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The proportionality of global warming to cumulative carbon emissions

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The global temperature response to increasing atmospheric CO(2) is often quantified by metrics such as equilibrium climate sensitivity and transient climate response. These approaches, however, do not account for carbon cycle feedbacks and therefore do not fully represent the net response of the Earth system to anthropogenic CO(2) emissions. Climate-carbon modelling experiments have shown that: (1) the warming per unit CO(2) emitted does not depend on the background CO(2) concentration; (2) the total allowable emissions for climate stabilization do not depend on the timing of those emissions; and (3) the temperature response to a pulse of CO(2) is approximately constant on timescales of decades to centuries. Here we generalize these results and show that the carbon-climate response (CCR), defined as the ratio of temperature change to cumulative carbon emissions, is approximately independent of both the atmospheric CO(2) concentration and its rate of change on these timescales. From observational constraints, we estimate CCR to be in the range 1.0-2.1 degrees C per trillion tonnes of carbon (Tt C) emitted (5th to 95th percentiles), consistent with twenty-first-century CCR values simulated by climate-carbon models. Uncertainty in land-use CO(2) emissions and aerosol forcing, however, means that higher observationally constrained values cannot be excluded. The CCR, when evaluated from climate-carbon models under idealized conditions, represents a simple yet robust metric for comparing models, which aggregates both climate feedbacks and carbon cycle feedbacks. CCR is also likely to be a useful concept for climate change mitigation and policy; by combining the uncertainties associated with climate sensitivity, carbon sinks and climate-carbon feedbacks into a single quantity, the CCR allows CO(2)-induced global mean temperature change to be inferred directly from cumulative carbon emissions.
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LETTERS
The proportionality of global warming to cumulative
carbon emissions
H. Damon Matthews
1
, Nathan P. Gillett
2
, Peter A. Stott
3
& Kirsten Zickfeld
2
The global temperature response to increasing atmospheric CO
2
is
often quantified by metrics such as equilibrium climate sensitivity
and transient climate response
1
. These approaches, however, do not
account for carbon cycle feedbacks and therefore do not fully
represent the net response of the Earth system to anthropogenic
CO
2
emissions. Climate–carbon modelling experiments have
shown that: (1) the warming per unit CO
2
emitted does not depend
on the background CO
2
concentration
2
; (2) the total allowable
emissions for climate stabilization do not depend on the timing
of those emissions
3–5
; and (3) the temperature response to a pulse
of CO
2
is approximately constant on timescales of decades to
centuries
3,6–8
. Here we generalize these results and show that the
carbon–climate response (CCR), defined as the ratio of temper-
ature change to cumulative carbon emissions, is approximately
independent of both the atmospheric CO
2
concentration and its
rate of change on these timescales. From observational constraints,
we estimate CCR to be in the range 1.0–2.16C per trillion tonnes of
carbon (Tt C) emitted (5th to 95th percentiles), consistent with
twenty-first-century CCR values simulated by climate–carbon
models. Uncertainty in land-use CO
2
emissions and aerosol
forcing, however, means that higher observationally constrained
values cannot be excluded. The CCR, when evaluated from climate
carbon models under idealized conditions, represents a simple yet
robust metric for comparing models, which aggregates both
climate feedbacks and carbon cycle feedbacks. CCR is also likely
to be a useful concept for climate change mitigation and policy; by
combining the uncertainties associated with climate sensitivity,
carbon sinks and climate–carbon feedbacks into a single quantity,
the CCR allows CO
2
-induced global mean temperature change to
be inferred directly from cumulative carbon emissions.
We propose a new measure of the climate response to anthro-
pogenic carbon dioxide emissions: the ‘carbon–climate response’
(CCR). The CCR is illustrated schematically in Fig. 1, which shows
the progression from carbon emissions to climate change. The CCR
incorporates the standard concept of climate sensitivity (the temper-
ature response to increased atmospheric CO
2
), in addition to a
‘carbon sensitivity’ (the amount by which atmospheric CO
2
concen-
trations increase in response to CO
2
emissions, as mediated by
natural carbon sinks, and including also the effect of feedbacks
between climate change and carbon uptake).
The CCR thus represents the net climate response to CO
2
emis-
sions, and can be defined as DT/E
T
, where DTis the global mean
temperature change over some period of time, and E
T
is the total
cumulative carbon dioxide emitted over that period. We assign units
of trillion tonnes of carbon to E
T
(1 Tt 51 teratonne, or 10
18
grams,
of carbon, which is equivalent to 3.7 trillion tonnes of CO
2
), so the
CCR as defined here carries units of uC per Tt C emitted. CCR can be
written as:
CCR 5DT/E
T
5(DT/DC
A
)3(DC
A
/E
T
)
where DC
A
is the change in atmospheric carbon (in Tt C). Written in
this way, CCR represents the product of the temperature change per
unit atmospheric carbon increase (DT/DC
A
) and the airborne frac-
tion of cumulative carbon emissions (DC
A
/DE
T
). If defined under
conditions of constant doubled pre-industrial atmospheric CO
2
,DT
is equal to the equilibrium climate sensitivity, and if defined under
doubled CO
2
conditions in a simulation in which CO
2
increases at
1% per year, DTis equal to the transient climate response
1
.
Both the airborne fraction of cumulative emissions and the tem-
perature change per unit atmospheric carbon increase are dependent
on the atmospheric CO
2
concentration and its rate of increase;
however, the CCR (as the product of the two) shows a remarkable
constancy with time. This can be seen in Fig. 2, which shows three
model simulations using the University of Victoria Earth System
Climate Model
9
(UVic ESCM, see Methods), an intermediate-
complexity coupled climate–carbon model. In all simulations, we
prescribed atmospheric CO
2
concentrations and used the model’s
interactive carbon sinks to diagnose the implied anthropogenic
CO
2
emissions consistent with the prescribed concentration
changes
10
. In the first simulation (Fig. 2a) we increased atmospheric
CO
2
by 1% per year for 70 years; in the second and third simulations
(Fig. 2b), atmospheric CO
2
was doubled (solid lines) or quadrupled
(dashed lines) instantaneously and held constant for 1,000 years. In
all simulations, the airborne fraction of cumulative emissions
decreased over time, whereas the temperature change per unit change
in atmospheric carbon increased with time. After an initial adjust-
ment period of about a decade, the CCR remained almost constant at
,1.7 uC per Tt C emitted.
1
Department of Geography, Planning and Environment, Concordia University, 1455 de Maisonneuve Blvd W., Montreal, Quebec, H3G 1M8, Canada.
2
Canadian Centre for Climate
Modelling and Analysis, Environment Canada, 3800 Finnerty Road, Victoria, British Columbia, V8P 5C2, Canada.
3
Met Office Hadley Centre, FitzRoy Road, Exeter, Devon, EX1 3PB, UK.
CO2 concentrationCO2 emission Climate change
Carbon sensitivity Climate sensitivity
Climate–carbon feedbacks
Carbon–climate response (CCR)
Figure 1
|
Schematic representation of the progression from CO
2
emissions
to climate change. We define ‘carbon sensitivity’ as the increase in
atmospheric CO
2
concentrations that results from CO
2
emissions, as
determined by the strength of natural carbon sinks. ‘Climate sensitivity’ is
shown here as a general characterization of the temperature response to
atmospheric CO
2
changes. Feedbacks between climate change and the
strength of carbon sinks are shown as the upper dotted arrow
(climate–carbon feedbacks). The CCR aggregates the climate and carbon
sensitivities (including climate–carbon feedbacks) into a single metric
representing the net temperature change per unit carbon emitted.
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In these simulations, the CCR is independent of both time and
CO
2
emission (or concentration) scenario. At a given CO
2
concen-
tration (see, for example, Fig. 2b), the time-independence of CCR
arises from a cancellation of a decreasing airborne fraction of cumu-
lative emissions, and an increasing temperature change per unit
atmospheric CO
2
over time. This may relate in part to the uptake
of heat and carbon by the ocean being driven by the same deep-ocean
mixing processes on long timescales
3,7
. However, as can be seen in
Fig. 2a and b, CCR is also independent of CO
2
concentration and, by
extension, of the CO
2
emission scenario. This scenario independence
emerges owing to the approximate cancellation of the saturation of
carbon sinks and the saturation of CO
2
radiative forcing with increas-
ing atmospheric CO
2
. As a result, at higher atmospheric concentra-
tions, a given CO
2
emission will lead to a larger increase in
atmospheric CO
2
, but the temperature change per unit change in
atmospheric CO
2
will be smaller
2
.
Even in the extreme case of instantaneous pulse emissions
8
, the
temperature change per unit carbon emitted in the UVic ESCM is
found to be constant to within 10% on timescales of between 20 and
1,000 years, and for cumulative emissions of up to 2 TtC (see
Supplementary Fig. 1). As is seen, however, in Fig. 2a, we expect
CCR to be more closely constrained in simulations in which cumu-
lative emissions vary smoothly. Nonetheless, if used as a metric for
model intercomparison, we recommend that CCR be defined under
standard conditions, such as at the time of CO
2
doubling in a tran-
sient simulation with 1% CO
2
increase per year. Defined in this way,
CCR generalizes previously proposed metrics (such as the temper-
ature response to a small pulse or constant sustained emission
6
—see
Supplementary Information for additional discussion) into a single
robust and versatile quantity which can be easily estimated from
current standard model experiments, and yet represents the climate
response to a wide range of CO
2
emissions scenarios.
In a given model, CCR is approximately constant with respect to
time and emissions scenario; however, we would expect the value of
CCR to vary among models owing to differences in both climate and
carbon sensitivities. Its time and scenario independence mean that
the CCR can be estimated from any model simulation with either
prescribed CO
2
emissions, or prescribed CO
2
concentrations and
prognostic model carbon sinks. Consequently, the simulations
performed as part of the Coupled Climate Carbon Cycle Model
Intercomparison Project (C4MIP
11
) provide a means of estimating
the range of CCR values among the current generation of coupled
climate–carbon models.
Figure 3 shows results from the 11 C4MIP models and the
ensemble mean, with global temperature change plotted as a function
of cumulative carbon emissions (Fig. 3a) and temperature change per
unit carbon emitted plotted as a function of time (Fig. 3b). Most
models (and the ensemble mean) show a nearly linear relationship
between temperature change and cumulative emissions (Fig. 3a),
suggesting that this may be a robust property of the coupled
climate–carbon system. Some models do deviate from linearity,
particularly early in the simulations, which is at least partly due to
the influence of decadal temperature variability. However, by the
middle of the twenty-first century, all models converge to an intrinsic
value of temperature change per unit carbon emitted, which remains
approximately stable for the remainder of the simulation (Fig. 3b).
CCR values calculated at the time of CO
2
doubling in each model
simulation are given in Supplementary Table 1. Model values of CCR
range from 1.0 to 2.1 uC per Tt C, with an ensemble mean value of
1.6 uC per Tt C (see Supplementary Information for additional dis-
cussion of model CCR values).
The CCR can also be estimated from historical carbon emissions
data and observed temperature changes. To calculate CCR from obser-
vations, we first estimated decadal-mean CO
2
-attributable warming
relative to 1900–09 by scaling an estimate of greenhouse-gas-
attributable warming
12
by the ratio of CO
2
to greenhouse-gas forcing.
We then calculated CCR by dividing CO
2
-attributable warming by
cumulative anthropogenic CO
2
emissions between 1900–09 and each
subsequent decade, including emissions from land-use change, fossil
fuels and cement production (see Methods).
Figure 4 shows an estimate of CCR for 1990–99 of 1.0–2.1uCper
Tt C (5 to 95% confidence interval), with a best estimate of 1.5 uCper
Tt C. Similar estimates of CCR, albeit with larger uncertainties, are
obtained for previous decades. We note that these estimates are less
contaminatedwith internal climate variability than those derived from
single simulations in Fig. 3 because the greenhouse-gas-attributable
warming is based on a scaled ensemble mean of 11 simulations.
Nonetheless, assuming the simulated temporal evolution of the green-
house gas response is realistic, these results provide further evidence
for the constancy of CCR as a function of time.
Recent climate–carbon model experiments have shown that elimi-
nating CO
2
emissions leads to approximately stable, or slowly
decreasing global temperatures over time
3,7,13
; this implies that close
to zero net anthropogenic carbon emissions are required to stabilize
global mean temperature
3
, and conversely that there may be neg-
ligible future warming commitment as a result of past CO
2
emis-
sions
3,7,13
. Consequently, the CCR, defined here as the ratio of
instantaneous temperature change to past CO
2
emissions, can also
Temperature change per unit carbon (ºC per Tt C)
Airborne fraction (Tt C per Tt C)
ΔT/ΔCA
ΔT/ΔCA
ΔCA/ET
CCR
ΔCA/ET
CCR
0 10203040506070
0 200 800 1,000
Model
y
ear
400 600
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
a
b
0
1
2
3
4
5
6
0
1
2
3
4
Figure 2
|
Idealized model simulations of the CCR. a, Simulation with a 1%
per year atmospheric CO
2
increase for 70 years, showing temperature change
per unit atmospheric carbon increase (DT/DC
A
: thin red line, right axis),
airborne fraction of cumulative carbon emissions (DC
A
/E
T
: thin blue line,
left axis) and CCR (thick red line, right axis). In this simulation, cumulative
airborne fraction decreased with time owing to a delayed carbon cycle
response to a rapid prescribed rate of atmospheric CO
2
increase. This is
consistent with saturating carbon sinks at higher atmospheric CO
2
, which
leads to an increased airborne fraction of annual emissions with increasing
atmospheric CO
2
.b, Simulations with an instantaneous doubling (solid
lines) and quadrupling (dashed lines) of atmospheric CO
2
for 1,000 years
(colours as in a). In all cases, the cumulative airborne fraction decreased with
time, whereas the temperature change per unit atmospheric carbon
increased with time; consequently, the CCR (defined as the product of these
two quantities) remained constant in time.
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be used as an estimate of the centennial-scale temperature legacy of
these emissions. As a result, our estimates of CCR can be inverted to
estimate the total allowable anthropogenic carbon emissions per
degree of long-term temperature change.
From our model-based estimate of CCR, we estimate allowable
emissions of 1.25 Tt C (range, 0.95–2 Tt C) for 2 uC warming relative
to pre-industrial temperature; our observationally based best estimate
of allowable emissions for 2 uC of warming is 1.4 Tt C (5–95% con-
fidence interval, 1.0 to 1.9 Tt C). Given total CO
2
emissions until now
of approximately 0.5Tt C from fossil fuels and land-use change
14,15
,
this implies that total future carbon emissions consistent with 2uCof
warming must be restricted to a best estimate of about 0.8Tt C
(0.7 Tt C based on the model ensemble mean; 0.9 Tt C based on obser-
vational constraints).
We emphasize, however, that the calculated uncertainty on this
number is quite large (0.4 to 1.5 Tt C). Furthermore, we are unable to
exclude the possibility of higher values of CCR (and consequently
lower values of allowable emissions), owing particularly to poorly
quantified uncertainties in historical land-use change emissions and
structural uncertainties in the simulated sulphate aerosol response.
For example, the allowable emissions for a particular warming
target calculated by ref. 5 were lower, because they used a higher
observational estimate of CO
2
-attributable warming as well as a
climate–carbon model which simulated non-negligible zero emis-
sions commitment under conditions of high climate sensitivity.
We note also that our analysis of allowable emissions applies specif-
ically to CO
2
-induced warming, and does not account for the effects
of other greenhouse gases or aerosols.
The CCR is a simple, yet robust representation of the global tem-
perature response to anthropogenic CO
2
emissions, and as such is
directly relevant to current policy negotiations surrounding inter-
national climate mitigation efforts. TheEuropean Union has proposed
restricting global warming to less than 2 uC above pre-industrial tem-
peratures
16
; however, large uncertainty in equilibrium climate sensi-
tivity
17
prevents confident estimates of the CO
2
stabilization level
required to avoid 2 uC warming, and climate sensitivity alone provides
no policy-useful information about the allowable CO
2
emissions for a
given stabilization level. The CCR represents a synthesis of previous
efforts to quantify the temperature response to anthropogenic CO
2
emissions by aggregating the uncertainties associated with climate
sensitivity, carbon sinks and climate–carbon feedbacks into a single
well-constrained metric of climate change that is related directly to
cumulative carbon emissions.
METHODS SUMMARY
For the idealized model experiments (1% per year CO
2
increase; doubled/quad-
rupled CO
2
) we used the UVic ESCM version 2.8 (refs 9, 18–20). The UVic
ESCM is a computationally efficient coupled climate–carbon model, with inter-
active representations of three-dimensional ocean circulation, atmospheric
energy and moisture balances, sea ice dynamics and thermodynamics, dynamic
vegetation and the global carbon cycle (including land and both inorganic and
organic ocean carbon). Version 2.7 of the UVic ESCM was one of the 11 par-
ticipating models in C4MIP
11
, in which models were driven by a common CO
2
emissions scenario and carbon sinks and atmospheric CO
2
concentrations were
calculated interactively until the year 2100. From the C4MIP simulations, we
estimated CCR using globally averaged temperature change and accumulated
carbon emissions at the year of CO
2
doubling in each simulation.
Our observational estimate of CCR was derived using estimates of CO
2
-attri-
butable warming and cumulative CO
2
emissions for each decade of the twentieth
century relative to 1900–09. We estimated CO
2
-attributable warming using an
estimate of greenhouse-gas-attributable warming
12
, scaled by the ratio of CO
2
to
1900 1920 1980 2000
Year
5th percentile
Best estimate
95th percentile
1940 1960
2
1
Carbon–climate response (ºC per Tt C)
3
0
Figure 4
|
Observational estimates of CCR. CCR was estimated for each
decade of the twentieth century after 1910 by scaling an observationally
constrained estimate of greenhouse-gas-attributable warming relative to
1900–09 by the ratio of CO
2
forcing to total greenhouse gas forcing, and
dividing by cumulative anthropogenic carbon emissions over the same
period. This observationally constrained estimate of CCR is both stable in
time and consistent with the estimates derived from model simulations.
Temperature change (ºC)
Cumulative carbon emissions (Tt C)
0 0.5 1.0 1.5 2.0
a
Model
y
ear
2050 2100
b
4
BERN-CC
CSM-1
CLIMBER2-LPJ
FRCGC
HADCM3LC
IPSL-CM2C
IPSL-CM4-LOOP
LLNL
MPI
UMD
UVIC-2.7
Mean
3
2
1
0
0
1
2
3
1900 1950 2000
Carbon–climate response (ºC per Tt C)
4
–1
Figure 3
|
CCR estimated from the C4MIP simulations
11
.a, Decadal-average
temperature change plotted as a function of cumulative carbon emissions,
showing a near-linear relationship for both individual models (coloured
lines) and the ensemble mean (black line). b, Temperature change per
cumulative carbon emitted for each decade from 1900 to 2100 relative to the
first decade of each model simulation. Over most of the twenty-first century
portion of the simulations, CCR values in each model are remarkably
constant in time.
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total greenhouse-gas forcing
21
, where greenhouse-gas forcing was first scaled by
an estimate of the mean efficacy of long-lived greenhouse gases
22
. We calculated
uncertainties in greenhouse-gas-attributable warming, accounting for internal
variability and inter-model uncertainty
12
, and assumed normally and Student-t
distributed uncertainties for radiative forcings and greenhouse-gas efficacy,
respectively
22
. We calculated cumulative carbon emissions from fossil fuels
and land-use change
13,14,23
, and assumed a one-sigma systematic uncertainty
on land-use emissions of 60.5 Pg C per year
24
. Our central estimates for CO
2
-
attributable warming and cumulative emissions at 1990–99 relative to 1900–09
were 0.492 uC and 0.338 Tt C, respectively. We calculated a probability density
function for CCR based on the probability distributions of the constituent terms,
which we used to estimate the mean and the 5th and 95th percentiles.
Full Methods and any associated references are available in the online version of
the paper at www.nature.com/nature.
Received 4 December 2008; accepted 14 April 2009.
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Supplementary Information is linked to the online version of the paper at
www.nature.com/nature.
Acknowledgements We thank A. Weaver, M. Eby, V. Arora, N. Ramankutty,
M. Allen, S. Solomon, K. Keller, K. Caldeira and S. Turner for commentary and
discussions on this work. We also thank P. Forster for providing radiative forcing
time series, and P. Friedlingstein and the C4MIP modelling community for the
availability of their model output. H.D.M. acknowledges support from the National
Science and Engineering Research Council of Canada, and the Canadian
Foundation for Climate and Atmospheric Sciences Project Grants. P.A.S. was
supported by the Joint DECC, Defra and MoD Integrated Climate Programme.
N.P.G. received support from the Leverhulme Trust. N.P.G. and P.A.S. acknowledge
support from the Climate Change Detection and Attribution Project, jointly funded
by NOAA’s Office of Global Programs and the US Department of Energy.
Author Contributions H.D.M. proposed the study, carried out model simulations
and analysis, and wrote most of the paper. N.P.G. proposed the inclusion of
observational constraints, N.P.G. and P.A.S. carried out this analysis, and N.P.G.
wrote the sections of the paper and methods describing these results. K.Z.
provided additional model simulations and analysis as described in the
Supplementary Information. All authors participated in discussions pertaining to
interpretation and presentation of results.
Author Information Reprints and permissions information is available at
www.nature.com/reprints. Correspondence and requests for materials should be
addressed to H.D.M. (dmatthew@alcor.concordia.ca).
LETTERS NATURE
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METHODS
UVic ESCM. The UVic ESCM is an intermediate-complexity coupled climate–
carbon model. The climate component consists of a reduced-complexity energy–
moisture balance atmosphere coupled to a general circulation ocean and
dynamic/thermodynamic sea-ice model
9
. The carbon cycle component of
version 2.8 consists of a biochemical dynamic vegetation model
18,19
and an
organic/inorganic ocean carbon cycle model
20
. Version 2.7 of the UVic ESCM
was one of the 11 participating models in the C4MIP
11
, as well as a contributing
model to the long-termclimate and carbon cycle projectionshighlighted in ref. 17.
C4MIP. The C4MIP compared the simulated climate and carbon cycle changes
from 11 coupled climate–carbon models (including seven atmosphere–ocean
general circulation models, and four intermediate-complexity models)
11
.
Models were driven by a common CO
2
emissions scenario (including specified
emissions from both fossil fuels and land-use change), with carbon sinks and
atmospheric CO
2
calculated interactively until the year 2100. To calculate the
CCR for each model, we used globally averaged temperature changes from the
coupled simulations, along with a running total of specified CO
2
emissions. The
values of CCR presented here and in the Supplementary Information were cal-
culated using a ten-year average of temperature increases and cumulative emis-
sions, centred at the time of CO
2
doubling in each simulation.
Observationally constrained CCR estimate. We calculated observational esti-
mates of CCR by taking the ratio of CO
2
-attributable warming and cumulative
emissions in the decade 1900–09 and each subsequent decade of the twentieth
century. We began with a multi-model estimate of greenhouse-gas-attributable
warming for each decade of the twentieth century. This was derived by scaling
the mean simulated temperature response to prescribed historical well-mixed
greenhouse-gas concentrations from HadCM3, GFDL and PCM to best-fit
HadCRUT2v temperature observations, based on a multiple regression together
with the response to sulphate aerosol and natural forcing
12
. The calculated un-
certainty in this greenhouse-gas-attributable warming includes an estimate of
internal variability based on control simulations and an estimate of model un-
certainty based on inter-model differences in forcings and simulated responses
12
.
We scaled the greenhouse-gas-attributable warming by the ratio of CO
2
forcing
to total well-mixed greenhouse gas forcing, with all forcings expressed as differ-
ences between 1900–09 and subsequent decades of the twentieth century
21
. Before
this scaling, we multiplied the well-mixed greenhouse-gas forcing by the mean
efficacy for long-lived greenhouse gases (shown in figure 2.19 of ref. 22) to
account for the larger temperature response per unit radiative forcing for other
greenhouse gases compared to CO
2
. Tropospheric ozone changes were not
specified in the simulations used by ref. 12, so we did not include them in our
estimate of total greenhouse gas forcing, under the assumption that the response
to troposphericozone is spatially and temporally dissimilarto that due to the well-
mixed greenhouse gases and is therefore unlikely to be aliased in the multiple
regression (the inclusion of tropospheric ozone forcing in the total greenhouse-
gas forcing estimate reduces our observational estimate of CCR to 0.9–1.8uC per
Tt C). Our calculation also assumes that climate forcings other than CO
2
emis-
sions have had little influence on atmospheric CO
2
concentration. This is a
reasonable assumption given a near-cancellationover the past century of positive
non-CO
2
greenhouse-gas forcing and negative aerosol forcing.
Uncertainties in greenhouse-gas-attributable warming were calculated follow-
ing ref.12; uncertainties in radiative forcings were estimated from ref. 22 (FAQ
2.1, Fig. 2) and were assumed to be normally distributed; uncertainties in effi-
cacies were estimated from figure 2.19 of ref. 22, and were assumed to be
Student-tdistributed. Land use, fossil fuel and cement emissions were taken
from CDIAC
14,15
. A one-sigma uncertainty on fossil fuel and cement emissions
of 65% was assumed following ref.23 and a one-sigma systematic uncertainty
on land-use emissions of 60.5 Pg C per year was assumed following ref. 24; both
were assumed to be normally distributed. A probability density function was
calculated for CCR based on the probability density functions of the constituent
terms, and this was used to derive the mean and the 5th and 95th percentiles. The
uncertainty in land-use emissions was the largest single contributor to the overall
uncertainty in CCR. Given this, we tested the sensitivity of our results to setting
land-use emissions to zero; this gave an estimate of CCR for the decade 1990–99
of 1.6–2.7 uC per Tt C, though we emphasize that this should not be taken as a
realistic upper bound for CCR, because zero land-use emissions are not consis-
tent with observed atmospheric CO
2
increases. Uncertainties in the overall
magnitude of aerosol forcing are fully accounted for in our estimate of green-
house-gas-attributable warming; however, uncertainties in the temporal or spa-
tial pattern of the response to aerosol forcing are only accounted for to the extent
that they are sampled in the three global climate models we used, and errors in
these patterns could lead to values of CCR outside our estimated uncertainty
range.
doi:10.1038/nature08047
Macmillan Publishers Limited. All rights reserved
©2009
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