J (2005) J Clim 18:4879– 4894.
19. Holland MM (2006) Geophys Res Lett 33:L23503.
20. Winton M (2006) Geophys Res Lett 33:L23504.
21. Saltzman B (2002) Dynamical Paleoclimatology (Academic, London).
22. Toniazzo T, Gregory JM, Huybrechts P (2004) J Clim 17:21–33.
23. Lunt DJ, De Noblet-Ducoudre N, Charbit S (2004) Clim Dyn 23:679 –694.
24. Otto-Bliesner BL, Marshall SJ, Overpeck JT, Miller GH, Hu A, CAPE Last Interglacial
Project Members (2006) Science 311:1751–1753.
25. Gregory JM, Huybrechts P (2006) Philos Trans R Soc A 364:1709 –1731.
26. Chylek P, Lohmann U (2005) Geophys Res Lett 32:L14705.
27. Mitrovica JX, Tamislea ME, Davis JL, Milne GA (2001) Nature 409:1026–1029.
28. Velicogna I, Wahr J (2006) Nature 443:329 –331.
29. Rignot E, Kanagaratnam P (2006) Science 311:986 –990.
30. Krabill W, Abdalati W, Frederick E, Manizade S, Martin C, Sonntag J, Swift R, Thomas
R, Wright W, Yungel J (2000) Science 289:428– 430.
31. Joughin I, Abdalati W, Fahnestock M (2004) Nature 432:608–610.
32. Bindschadler R (2006) Science 311:1720 –1721.
33. Johannessen OM, Khvorostovsky K, Miles MW, Bobylev LP (2005) Science 310:1013–
1016.
34. Hansen JE (2005) Clim Change 68:269–279.
35. Mercer JH (1978) Nature 271:321–325.
36. Oppenheimer M (1998) Nature 393:325–332.
37. Oppenheimer M, Alley RB (2004) Clim Change 64:1–10.
38. Scherer RP, Aldahan A, Tulaczyk S, Possnert G, Engelhardt H, Kamb B (1998) Science
281:82–85.
39. Velicogna I, Wahr J (2006) Science 311:1754 –1756.
40. Thomas R, Rignot E, Casassa G, Kanagaratnam P, Acun˜ a C, Akins T, Brecher H,
Frederick E, Gogineni P, Krabill W, et al. (2004) Science 306:255–258.
41. Stocker TF, Wright DG (1991) Nature 351:729 –732.
42. Rahmstorf S (2002) Nature 419:207–214.
43. Ganopolski A, Rahmstorf S (2001) Nature 409:153–158.
44. Rahmstorf S, Crucifix M, Ganopolski A, Goosse H, Kamenkovich I, Knutti R, Lohmann
G, Marsh R, Mysak LA, Wang Z, Weaver AJ (2005) Geophys Res Lett 32:L23605.
45. Stommel H (1961) Tellus 13:224 –230.
46. Lenton TM, Marsh R, Price AR, Lunt DJ, Aksenov Y, Annan JD, Cooper-Chadwick T, Cox
SJ, Edwards NR, Goswami S, et al. (2007) Clim Dyn 29:591–613.
47. Vellinga M, Wood RA (2002) Clim Change 54:251–267.
48. Mikolajewicz U, Gro¨ ger M, Maier-Reimer E, Schurgers G, Vizcaı´no M, Winguth AME
(2007) Clim Dyn 28:599 –633.
49. Curry R, Dickson B, Yashayaev I (2003) Nature 426:826–829.
50. Peterson BJ, Holmes RM, McClelland JW, Vo¨ro¨ smarty CJ, Lammers RB, Shiklomanov
AI, Shiklomanov IA, Rahmstorf S (2002) Science 298:2171–2173.
51. Stocker TF, Schmittner A (1997) Nature 388:862– 865.
52. Palmer TN (1999) J Clim 12:575–591.
53. Philander SG, Federov A (2003) Annu Rev Earth Planet Sci 31:579 –594.
54. Guilyardi E (2006) Clim Dyn 26:329–348.
55. Timmermann A, Oberhuber J, Bacher A, Esch M, Latif M, Roeckner E (1999) Nature
398:694–697.
56. Cane MA, Clement AC, Kaplan A, Kushnir Y, Pozdnyakov D, Seager R, Zebiak SE,
Murtugudde R (1997) Science 275:957–960.
57. Brown J, Collins M, Tudhope A (2006) Adv Geosci 6:29 –33.
58. Koutavas A, deMenocal PB, Olive GC, Lynch-Stieglitz J (2006) Geology 34:993–996.
59. Wara MW, Ravelo AC, Delaney ML (2005) Science 309:758–761.
60. Rickaby REM, Halloran P (2005) Science 307:1948 –1952.
61. Collins M, Groups TCM (2005) Clim Dyn 24:89–104.
62. van Oldenborgh GJ, Philip SY, Collins M (2005) Ocean Sci 1:81–95.
63. Zickfeld K, Knopf B, Petoukhov V, Schellnhuber HJ (2005) Geophys Res Lett 32:
L15707.
64. Burns SJ, Fleitmann D, Matter A, Kramers J, Al-Subbary AA (2003) Science 301:1365–
1367.
65. Gupta AK, Anderson DM, Overpeck JT (2003) Nature 431:354–357.
66. Anderson DM, Overpeck JT, Gupta AK (2002) Science 297:596–599.
67. Webster PJ, Magan˜ a VO, Palmer TN, Shukla J, Tomas RA, Yanai M, Yasunari T (1998)
J Geophys Res 103:14451–14510.
68. Meehl GA, Arblaster JM (2003) Clim Dyn 21:659– 675.
69. Lal M, Cubasch U, Voss R, Waszkewitz J (1995) Curr Sci India 69:752–763.
70. Mittal AK, Dwivedi S, Pandey AC (2003) Indian J Radio Space Phys 32:209 –216.
71. Claussen M, Kubatzki C, Brovkin V, Ganopolski A, Hoelzmann P, Pachur H-J (1999)
Geophys Res Lett 26:2037–2040.
72. de Menocal P, Oritz J, Guilderson T, Adkins J, Sarnthein M, Baker L, Yarusinsky M
(2000) Quat Sci Rev 19:347–361.
73. Patricola CM, Cook KH (2007) J Clim 20:694–716.
74. Brovkin V, Claussen M, Petoukhov V, Ganopolski A (1998) J Geophys Res 103:31613–31624.
75. Held IM, Delworth TL, Lu J, Findell KL, Knutson TR (2005) Proc Natl Acad Sci USA
102:17891–17896.
76. Cook KH, Vizy EK (2006) J Clim 19:3681–3703.
77. Lucht W, Schaphoff S, Erbrecht T, Heyder U, Cramer W (2006) Carbon Balance Manage 1:6.
78. Zeng N, Dickinson RE, Zeng X (1996) J Clim 9:859–883.
79. Kleidon A, Heimann M (2000) Clim Dyn 16:183–199.
80. Cox PM, Betts RA, Collins M, Harris PP, Huntingford C, Jones CD (2004) Theor Appl
Climatol 78:137–156.
81. Betts RA, Cox PN, Collins M, Harris PP, Huntingford C, Jones CD (2004) Theor Appl
Climatol 78:157–175.
82. White A, Cannell MGR, Friend AD (1999) Global Environ Change 9:S21–S30.
83. Li W, Fu R, Dickinson RE (2006) J Geophys Res 111:D02111.
84. Schaphoff S, Lucht W, Gerten D, Sitch S, Cramer W, Prentice IC (2006) Clim Change
74:97–122.
85. Cook KH, Vizy EK (2008) J Clim, in press.
86. Joos F, Prentice IC, Sitch S, Meyer R, Hooss G, Plattner G-K, Gerber S, Hasselmann K
(2001) Global Biogeochem Cycles 15:891–907.
87. Hogg EH, Schwarz AG (1997) J Biogeogr 24:527–534.
88. Morgan MG, Henrion M (1990) Uncertainty: A Guide to Dealing with Uncertainty in
Quantitative Risk and Policy Analysis (Cambridge Univ Press, New York).
89. Kadane JB, Wolfson LJ (1998) J R Stat Soc Ser D 47:3–17.
90. O’Hagan A (1998) J R Stat Soc Ser D 47:21–35.
91. Cooke RM (1991) Experts in Uncertainty (Oxford Univ Press, Oxford).
92. Apostolakis G (1990) Science 250:1359 –1364.
93. National Research Council (2002) Estimating the Public Health Benefits of Proposed
Air Pollution Regulations (Natl Acad Press, Washington, DC).
94. Oppenheimer M, O’Neill BC, Webster M, Agrawala S (2007) Science 317:1505–
1506.
95. Morgan MG, Keith DW (1995) Environ Sci Technol 29:468 – 476.
96. Morgan MG, Pitelka LF, Shevliakova E (2001) Clim Change 49:279 –307.
97. Vaughan DG, Spouge JR (2002) Clim Change 53:65–91.
98. Morgan MG, Adams PJ, Keith DW (2006) Clim Change 75:195–214.
99. Zickfeld K, Levermann A, Morgan MG, Kuhlbrodt T, Rahmstorf S, Keith DW (2007)
Clim Change 82:235–265.
100. Wiesenfeld K (1985) Phys Rev A 32:1744 –1751.
101. Kleinen T, Held H, Petschel-Held G (2003) Ocean Dyn 53:53– 63.
102. Held H, Kleinen T (2004) Geophys Res Lett 31:L23207.
103. Rietkerk M, Dekker SC, de Ruiter PC, van de Koppel J (2004) Science 305:1926 –
1929.
104. Schmittner A, Latif M, Schneider B (2005) Geophys Res Lett 32:L23710.
105. IPCC (2007) Climate Change 2007: Mitigation of Climate Change. Contribution of
Working Group III to the Fourth Assessment Report of the Intergovernmental Panel
on Climate Change, eds Metz B, Davidson OR, Bosch PR, Dave R, Meyer LA (Cambridge
Univ Press, Cambridge, UK).
106. IPCC (2007) Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribu-
tion of Working Group II to the Fourth Assessment Report of the Intergovernmental
Panel on Climate Change, eds Parry ML, Canziani OF, Palutikof JP, van der Linden PJ,
Hanson CE (Cambridge Univ Press, Cambridge, UK).
107. Janssen MA, Ostrom E (2006) Global Environ Change 16:237–239.
108. Eakin H, Luers AL (2006) Annu Rev Environ Resour 31:365–394.
109. Dasgupta P, Ma¨ ler K-G (2003) Environ Resour Econ 26:499 –525.
110. Dasgupta P (2008) Rev Environ Econ Policy, in press.
111. Edenhofer O, Lessman K, Kemfert C, Grubb M, Ko¨ hler J (2006) Energy J: Special Issue
on Endogenous Technological Change and the Economics of Atmospheric Stabilisa-
tion Special Issue 1:57–108.
112. Scientific Expert Group on Climate Change (2007) Confronting Climate Change:
Avoiding the Unmanageable and Managing the Unavoidable, Report prepared for
the United Nations Commission on Sustainable Development, eds Bierbaum RM,
Holdren JP, MacCracken MC, Moss RH, Raven PH (Sigma Xi, Research Triangle Park,
NC, and United Nations Foundation, Washington, DC).
Lenton et al. PNAS
兩
February 12, 2008
兩
vol. 105
兩
no. 6
兩
1793