PERSPECTIVE
doi:10.1038/nature11574
Making sense of palaeoc limate sensitivity
PALAEOSENS Project Members*
Many palaeoclimate studies have quantified pre-anthropogenic climate change to calculate climate sensitivity (equi-
librium temperature change in response to radiative forcing change), but a lack of consistent methodologies produces a
wide range of estimates and hinders comparability of results. Here we present a stricter approach, to improve
intercomparison of palaeoclimate sensitivity estimates in a manner compatible with equilibrium projections for future
climatechange.Overthe past65 million years,thisrevealsa climatesensitivity(in K W
21
m
2
)of0.3–1.9 or0.6–1.3 at95% or
68% probability, respectively. The latter implies a warming of 2.2–4.8K per doubling of atmospheric CO
2
, which agrees
with IPCC estimates.
C
haracterizing the complex responses of climate to changes in the
radiation budget requires the definition of climate sensitivity:
this is the global equilibrium surface temperature response to
changes in radiative forcing (an alteration to the balance of incoming and
outgoing energy in the Earth–atmosphere system) caused by a doubling
of atmospheric CO
2
concentrations. Despite progress in modelling and
data acquisition, uncertainties remain regarding the exact value of cli-
mate sensitivity and its potential variability through time. The range of
climate sensitivities in climate models used for Intergovernmental Panel
for Climate Change Assessment Report 4 (IPCC-AR4) is 2.1–4.4 K per
CO
2
doubling
1
, or a warming of 0.6–1.2 K per W m
–2
of forcing.
Observational studies have not narrowed this range, and the upper limit
is particularly difficult to estimate
2
.
Large palaeoclimate changes can be used to estimate climate sensi-
tivity on centennial to multi-millennial timescales, when estimates of
both global mean temperature and radiative perturbations linked with
slow components of the climate system (for example, carbon cycle, land
ice) are available (Fig. 1). Here we evaluate published estimates of climate
sensitivity from a variety of geological episodes, but find that intercom-
parison is hindered by differences in the definition of climate sensitivity
between studies (Table 1). There is a clear need for consistent definition
of which processes are included and excluded in the estimated sensitivity,
like the need for strict taxonomy in biology. The definition must agree
as closely as possible with that used in modelling studies of past and
future climate, while remaining sufficiently pragmatic (operational) to
be applicable to studies of different climate states in the geological past.
Here we propose a consistent operational definition for palaeoclimate
sensitivity and illustrate how a tighter definition narrows the range of
reported estimates. Consistent intercomparison is crucial to detect sys-
tematic differences in sensitivity values—for example, due to changing
continental configurations, different climate background states, and the
types of radiative perturbations considered. These differences may then
be evaluated in terms of additional controls on climate sensitivity, such
as those arising from plate tectonics, weathering cycles, changes in
ocean circulation, non-CO
2
greenhouse gases (GHGs), enhanced water-
vapour and cloud feedbacks under warm climate states. Palaeoclimate
data allow such investigations across geological episodes with very dif-
ferent climates, both warmer and colder than today. Clarifying the
dependence of feedbacks, and therefore climate sensitivity, on the back-
ground climate state is a top priority, because it is central to the utility of
past climate sensitivity estimates in assessing the credibility of future
climate projections
1,3
.
Quantifying climate sensitivity
‘Equilibrium climate sensitivity’ is classically defined as the simulated
global mean surface air temperature increase (DT, in K) in response to a
doubling of atmospheric CO
2
, starting from pre-industrial conditions
(which corresponds to a radiative perturbation, DR, of 3.7 W m
–2
; refs 1,
3). We introduce the more general definition of the ‘climate sensitivity
parameter’ as the mean surface temperature response to any radiative
perturbation (S 5 DT/DR; where DT and DR are centennial to multi-
millennial averages), which facilitates comparisons between studies
from different time-slices in Earth history. For brevity, we refer to S as
‘climate sensitivity’. In the definition of S, an initial perturbation DR
0
leads to a temperature response DT
0
following the Stefan–Boltzmann
law, which is the temperature-dependent blackbody radiation response.
This is often referred to as the Planck response
4
, with a value S
0
of about
0.3 K W
21
m
2
for the present-day climate
5,6
. The radiative perturbation
of the climate system is increased (weakened) by various positive (nega-
tive) feedback processes, which operate at a range of different timescales
(Fig. 1). Because the net effect of positive feedbacks is found to be greater
than that of negative feedbacks, the end result is an increased climate
sensitivity relative to the Planck response
4
.
*Lists of participants and their affiliations appear at the end of the paper.
Timescale
Years Decades Centuries Millennia Multi-millennia // Myr
Clouds, water vapour,
lapse rate, snow/sea ice
Upper ocean
CH
4
CH
4
(major gas-hydrate feedback;
for example, PETM)
Vegetation
Dust/aerosol
Dust (vegetation mediated)
Entire oceans
Land ice sheets
Carbon cycle
Weathering
Biological evolution
of ve
g
etation t
y
pes
Plate tectonics
Figure 1
|
Typical timescales of different feedbacks relevant to equilibrium
climate sensitivity, as discussed in this work. Modified and extended from
previous work
98
. Ocean timescales were extended to multi-millennial timescales
99
.
29 NOVEMBER 2012 | VOL 491 | NATURE | 683
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©2013
Table 1
|
Summary of key studies.
Label in Fig. 3 Source Time window Explicitly considered
forcings
Temperature data used S and 1s bounds
(K W
21
m
2
)
Notes
1 Ref. 2 LGM Various Various 0.81 6 0.27
(data);
0:81
z0:4
{0:27
(models)
LGM compilation based
on ref. 15
2 Ref. 6 LGM GHG (CO
2
,CH
4
,N
2
O),
LI, AE, VG
DT
global
525.8 6 1.4 K;
GLAMAP extrapolated
with model
82
0:72
z0:33
{0:23
Scaling factor (0.85) for
smaller S at LGM compared
to 2 3 CO
2
(refs 12, 16)
3 Ref. 86 LGM GHG (CO
2
,CH
4
),
LI, AE, VG
CLIMAP and DT
aa&gld
0.80 6 0.14 Value after authors’ sugge sted
correction of CLIMAP
temperatures
4 Ref. 79 LGM GHG (CO
2
,CH
4
),
LI, AE, VG
MARGO
81
SST based
DT 5 {3:0
z1:3
{0:7
K
0:62
z0:08
{0:12
Model-based global estimate
5 Ref. 76 GC GHG (CO
2
,CH
4
) DT
trop
1.1 6 0.05 Author’s linear regression case.
Value based on single-site tropical
SST, and representation of global
changes will be more uncertain
6 Ref. 74 GC GHG (CO
2
,CH
4
),
LI, AE
DT
aa
(with 1.5 3 polar
amplification)
0.88 6 0.13 Author used a single value for
polar amplification. If 2 3 were
used
52
, then the central estimate
is closer to 0.7
7 Ref. 52 GC GHG (CO
2
,CH
4
,
N
2
O), LI
DT
aa
(with 2 3 polar
amplification)
0.75 6 0.13 Authors used a single value for
polar amplification. If 1.5 3 were
used
74
, then the central estimate
becomes 1.0
8 Ref. 52 GC GHG
(CO
2
,CH
4
,N
2
O)
DT
aa
(with 2 3 polar
amplification)
1.5 6 0.25 Authors used a single value for
polar amplification. If 1.5 3 were
used
74
, then the central estimate
becomes 2.0
23–32 This work,
based on ref. 6
GC (,800 kyr ago) GHG (CO
2
,CH
4
,N
2
O),
LI, AE, VG
DT
NH
5 model-based
deconvolution of benthic
d
18
O (ref. 51), scaled to
global DT using a NH
polar amplification on
land of 2.75 6 0.25
0.66 6 0.22 to
2.26 6 0.78
This covers the range of
S
[GHG,X]
given in Table 2
9 Ref. 85 GC GHG (CO
2
,CH
4
,
N
2
O), LI
DT
aa
(with 2 3 polar
amplification) and
1.5 3 DT
ds
0.75 6 0.13 Authors used a single value for
polar amplification. If 1.5 3 were
used
73
, then the central estimate
becomes 1.0
10 Ref. 39 GC GHG (CO
2
,CH
4
,
N
2
O), LI, AE
36-record global SST
synthesis along with
DT
aa&gld
.
0:85
z0:25
{0:2
Polar amplification diagnosed,
not imposed. Estimates made
both in a spatially explicit sense
and as direct global means
11 Ref. 39 GC GHG (CO
2
,CH
4
,
N
2
O), LI
36-record global SST
synthesis along with
DT
aa&gld
.
1.05 6 0.25 As above
12 Ref. 87 Early to Middle
Pliocene (4.2–3.3
Myr ago)
CO
2
, ESS Using model-based
DT for Middle and
Early Pliocene of
2.4–2.9 uC and 4 uC.
DCO
2
alkenone
1.92 6 0.14 to
2.35 6 0.18
(3.3 Myr ago);
2.60 6 0.19
(4.2 Myr ago)
Forcing in ref. 44; temperature
in ref. 87. Both derived in global
sense from model experiments
13 Ref. 61 Miocene optimum
to present day
Slow feedbacks Deconvolution of
benthic d
18
O (ref. 63)
0.78 6 10% f 5 0.71, b 5 5.35, c 5 1.3. Details
in Supplementary Information
14 This work
(compilation)
Eocene–Oligocene
transition (,34 Myr
ago)
CO
2
. ESS (in the
sense of ref. 44)
Model-based DT,
with range of CO
2
values
1:72
z0:9
{0:54
Details in Supplementary
Information
15 This work
(compilation)
Late Eocene
versus present
CO
2
. ESS (in the
sense of ref. 44)
Model-based DT,
with range of CO
2
values
1:82
z0:26
{0:49
Details in Supplementary
Information
16 Ref. 78 Middle Eocene
Climatic Optimum
(,40 Myr ago)
CO
2
. Ice-free world.
Event study (not
affected by plate
tectonics and
evolution effects)
DT
ds
(2 records) and
DT
mg
(7 records).
DCO
2
from alkenones
0.95 6 0.3 500 kyr timescale. DT
ds
5 DT
mg
.
Temperatures from subtropics to
high latitudes; no tropical data.
Hence biased to high-latitude
sensitivity
17 Ref. 78 Mid to Late Eocene
transition (41–35
Myr ago)
CO
2
. Largely ice-free
world. Event study
(not affected by
plate tectonics and
evolution effects)
DT
ds
(ref. 71) and DT
mg
.
DCO
2
5 difference mid
Eocene alkenone and
late Eocene d
11
B
0.95 6 0.3 Multi-million-year timescale.
Adding uncertainty of 61 uC
to DT would enhance 1s limits
to 60.45 K W
21
m
2
18 Ref. 88 Early Eocene
(,55–50 Myr ago)
CO
2
. Ice-free world.
(potential influences
of plate tectonics and
biological evolution
not considered)
DT
mg
(refs 89–91). DCO
2
based on modelling
91
marine organic carbon
isotope fractionation
92
and soil nodules
93
0.65 6 0.25 Central value recalculated in
ref. 94.
Note ref. 89 underestimate d
tropical SST
19 This work
(compilation)
PETM
(,56 Myr ago)
CO
2
. Ice-free world.
Event study (not
affected by plate
tectonics and
evolution effects)
DT
ds
(.6 records) and
DT
mg
(.11 records;
equatorial to polar).
DCO
2
based on deep ocean
carbonate chemistry
72, 95
1.0–1.8 Details in Supplementary
Information. Assumes all warming
due to C input, and range of
background CO
2
and C-injection
scenarios. DT
ds
5 DT
mg
. Total
range of S is 0.7–2.2 K W
21
m
2
.
RESEARCH PERSPECTIVE
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We emphasize that all feedbacks, and thus the calculated climate
sensitivity, may depend in a—largely unknown—nonlinear manner
on the state of the system before perturbation (the ‘background climate
state’) and on the type of forcing
7–15
. The relationship of S with back-
ground climate state differs among climate models
12,16–18
. A suggestion
of state dependence is also found in a data comparison (Table 2)
6
, where
climate sensitivity for the past 800,000 years (800 kyr) shows substantial
fluctuations through time (Fig. 2). In contrast, its values for the Last
Glacial Maximum (LGM) alone occupy only the lower half of that range
(Fig. 2). That evaluation also suggests that the relationship of S with the
general climate state may not be simple.
‘Fast’ versus ‘slow’ processes
Climate sensitivity depends on processes that operate on many different
timescales, from seconds to millions of years, due to both direct response
to external radiative forcing, and internal feedback processes (Fig. 1).
Hence, the timescale over which climate sensitivity is considered is
critical. An operationally pragmatic decision is needed to categorize a
process as ‘slow’ or ‘fast’, depending on the timescale of interest, the
resolution of the (palaeo-)records considered and the character of
changes therein
19
. If a process results in temperature changes that reach
steady state slower than the timescale of the underlying radiative per-
turbation, then it is considered ‘slow’; if it is faster or coincident, then it is
‘fast’. Present-day atmospheric GHG concentrations and the radiative
perturbation due to anthropogenic emissions increase much faster than
observed for any natural process within the Cenozoic era
20–22
.
For the present, the relevant timescale for distinguishing between fast
and slow processes can be taken as 100 yr (ref. 23). Ocean heat uptake
plays out over multiple centuries. Combined with further ‘slow’ pro-
cesses, it causes climate change over the next few decades to centuries to
be dominated by the so-called ‘transient climate response’ to radiative
changes that result from changing GHG concentrations and aerosols
5,19,24
.
After about 100 yr, this transient climate response is thought to amount to
roughly two-thirds of the equilibrium (see below) climate sensitivity
5,25
.
Climate models account for the fast feedbacks from changes in water-
vapour content, lapse rate, cloud cover, snow and sea-ice albedo
26
, and
the resulting response is often referred to as the ‘fast-feedback’ or
‘Charney’ sensitivity
23
. To approximate the ‘equilibrium’ value of that
climate sensitivity, accounting for ocean heat uptake and further slow
processes, models might be run over centuries with all the associated
computational difficulties
27–30
, or alternative approaches may be used
that exploit the energy balance of the system for known forcing or
extrapolation to equilibrium
31
.
In palaeoclimate studies, an operational distinction has emerged to
distinguish ‘fast’ and ‘slow’ processes relative to the timescales of tempera-
ture responses measured in palaeodata, where ‘fast’ is taken to apply to
processes up to centennial scales, and ‘slow’ to processes with timescales
closeto millennial or longer. Thus, changesin natural GHG concentrations
are dominated by ‘slow’ feedbacks related to global biogeochemical cycles
(Fig. 1). Similarly slow are the radiative influences of albedo feedbacks that
are dominated by centennial-scale or longer changes in global vegetation
cover and global ice area/volume (continental ice sheets) (Fig. 1).
Label in Fig. 3 Source Time window Explicitly considered
forcings
Temperature data used S and 1s bounds
(K W
21
m
2
)
Notes
20 Ref. 96 Cretaceous and
early Palaeogene
CO
2
. Largely ice-free
world. (potential
influences of plate
tectonics and biological
evolution not
considered)
1 Recalculated in ref. 94. No
uncertainty range was reported,
nor salient details for assessment.
Figure 3b, c assumes 625%
21 Ref. 94 Cretaceous and
early Palaeogene
CO
2
. Largely ice-free
world. ESS in the
sense of ref. 44
DT after refs 52, 71.
DCO
2
based on ref. 60.
.0.8 No uncertainty range reported.
This is a lower bound estimate
only
22 Ref. 97 Phanerozoic CO
2
. Ice-free situation.
(Potential influen ces
of plate tectonics and
biological evolution
not considered).
DT
mg,
DCO
2
based
on GEOCARBSULF
0.8–1.08 Model-based with extensive
uncertainty analysis
These studies have empirically determined S for the Pleistocene and some deep-time periods from comparison between data-derived time series for temperature and for radiative change. Comparison of results
between studies is greatly hindered by the different ‘versions’ of S used, as related to different notions of which processes should be explicitly accounted for, and by the different approaches taken to approximate
global mean surfacetemperature. All uncertainties are as originally reported, but shown here at the level equivalent to 1s, estimated where necessary by dividing total range values by a factor of 2. All values for S are
reported in K W
21
m
2
, where necessary after transformation using 3.7 W m
–2
per doubling of CO
2
, bearing in mind the caveats for this at high CO
2
concentrations as elaborated in the main text. GC, glacial cycles;
LGM, Last Glacial Maximum; PETM, Palaeocene/Eocene thermal maximum; SST, sea surface temperature. See main text for details of forcings. Subscripts: aa, Antarctica; gld, Greenland; trop, tropical; ds, deep
sea; global, global mean; mg, Mg/Ca; NH, Northern Hemisphere.
Table 1 j Continued
Table 2
|
Common permutations of S that may be encountered in palaeostudies
Label in
Fig. 3
S definition Explicitly considered
radiative perturbation
Period in which it is practical
to use the definition
S 6 1s for 800 kyr
(K W
21
m
2
)
S 6 1s
for LGM (K W
21
m
2
)
S
for Pliocene (K W
21
m
2
)
23 S
[CO2]
DR
[CO2]
All (especially pre-35 Myr ago
when LI < 0)
3.08 6 0.96 2.63 6 0.57 1.2
24 S
[CO2, LI]
DR
[CO2, LI]
,35 Myr ago 1.07 6 0.40 0.95 6 0.22 0.97
25 S
[CO2, LI, VG]
DR
[CO2, LI, VG]
,35 Myr ago 0.86 6 0.27 0.80 6 0.19 0.82
26 S
[CO2, LI, AE]
DR
[CO2, LI, AE]
,35 Myr ago, but mainly ,800 kyr ago 0.90 6 0.42 0.72 6 0.18
27 S
[CO2, LI, AE, VG]
DR
[CO2, LI, AE, VG]
,35 Myr ago, but mainly ,800 kyr ago 0.75 6 0.29 0.63 6 0.15
28 S
[GHG]
DR
[GHG]
,800 kyr ago 2.32 6 0.76 1.97 6 0.41
29 S
[GHG, LI]
DR
[GHG, LI]
,800 kyr ago 0.96 6 0.36 0.85 6 0.19
30 S
[GHG, LI, VG]
DR
[GHG, LI, VG]
,800 kyr ago 0.78 6 0.23 0.73 6 0.16
31 S
[GHG, LI, AE]
DR
[GHG, LI, AE]
,800 kyr ago 0.82 6 0.36 0.66 6 0.16
32 S
[GHG, LI, AE, VG]
DR
[GHG, LI, AE, VG]
,800 kyr ago 0.68 6 0.24 0.58 6 0.14
S (second column) is presented with a subscript that identifies the explicitly considered radiative perturbations DR (third column, same subscripts as for S); all other processes are implicitly resolved as feedbacks
within S. The period in which the various definitions of S are practical is determined by the availability of data for the explicitly considered processes. Subscript CO2 indicates the radiative impact of atmospheric
CO
2
concentration changes; LI represents the radiative impact of global land ice-volume changes; VG stands for the radiative impact of global vegetation cover changes; AE indicates the radiative impact of aerosol
changes; GHG stands for the impact of changes in all non-water natural greenhouse gases (notably CO
2
,CH
4
and N
2
O). Columns 5 and 6 give calculated values for all suggested permutations of S for the past
800 kyr or the LGM, respectively, based on a previous data compilation
6
. Mean values of all S
[X]
for the LGM are about 13% smaller than for the whole 800 kyr, but lie well within the given uncertainties. This offset
illustrates the state-dependence of S (see Supplementary Information). Column 7 gives examples for the Pliocene
13,44
; Fig. 3b, c assumes 625% uncertainty in these. In these values the effects of orographic
changes have been taken into account (see Supplementary Information section B2).
PERSPECTIVE RESEARCH
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Other processes clearly have both fast and slow components. For
example, palaeorecords of atmospheric dust deposition imply important
aerosol variations on decadal to astronomical (orbital) timescales
32–36
,
reflecting both slow controlling processes related to ice-volume and
land-surface changes, and fast processes related to changes in atmo-
spheric circulation. A further complication arises from the lack of ade-
quate global atmospheric dust data for any geological episode except the
LGM
37,38
, even though that is essential because the spatial distribu-
tion of dust in the atmosphere tends to be inhomogeneous and because
temporal variationsin some locations tend to take place over several orders
of magnitude
32–36
. Moreover, palaeoclimate models generally struggle to
account for aerosols, with experiments neither prescribing nor implicitly
resolving aerosol influences. So far, understanding of aerosol/dust feed-
backs remains weak and in need of improvements in both data coverage
and process modelling, especially because dust forcing may account for
some 20% of the glacial–interglacial change in the radiative budget
6,39
.
So for comparison of results between studies, it is most effective to
consider only the classical ‘Charney’ water-vapour, cloud, lapse rate, and
snow and sea-ice feedbacks
23
as ‘fast’, and all other feedbacks as ‘slow’. In
addition, results from palaeoclimate sensitivity studies generally do not
address the transient climate response that dominates present-day
changes, but capture a more complete longer-term system response
comparable with equilibrium climate sensitivity in climate models.
Forcing and slow feedbacks
The external drivers of past natural climate changes mainly resulted
from changes in solar luminosity over time
40
, from temporal and spatial
variations in insolation due to changes in astronomical parameters
41–43
,
from changes in continental configurations
14,44
, and from geological
processes that directly affect the carbon cycle (for example, volcanic
outgassing).However, the completeEarthsystemresponse to suchforcings
as recorded by palaeodata cannot be immediately deduced from the
(equilibrium) ‘fast feedback’ sensitivity of climate models, because of
the inclusion of slow feedback contributions. When estimating climate
sensitivity from palaeodata, agreement is therefore needed about which
of the slower feedback processes are viewed as feedbacks (implicitly
accounted for in S), and which are best considered as radiative forcings
(explicitly accounted for in DR).
We employ an operational distinction
31,45
in which a process is con-
sidered as a radiative forcing if its radiative influence is not changing
with temperature on the timescale considered, and as a feedback if its
impact on the radiation balance is affected by temperature changes on
that timescale. For example, the radiative impacts of GHG changes over
the past 800 kyr may be derived from concentration measurements of
CO
2
,CH
4
and N
2
O in ice cores
46–48
, and the radiative impacts of land-ice
albedo changes may be calculated from continental ice-sheet estimates,
mainly based on sea-level records
49–51
. Thus, the impacts of these slow
feedbacks can be explicitly accounted for before climate sensitivity is
calculated. This leaves only fast feedbacks to be considered implicitly in
the calculated climate sensitivity, which so approximates the (equilib-
rium) ‘Charney’ sensitivity from modelling studies
6,39,52
.
Operational challenges
All palaeoclimate sensitivity studies are affected by limitations of data
availability. Below we discuss such limitations to reconstructions of
forcings and feedbacks, and of global surface temperature responses.
First, however, we re-iterate a critical caveat, namely that the climate
response depends to some degree on the type of forcing (for example,
shortwave versus longwave, surface versus top-of-atmosphere, and local
versus global). The various radiative forcings with similar absolute mag-
nitudes have different spatial distributions and physics, so that the con-
cept of global mean radiative forcing is a simplification that introduces
some (difficult to quantify) uncertainty.
Astronomical (orbital) forcing is a key driver of climate change. In
global annual mean calculations of radiative change, astronomical forcing
is very small and often ignored
39,52
. Although this obscures its importance,
mainly concerning seasonal changes in the spatial distribution of inso-
lation over the planet
41,42,53–55
, we propose that the contribution of the
astronomical forcing to DR may be neglected initially. When other com-
ponents of the system respond to the seasonal aspects of forcing, such as
Quaternary ice-sheet variations, these may be accounted for as forcings
themselves.
GHG concentrations from ice cores are not available for times before
800 kyr ago, when CO
2
levels instead have to be estimated from indirect
methods. These employ physico-chemical or biological processes that
depend on CO
2
concentrations, such as the abundance of stomata on
fossil leaves
56
, fractionation of stable carbon isotopes by marine phyto-
plankton
57
, boron speciation and isotopic fractionation in sea water as a
function of pH and preserved in biogenic calcite
58
, and the stability fields
of minerals precipitated from waters in contact with the atmosphere
59
.
–8
–6
–4
–2
0
2
ΔT (K)
a
–8
–6
–4
–2
0
2
ΔR
[CO2, LI]
(W m
–2
)
b
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Time (kyr BP)
S
[CO2, LI]
(K W
–1
m
2
)
800 700 600 500 400 300 200 100 0
σ
1
100-kyr running mean of S
i
Mean of S
i
± σ
0
S
i
± σ
1
at LGM
c
Figure 2
|
Illustration of variability of climate sensitivity using a calculation
of
S
[CO2,LI]
, as defined in this work, for the past 800 kyr. a, Changes in global
temperature. b, Changes in radiative forcing due to changes in CO
2
and surface
albedo due to land ice. c, Calculated S
[CO2,LI]
, which is only considered robust
and calculated when DT , 21.5 K and DR
[CO2,LI]
, 20.5 W m
–2
, as indicated
by the dotted red lines in a and b.Inc,meanofS
i
6 s
0
(dashed black lines
indicate s
0
, the uncertainty of averaging) and 100-kyr running mean (blue line)
are shown. Magenta marker in c denotes S
i
6 s
1
for the LGM only (23–19 kyr
ago) (s
1
is the square root of the sum of squares of individual uncertainties
connected with different processes contributing to S
i
). The grey areas in
a–c denote s
1
(standard deviation) uncertainties of S
i
for single points in time
(points themselves are omitted for clarity). Details of data and the definition of
the calculated uncertainties presented in this figure are available in
Supplementary Information. In a and b, the dashed black lines indicate the
preindustrial reference case (DT 5 0K,DR
[CO2,LI]
5 0Wm
–2
).
RESEARCH PERSPECTIVE
686 | NATURE | VOL 491 | 29 NOVEMBER 2012
Macmillan Publishers Limited. All rights reserved
©2013
Considerable uncertainties remain in such reconstructions, but improve-
ments are continually made to the methods, their temporal coverage and
their mutual consistency
60
. Recent work has synthesized a high-resolu-
tion CO
2
record for the past 20 million years (Myr; ref. 61), but new data
and updated syntheses remain essential, particularly for warmer climate
states. Also, proxies are needed for reconstruction of CH
4
and N
2
O con-
centrations in periods pre-dating the ice-core records
62
.
Regarding the assessment of land-ice albedo changes, good methods
exist for the generation of continuous centennial- to millennial-scale
sea-level (ice-volume) records over the past 500 kyr (refs 49–51), but
such detailed information remains scarce for older periods. A model-
based deconvolution of deep-sea stable oxygen isotope records into
their ice-volume and deep-sea temperature components
51
was recently
extended to 35 Myr ago
63
, but urgently requires independent validation,
especially to address uncertainties about the volume-to-area relation-
ships that would be different for incipient ice sheets than for mature
ice sheets
64,65
. Before 35 Myr ago, there is thought to have been (virtually)
no significant land-ice volume
66
, but this does not exclude the potential
existence of major semi-permanent snow/ice-fields
67,68
, and there remain
questionswhether these would constitute ‘fast’ (snow) or ‘slow’ (land-ice)
feedbacks. The contribution of the sea-ice albedo feedback also remains
uncertain, with little quantitative information beyond the LGM.
Similar examples of uncertainties and limited data availability could
be listed for all feedbacks. However, a ‘deep-time’ (before 1 Myr ago)
geological perspective must be maintained because it offers access to the
nearest natural approximations of the current rate and magnitude of
GHG emissions
69,70
, and because only ancient records provide insight
into climate states globally warmer than the present. Given that no past
perturbation will ever present a perfect analogue for the continuing
anthropogenic perturbation, it may be more useful to consider past
warm climate states as test-beds for evaluating processes and responses,
and for challenging/validating model simulations of those past climate
states. Such data–model comparisons will drive model skill and under-
standing of processes, improving confidence in future multi-century
projections. For such an approach, palaeostudies may minimize the
impacts of very long-term influences on climate sensitivity (for example,
due to changes in orography, or biological evolution of vegetation)
through a focus on highly resolved documentation of specific perturba-
tions that are superimposed upon differentlong-term backgroundclimate
states. An example is the pronounced transient global warming and
carbon-cycle perturbation during the Palaeocene/Eocene thermal maxi-
mum (PETM) anomaly
71,72
, which punctuated an already warm climate
state
73
. Note that deep-time case studies need to consider one further
complication, namely that the radiative forcing per CO
2
doubling may
be about 3.7 W m
–2
when starting from pre-industrial concentrations,
but increases at higher CO
2
levels
11
. Data-led studies may help with a
first-order documentation of this dependence. Calculation of S from CO
2
and temperature measurements using a constant 3.7 W m
–2
per CO
2
doubling would (knowingly) overestimate S for high-CO
2
episodes.
The difference with other, identically defined, S values for different cli-
mate background states may then be used to assess any deviation from
3.7 W m
–2
per CO
2
doubling.
Regarding the reconstruction of past global surface temperature res-
ponses (that is, DT in equation (1) below), again much remains to be
improved. Most work to date (see Table 1) relies on one or more of the
following: polar temperature variations from Antarctic ice cores (since
800 kyr ago) with a multiplicative correction for ‘polar amplification’
(usually estimated at 1.5–2.0; refs 74, 75); deep-sea temperature varia-
tions from marine sediment-core data with a correction for the ratio
between global surface temperature and deep-sea temperature changes
(often estimated at 1.5); single-site sea surface temperature (SST) records
from marine sediment cores; or compilations of SST data of varying
geographic coverage from marine sediment cores
6,39,52,76–78
. So far, few
studies have included terrestrial temperature proxy records other than
those from ice cores
79
, yet better control on land-surface data is crucial
because of seasonal and land-sea contrasts. Continued development is
needed of independently validated (multi-proxy) and spatially represent-
ative (global) data sets of high temporal resolution relative to the climate
perturbations studied.
Uncertainties in individual reconstructions of temperature change
may in exceptional cases be reported to 60.5 K, but more comprehensive
uncertainty assessments normally find them to be larger
80,81
. Compilation
of such records to determine changes in global mean surface tempera-
ture involves the propagation of further assumptions/uncertainties, for
example due to interpolation from limited spatial coverage, and the end
result is unlikely to be constrained within narrower limits than 61 K even
for well-studied intervals. Finally, comparisons between independent
reconstructions for the same episode reveal ‘hidden’ uncertainties due
to differences between each study’s methodological choices, uncertainty
determination, and data-quality criteria, which are hard to quantify and
often poorly elucidated. Take the LGM for example, which for tempera-
ture is among the best-studied intervals. The MARGO compilation
81
inferred a global SST reduction of –1.9 6 1.8 K relative to the present.
Another spatially explicit study
79
used that range to infer a global mean
surface air temperature anomaly of {3
z1:3
{0:7
K. The latter contrasts with a
previous estimate of 25.8 6 1.4 K (ref. 82), which is consistent with
tropical (30u Sto30u N) SST anomalies of 22.7 6 1.4 K (ref. 83).
However, that tropical range itself is also contested; the MARGO
81
study suggested such cooling in the Atlantic Ocean, but less in the
tropics of the Indian and Pacific Oceans (giving a global tropical
cooling of only 21.7 6 1.0 K). Clearly, even a well-studied interval
gives rise to a range of estimates for temperature, and therefore for
climate sensitivity.
It is evident that progress in quantifying palaeoclimate sensitivity
will not only rely on a common concept and terminology that allows
like-for-like comparisons (see below); it will also rely on an objective,
transparent and hence reproducible discussion in each study of the
assumptions and uncertainties that affect the values determined for
change in both temperature and radiative forcing.
A way forward
Here we propose a new terminology to help palaeoclimate sensitivity stud-
ies adopt common concepts and approaches, and thus improve the poten-
tial for like-for-like comparisons between studies. First we outline how our
concept of ‘equilibrium’ S for palaeo-studies relates to ‘equilibrium’ S for
modern studies. Then, we present a notation system that is primarily of
value to data-based palaeo studies to clarify which slow feedbacks are
explicitly acco unted for. We finish with an application of the new frame-
work, calculating climate sensitivity from a representative selection of
palaeoclimate sensitivity estimates over the past 65 Myr, with a fair balance
of climates warmer than the present to those colder than the present.
When the DT response to an applied GHG radiative forcing DR is
small relative to ‘pre-perturbation’ reference temperature, the ‘equilib-
rium’ climate sensitivity S
a
(where a indicates actuo, for present-day)
takes the form (see, for example, refs 4, 84):
S
a
~
DT
DR
~
{1
l
P
z
P
N
i~1
l
f
i
ð1Þ
Here l
P
is the Planck feedback parameter (23.2 W m
22
K
21
) and l
f
i
(in W m
22
K
21
) represents the feedback parameters of any number
(N) of fast (f ) feedbacks. We define feedback parameters in the form
l
f
i
5 DR
i
/DT. S
a
is the ‘Charney’ sensitivity calculated by most cli-
mate models in ‘2 3 CO
2
’ equilibrium simulations, with a range of
0.6–1.2 K W
21
m
2
in IPCC-AR4. However, the Earth system in reality
responds to a perturbation according to an equilibrium climate sen-
sitivity parameter S
p
(where p indicates palaeo), but the timescales to
reach this equilibrium are long, so that the forcing normally changes
before equilibrium is reached. To obtain S
a
from palaeoclimate sens-
itivity S
p
, a correction is therefore needed for the slow feedback influ-
ences. Using l
s
j
to represent any number (M) of slow (s) feedbacks, we
derive the general expression (see Supplementary Information):
PERSPECTIVE RESEARCH
29 NOVEMBER 2012 | VOL 491 | NATURE | 687
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©2013
![Figure 2 | Illustration of variability of climate sensitivity using a calculation of S[CO2,LI], as defined in this work, for the past 800kyr. a, Changes in global temperature. b, Changes in radiative forcing due to changes in CO2 and surface albedo due to land ice. c, Calculated S[CO2,LI], which is only considered robust and calculated when DT,21.5K and DR[CO2,LI],20.5Wm –2, as indicated by the dotted red lines in a and b. In c, mean of Si 6 s0 (dashed black lines indicate s0, the uncertainty of averaging) and 100-kyr runningmean (blue line) are shown. Magenta marker in c denotes Si 6 s1 for the LGM only (23–19 kyr ago) (s1 is the square root of the sum of squares of individual uncertainties connected with different processes contributing to Si). The grey areas in a–c denote s1 (standard deviation) uncertainties of Si for single points in time (points themselves are omitted for clarity). Details of data and the definition of the calculated uncertainties presented in this figure are available in](/figures/figure-2-illustration-of-variability-of-climate-sensitivity-ilb4ojax.webp)