Clim Dyn (2010) 35:1461–1475
DOI 10.1007/s00382-010-0798-y

Climate forcings and climate sensitivities diagnosed
from atmospheric global circulation models
Bruce T. Anderson • Jeff R. Knight •Mark A. Ringer • Clara Deser • Adam S. Phillips •Jin-Ho Yoon • Annalisa Cherchi

Received: 30 March 2009 / Accepted: 15 March 2010 / Published online: 31 March 2010
Ó Springer-Verlag 2010

Abstract Understanding the historical and future responseof the global climate system to anthropogenic emissions ofradiatively active atmospheric constituents has become atimely and compelling concern. At present, however, there
are uncertainties in: the total radiative forcing associatedwith changes in the chemical composition of the atmosphere; the effective forcing applied to the climate system
resulting from a (temporary) reduction via ocean-heatuptake; and the strength of the climate feedbacks that subsequently modify this forcing. Here a set of analyses derived
from atmospheric general circulation model simulations areused to estimate the effective and total radiative forcing of
the observed climate system due to anthropogenic emissions
over the last 50 years of the twentieth century. They are also
used to estimate the sensitivity of the observed climate
system to these emissions, as well as the expected change inglobal surface temperatures once the climate system returns
to radiative equilibrium. Results indicate that estimates ofthe effective radiative forcing and total radiative forcing
associated with historical anthropogenic emissions differ
across models. In addition estimates of the historical sensitivity of the climate to these emissions differ across models.
However, results suggest that the variations in climate sensitivity and total climate forcing are not independent, andthat the two vary inversely with respect to one another. As
such, expected equilibrium temperature changes, which are
given by the product of the total radiative forcing and theclimate sensitivity, are relatively constant between models,particularly in comparison to results in which the total
radiative forcing is assumed constant. Implications of theseresults for projected future climate forcings and subsequent
responses are also discussed.

B. T. Anderson (&)
Department of Geography and Environment,
Boston University, Boston, MA 02215, USAe-mail: brucea@bu.edu

1 Introduction

J. R. Knight  M. A. Ringer
Met Office Hadley Centre, Exeter EX1 3PB, UK
C. Deser  A. S. Phillips
National Center for Atmospheric Research,
Boulder, CO 80307, USA
J.-H. Yoon
Cooperative Institute for Climate and Satellites, Earth System
Science Interdisciplinary Center, University of Maryland,College Park, MD 20742, USA
A. Cherchi
Centro Euro-Mediterraneo per i Cambiamenti Climatici,
and Istituto Nazionale di Geofisica e Vulcanologia,
Bologna, Italy

While the complexity of the fully coupled Earth system
introduces numerous sources of uncertainty in its response
to historical and future global climate-change influences,
three stand out with respect to anthropogenically inducedchanges in global-mean surface temperatures: (1) theradiative forcing associated with changing concentrationsof atmospheric chemical constituents; (2) the rate of ocean
heat uptake and associated lag in the response of the climate system to this radiative forcing; and (3) the responseof the climate system itself to this radiative forcing, vis a
vis feedbacks within various Earth subsystems (e.g. Stottand Kettleborough 2002). Here we briefly describe each.
Recent analyses of coupled-climate model simulations
suggest that the climate forcing associated with increased
anthropogenic emissions of greenhouse gases and aerosols

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1462

may differ between models (Collins et al. 2006). Much ofthis uncertainty is related to the influence that historicaland future aerosol concentrations have upon the global
climate system (Schwartz 2004), which arises fromuncertainties in their impact on the reflection (Penner et al.
1994; Boucher et al. 1998) and absorption (Ramanathan
and Carmichael 2008) of incoming solar radiation, as wellas the indirect effects of aerosols upon cloud characteristics(Knutti et al. 2002; Quaas et al. 2006; Lohmann et al.
2007). More recently, however, it has been suggested that
there also exist uncertainties in the direct forcing of theclimate system associated with increasing concentrationsof CO2 and other greenhouse gases, even for the sameprescribed changes in radiatively active emissions/concentrations (Forster and Taylor 2006; Collins et al. 2006;
IPCC 2007).
In addition, how this radiative forcing is partitioned
between an effective radiative heating term which produces
concurrent changes in the climate system, and ocean-heatuptake which results in a time-lag within the climate system to changes in the chemical composition of the atmosphere,
depends
upon
ocean
dynamics
andthermodynamics (for instance related to the mixed-layer
depth, diffusion rates, and mixing to the deeper ocean:
Sokolov et al. 2003). While uncertainties in estimates ofthe observed ocean heat content over the course of the lastcentury contribute to uncertainty in the effective heat
capacity of the global Earth system and hence its responsetime to any applied forcing (Forest et al. 2002; Schwartz
2007; Knutti et al. 2008), research also suggests that these
uncertainties tend to be small compared with uncertainties
in the applied forcing over this time and in the climate
response to this forcing (Wigley et al. 2005; Collins et al.
2007; Knutti and Tomassini 2008; Dufresne and Bony2008).
Finally, it is well known that the climate response tochanges in radiatively active atmospheric constituents—
typically measured by the change in globally averaged
surface temperatures and usually referred to as the climate
sensitivity—is highly variable across model systems (IPCC
2007; Roe and Baker 2007). It is difficult to deduce theseestimates from either short-term (Frame et al. 2005; Annan
and Hargreaves 2006) or long-term (Hegerl 2006; Edwards
et al. 2007) observational products. In addition, intermediate-complexity (Knutti et al. 2002) and fully coupled(Murphy et al. 2004; Soden and Held 2006; Sanderson
et al., 2008) numerical model simulations also give wide
ranges of uncertainty in how the global climate system may
respond to a given forcing factor.
As discussed, much of the previous research into these
uncertainties, particularly with regard to the sensitivity of
the global climate system to imposed radiative forcing, hasbeen based on the analysis of available observations

123

B. T. Anderson et al.: Climate forcings and climate sensitivities(e.g. Annan and Hargreaves 2006) or projections from fully
coupled numerical model simulations (e.g. Murphy et al.
2004). Alternatively, atmosphere-only general circulation
models (AGCM) can also be used to estimate the sensitivity of the climate system by prescribing the climatechange via the sea-surface temperatures (SSTs) and thenusing the top-of-atmosphere (TOA) radiative fluxes todeduce the necessary forcing needed to balance theimposed climate change (e.g. Cess et al. 1990; Ringer et al.
2006). This method has the advantage that it tests thesensitivity of the atmospheric and land-surface componentsof the climate system while ignoring (both numerically andphysically) the details of the ocean system. In particular,
these AGCMs overcome the problems associated with
underestimation of natural (or internal) coupled ocean/
atmosphere variability because the sea-surface temperature
evolution is specified from observations (Folland et al.
1998; Sexton et al. 2001). One disadvantage however isthat they assume an equilibrium between the forcing of theclimate system and the radiative response (see Cess et al.
1990, Eq. 1). In this sense, this method does not accountfor the time-lag arising from a radiative imbalance within
the Earth’s climate system associated with increased ocean
heat content (Levitus et al. 2005; Hansen et al. 2005; Wonget al. 2006).
Here, we will use the Cess et al. (1990) methodology toestimate the historical climate sensitivity of the observed
system to the effective radiative forcing over the last
50 years of the twentieth century. At the same time, wewill utilize a modified version of the methodology thatallows the atmospheric general circulation models toaccount for historical ocean heat uptake over the same time
period and hence provide estimates of the historical evolution of the full radiative forcing fields as well. We willthen compare the model estimates of climate sensitivity
with estimates of full radiative forcing and show that thetwo are not independent, in agreement with previous
findings (Web et al. 2006; Kiehl 2007; Knutti 2008). This
result has important implications for the range of projections of climate variability associated with future anthropogenic emissions of greenhouse gases and aerosols.

2 DataFor this study, we will use output from AGCM simulations
produced from the Community Atmosphere Model(CAM3.0—Collins et al. 2006); the Hadley Centre
atmospheric model (HadAM3—Pope et al. 2000); theatmospheric component of the Coupled-Atmosphere–
Biosphere–Ocean model (CABO—Zeng et al. 2004); andthe Euro-Mediterranean Centre for Climate Change model(CMCC), which is based upon the ECHAM4 AGCM

B. T. Anderson et al.: Climate forcings and climate sensitivities

1463(Roeckner et al. 1996). For the CAM3, CABO and CMCC
models, two scenarios are considered. In the first, multiple
simulations (5, 6, and 5, respectively) of the AGCM areforced only by historical changes in global SSTs (termed
the AMIP simulation). In the second scenario, multiple
simulations (again, 5, 6, and 5, respectively) are forced byhistorical changes in global SSTs, along with Greenhousegas (GHG) concentrations, sulfate aerosols, volcanic
particulates (CAM3 and CABO only), stratospheric andtropospheric ozone, and solar activity (termed the AMIPATM simulation). For the HadAM3 model, two scenarios
are considered as well. In the first, five simulations of the
AGCM are forced by historical changes in global SSTs as
well as volcanic particulates and solar activity. These runs
will be referred to as AMIP simulations with the understanding that they also include certain natural radiative
forcings. In the second, five simulations are forced byhistorical changes in global SSTs, volcanic particulates,and solar activity, as well as GHG concentrations, sulfate
aerosols, and stratospheric and tropospheric ozone (again,
termed the AMIP-ATM simulation). For all the experiments we examine the period from 1950 to 1999. Table 1
provides a summary description of the atmosphere-onlymodel simulations used in the study.
To characterize changes in the overall planetary energybalance, this study will principally analyze top of atmosphere (TOA) outgoing longwave radiation (OLR) and net
solar radiation (incoming minus outgoing). In addition wewill analyze the simulated global near-surface temperaturefields from the four models and two experimental set-ups.
For comparison, observational estimates of global nearsurface temperatures are taken from the Hadley Centre’s
Climate Research Unit (CRU) gridded combined land/marine data product (Jones et al. 1999; Brohan et al. 2006).
All values presented here represent ensemble-mean, globally averaged estimates with a 12-month running-meantime-filter applied.

3 Methods
Previously, Cess et al. (1990) deduced the radiative forcing, DQtot, needed to produce a given climate change by
imposing changes in SSTs within an AGCM and thenexamining the resulting change in TOA net radiative
fluxes, DRTOA
AMIP . In these simulations, the model is provided
with no information about the forcing of the climate system, only the observed response of the climate to that
forcing (as determined by the change in SST fields). Thechange in TOA net radiative fluxes then provides an estimate of the radiative forcing needed to produce the(imposed) climate change, DQtot , such that DQtot ¼
DRTOA
AMIP (e.g. Cess et al. 1990; Ringer et al. 2006).
However, their study assumes that the ocean state is inequilibrium with the radiative forcing itself. As evidenced
from recent analyses of observations (Levitus et al. 2005),
coupled-climate model simulations (Hansen et al. 2005),
and remotely sensed data (Wong et al. 2006), there has

Table 1 Name and characteristics of model simulations used in this analysis
Name

Resolution

Forcing

Duration# in ensemble

CAM3.0 AMIP
CABO AMIP

T85 (about 1.4°)
Latitude–Longitude: 5.625° 9 3.75°

SSTs

1950–2000

56CMCC AMIP

T42 (about 2.8°)

CAM3.0 AMIP-ATM

T85 (about 1.4°)

SSTs

CABO AMIP-ATM

Latitude–Longitude: 5.625° 9 3.75°

GHGs

6

CMCC AMIP-ATM

T42 (about 2.8°)

Sulfate aerosols

55
1950–2000

5

Volcanic particulates (CAM3.0, CABO)
Ozone
Solar activity
HadAM3 AMIP

Latitude–Longitude: 3.75° 9 2.5°

SSTs

1950–2000

5

1950–2000

5

Volcanic particulates
Solar activity
HadAM3 AMIP-ATM

Latitude–Longitude: 3.75° 9 2.5°

SSTs
GHGs
Sulfate aerosols
Volcanic particulates
Ozone
Solar activity

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B. T. Anderson et al.: Climate forcings and climate sensitivities

been an increase in the heat content of the ocean arisingfrom a radiative imbalance within the Earth’s climate
system. These results suggest that the full anthropogenic
radiative forcing applied over the last 50? years, DQtot, isbeing partitioned between an effective radiative heating
term, DQeff, and ocean-heat uptake, DQocn (Sokolov et al.
2003):
DQtot ¼ DQeff þ DQocn :ð1Þ

In this case, the historical changes in SSTs are assumed
to be responding to the effective radiative forcing, DQeff,
not the full radiative forcing. Hence, we modify the Cesset al. (1990) methodology by replacing DQtot with DQeff.
The relation between DRTOA
AMIP and DQeff then becomes:
DQeff ¼ DRTOA
AMIP :

ð2Þ

In comparison, when an AGCM is run with explicit
changes in both SSTs and atmospheric chemical
constituents, the model is provided with information
about both the forcing of the climate system (asdetermined by the historical evolution of radiatively
active chemical constituents) as well as the observed
response of the climate to that forcing (as determined by
the historical evolution of the SST fields). Hence, thechange in TOA radiation (DRTOA
AMIPATM ) represents the sumof the explicitly imposed radiative forcing (DQtot) and theimposed SST forcing (given by [-DQeff]). As discussed in
Hansen et al. (2002) (and as is evident from Eqs. 1, 2), thissum represents the ocean-heat uptake of the full radiative
forcing:
DRTOA
AMIPATM ¼ DQtot þ ðDQeff Þ ¼ DQtot  DQeff¼ DQocn :ð3Þ

From this equation, we also see that DRTOA
AMIPATM
represents the difference between the explicitly imposedradiative forcing associated with changing chemical
constituents (DQtot) and the effective radiative forcing
needed to produce the historical evolution of SSTs (DQeff).
Hence, an estimate of the total forcing of the climate
system can be derived by taking the difference between the
TOA net radiative-flux terms from the two AGCM
simulations:
TOA
DRTOA
AMIPATM  DRAMIP ¼ DQocn  ðDQeff Þ ¼ DQtot

ð4Þ
Another way to arrive at this equation is to consider thedifference of the two simulations as a modification of thearchetypical ‘‘cloud radiative forcing’’ methodology (Cesset al. 1990). In that setting, the net incoming TOA radiation
for cloudy conditions is compared with that from clear
conditions; the imbalance gives the radiative forcing
imparted by the clouds. In the case presented here, the123

AMIP simulation can be considered the ‘‘clear’’ conditions
in which no changes in radiatively active chemical
constituents are introduced; analogously, the AMIP-ATM
simulation can be considered the ‘‘cloudy’’ conditions inwhich a radiatively active profile is introduced. The
difference between AMIP-ATM net incoming TOA
radiation and the AMIP net incoming TOA radiation thengives the radiative forcing associated with changes in theradiatively active chemical composition of the atmosphere,
TOA
i.e. DQtot ¼ DRTOA
AMIPATM  DRAMIP .
These relationships are confirmed by taking the differTOA
ence between DRTOA
AMIPATM and DRAMIP , and comparing itwith globally averaged TOA net radiative fluxes from amodel that is forced only by historical changes in GHG
concentrations, sulfate aerosols, volcanic particulates,
stratospheric and tropospheric ozone, and solar activity,
while keeping the sea-surface temperatures at their climatological values (termed the ATM simulation). These
globally averaged TOA net radiative fluxes, DRTOA
ATM , provide a direct estimate of the explicitly imposed radiative
forcing, DQtot, associated with changing chemical constituents (Hansen et al. 2002; Shine et al. 2003; Gregory andWebb 2008). Figure 1 shows that the direct estimates of
DQtot ¼ DRTOA
ATM from the CAM3.0 model match the indirect estimates derived by taking the difference between
TOA
DRTOA
AMIPATM and DRAMIP values.
When estimated in this manner, the total radiative
forcing accounts for the adjustment of the stratosphere andtroposphere and is sometimes referred to as ‘‘fixed sea
surface temperature forcing’’ (Hansen et al. 2002). It
should be noted, however, that this experiment differs fromthat of Shine et al. (2003), in which both the SSTs andland-surface temperatures (LST) are prescribed. In thoseexperiments it was found that the magnitude of radiative
forcing estimated from the ATM-type GCM experiments is
too high if only SSTs are prescribed. However, Shine et al.
(2003) found that this excess forcing was most pronounced
for processes affecting the shortwave component of the
Earth’s radiation budget (either due to solar or aerosol
effects); the estimates for forcing associated with increasing GHGs were identical. In addition, Fig. 1b suggests thatthe total radiative forcing estimated directly from the ATM
simulations (in which the excess forcing is present) is
nearly identical to that estimated from the AMIP and
AMIP-ATM simulations (in which the excess forcing
cancels itself), suggesting that any net excess forcing
associated with solar (positive) and aerosol (negative)
effects may in fact be small for these historicalsimulations.
Based upon these results, and the above theoreticalconsiderations, we will now use AGCM-only simulations—incorporating SST-only and SST and radiatively
active atmospheric forcing—to estimate the historicalB. T. Anderson et al.: Climate forcings and climate sensitivities

1465

Fig. 1 a Change in globally
averaged net incoming top of
atmosphere (TOA) radiation(W m-2) from the ensemble
mean CAM3.0 AMIP (blue),
AMIP-ATM (red), and ATM(black) simulations. Time-series
are smoothed using a 12-monthbox-filter and plotted such thatthe 5-year period at the
beginning of the time-series iscentered on 0. b Change inhistorical radiative forcing,
DRtot, as derived from thedifference between the globally
averaged net incoming TOA
radiation from the CAM3.0
AMIP-ATM and AMIP
simulations (blue), and from theCAM3.0 ATM simulations(black)effective radiative forcing, total radiative forcing, and climate sensitivities for various atmospheric modelingsystems.

4 AGCM results
Figure 2 shows the global-average surface temperatures
taken from the CRU observational product, along with the
AGCMs. Global temperature changes in both the AMIP
and AMIP-ATM simulations approximate the observed
global temperature changes, which is to be expected since
the SST evolution is prescribed in these simulations(Compo and Sardeshmukh 2009). At the same time it isimportant to note that the atmosphere-only models are
not explicitly ‘‘tuned’’ to match the observed surface
temperature changes (although they may be implicitly
tuned to reproduce observed climatological patterns oftemperature and precipitation, for instance), which are
instead to first order dictated by the historical changes in
SSTs. Our interest here is in diagnosing the models’
responses to these changing SSTs (and atmosphericchemical constituents).
Figure 3 shows the globally averaged net incoming
TOA radiation from the ensemble-mean AMIP and AMIPATM simulations. The largest variations are associatedwith the volcanic eruptions of Agung (1963), El Chichon(1982), and Pinatubo (1991—Robock 2000). However,results also indicate that all four AMIP simulations, which

do not contain explicit anthropogenic changes in thechemical composition of the atmosphere, produce a net lossof radiative energy through the top of the atmosphereassociated with global-scale increases in SSTs (Cess et al.
1990; Trenberth et al. 2002). In contrast, for the AMIPATM simulations there is a long-term increase in the net
incoming TOA radiation, indicating a net retention ofenergy within the earth system despite the increase in SST
fields (Kiehl 1983; Goody et al. 1996; Mitchell et al. 1987;
Harries et al. 2001; Brindley and Allan 2003). As mentioned above, the differences in the net TOA radiative flux
fields from the two simulations gives the total radiative
forcing, DQtot (Fig. 3b). This figure indicates that the fourmodels contain variable estimates of the radiative forcing
associated with the historical evolution of radiatively active
chemical constituents. Part of this variability is due to the
exclusion of certain chemical constituents (volcanic particulates) from the CAM3 and CABO AMIP simulations,which is manifested as significant decreases in the net
radiation difference curves in the early 1960s, 1980s, and1990s (again, associated with the eruptions of Agung, El
Chichon, and Pinatubo, respectively). However, there arealso inter-model variations in the long-term trends in theradiative forcing, which we investigate in more detailbelow.
To better analyze the changes in each model, Fig. 4
shows the overall trends in various surface and TOA fields,
derived by taking the difference between the 5-year meanvalues at the beginning and end of each integration; we

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Fig. 2 Change in globally averaged surface temperatures (K) for the
CAM3, HAD3, CABO and CMCC simulations (thin, colored lines)
and the CRU observations (thick, black line). Solid (dashed) lines
indicate surface temperatures derived from the AMIP (AMIP-ATM)

B. T. Anderson et al.: Climate forcings and climate sensitivities

simulations. Time-series are smoothed using a 12-month box filter
and plotted such that the 5-year period at the beginning of the timeseries is centered on 0

Fig. 3 a Change in globally
averaged net incoming top of
atmosphere (TOA) radiation(W m-2) for the CAM3, HAD3,
CABO and CMCC derived from
AMIP (solid) and AMIP-ATM(dashed) simulations. Timeseries are smoothed using a
12-month box filter and plottedsuch that the 5-year period atthe beginning of the time-series
is centered on 0. b Difference
between the globally averaged
net incoming TOA radiationfrom AMIP-ATM and AMIP
simulations for the CAM3,
HAD3, CABO and CMCC

performed the analysis in this manner to avoid end-effects(associated with Pinatubo-related volcanic signatures near
the end of the CAM3 and CABO simulations) that arosewhen applying simple linear trends across the entire timeseries. Figure 4a shows the historical trends in global surface temperatures, both from the AMIP and AMIP-ATM
simulations. The slightly larger global surface temperaturechanges found in the AMIP-ATM simulations comparedwith the AMIP simulations (except for CMCC) are related
to climate changes that are forced directly by the inclusionof anthropogenic chemical constituents, separate fromthose that arise indirectly from the anthropogenic chemical
constituents’ impact upon SST and sea-ice changes

123(Folland et al. 1998; Sexton et al. 2001). The ATM-AMIP
global surface temperature trends generally have similarvalues across the models with an average of 0.41 K; for the
AMIP simulations the global surface temperature trends
average 0.35 K. The observed temperature change for thisperiod, taken from the CRU data, is 0.43 K.
Examining the trends in TOA radiation fields from theAMIP runs next (Fig. 4b), we find that the effective radiative forcing, DQeff ¼ DRTOA
AMIP , needed to produce theobserved historical climate change over the last 50 years of
the twentieth century differs in each model. These differences arise both because of differences in the longwave
response, as well as the shortwave response (Cess et al.

B. T. Anderson et al.: Climate forcings and climate sensitivities

1467

Fig. 4 a Trends in globally
averaged surface temperatures(K) from the AMIP (blue) and
AMIP-ATM (red) simulations
from CAM3, HAD3, CABO and
CMCC. b Trends in globally
averaged incoming top of theatmosphere radiation (longwave
in blue, shortwave in red, andnet in green; W m-2) from theAMIP simulations for CAM3,
HAD3, CABO and CMCC.
Positive values indicate
increases in downward
radiation. c Same as b except
for AMIP-ATM simulations.
d Same as b except fordifference between AMIP-ATM
and ATM simulations

1990; Ringer et al. 2006), and differ by a factor of two(from 0.6 to 1.16 W m-2). If we examine the trends in
TOA radiation fields from the AMIP-ATM runs (Fig. 4c),
we find that there are still inter-model differences in boththe longwave and shortwave trends. However, as with thesurface temperature estimates, the net trends are fairly
similar in all four models (0.38–0.50 W m-2). As before,
the changes in TOA radiation (DRTOA
AMIPATM ) from thesemodels give an estimate of the associated energy fluxes
from the atmosphere to the underlying surface (predominantly the ocean surface, and to a lesser extent the land
surface: Levitus et al. 2005) over the course of the simulation, represented by DQocn .
As suggested above, if we take the difference between
the TOA radiation from the AMIP-ATM DRTOA
AMIPATMsimulations, we arrive at an
and the AMIP DRTOA
AMIP
estimate of the total radiative forcing associated withchanging anthropogenic chemical constituents (DQtot—
Fig. 4d). As suggested by the time-evolution of theseestimates in Fig. 2b, the overall trend of the total historicalradiative forcing over the 50-year period differs in eachmodel, and ranges from 1.00 to 1.67 W m-2 or a factor of
two-thirds. In addition, the longwave and shortwave components of this forcing also differ (ranging from 0.98 to
1.93 and -0.42 to 0.09 W m-2 respectively). These results
agree with those of Forster and Taylor (2006), whichindicate that a factor of two difference can be found in the

longwave forcing of coupled-climate models, even given
the same future changes in GHG concentrations.
From these results we find that both the effective radiative forcing and total radiative forcing within each model
seem to differ (see Fig. 4b, d). Plotting the two against one
another (Fig. 5a), we find that there is a nearly uniform
offset between the effective radiative forcing and total
radiative forcing within each model. Fitting these data
points with a linear trend, DQtot = aDQeff ? b, we findthat a = 1.02 and b = 0.42 W m-2. The offset value, b, isnearly equivalent to the mean estimated ocean-heat uptake
found in Fig. 4c (DQocn = 0.44 W m-2), as expected.
Given estimates of the change in effective radiative
forcing from the AMIP simulations and the associatedglobal temperature change, we can derive an estimate of
the sensitivity, k, for each of the AGCMs, defined here ask = DTeff/DQeff (Cess et al. 1990), where DTeff is theeffective (i.e. realized) global temperature change overthe course of the simulation period. If we then plot themodel sensitivities against the total radiative forcing
estimates, we find an inverse relation between the two(Fig. 5b). This result suggests that a given atmosphericmodel’s radiative response to imposed radiatively active
chemical constituents (i.e. the total radiative forcing) isinversely related to the model’s internal climate sensitivity. A similar inverse relation between climate-sensitivity and radiative forcing has been found in historical

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B. T. Anderson et al.: Climate forcings and climate sensitivities

Fig. 5 a Effective radiative forcing (DQeff—W m-2) derived fromtrends in globally averaged incoming top of the atmosphere (TOA)
radiation from the AMIP simulations, plotted against the total
radiative forcing (DQtot—W m-2) derived from the difference
between trends in the AMIP-ATM and AMIP globally averaged
incoming TOA radiation for the CAM3, HAD3, CABO and CMCC.
Also shown are the one-to-one line (black) and a linear trend fitted tothe individual model data (red). b Sensitivity of the AGCM, plottedagainst DQtot for the CAM3, HAD3, CABO and CMCC. Sensitivity
calculated as the trend in globally averaged surface temperatures fromthe AMIP-ATM simulations, divided by DQeff. Also shown is theinterpolated sensitivity derived from the linearly fitted total radiative
forcing in a (red line)

coupled-climate model simulations of the twentieth century climate system (Kiehl 2007), which is attributed tothe differences in aerosol forcings (i.e. changes inincoming absorbed shortwave radiation) imposed in different models. However, from the AGCM results it
appears that there are also significant differences in the
longwave radiative forcing component (see Fig. 4d);
generally, the inter-model differences in total radiative
forcing presented here are better correlated with the
longwave radiative forcing component (r = 0.80) thanthey are with the shortwave radiative forcing component(r = -0.03). We discuss the contributions of each component to the total radiative forcing further in Sect. 5.
Before going on, it is important to note that the apparent
inverse relation between total radiative forcing and climate
sensitivity within these AGCMs is not a consequence of themodels using the same prescribed temperature evolution(via historical SSTs). Indeed, when the model comparison
was first performed, it was expected that each of the AGCMs would have very similar estimates of total radiative
forcing, which would be partitioned differently into
effective heating (as determined from the AMIP simulations) and ocean-heat uptake (as determined from theAMIP-ATM simulations) by each model. Alternatively,
each model could have provided independent estimates ofeffective radiative heating, ocean-heat uptake, and total
radiative forcing, based upon the numerical specifics ofeach model itself. Instead, we find that the various estimates from each model are not independent and that in fact
there are significant inter-model differences in total radiative forcing, which vary inversely with respect to theirdifferences in climate sensitivity.

Based upon these results, we can find the equilibrium
temperature change—the temperature change expected forthe present total radiative forcing once the system comesback into equilibrium—by taking the product of the sensitivity and the total radiative forcing from a given model(Fig. 6a). Because the total radiative forcing and sensitivity
are inversely related to one another, the equilibrium temperatures across the models show a smaller range thanwould be expected if a fixed total radiative forcing waspresumed (here set to the average total radiative forcing
from the four models, *1.35 W m-2). Based upon thelinear relation found earlier, we can derive the hypothetical
relation between the equilibrium temperature and themodel sensitivity:

123

DTeq ¼ aDTeff þ bk

ð5Þ

where a, b are the same as above. Since a = 1.02 andb = 0.42 W m-2 \ 1, we find that when accounting forthe relation between the radiative forcing and climate
sensitivity of a given model, the range of equilibrium
temperatures is significantly less than if a fixed radiative
forcing is assumed. This result is also shown in Fig. 6b, inwhich the estimated equilibrium temperature response
from the models, based upon the model-specific total
radiative forcing and climate sensitivity, is compared withthe estimated equilibrium temperature response based only
upon the model’s climate sensitivity and a fixed total
radiative forcing equal to the average total radiative forcing
from the four models.
If we next assume that the longwave component ofradiative forcing scales (approximately) linearly withchanges in greenhouse gas concentrations, as represented

B. T. Anderson et al.: Climate forcings and climate sensitivities

1469

Fig. 6 a Sensitivity of the AGCM, plotted against the equilibrium
temperature response of the AGCM (DTeq—K) for the CAM3, HAD3,
CABO and CMCC. Equilibrium temperature response calculated as
the product of the sensitivity and the total radiative forcing (DQtot) of
the AGCM. Also shown is the equilibrium temperature response
assuming a fixed total radiative forcing equal to the mean of the fourmodels (black line) and the interpolated equilibrium temperature
response derived from the linearly fitted total radiative forcing in
Fig. 5a (red line). b DTeq calculated as the product of the sensitivity
and the globally averaged total radiative forcing of the AGCM (Simu)
and as the product of the sensitivity and a fixed total radiative forcing
equal to the mean of the four models [Fix Q(tot)]

Fig. 7 a Total (red line) and effective (blue line) radiative forcing(W m-2) associated with a doubling of pre-industrial CO2 concentrations, as derived from the linearly fitted total radiative forcing in
Fig. 5a, scaled by the ratio of the future to historical changes in CO2
concentrations, relative to fixed total radiative forcing of 4 W m-2(black line). b Sensitivity of the AGCM, plotted against theequilibrium temperature response (DTeq—K) for a doubling of preindustrial CO2 concentrations. Equilibrium temperature response
calculated as the product of the sensitivity and the linearly fitted(fixed) total radiative forcing shown in red (black)by changes in CO2, we can estimate the relation between
climate sensitivity and the total radiative forcing in
response to a doubling of pre-industrial CO2 concentrations. This relation is shown in Fig. 7a. Here, the linearlyfitted total radiative forcing curve (seen in Fig. 5b) is
scaled by the ratio of the changing concentrations associated with a doubling of CO2 (e.g. an increase of 280 ppm)
to the historical changes during the period of investigation(which is approximately 58 ppm over the time-period
1950–2000). If we then assume that the same linear relationship holds between effective radiative forcing and total
radiative forcing, we can estimate the effective radiative
forcing as well. Note that depending upon the model sensitivity, the total radiative forcing associated with a doubling of pre-industrial CO2 concentrations can be muchgreater (or less) than the commonly assumed value of
4 W m-2.
We subsequently estimate the equilibrium temperaturechange associated with a doubling of pre-industrial CO2
concentrations, DTeq(2xCO2), by taking the product of k
and DQtot(2xCO2) from above (Fig. 7b). We find that
because of the inverse relation between climate sensitivity
and total (and effective) radiative forcing, the overall rangeof estimated temperature changes is reduced comparedwith those found by assuming a fixed radiative forcing(equal to 4 W m-2) for all climate sensitivities. In theexample here, the range, when accounting for the dependency of the total radiative forcing to the climate sensitivity, is 2.5–3 K, compared with a range of 1.25–4 K
when using fixed estimates of total radiative forcing.

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5 Coupled climate model results
In the previous section we discussed how AGCM-only
simulations, incorporating SST-only and SST and radiatively active atmospheric forcing, can be used to estimate
the historical effective radiative forcing, total radiative
forcing, and climate sensitivities for various models. Oneof the more intriguing results is that the total (and effective) radiative forcing applied to the climate differs fromone model to another, in agreement with independent
coupled-climate model results (Forster and Taylor 2006;
Collins et al. 2006; IPCC 2007). In addition, our results
suggest that the strength of this total radiative forcing is afunction of the internal climate sensitivity of the model
itself, such that more sensitive climate models also impose
less total radiative forcing.
To see whether this result is more generally applicablewithin coupled-climate model simulations (as suggested by
Web et al. 2006; Kiehl 2007; Knutti 2008), we use theresults from Forster and Taylor (2006), which compute thetotal radiative forcing and climate sensitivity (asFig. 8 Total radiative forcing (W m-2) associated with a 1%/year
increase in CO2 concentrations for 20 coupled-climate models plottedagainst their respective climate sensitivities (black circles) from
Forster and Taylor (2006) Table 3, along with the associatedequilibrium temperature response (K) estimated from the product of
the total radiative forcing and climate sensitivity. Also shown is theradiative-forcing/climate-sensitivity curve (solid line) that passes
through each coupled-climate model data point, assuming an inverse

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B. T. Anderson et al.: Climate forcings and climate sensitivities

represented by the inverse of the climate feedback term, Y)
for 20 coupled-climate models forced solely by 1%/year
increases in CO2 concentrations. Plotting the total radiative
forcing against the model climate sensitivities (Fig. 8), we
find that not all models have the same inverse relationship,
as seen in the AGCM results. However, by plotting theassumed inverse relation that passes through each individual model estimate, we can see that two groups ofmodels appear to have very similar radiative-forcing/climate-sensitivity relationships. If we also plot the equilibrium temperature response for each model, calculated as
the product of the total radiative forcing and the climate
sensitivity, we find that the models that have similar
inverse relationships also have similar equilibrium temperature responses (to be expected since the individual
curves are representative of all climate-forcing/climatesensitivity combinations that give the same equilibrium
temperature response as the individual model value
through which the curve passes). The partitioning between
models with low, high, and outlying equilibrium temperature responses is confirmed by performing a K-means

relation that maintains the same equilibrium temperature response.
Two subsets of models are grouped together (green and red) based
upon the similarity in their radiative-forcing/climate-sensitivity
curves; outlier curves are shown in light/dark blue. Designations
determined using a K-means clustering algorithm with four designated clusters, applied to the equilibrium temperature response fromthe 20 models—see text

B. T. Anderson et al.: Climate forcings and climate sensitivities

clustering (Gong and Richman, 1995) applied to theequilibrium temperature response from the 20 separate
models. In addition, the selection of four clusters is confirmed by calculating the marginal improvement in unexplained variance between Cluster n and Cluster n ? 1,
which reaches a local minimum (and near-zero values) forn C 4, indicating that the inclusion of additional clusters
provides little additional reduction in unexplained variance(not shown).
Figure 9 shows the individual model estimates of theequilibrium temperature response, plotted against themodel’s sensitivity. In addition, the plot shows the expected equilibrium temperature response if the total radiative
forcing were the same in all models (and set equal to themean of the 20 models, *6.2 W m-2). Those models thathave very similar radiative-forcing/climate-sensitivity
relationships show small variations in their estimatedequilibrium temperature responses. At the same time, thepresence of outlier models does suggest that the radiativeforcing/climate-sensitivity relationship is not robust acrossall models, raising the possibility of much greater (orsmaller) equilibrium temperature responses to increasing
concentrations of CO2 (which we discuss further below).
As mentioned, a similar inverse relation between climate sensitivity and historical radiative forcing has beenfound in coupled climate-model runs (Kiehl 2007). Previously, this inverse relation was attributed mainly to intermodel differences in the radiative forcing associated with

1471

historical increases in aerosols. Projections of future climate change incorporating this climate-sensitivity/climateforcing relation found that, unlike the results presented
here, the inverse relation did not reduce uncertainties infuture global temperature responses (Knutti 2008), mainly
because the future longwave component to total radiative
forcing (associated with future projections of greenhousegas concentrations)—which was fixed across the model
runs—overwhelms any future forcing associated withchanging aerosol concentrations. However, from resultspresented above and in Forster and Taylor (2006), IPCC
(2007), and Gregory and Webb (2008) it is emphasized that
there are inter-model differences in the radiative forcing
associated with increasing CO2 concentrations as well, andthat these differences in radiative forcing may also have an
inverse relation to a given model’s climate sensitivity.
To further analyze why these inter-model differences intotal radiative forcing arise, we plot the total radiative
forcing estimates taken from Forster and Taylor (2006)
against the longwave and shortwave radiative forcing
estimates from the same study (Fig. 10). As before themodels are segregated into those that have a low equilibrium temperature response, a high equilibrium temperature response, and those that have outlying equilibrium
temperature responses. For the models that have similar
low and high equilibrium temperature responses, it appears
that there is a quasi-linear relation between the longwave
and total radiative forcing estimates (r = 0.87 and 0.89,

Fig. 9 Equilibrium temperaturechange (K) associated with a
1%/year increase in CO2
concentrations for 20 coupledclimate models plotted against
their respective climate
sensitivities for low/high/outlier(green/red/blue) equilibrium
temperature groupings—see
Fig. 8 for subsets of radiativeforcing/climate-sensitivity
curves. Equilibrium temperature
response calculated as the
product of the sensitivity andthe globally averaged total
radiative forcing in Fig. 8. Also
shown is equilibrium
temperature response assuming
a fixed total radiative forcing
equal to the mean of the 20
coupled climate models(*6.2 W m-2—black line)

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B. T. Anderson et al.: Climate forcings and climate sensitivities

Fig. 10 a Total radiative forcing (W m-2) associated with a 1%/year
increase in pre-industrial CO2 concentrations for 20 coupled-climate
models plotted against their respective longwave radiative forcing
component (W m-2) for low/high/outlier (green/red/blue)

equilibrium temperature groupings—see Fig. 8 for subsets ofradiative-forcing/climate-sensitivity curves. b Same as a except for
the respective shortwave radiative forcing component

respectively—Fig. 10a); however there is no similar relation between the shortwave and total radiative forcing
estimates (r = 0.20 and 0.22, respectively—Fig. 10b).
These results suggest that the inverse relation between
radiative forcing (both historical and future) and climate
sensitivity may be associated with changing greenhousegas concentrations as well as aerosols; as such this inverse
relation may be more important for future climate change
projections than is currently thought (e.g. Knutti 2008).

modifying the total radiative forcing associated withchanges in the chemical composition of the atmosphere; in
addition it is unclear whether the affected component of
total radiative forcing is associated with instantaneousradiative forcing by CO2 or adjustments to the stratosphere,
troposphere (Hansen et al. 2002; Shine et al. 2003) or
possibly clouds (Gregory and Webb 2008).
An explicit test of the above hypothesis will require
additional experiments: in particular, a single AGCM could
be integrated after modifying the parameters that affectwater vapor/lapse rate and/or cloud processes to produce
enhanced feedback (or forcing) effects. As mentioned,
atmosphere-only models are not explicitly ‘‘tuned’’ tomatch the observed surface temperatures, which are to firstorder dictated by the historical changes in SSTs. By analyzing the differences in model responses to changing SSTs
and atmospheric chemical constituents, as conditioned onchanges in relevant parameters, it will be possible todetermine whether the above hypothesis is valid. Alternatively, similar experiments could be performed using asingle coupled-climate model with modified longwave
feedback parameters, but in that case the total radiative
forcing from the model would have to be re-derived using
the method of Forster and Taylor (2006).
Finally we note that the above hypothesis only holds for
feedback processes that affect the longwave component of
the global radiation budget. While there also appears to be
an inverse relation between feedback and radiative forcing
processes that affect the shortwave component of the global radiation budget (Kiehl 2007), it is expected that thisinverse relation will weaken or disappear with a reductionof anthropogenic aerosol forcing (Kiehl 2007; Knutti2008). In that case, model differences in the shortwaverelated feedback processes, which would no longer be
offset by compensating changes in shortwave radiative

6 Discussion
One of the most important findings of the present analysis
is an inverse relation between climate sensitivity and total
radiative forcing within both historical AGCM simulations
and forced coupled climate-model runs. This inverse relationship appears to be manifested in inter-model differences in the longwave component of the total radiative
forcing. From the experiments we used and the analyses we
performed, we construct the following hypothesis: Models
that have enhanced longwave feedback processes—e.g.
water vapor/lapse rate and/or cloud feedbacks (Bony et al.,2006)—by nature attenuate the transfer of outgoing longwave radiation more so than in models with less robust
feedbacks. As such, in models with enhanced longwave
feedbacks, the change in outgoing longwave radiation
attributable to an increase in CO2 (and other greenhousegases), above and beyond what is already being retained
within the system by feedback processes, is expected to be
less; e.g. the total radiative forcing attributable to theinclusion of additional CO2 in models with enhanced
feedback processes is less than in those models with lessrobust feedbacks, as found here. Of course, it is still unclear
which longwave feedback processes may be involved in123B. T. Anderson et al.: Climate forcings and climate sensitivities

forcing, could give rise to model differences in the overall
equilibrium temperature response to enhanced GHG forcing. This may help explain why many model studies findthat differences in model responses to enhanced greenhouse gas concentrations appear most sensitive to feedbacks involving changes in shortwave radiation (Bony andDufresne 2005; Web et al. 2006; Ringer et al. 2006;
Williams and Tselioudis 2007), as well as why there arestill differences in equilibrium temperature responses in
the coupled-climate models analyzed here (as seen in
Figs. 8, 9).

7 Conclusions
Understanding the historical and future sensitivity of the
global climate system to anthropogenic emissions of heattrapping gases and aerosols has become a timely andcompelling concern. Presently, uncertainties in the magnitude of the historical climate response to anthropogenic
emissions arise because of uncertainties in the strength of
the feedbacks that subsequently modify this forcing, andhence in the sensitivity of the climate system to this forcing. In addition, some of the heat trapped by these emissions has been absorbed by the ocean, leading to
uncertainties in their effective forcing of the climate.
Finally, there exist uncertainties in the total radiative
forcing itself associated with the increased concentrationsof greenhouse gases and aerosols. Here we propose amethodology utilizing atmosphere-only general circulation
models to estimate the historical radiative forcing arisingfrom increased emissions of radiatively active atmosphericconstituents, as well as the ocean-heat uptake associatedwith this radiative forcing and the expected climate change.
This methodology is a modification of the Cess et al.
(1990) climate-sensitivity studies and involves different
AGCMs forced with observed changes in global-scale SST
anomalies, and then forced with both global-scale SSTs
and radiatively active atmospheric constituents.
Based upon TOA radiative fluxes from these two sets ofsimulations, we find that while the different modeling systems produce approximately the same historical global
surface temperature response (*0.4 K over the period
1950–2000), their estimates of the total radiative forcing
associated with the changing chemical composition of theatmosphere differ by a factor of two-thirds (from approximately 1.00–1.67 W m-2). In addition results suggest arange of global climate sensitivities in response to thisforcing, from approximately 0.3–0.7 K/(W m-2). However,
the model estimates’ of global climate sensitivities and total
radiative forcing are not independent from one another but
vary in a quasi-inverse way such that models with higher
global climate sensitivities have lower total radiative

1473

forcings. Because of this inverse relationship, the model
estimates of total expected surface temperature changes(compared with the mid-1950s) are similar across models(approximately 0.15 K difference between models), andshow a much smaller range than if the total radiative forcing
in each model is assumed to be the same (approximately
0.55 K difference).
Initial results from coupled ocean–atmosphere models,
forced by 1%/year increases in CO2 concentrations, also
indicate large inter-model differences in estimates of total
radiative forcing and climate sensitivity. However, inagreement with the atmosphere-only general circulation
models, results also suggest that certain models may have
similar relationships between the total radiative forcing andclimate sensitivity. For these models, the range of equilibrium temperature responses to future emissions of radiatively active chemical constituents is again less than if thefull range of climate sensitivities, applied to a constant total
radiative forcing estimate, is assumed.
It is important to note that in many current numericalmodel forecasts, the apparent offset between total radiative
forcing and climate sensitivity may be accounted for if themodel uses some form of radiative transfer code (e.g.
Collins et al. 2006). However, it may not be accounted forin many probability studies, which treat the radiative
forcing term as a fixed function of the GHG concentrations
and then combine it with a range of sensitivities as determined from short-term or long-term observational products(Annan and Hargreaves 2006), or intermediate-complexity(Hegerl 2006; Knutti and Tomassini 2008) and fully coupled numerical model simulations (Murphy et al. 2004).
Such an approach assumes that the radiative forcing is
independent of all feedback processes; our results showthat this may not be the case and that the temperaturechange may be more constant than is derived from suchcalculations.
Acknowledgments Dr. Anderson’s research was supported by aVisiting Scientist appointment to the Grantham Institute for Climate
Change, administered by Imperial College of Science, Technology,
and Medicine.

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