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© 2008 Macmillan Publishers Limited. All rights reserved.
© 2008 Macmillan Publishers Limited. All rights reserved.
REVIEW ARTICLE
The equilibrium sensitivity of the Earth’s
temperature to radiation changes
The Earth’s climate is changing rapidly as a result of anthropogenic carbon emissions, and damaging
impacts are expected to increase with warming. To prevent these and limit long-term global surface
warming to, for example, 2 °C, a level of stabilization or of peak atmospheric CO2 concentrations
needs to be set. Climate sensitivity, the global equilibrium surface warming after a doubling of
atmospheric CO2 concentration, can help with the translation of atmospheric CO2 levels to warming.
Various observations favour a climate sensitivity value of about 3 °C, with a likely range of about
2–4.5 °C. However, the physics of the response and uncertainties in forcing lead to fundamental
diffi culties in ruling out higher values. The quest to determine climate sensitivity has now been going
on for decades, with disturbingly little progress in narrowing the large uncertainty range. However,
in the process, fascinating new insights into the climate system and into policy aspects regarding
mitigation have been gained. The well-constrained lower limit of climate sensitivity and the transient
rate of warming already provide useful information for policy makers. But the upper limit of climate
sensitivity will be more diffi cult to quantify.
RETO KNUTTI1* AND GABRIELE C. HEGERL2
1Institute for Atmospheric and Climate Science, ETH Zurich,
CH-8092 Zurich, Switzerland
2School of Geosciences, University of Edinburgh, Edinburgh,
EH9 3JW, UK
*e-mail: reto.knutti@env.ethz.ch
When the radiation balance of the Earth is perturbed, the
global surface temperature will warm and adjust to a new
equilibrium state. But by how much? The answer to this
seemingly basic but important question turns out to be a tricky
one. It is determined by a number termed equilibrium climate
sensitivity, the global mean surface warming in response to
a doubling of the atmospheric CO2 concentration after the
system has reached a new steady state. Climate sensitivity
cannot be measured directly, but it can be estimated from
comprehensive climate models. It can also be estimated from
climate change over the twentieth century or from short-term
climate variations such as volcanic eruptions, both of which were
observed instrumentally, and from climate changes over the
Earth’s history that have been reconstructed from palaeoclimatic
data. Many model-simulated aspects of climate change scale
approximately linearly with climate sensitivity, which is therefore
sometimes seen as the ‘magic number’ of a model. This view is
too simplistic and misses many important spatial and temporal
aspects of climate change. Nevertheless, climate sensitivity is the
largest source of uncertainty in projections of climate change
beyond a few decades1–3 and is therefore an important diagnostic
in climate modelling4,5.
THE CONCEPT OF FORCING, FEEDBACK AND CLIMATE SENSITIVITY
e concept of radiative forcing, feedbacks and temperature
response is illustrated in Fig. 1. Anthropogenic emissions of
greenhouse gases, aerosol precursors and other substances, as
well as natural changes in solar irradiance and volcanic eruptions,
a ect the amount of radiation that is re ected, transmitted and
absorbed by the atmosphere. is externally imposed (naturally
or human-induced) energy imbalance on the system, such as
the increased long-wave absorption caused by the emission of
anthropogenic CO2, is termed radiative forcing (ΔF). In a simple
global energy balance model, the di erence between these
(positive) radiative perturbations ΔF and the increased outgoing
long-wave radiation that is assumed to be proportional to the
surface warming ΔT leads to an increased heat ux ΔQ in the
system, such that
ΔQ = ΔF − λΔT (1)
Heat is taken up largely by the ocean, which leads to increasing
ocean temperatures6. The changes in outgoing long-wave
radiation that balance the change in forcing are influenced by
climate feedbacks. For a constant forcing, the system eventually
approaches a new equilibrium where the heat uptake ΔQ is
zero and the radiative forcing is balanced by additional emitted
long-wave radiation. Terminology varies, but commonly the
ratio of forcing and equilibrium temperature change λ = ΔF/ΔT
is defined as the climate feedback parameter (in W m−2 °C−1),
its inverse Sʹ = 1/λ = ΔT/ΔF the climate sensitivity parameter
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REVIEW ARTICLE
(in °C W−1 m2) and S = ΔT2×CO2 the equilibrium climate sensitivity,
the equilibrium global average temperature change for a
doubling (usually relative to pre-industrial) of the atmospheric
CO2 concentration, which corresponds to a long-wave forcing
of about 3.7 W m−2 (ref. 7). The beauty of this simple conceptual
model of radiative forcing and climate sensitivity (equation (1))
is that the equilibrium warming is proportional to the radiative
forcing and is readily computed as a function of the current CO2
relative to the pre-industrial CO2: ΔT = S ln(CO2/CO2(t=1750))/ln2.
The total forcing is assumed to be the sum of all individual
forcings. The sensitivity S can also be phrased as8–10
S = ΔT0/(1 − f) (2)
where f is the feedback factor amplifying (if 0 < f < 1) or damping
the initial blackbody response of ΔT0 = 1.2 °C for a CO2 doubling.
e total feedback can be phrased as the sum of all individual
feedbacks9 (see Fig. 2; examples of feedbacks are increases in
the greenhouse gas water vapour with warming; other feedbacks
are associated with changes in lapse rate, albedo and clouds). To
rst order, the feedbacks are independent of T, yielding a climate
sensitivity that is constant over time and similar between many
forcings. e global temperature response from di erent forcings is
therefore approximately additive11. However, detailed studies nd
that some feedbacks will change with the climate state12–14, which
means that the assumption of a linear feedback term λΔT is valid
only for perturbations of a few degrees. ere is a di erence in the
sensitivity to radiative forcing for di erent forcing mechanisms,
which has been phrased as their ‘e cacy’7,15. ese e ects are
represented poorly or not at all in simple climate models16. A more
detailed discussion of the concepts and the history is given in
refs 5, 7, 17–20.
Note that the concept of climate sensitivity does not quantify
carbon-cycle feedbacks; it measures only the equilibrium surface
response to a speci ed CO2 forcing. e timescale for reaching
equilibrium is a few decades to centuries and increases strongly
with sensitivity21. e transient climate response (TCR, de ned as
the warming at the point of CO2 doubling in a model simulation in
which CO2 increases at 1% yr−1) is a measure of the rate of warming
while climate change is evolving, and it therefore depends on the
ocean heat uptake ΔQ. e dependence of TCR on sensitivity
decreases for high sensitivities9,22,23.
ESTIMATES FROM COMPREHENSIVE MODELS AND PROCESS STUDIES
Ever since concern arose about increases of CO2 in the atmosphere
causing warming, scientists have attempted to estimate how
much warming will result from, for example, a doubling of the
atmospheric CO2 concentration. Even the earliest estimates ranged
remarkably close to our present estimate of a likely increase of
between 2 and 4.5 °C (ref. 24). For example, Arrhenius25 and
Callendar26, in the years 1896 and 1938, respectively, estimated that
a doubling of CO2 would result in a global temperature increase of
5.5 and 2 °C. Half a century later, the rst energy-balance models,
radiative convective models and general circulation models
(GCMs) were used to quantify forcings and feedbacks, and with
Temperature
profile
Tropopause
Ice sheets
and vegetation
Instantaneous RF
Whole
atmosphere fixed
Ocean
Initial state
Stratospheric adjustments
Stratospheric
adjusted RF
Fixed troposphere
Fixed surface
Timescale:
days to months
Tropospheric adjustments
Effective RF/
zero surface
temperature change RF
Non-radiative effects
Fixed surface
Timescale:
days to months
ΔF from 2 × CO2
Climate
feedbacks
Equilibrium
warming S
Very little
ocean heat
uptake
Timescale:
centuries
Timescale:
millennia
Additional forcing
from slow feedbacks Equilibrium
warming
with slow
feedbacks
Climate
feedbacks
Transient
warming ΔT
Large
ocean heat
uptake
Timescale:
decades
ΔF
ΔQ
ΔQ = ΔF – λ ΔT
Figure 1 The concept of radiative forcing, feedbacks and climate sensitivity. a, A change in a radiatively active agent causes an instantaneous radiative forcing (RF). b, The
standard defi nition of RF includes the relatively fast stratospheric adjustments, with the troposphere kept fi xed. c, Non-radiative effects in the troposphere (for example of
CO2 heating rates on clouds and aerosol semi-direct and indirect effects) occurring on similar timescales can be considered as fast feedbacks or as a forcing. d–f, During
the transient climate change phase (d), the forcing is balanced by ocean heat uptake and increased long-wave radiation emitted from a warmer surface, with feedbacks
determining the temperature response until equilibrium is reached with a constant forcing (e, f). The equilibrium depends on whether additional slow feedbacks (for
example ice sheets or vegetation) with their own intrinsic timescale are kept fi xed (e) or are allowed to change (f).
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REVIEW ARTICLE
nature geoscience | VOL 1 | NOVEMBER 2008 | www.nature.com/naturegeoscience 737
it the climate sensitivity S (refs 9, 21, 27–31). Climate sensitivity
is not a directly tunable quantity in GCMs and depends on many
parameters related mainly to atmospheric processes. Di erent
sensitivities in GCMs can be obtained by perturbing parameters
a ecting clouds, precipitation, convection, radiation, land surface
and other processes. Two decades ago, the largest uncertainty in
these feedbacks was attributed to clouds32. Process-based studies
now nd a stronger constraint on the combined feedbacks from
increases in water vapour and changes in the lapse rate. ese
studies still identify low-level clouds as the dominant uncertainty
in feedback4,5,33.
Requiring that climate models reproduce the observed
present-day climatology (spatial structure of the mean climate
and its variability) provides some constraint on model climate
sensitivity. Starting in the 1960s (ref. 27), climate sensitivities in
early GCMs were mostly in the range 1.5–4.5 °C. at range has
changed very little since then, with the current models covering
the range 2.1–4.4 °C (ref. 5), although higher values are possible34.
is can be interpreted as disturbingly little progress or as a
con rmation that model simulations of atmospheric feedbacks
are quite robust to the details of the models. ree studies have
calculated probability density functions (PDFs) of climate
sensitivity by comparing di erent variables of the present-day
climate against observations in a perturbed physics ensemble of
an atmospheric GCM coupled to a slab ocean model35–37. ese
distributions re ect the uncertainty in our knowledge of sensitivity,
not a distribution from which future climate change is sampled.
e estimates are in good agreement with other estimates (Fig. 3).
e main caveat is that all three studies are based on a version of
the same climate model and may be similarly in uenced by biases
in the underlying model.
CONSTRAINTS FROM THE INSTRUMENTAL PERIOD
Many recent estimates of the equilibrium climate sensitivity
are based on climate change that has been observed over the
instrumental period (that is, about the past 150 years). Wigley et al.38
pointed out that uncertainties in forcing and response made it
impossible to use observed global temperature changes during
that period to constrain S more tightly than the range explored
by climate models (1.5–4.5 °C at the time), and that the upper
end of the range was particularly di cult to estimate, although
qualitatively similar conclusions appear in earlier pioneering
work9,10,21,39. Several studies subsequently used the transient
evolution of surface temperature, upper air temperature, ocean
temperature or radiation in the past, or a combination of these,
to constrain climate sensitivity. An overview of ranges and PDFs
of climate sensitivity from those methods is shown in Fig. 3.
Several studies used the observed surface and ocean warming
over the twentieth century and an estimate of the radiative forcing
to estimate sensitivity, either by running large ensembles with
di erent parameter settings in simple or intermediate-complexity
models3,38,40–46, by using a statistical model47 or in an energy balance
calculation48. Satellite data for the radiation budget were also used
to infer climate sensitivity49. e advantage of these methods is
that they consider a state of the climate similar to today’s and
use similar timescales of observations to the projections we are
interested in, thus providing constraints on the overall feedbacks
operating today. However, the distributions are wide and cannot
exclude high sensitivities. e main reason is that it cannot be
excluded that a strong aerosol forcing or a large ocean heat uptake
might have hidden a strong greenhouse warming.
Some recent analyses have used the well-observed forcing
and response to major volcanic eruptions during the twentieth
century, notably the eruption of Mount Pinatubo. e constraint
is fairly weak because the peak response to short-term volcanic
forcing has a nonlinear dependence on equilibrium sensitivity,
yielding only slightly enhanced peak cooling for higher values of
S (refs 42, 50, 51). Nevertheless, models with climate sensitivity
in the range 1.5–4.5 °C generally perform well in simulating the
climate response to individual volcanic eruptions and provide an
opportunity to test the fast feedbacks in climate models5,52,53.
PALAEOCLIMATIC EVIDENCE
Some early estimates of climate sensitivity drew on palaeoclimate
information. For example, the climate of the Last Glacial Maximum
(LGM) is a quasi-equilibrium response to substantially altered
boundary conditions (such as large ice sheets over landmasses of
the Northern Hemisphere, and di erent vegetation) and di erent
atmospheric CO2 levels. Simple calculations relating the peak
cooling to changes in radiative forcing yielded estimates mostly
between 1 and 6 °C, which turned out to be close to Arrhenius’s
estimates9,54–56. Simulations of the LGM are still an important
testbed for the response of climate models to radiative forcing57.
In some recent studies, parameters in climate models have been
perturbed systematically to estimate S (refs 14, 58, 59). e idea
is to estimate the sensitivity of a perturbed model by running it
to equilibrium with doubled CO2 and then evaluate whether the
same model yields realistic simulations of the LGM conditions.
is method avoids directly estimating the relationship between
0 0.2 0.4 0.6 0.8 1.0
Feedback
10
8
6
4
2
0
Climate sensitivity (ºC)
Figure 2 Relation between amplifying feedbacks f and climate sensitivity S. A
truncated normal distribution with a mean of 0.65 and standard deviation of 0.13
for the feedback f (solid blue line) is assumed here for illustration. These values are
typical for the current set of GCMs8,33. Because f is substantially positive and the
relation between f and S is nonlinear (black line, equation (2)), this leads to a skewed
distribution in S (solid red line) with the characteristic long tail seen in most studies.
Horizontal and vertical lines mark 5–95% ranges. A decrease in the uncertainty of
f by 30% (dashed blue line) decreases the range of S, but the skewness remains
(dashed red line). The uncertainty in the tail of S depends not only on the uncertainty
in f but also on the mean value of f. Note that the assumption of a linear feedback
(equation (1)) is not valid for f near unity. Feedbacks of 1 or more would imply
unphysical, catastrophic runaway effects. (Modifi ed from ref. 8.)
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REVIEW ARTICLE
Instrumental
period
Current mean
climate state
General circulation
models
Last millennium
Volcanic eruptions
Last Glacial Maximum, data
Last Glacial Maximum, models
Proxy data from
millions of years ago
Combining different
lines of evidence
Expert elicitation
012345678910
Climate sensitivity (ºC)
Most likely
Very likely
Likely
Extreme estimates
Extreme estimates beyond
the 0–10 ºC range
Yes, well understood, small uncertainty,
many studies, good agreement,
high confidence
Partly yes, partly understood, medium
uncertainty, few studies, known limitations,
partial agreement, medium confidence
No, poorly understood, large uncertainties,
very few studies or poor agreement, (un)known
limitations, low confidence
Unclear, ambiguous, criteria do not apply,
not considered, cannot be quantified
Similar climate
base state
Similar feedbacks
and timescales
Near equilibrium
state
Most uncertainties
considered
Quality/number of
observations
Uncertainty in
forcing
Confidence from
multiple estimates
Overall LOSU
and confidence
Constraint on
upper bound
Figure 3 Distributions and ranges for climate sensitivity from different lines of evidence. a, The most likely values (circles), likely (bars, more than 66% probability)
and very likely (lines, more than 90% probability) ranges are subjective estimates by the authors based on the available distributions and uncertainty estimates from
individual studies, taking into account the model structure, observations and statistical methods used. Values are typically uncertain by 0.5 °C. Dashed lines indicate
no robust constraint on an upper bound. Distributions are truncated in the range 0–10 °C; most studies use uniform priors in climate sensitivity. Details are discussed
in refs 18, 24, 75 and in the text. Single extreme estimates or outliers (some not credible) are marked with crosses. The IPCC24 likely range and most likely value are
indicated by the vertical grey bar and black line, respectively. b, A partly subjective classifi cation of the different lines of evidence for some important criteria. The
overall level of scientifi c understanding (LOSU) indicates the confi dence, understanding and robustness of an uncertainty estimate towards assumptions, data and
models. Expert elicitation90 and combined constraints are diffi cult to assess; both should have a higher LOSU than single lines of evidence, but experts tend to be
overconfi dent and the assumptions are often not clear.
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forcing and response, and thus avoids the assumption that the
feedback factor is invariant for this very di erent climatic state.
Instead, the assumption is that the change in feedbacks with climate
state is simulated well in a climate model. e resulting estimates
of climate sensitivity are quite di erent for two such attempts58,59,
illustrating the crucial importance of the assumptions in forcings
(dust, vegetation or ice sheets) and of di erences in the structure
of the models used60.
A few people have used palaeoclimate reconstructions from
the past millennium to gain insight into climate sensitivity on
the basis of a large sample of decadal climate variations that
were influenced by natural forcing, and particularly volcanic
eruptions61,62. Because of a weak signal and large uncertainties in
reconstructions and forcing data (particularly solar and volcanic
forcing), the long time horizon yielded a weak constraint on
S (ref. 62) (see Fig. 3), arising mainly from low-frequency
temperature variations associated with changes in the frequency
and intensity of volcanism. Direct estimates of the equilibrium
sensitivity from forcing between the Maunder Minimum period
of low solar forcing and the present are also broadly consistent
with other estimates63.
Some studies of other, more distant palaeoclimate periods64,65
seem to be consistent with the estimates from the more recent
past. For example, the relationship between temperature over the
past 420 million years64 supports sensitivities that are larger than
1.5 °C, but the upper tail is poorly constrained and uncertainties in
the models that are used are signi cant and di cult to quantify.
ere are few studies that yield estimates of S that deviate
substantially from the consensus range, mostly towards very
low values. ese results can usually be attributed to erroneous
forcing assumptions (for example hypothesized external processes
such as cosmic rays driving climate66), neglect of internal climate
variability67, overly simpli ed assumptions, neglected uncertainties,
errors in the analysis or dataset, or a combination of these68–71.
ese results are typically inconsistent with comprehensive
models. In some cases they were refuted by testing the method of
estimation with a climate model with known sensitivity50,72–74.
Several studies and assessments have discussed the available
estimates for climate sensitivity in greater detail4,5,17,18,23,24,75. In
summary, most studies nd a lower 5% limit between 1 and 2 °C
(Fig. 3). e combined evidence indicates that the net feedbacks
f to radiative forcing (equation (2)) are signi cantly positive and
emphasizes that the greenhouse warming problem will not be
small. Figure 3 further shows that studies that use information
in a relatively complete manner generally nd a most likely value
between 2 and 3.5 °C and that there is no credible line of evidence
that yields very high or very low climate sensitivity as a best
estimate. However, the gure also quite dramatically illustrates
that the upper limit for S is uncertain and exceeds 6 °C or more in
many studies. e reasons for this, and the caveats and limitations,
are discussed below.
On the basis of the available evidence, the IPCC Fourth
Assessment Report concluded that constraints from observed
recent climate change18 support the overall assessment that climate
sensitivity is very likely (more than 90% probability) to be larger
than 1.5 °C and likely (more than 66% probability) to be between
2 and 4.5 °C, with a most likely value of about 3 °C (ref. 24). More
recent studies support these conclusions8,45,51,64, with the exception of
estimates based on problematic assumptions discussed above67,69,71.
A LACK OF PROGRESS?
e large uncertainty in climate sensitivity seems disturbing
to many. Have we not made any progress? Or are scientists just
anchored on a consensus range76? Indeed, observations have
not strongly constrained climate sensitivity so far. e latest
generation of GCMs, despite clear progress in simulating past and
present climate5,18,24,77, covers a range of S of 2.1–4.4 °C (ref. 5),
which is very similar to earlier models and not much di erent
from the canonical range of 1.5–4.5 °C rst put forward in 1979 by
Charney78 and later adopted in several IPCC reports20,79.
e fact that high sensitivities are di cult to rule out was
recognized more than two decades ago9,21,39,80. One reason is that
the observed transient warming relates approximately linearly to S
only for small values but becomes increasingly insensitive to S for
shorter timescales and higher S, largely because ocean heat uptake
prevents a linear response in S (equation (1))21–23,81. In addition,
the uncertainty in aerosol forcing prevents the conclusions that
the total forcing ΔF is strongly positive7; if ΔF were close to zero,
S would have to be large to explain the observed warming. is is
illustrated in Fig. 4, showing that both a low sensitivity combined
with a high forcing and a high sensitivity with a low forcing can
reproduce the forced component of the observed warming3,40–45,48.
A high sensitivity can also be compensated for by a high value of
ocean heat uptake. Di erent combinations of forcing, sensitivity,
ocean heat uptake and surface warming (all of which are uncertain)
can therefore satisfy the global energy balance (equation (1)).
A further fundamental reason for the fat tail of S is that S is
proportional to 1/(1 − f) (equation (2))8–10. is relation goes
remarkably far in explaining the PDFs of S on the basis of the
range of the feedback f estimated in GCMs33, if the uncertainty in
f is assumed to be Gaussian. Reducing the uncertainty in f reduces
the range of S, in particular the upper bound, but the skewness
remains8 (see Fig. 2). Recent work on constraining individual
feedbacks4 is promising and helps in isolating model uncertainties
and de ciencies, but it has not yet narrowed the range of f
1900 1950 2000 2050 2100
Year
6
5
4
3
2
1
0
Surface warming (ºC)
Figure 4 The observed global warming provides only a weak constraint on climate
sensitivity. A climate model of intermediate complexity3, forced with anthropogenic
and natural radiative forcing, is used to simulate global temperature with a low
climate sensitivity and a high total forcing over the twentieth century (2 °C, 2.5 W m−2
in the year 2000; blue line) and with a high climate sensitivity and low total
forcing (6 °C, 1.4 W m−2; red line). Both cases (selected for illustration from a large
ensemble) agree similarly well with the observed warming (HadCRUT3v; black line)
over the instrumental period (inset), but show very different long-term warming for
SRES scenario A2 (ref. 101). For simplicity, ocean parameters are kept constant here.
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REVIEW ARTICLE
substantially. In the example of Fig. 2, reducing the 95th centile
of S from about 8.5 °C to 6 °C requires a decrease in the total
feedback uncertainty of about 30%.
Although uncertainties remain large, it would be presumptuous
to say that science has made no progress, given the improvements in
our ability to understand and simulate past climate variability and
change18 as well as in our understanding of key feedbacks4,5. Support
for the current consensus range on S now comes from many di erent
lines of evidence, the ranges of which are consistent within the
uncertainties, relatively robust towards methodological assumptions
(except for the assumed prior distributions; see below) and similar
for di erent types and generations of models. e processes
contributing to the uncertainty are now better understood.
LIMITATIONS AND WAYS FORWARD
ere are known limitations to the concept of forcing and feedback
that are important to keep in mind. e concept of radiative forcing
is of rather limited use for forcings with strongly varying vertical
or spatial distributions7,19. In addition, the equilibrium response
depends on the type of forcing15,82,83. As mentioned above, climate
sensitivity may also be time-dependent or state-dependent12,14,16,84;
for example, in a much warmer world with little snow and ice,
the surface albedo feedback would be di erent from today’s. Some
models indicate that sensitivity depends on the magnitude of the
forcing or warming84,85. ese e ects are poorly understood and are
mostly ignored in simpler models that prescribe climate sensitivity.
e y are likely to be particularly important when estimating climate
sensitivity directly from climate states very di erent from today’s
(for example palaeoclimate), for forcings other than CO2, and in
simple models in which climate sensitivity is a prescribed xed
number and all radiative forcings are treated equally as a change
in the ux at the top of the atmosphere. Structural problems in
the models, for example in the representation of cloud feedback
processes or the physics of ocean mixing5, in particular in cases
in which all models make similar simpli cations, will also a ect
results for climate sensitivity and are very di cult to quantify.
e classical ‘Charney’ sensitivity that results from doubling
CO2 in an atmospheric GCM coupled to a slab ocean model
includes the feedbacks that occur on a timescale similar to that
of the surface warming (namely mainly water vapour, lapse rate,
clouds and albedo feedbacks). ere is an unclear separation
between forcing and fast feedbacks (for example clouds changing
as a result of CO2-induced heating rates rather than the slower
surface warming86,87). Additionally, slow feedbacks with their own
intrinsic timescale, for example changes in vegetation or the retreat
of ice sheets and their e ect on the ocean circulation, could increase
or decrease sensitivity on long timescales88,89 but are kept xed in
models (see Fig. 1). Currently, the climate sensitivity parameter
(the response to 1 W m−2 of any forcing) times the forcing at the
time of CO2 doubling, the equilibrium climate sensitivity for CO2
doubling in a fully coupled model, the ‘Charney’ sensitivity of a
slab model and the e ective climate sensitivity determined from a
transient imbalance are all mostly assumed to be the same number
and are all termed ‘climate sensitivity’. Because few coupled models
have been run to equilibrium and the validity of these concepts
for high forcings is not well established, care should be taken in
extrapolating observationally constrained e ective sensitivities
or slab model sensitivities to long-term projections for CO2 levels
beyond doubling, because feedbacks should be quite di erent in a
substantially warmer climate.
Despite these limitations, S is a quantity that is useful in
estimating the level of CO2 concentrations consistent with an
equilibrium temperature change below some ‘dangerous’ threshold,
as shown in Fig. 5, although the lack of a clear upper limit on S
makes it di cult to estimate a safe CO2 stabilization level for a
given temperature target. What are the options for learning more
about climate sensitivity? Before discussing this, a methodological
point a ecting estimates of S needs to be mentioned: results from
methods estimating a PDF of climate sensitivity depend strongly
on their assumptions of a prior distribution from which climate
models with di erent S are sampled42. Studies that start with climate
sensitivity being equally distributed in some interval (for example
1–10 °C) yield PDFs of S with longer tails than those that sample
models that are uniformly distributed in feedbacks (that is, the
inverse of S (refs 35, 49)). Truly uninformative prior assumptions
do not exist, because the sampling of a model space is ambiguous
(that is, there is no single metric of distance between two models).
Subjective choices are part of Bayesian methods, but because the
data constraint is weak here, the implications are profound. An
alternative prior distribution that has been used occasionally is an
estimate of the PDF of S based on expert opinion43,44,90 (Fig. 3).
However, experts almost invariably know about climate change
in di erent periods (for example the observed warming, or the
temperature at the LGM), which introduces concern about the
independence of prior and posterior information.
01 23456
1,000
900
800
700
600
500
400
300
Equivalent CO2 concentration (p.p.m.v.)
1.5 ºC 2 ºC
3 ºC
4.5 ºC
6 ºC
Likely warming for 450 p.p.m.
E
q
uilibrium tem
p
erature increase from
p
re-industrial
(
ºC
)
Water
Eco-
systems
Food
Health
Coast
Hundreds of millions exposed to increased water stress
Changes in water availability, increased droughts in mid latitudes
Increased coral bleaching
Increased extinction risk for many species
Changes in cereal production patterns
Localized negative impacts on food production
Increased damage from floods and storms
One-third of coastal wetlands lost
Millions experience coastal flooding each year
Substantial burden on health services
Increased burden from malnutrition and diseases
Increased mortality from extreme events
Ecosystem changes from ocean circulation changes
Biosphere may turn into carbon source
Figure 5 Relation between atmospheric equivalent CO2 concentration chosen
for stabilization and key impacts associated with equilibrium global temperature
increase. According to the concept of climate sensitivity, equilibrium temperature
change depends only on climate sensitivity S and on the logarithm of CO2. The
most likely warming is indicated for S = 3 °C (black solid), the likely range (dark
grey) is for S = 2–4.5 °C (ref. 24) (see Fig. 3). The 2 °C warming above the
pre-industrial temperature, often assumed to be an approximate threshold for
dangerous interference with the climate system, is indicated by the black vertical
dashed line for illustration. Stabilization at 450 p.p.m. by volume (p.p.m.v.)
equivalent CO2 concentration (horizontal dashed line) has a probability of less
than 50% of meeting the 2 °C target, whereas 400 p.p.m. would probably meet
it22. Selected key impacts (some delayed) for several sectors and different
temperatures are indicated in the top part of the fi gure, based on the recent
IPCC report (Fig. SPM.2 in ref. 100). For high CO2 levels, limitations in the climate
sensitivity concept introduce further uncertainties in the CO2–temperature
relationship not considered here (see the text).
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Another option that makes use of this Bayesian framework is
to combine some of the individually derived distributions to yield
a better constraint62,91. Combining pieces of information about S
that are independent of each other and arise from di erent time
periods or climatic states should provide a tighter distribution.
e similarity of the PDFs arising from various lines of evidence
shown in Fig. 3 substantially increases con dence in an overall
estimate. However, the di culty in formally combining lines of
evidence lies in the fact that every single line of evidence needs
to be entirely independent of the others, unless dependence is
explicitly taken into account. Additionally, if several climate
properties are estimated simultaneously that are not independent,
such as S and ocean heat uptake, then combining evidence requires
combining joint probabilities rather than multiplying marginal
posterior PDFs62. Neglected uncertainties will become increasingly
important as combining multiple lines of evidence reduces
other uncertainties, and the assumption that the climate models
simulate changes in feedbacks correctly between the di erent
climate states may be too strong, particularly for simpler models.
All of this may lead to unduly con dent assessments, which is a
reason that results combining multiple lines of evidence are still
treated with caution. Figure 3b is a partly subjective evaluation of
the di erent lines of evidence for several criteria that need to be
considered when combining lines of evidence in an assessment.
e prospect for the success of these combined constraints may
be better than that of arriving at a tight constraint from a single
line of observations. Additionally, rather than evaluating models
by using what is readily observed (but may be weakly related to
climate sensitivity)34, ensembles of models could help to identify
which observables are related to climate sensitivity and could thus
provide a better constraint36,92. Future observations of continued
warming of atmosphere and ocean, along with better estimates of
radiative forcing, will eventually provide tighter estimates. New
data may open additional opportunities for evaluating climate
models. Finally, for the particular purpose of understanding
climate sensitivity and characterizing uncertainty, large ensembles
of models with di erent parameter settings34 probably provide
more insight than a small set of very complex models.
POLICY IMPLICATIONS
Whether the uncertainty in climate sensitivity matters depends
strongly on the perspective. ere is no consensus on whether the
goal of the United Nations Framework Convention on Climate
Change of ‘stabilization of greenhouse gas concentrations in the
atmosphere at a level that would prevent dangerous anthropogenic
interference with the climate’ is a useful target to inform policy.
But if certain levels of warming are to be prevented even in the
long run (for example to prevent the Greenland ice sheet from
melting), then climate sensitivity, particularly the upper bound93, is
critical. For example, if the damage function is assumed to increase
exponentially with temperature and the tail of climate sensitivity is
fat (that is, the damage with temperature increases faster than the
probability of such an event), then the expected damage could be
in nite, entirely dominated by the tiny probability of a disastrous
event94. In contrast, if a cost–bene t framework with su ciently
large discounting is adopted, climate change beyond a century is
essentially irrelevant; if the exponential discounting dominates the
increasing damage, then climate sensitivity is unimportant simply
because the discounted damage is insensitive to the stabilization
level. us, the policy relevance of climate sensitivity for mitigation
depends on an assumed economic framework, discount rate and
the timescale of interest.
For short-term scenario projections, the transient climate
response and peak warming in a CO2 overshoot scenario are better
constrained than equilibrium changes, because they are linearly
related to observations and show much less skewed distributions81,95–98.
e prospects for well-constrained projections on the timescales of
a few decades are thus brighter1, and these may be more useful for
decision makers in the short term. Furthermore, for a stabilization
at, for example, 450 p.p.m. CO2 equivalent forcing, which is a level
that would avoid a long-term warming of 2 °C above pre-industrial
temperatures with a probability of rather less than 50% (Fig. 5), the
necessary emission reductions are large and not strongly a ected by
the uncertainty in S. e uncertainties in such an emission pathway
are shown in Fig. 6, considering only CO2. Taking non-CO2 forcings
into account requires even lower emissions.
Long-term stabilization targets depend on climate sensitivity
and on carbon-cycle–climate feedbacks99. e uncertainty in both
of these, if the past is indicative of the future, may not decrease
quickly. However, the tight constraint on the lower limit of sensitivity
indicates a need for strong and immediate mitigation e orts if the
world decides that large climate change should be avoided (Figs 5
and 6). e uncertainty in short-term targets is quite small, and as
scientists continue to narrow the estimates of the climate sensitivity,
and as the feasibility of emission reductions is explored, long-term
emission targets can be adjusted on the basis of future insight.
doi:10.1038/ngeo337
Published online: 26 October 2008.
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Acknowledgements
The International Detection and Attribution Working Group (IDAG) acknowledges support from the
US Department of Energy’s Offi ce of Science, Offi ce of Biological and Environmental Research and the
National Oceanic and Atmospheric Administration’s Climate Program Offi ce.
Correspondence and requests for materials should be addressed to R.K.
