Origins of differences in climate sensitivity, forcingand feedback in climate models
Mark J. Webb • F. Hugo Lambert •
Jonathan M. Gregory
Received: 31 October 2011 / Accepted: 8 March 2012 / Published online: 12 April 2012
� Crown Copyright 2012
Abstract We diagnose climate feedback parameters and
CO2 forcing including rapid adjustment in twelve atmo-
sphere/mixed-layer-ocean (‘‘slab’’) climate models from
the CMIP3/CFMIP-1 project (the AR4 ensemble) and fif-
teen parameter-perturbed versions of the HadSM3 slab
model (the PPE). In both ensembles, differences in climate
feedbacks can account for approximately twice as much of
the range in climate sensitivity as differences in CO2
forcing. In the AR4 ensemble, cloud effects can explain the
full range of climate sensitivities, and cloud feedback
components contribute four times as much as cloud com-
ponents of CO2 forcing to the range. Non-cloud feedbacks
are required to fully account for the high sensitivities of
some models however. The largest contribution to the high
sensitivity of HadGEM1 is from a high latitude clear-sky
shortwave feedback, and clear-sky longwave feedbacks
contribute substantially to the highest sensitivity members
of the PPE. Differences in low latitude ocean regions
(30�N/S) contribute more to the range than those in mid-
latitude oceans (30–55�N/S), low/mid latitude land (55�N/
S) or high latitude ocean/land (55–90�N/S), but contribu-
tions from these other regions are required to account fully
for the higher model sensitivities, for example from land
areas in IPSL CM4. Net cloud feedback components over
the low latitude oceans sorted into percentile ranges of
lower tropospheric stability (LTS) show largest differences
among models in stable regions, mainly due to their
shortwave components, most of which are positive in spite
of increasing LTS. Differences in the mid-stability range
are smaller, but cover a larger area, contributing a com-
parable amount to the range in climate sensitivity. These
are strongly anti-correlated with changes in subsidence.
Cloud components of CO2 forcing also show the largest
differences in stable regions, and are strongly anticorre-
lated with changes in estimated inversion strength (EIS).
This is qualitatively consistent with what would be
expected from observed relationships between EIS and
low-level cloud fraction. We identify a number of cases
where individual models show unusually strong forcings
and feedbacks compared to other members of the ensem-
ble. We encourage modelling groups to investigate unusual
model behaviours further with sensitivity experiments.
Most of the models fail to correctly reproduce the observed
relationships between stability and cloud radiative effect in
the subtropics, indicating that there remains considerable
room for model improvements in the future.
Keywords Cloud � Climate models � Climate sensitivity �Feedback � Effective forcing � Rapid adjustment �Carbon dioxide � CO2
1 Introduction
Clouds remain a major source of uncertainty in climate
model projections of future changes in global mean surface
temperatures (Randall et al. 2007; Bony et al. 2006). In the
IPCC AR4 generation of climate models, all types of
M. J. Webb (&) � J. M. Gregory
Hadley Centre, Met Office, FitzRoy Road,
Exeter EX1 3PB, UK
e-mail: [email protected]
F. H. Lambert
College of Engineering, Mathematics and Physical Sciences,
University of Exeter, Exeter, UK
J. M. Gregory
National Centre for Atmospheric Science,
Reading University, Reading, UK
123
Clim Dyn (2013) 40:677–707
DOI 10.1007/s00382-012-1336-x
clouds contribute to this uncertainty, but low clouds have
been shown to make the largest contribution, mainly
through their impact on shortwave radiation (Bony and
Dufresne 2005; Webb et al. 2006; Wyant et al. 2006;
Williams and Tselioudis 2007; Medeiros et al. 2008; Soden
and Vecchi 2011).
Perturbed parameter ensembles have also been used to
explore inter-model differences in feedbacks and equilib-
rium climate sensitivity (Murphy et al. 2004; Stainforth
et al. 2005; Webb et al. 2006; Sanderson et al. 2008a, b;
Rougier et al. 2009; Joshi et al. 2008; Yokohata et al.
2010) and in transient climate change (Collins et al. 2006a,
2010; Harris et al. 2006). As in the case of the AR4
ensemble, shortwave cloud feedbacks in regions where low
level cloud changes dominate make the largest contribution
to inter-model spread in climate sensitivity (Webb et al.
2006; Yokohata et al. 2010).
A number of studies have looked for evidence to support
a dominant contribution from one type of marine boundary
cloud over another. Bony and Dufresne (2005) divided 15
atmosphere–ocean general circulation models (AOGCMs)
into high and low sensitivity groups, and showed that, over
the tropical oceans, the largest differences in cloud feed-
backs between these were found in regions of weak sub-
sidence. Medeiros et al. (2008) compared atmosphere-only
experiments from three models forced with observed SSTs
and with zonally uniform ‘aquaplanet’ SSTs with no land,
diagnosing cloud feedbacks induced by a uniform ?2K
SST perturbation. The difference in the average cloud
feedback over the tropical oceans between the realistic
NCAR and GFDL models was reproduced in the aqua-
planet configurations, despite their lack of persistent
stratocumulus.
Both of these results support the idea that trade cumulus
clouds (which cover large areas of the tropics) contribute as
much (or more) than persistent stratocumulus clouds to
inter-model spread in tropical cloud feedback. However,
Williams and Webb (2009) examined cloud feedbacks in
10 CO2 doubling experiments with atmosphere-mixed-
layer ocean ‘‘slab’’ models from the Cloud Feedback
Model Intercomparison Project, and found that stratocu-
mulus and stratocumulus/trade-cumulus transition clouds
make a larger contribution to inter-model spread in cloud
feedback than trade cumulus in those models. A weakness
of the Williams and Webb (2009) study is the fact that,
although 10 model versions were analysed, two of these
were versions of the MIROC3.2 model, and four were
versions of the Hadley Centre model, meaning that only six
distinct models were analysed [far fewer than Bony and
Dufresne (2005)]. This in part motivates the present study,
which analyses a larger set of slab models.
Another development since IPCC AR4 has been the
realisation that instantaneous CO2 forcing can lead to rapid
adjustments in the structure of the troposphere (on time-
scales of weeks rather than years), leading to equally rapid
adjustments in cloud and hence radiation at the top of the
atmosphere (Gregory and Webb (2008), hereafter GW08).
For analysis purposes these can be treated as a components
of an ‘effective’ radiative CO2 forcing (analogous to
stratospheric adjustment or indirect aerosol forcing) which
includes the effect of adjustments on short atmospheric
response time scales, in contrast to conventional climate
feedbacks which scale with global temperature, operating
on longer ocean response time scales. GW08 suggested that
tropospheric adjustment to CO2 may be responsible for
some of the model spread in equilibrium climate sensitiv-
ity. They also showed that CO2 forcing diagnosed in this
way was in good agreement with that diagnosed by dou-
bling CO2 while holding SST’s fixed (Hansen et al. 2002,
2005; Shine et al. 2003) in one model, HadSM3. Andrews
and Forster (2008) drew similar conclusions, and high-
lighted the role of cloud masking effects (Soden et al.
2004) on the cloud adjustment term.
More recently Colman and McAvaney (2011), Wyant
et al. (in press) and Watanabe et al. (2011) have analysed
cloud adjustments in individual models. Colman and
McAvaney (2011) found that a positive shortwave cloud
adjustment in a version if the Australian Bureau of Mete-
orology Research Centre (BMRC) climate model was due
to reductions in low-mid level cloud fraction associated
with enhanced heating rates, increased temperatures from
increased CO2, and associated reductions in relative
humidity. Meanwhile, Wyant et al. (in press) and Watan-
abe et al. (2011) have found positive adjustments in the
SP-CAM and MIROC models respectively, coincident with
a shallowing of the boundary layer in subtropical regions.
GW08 also examined a parameter-perturbed version of
HadSM3, and showed that its low climate sensitivity was
due to a smaller global effective CO2 forcing term than
standard HadSM3 because of shortwave cloud effects.
Geographical maps of the forcing terms showed substantial
differences in the tropics and in mid-latitudes. Doutriaux-
Boucher et al. (2009) applied a similar analysis to a fully
coupled AOGCM related to HadSM3 including an
interactive carbon cycle (HadCM3LC) and found a sub-
stantial effect on the shortwave cloud adjustment over
northern hemisphere land areas. They attributed this to
the sensitivity of stomatal conductance to CO2 increases,
which affects low level cloudiness through suppressed
evapotranspiration.
Pincus et al. (2008) and Collins et al. (2010) correlated
global feedbacks from the AR4 models with various
measures of present-day model skill, including global mean
bias and root mean square error, but found no statistically
significant relationships. Klocke et al. (2011) argue that
global measures of model skill such as these may be
678 M. J. Webb et al.
123
unrelated to climate sensitivity because they are influenced
not only by the regions controlling the sensitivity, but also
by other regions with large present-day biases. Trenberth
and Fasullo (2010) do however find a statistically signifi-
cant anti-correlation between the global climate sensitivity
and the net downward top-of-atmosphere radiation at the
top of atmosphere averaged over the Southern Hemisphere
in the AR4 models.
GW08 did not examine the contributions of different
geographical regions to the differences in forcings and
feedbacks in the multi-model ensemble. Here we apply the
analysis of GW08 to a larger ensemble of slab models to
highlight the contributions of different regions of the globe
to inter-model differences in effective forcings, feedbacks
and climate sensitivity. This also enables us to look for
relationships between regional biases and forcings and
feedbacks arising in those same regions.
Although GW08 argued that cloud adjustments occur as
a response to changes in the structure of the troposphere in
direct response to CO2 increases, the possibility remains
that some of these changes are driven by rapid land
warming. Dong et al. (2009) show evidence of a warming
in the free troposphere spreading out from land regions in a
CO2 doubling experiment with the atmosphere component
of HadSM3, and Williams et al. (2008) show evidence of
rapid warming over land in the slab versions of HadSM3
and HadGEM1. Here we use the term ‘effective forcing’ to
encompass the effects of rapid adjustments (in the tropo-
sphere or the land surface), which happen on timescales
which are short compared to the timescale of the ocean
temperature response. Defining forcing and feedback in
this way is a pragmatic approach, which diagnoses the
climate feedback parameter in a way which is more
accurately applicable to a wider range of forcings. Another
benefit of this approach is that it can be applied consistently
across models, and yields forcing and feedback values
which will reproduce the correct time variation of the
global temperature response in simple energy balance
models used to emulate AOGCMs.
This study also aims to address certain questions in rela-
tion to CFMIP-2, the second phase of the Cloud Feedback
Model Intercomparison Project. CFMIP-2 aims to make
better use of observations to evaluate clouds in climate
models, and to gain a better understanding of the physical
mechanisms responsible for the inter-model spread in cli-
mate sensitivity attributable to clouds. Plans for these dif-
ferent activities are detailed on the project website at
http://www.cfmip.net, and summarised in Bony et al. (2011)
(CLIVAR Exchanges, May 20111). CFMIP-2 includes an
activity co-organised with the GEWEX Cloud System Study
(GCSS) Boundary Layer Cloud Working Group called
CGILS (CFMIP/GCSS Intercomparison of LES and SCM,
Zhang et al. May 2010, GEWEX News2). This intercom-
parison uses a set of idealised SCM/LES forcings designed to
represent the changes in the local environment of subtropical
clouds in the warmer climate, building on the work of Zhang
and Bretherton (2008), Wyant et al. (2009) and Blossey
et al. (2009), and aims to establish whether or not idealised
SCM experiments can reproduce the different feedbacks
seen in the global models, and whether or not the cloud
resolving models show a smaller spread. For activities such
as CGILS, it is useful to know not only which type of cloud to
focus on (e.g. persistent stratocumulus, fairweather cumulus
or stratocumulus-trade cumulus transition) but also the rel-
ative importance of CO2 forced cloud adjustments and cloud
feedbacks. It is also useful to know the extent to which dif-
ferent cloud-climate responses are due to different changes
in large-scale variables such as stability and vertical velocity.
Wyant et al. (2009) investigated this question in the SP-
CAM, by sorting a number of model variables into percen-
tiles of lower tropospheric stability (LTS) over the low
latitude oceans. We apply their technique to a wider range of
models here to inform CGILS and future related activities.
An outline of the present study follows. Section 2
describes the twelve atmosphere/mixed layer ocean ‘slab’
models from CMIP3/CFMIP-1 and fifteen parameter-per-
turbed versions of HadSM3 analysed, the observations, and
the variant of the GW08 method which we employ. In Sect.
3 we compare the relative sizes of the contributions of
inter-model differences in global effective forcings and
feedbacks (and their cloud components) to the range in
climate sensitivity in both ensembles. In Sect. 4 we com-
pare the contributions from low latitude oceans (30�N/S),
mid-latitude oceans (30–55�N/S), low/mid latitude land
(55�N/S) and high latitude ocean/land (55–90�N/S), and
look for relationships between them and biases in the
control simulations compared to observed climatologies in
those same regions. Section 5 highlights some unusual
behaviours in individual models which we consider worthy
of future investigation by the modelling groups. In Sect. 6
we sort cloud components of feedback and forcing terms
over the low latitude oceans into percentile ranges of LTS,
following the approach of Wyant et al. (2009). Composite
responses of LTS, EIS [estimated inversion strength, Wood
and Bretherton (2006)] and pressure velocity at 500 hPa are
also examined to see if any relationships are present
between these large scale forcings and the cloud terms. We
also examine composites from the control simulations and
compare them with observational estimates of the equiva-
lent quantities. We present our conclusions and plans for
future work in Sect. 7.
1 See http://www.clivar.org/publications/exchanges/exchanges.php. 2 See http://www.gewex.org.
Climate sensitivity, forcing and feedback in climate models 679
123
2 Model descriptions and analysis methods
Two slab model ensembles are analysed. The first is the
AR4 multi-model ensemble combining experiments from
the CFMIP-1 and CMIP3 archives at PCMDI. These are
summarised in Table 1, and are a combination of those
analysed in Webb et al. (2006), Gregory and Webb (2008)
and Williams and Webb (2009). Selected members of the
HadSM3 perturbed physics ensemble (PPE) from Webb
et al. (2006) are also analysed. These are the slab model
equivalents of the 17 AOGCM experiments described in
Collins et al. (2010), with the exception of the standard
unperturbed experiment (for which the response immedi-
ately following CO2 doubling required for the GW08
analysis is unavailable) and one other which has data
missing.
Earth radiation budget (ERB) observational estimates
are taken from the ERBE-S4G (Harrison et al. 1990) and
ISCCP-FD (Zhang et al. 1995) datasets. The same period
(February 1985–January 1990) is used in both cases. We
note that these datasets are not pure observations and that
they should be considered to be subject to an observational
uncertainty which may be greater than the differences
between them. We also use analyses from MERRA
(Rienecker et al. 2011) and ERA40 (Uppala et al. 2005)
for the same period.
We apply the analysis method of Gregory et al. (2004)
and GW08, with some modifications. We quantify the
magnitude of climate change in the CO2 doubling experi-
ments using the change in the global-mean near surface
temperature DT relative to the control state. We can
express the climate sensitivity (DT at equilibrium) as a
function of a radiative forcing f and a climate feedback
parameter K such that f þ KDT ¼ 0. Note that K has the
opposite sign convention to the a feedback parameter used
in GW08; i.e. K ¼ �a. Thus defined, a stable system will
have a negative climate feedback parameter. Positive
increments to f and K tend to increase climate sensitivity,
making f more positive and K less negative, while negative
increments tend to decrease climate sensitivity. Gregory
et al. (2004) showed that f and K can be estimated in CO2
doubling experiments by linearly regressing the 2CO2
minus control difference of the annual-mean time series of
the net downward radiation at the top of the atmosphere (N)
against DT . The intercept of the regression line with the
line DT ¼ 0 gives an estimate for f and its slope gives an
estimate of K. The effective climate sensitivity is an esti-
mated value for the climate sensitivity defined as �f=Kusing the values from the regression. This may differ
slightly from the actual equilibrium climate sensitivity, but
we use it for consistency. To improve signal-to-noise in the
regressions we use the full time series of model outputs in
the 2CO2 experiments, ranging from 25 years in HadSM3
to 95 years in GFDL AM2.0 (GW08 used the first 20 years
only). Ordinary least squares regression is used as in
GW08, but we perform our error analysis using the case
resampling bootstrap method (Efron and Tibshirani 1993).
The annual-mean time series is randomly sampled ‘with
replacement’, producing a sample the same size as the
original time series, in which some values will be usually
be duplicated and some not sampled. The regression is
applied to this sample, and the procedure is repeated 1,000
times, to produce 95 % (2.5–97.5 %) confidence intervals
on the slope and intercept values.
Figure 1 shows a scatterplot of global forcing versus
feedback values from the AR4 ensemble, and Fig. 2 shows
the equivalent for the PPE. Statistical uncertainties in the
estimation of the forcing and feedback values for each
model are illustrated by a cloud of points sampled using the
bootstrap method. Rather than being ellipses with hori-
zontal and vertical axes of symmetry, as would be expected
for two independent variables, these clouds of points tend
Table 1 List of AR4 CMIP3/
CFMIP-1 models used in this
study
Atmospheric model References
IPSL-CM4 (CFMIP-1) Hourdin et al. (2006)
HadGEM1 (CMIP3) Martin et al. (2006), Johns et al. (2006)
MIROC3.2 medres (CMIP3) Hasumi and Emori (2004)
CCCMA CGCM4 (CFMIP-1) von Salzen et al. (2005)
HadCM3 (CFMIP-1) Pope et al. (2000), Gordon et al. (2000)
ECHAM5/MPI-OM (CFMIP-1) Roeckner et al. (2003)
MRI-CGCM2.3.2a (CMIP3) Yukimoto et al. (2006)
CSIRO-Mk3.0 (CMIP3) Gordon et al. (2002)
CCCMA CGCM3.1(T63) (CMIP3) http://www.cccma.bc.ec.gc.ca/models/
cgcm3.shtml
GFDL-CM2.0 (CMIP3) Delworth et al. (2006)
NCAR CCSM3 (CMIP3) Collins et al. (2006b)
GISS-ER (CMIP3) Schmidt et al. (2006)
680 M. J. Webb et al.
123
to be roughly aligned with and confined to be close to lines
of constant climate sensitivity. This indicates that the
uncertainties in the forcing and feedback estimates for each
model are anti-correlated. Our interpretation of this is as
follows. Firstly, the climate sensitivity for each model is
well estimated because we include all years of model data
at equilibrium. This means that the intercept of the
regression line with the line y = 0 on the Gregory plot (e.g.
Figure 1 of GW08) will be well constrained. However,
models warm fastest in the first few years after CO2 dou-
bling, so relatively few sample points are available to
constrain the estimated forcing value, allowing interannual
variability to have a bigger impact on its uncertainty. Since
the climate sensitivity is well known, any uncertainty in the
forcing will lead to the regression line ‘pivoting’ around
the intercept with the line y = 0, so that a more positive
forcing/intercept produces a more negative feedback/slope,
consistent with the anti-correlation seen in the forcing and
feedback values errors here. This estimation uncertainty
can be reduced in future model intercomparisons by
increasing the signal-to-noise ratio. In the forthcoming
CMIP5 experiments this will be achieved by running fully
coupled AOGCM experiments subject to a stronger forcing
(CO2 quadrupling rather than doubling). These experi-
ments will be run for 150 years and will equilibrate more
slowly than the slab models analysed here, providing a
larger number of sample points spread out along the
regression line. Dividing the forcing estimate for CO2
quadrupling by two will give an estimate of the forcing due
to CO2 doubling with smaller error bars. This will also
result in a smaller uncertainty in the feedback parameter, as
the pivoting effect described above will be reduced by the
smaller uncertainty in the forcing. It will be interesting to
see whether the forcings and feedbacks diagnosed in these
experiments are consistent with those under CO2 doubling.
An initial condition ensemble will also be run for each
model, staggered at one month intervals to diagnose
responses on time scales of less than one year (Doutriaux-
Boucher et al. 2009), which will provide a more accurate
estimate of the forcing intercept value, and fixed SST
experiments subject to CO2 quadrupling will also provide
forcing estimates using the Hansen et al. (2002) method.
As in GW08, we use the difference between all-sky and
clear-sky fluxes to measure the effect of clouds on CO2
forcing and feedback. This difference is often referred to as
the ‘cloud radiative forcing’, but we prefer the term cloud
radiative effect (CRE) which is analogous to ‘greenhouse
effect’. As pointed out by Soden et al. (2004), the change
in the CRE is not the same as the cloud feedback diagnosed
using the partial radiative perturbation (PRP) method (e.g.
Wetherald and Manabe 1988; Colman 2003), or approxi-
mate versions of it (e.g. Soden and Held 2006; Taylor et al.
2007). PRP defines the cloud feedback as the partial
derivative of the TOA radiative flux with respect to a
change in cloud where all other quantities (e.g. water
vapour, surface albedo) are artificially held fixed. PRP also
diagnoses non-cloud feedbacks using partial derivatives,
including the effects of climatological cloud masking, for
example where the effect of a change in surface albedo is
not seen at the TOA because of persistent cloudiness. In
contrast, the CRE method diagnoses the non-cloud feed-
backs as they would be seen in clear-sky conditions with-
out the effects of cloud masking, while the cloud masking
effects on the non-cloud feedbacks are included in the
change in CRE along with the effect of any cloud changes.
Climatological cloud masking clearly has a substantial
impact on CO2 forcing, climate feedback and climate
-2.0 -1.5 -1.0 -0.5 0.0
Feedback (W/m2/K)
0
1
2
3
4
5
Eff
ectiv
e Fo
rcin
g (W
/m2 )
Δ T=2Δ T=3Δ T=4Δ T=5Δ T=6Δ T=7
GISS-ERCCSM3GFDL AM2.0CCCMA-CGCM3.1MRI-CGCM2.3.2ACSIRO Mk3.0MPI ECHAM5UKMO-HadSM3CCCMA CGCM4MIROC3.2(medres)HadGEM1IPSL-CM4
Fig. 1 Global mean forcings and feedbacks in the AR4 slab
ensemble. Squares and coloured ticks on the axes show the best
estimates, dots show the individual bootstrap values and the diamonds
show the 95 % (2.5–97.5 %) confidence intervals. The ensemble
mean forcing and feedback values and their ranges are shown using
horizontal and vertical black lines. Sloping lines of constant climate
sensitivity are shown in black. The legend shows the names of the
models ordered from highest to lowest climate sensitivity
-2.0 -1.5 -1.0 -0.5 0.0
Feedback (W/m2/K)
0
1
2
3
4
5
Eff
ectiv
e Fo
rcin
g (W
/m2 )
ΔT=2ΔT=3ΔT=4ΔT=5ΔT=6ΔT=7
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
Fig. 2 As Fig. 1, but for the PPE
Climate sensitivity, forcing and feedback in climate models 681
123
sensitivity. If, say, in a particular climate model, the sea ice
feedback were to be masked by a climatological excess of
cloud, then this would have as much potential to affect the
total feedback and climate sensitivity of that model as an
unusually large or small change in cloud. We consider the
CRE method acceptable for the purpose employed here,
although it does not separate these two effects. Our reason
for using the CRE method rather than the other possibilities
is mainly a practical one, in that the other methods require
additional diagnostics which are not available in all mod-
els. We wish to include as many models in our analysis as
possible, and all-sky plus clear-sky fluxes at TOA are
universally available. In the following text we refer to the
change in the CRE as the cloud component of the total
feedback or forcing, noting that this includes the net effect
of the cloud responses and cloud masking.
Although we regress various quantities against global
mean near-surface temperature, this does not mean that we
think that clouds respond to this quantity directly. This is
more a convenient analysis method which takes advantage
of the observation that top of atmosphere radiative fluxes
do respond quite linearly with global temperature in slab
models, as shown in Figure 2 of Gregory and Webb (2008).
Since this is the case, it seems likely that those factors
which are thought to influence the large scale cloud
response (e.g. stability, subsidence, moist physics) do also
scale linearly with the system warming. Defining forcing
and feedback in this way is a pragmatic approach, which
diagnoses the climate feedback parameter in a way which
is more accurately applicable to a wider range of forcings.
Another benefit of this approach is that it yields forcing and
feedback values which will reproduce the correct time
variation of the global temperature response in simple
energy balance models used to emulate AOGCMs. Given
that global top-of-atmosphere fluxes do respond quite lin-
early with temperature increases in slab models, we think
that this approach is justified here.
3 Global forcings and feedbacks
In this section we compare the relative sizes of the con-
tributions of inter-model differences in global effective
forcings and feedbacks (and their cloud components) to the
range in climate sensitivity in both ensembles.
For the AR4 ensemble the range in effective climate
sensitivity is 2.3 K (2.7–5.0 K) (Fig. 1; Table 2). If there
were no inter-model differences in climate feedback, and
all models had a feedback value equal to ensemble mean,
then the remaining range (due to forcing differences alone)
would be 1.5 K (2.9–4.3 K). This estimate of the contri-
bution of forcing differences to the spread in climate sen-
sitivity can be seen graphically in Fig. 1 by comparing the
full range of sensitivities with those spanned by the thick
black vertical line, which covers the range of model forcing
values at the ensemble mean value of the feedback
parameter. Conversely, if there were no inter-model dif-
ferences in CO2 forcing, and all models had a forcing value
equal to the ensemble mean, then the resulting range (due
to feedback differences alone) would be 2.9 K (2.6–5.4 K).
(See the thick black horizontal line.) The range in climate
sensitivity in the presence of global feedback differences
Table 2 Global effective
forcings, feedbacks and
effective climate sensitivities
for the AR4 ensemble
The values in brackets indicate
95 % (2.5–97.5 %) confidence
intervals relative to the best
estimate. Note that the ensemble
mean climate sensitivity is not
exactly the same as the climate
sensitivity predicted by the
ensemble mean forcing and
feedback
Model Forcing, f (W m-2) Feedback, K(W m-2 K-1)
Effective climate
sensitivity, DT (K)
IPSL CM4 3.70 (-0.51, 0.43) -0.75 (-0.11, 0.13) 4.96 (-0.18, 0.25)
HadGEM1 3.13 (-0.35, 0.24) -0.67 (-0.06, 0.09) 4.68 (-0.16, 0.19)
MIROC 3.2 medres 4.27 (-0.47, 0.25) -1.04 (-0.07, 0.12) 4.11 (-0.07, 0.08)
CCCMA CGCM4 4.02 (-0.82, 0.24) -1.00 (-0.07, 0.24) 4.03 (-0.11, 0.19)
HadSM3 3.71 (-0.94, 0.34) -1.00 (-0.12, 0.28) 3.73 (-0.17, 0.23)
MPI ECHAM5 4.49 (-0.65, 0.65) -1.28 (-0.20, 0.22) 3.52 (-0.11, 0.13)
CSIRO Mk3 3.00 (-0.55, 0.26) -0.89 (-0.09, 0.19) 3.37 (-0.09, 0.18)
MRI CGCM2 3.06 (-0.89, 0.62) -0.96 (-0.20, 0.30) 3.19 (-0.10, 0.14)
CCCMA CGCM3.1 4.40 (-0.61, 0.42) -1.42 (-0.13, 0.19) 3.11 (-0.05, 0.05)
GFDL AM2.0 2.97 (-0.69, 0.26) -1.02 (-0.09, 0.24) 2.90 (-0.05, 0.06)
NCAR CCSM3.0 3.03 (-0.38, 0.16) -1.12 (-0.07, 0.16) 2.72 (-0.05, 0.06)
GISS-ER 3.64 (-0.60, 0.31) -1.35 (-0.11, 0.24) 2.69 (-0.03, 0.04)
Ensemble mean 3.62 -1.04 3.58
Effective climate sensitivity 3.48
predicted by ��f=�K
Ensemble range 1.52 0.75 2.27
682 M. J. Webb et al.
123
alone is almost twice that with global effective forcing
differences alone, indicating that feedback differences
make the largest contribution. This result is qualitatively
consistent with those obtained by earlier studies which did
not allow for the effects of rapid cloud adjustments on
radiative forcing (Webb et al. (2006) using a subset of the
models examined here and Dufresne and Bony (2008)
using the CMIP-3 AOGCMs). The contribution from
forcing differences is substantial however, and 50 % larger
than the equivalent estimate from Webb et al. (2006).
Climate sensitivity range is a statistic commonly quoted for
climate models, but it has the disadvantage of being
determined by the models at the extremes, and contains no
information on the distribution of values within. Consid-
ering ensemble variance in climate sensitivity yields fairly
similar results to those described above (Table 4).
There is an anti-correlation (r = - 0.52) between
feedbacks and forcings in the AR4 ensemble, which can be
seen in Fig. 1 as a tendency for models with more negative
feedbacks to have more positive forcing values and those
with less negative feedback values to have less positive
forcing values. This anti-correlation is not significant at the
95 % level however, and so may simply be due to a chance
distribution of feedback and forcing values arising from the
different physical assumptions in the models. The range of
climate sensitivities calculated using feedback differences
alone is larger than that with forcing and feedback differ-
ences considered together. Contributions from the cloud
components of the feedback also give a larger range than
cloud components of the feedback and forcing taken
together (Table 4). This is not the case for the clear-sky
equivalents, so we conclude that cloud effects are the main
cause.
Note that it is important not to confuse the anti-corre-
lation between the best estimates of the forcings and
feedbacks across the ensemble with the much stronger anti-
correlations seen between regression error estimates for the
forcing and feedback in each individual model. The latter is
a consequence of using the Gregory et al. (2004) method
while the former is a property of the ensemble. We know
this because Webb et al. (2006) previously found the range
in climate sensitivities calculated using feedback differ-
ences alone to be larger than that with forcing and feedback
differences in a subset of the AR4 ensemble, but using a
more conventional forcing diagnosis method which did not
use regression and made no allowance for rapid cloud
adjustment.
For the PPE, the range in effective climate sensitivity is
4.6 K (2.2–6.9 K) (Fig. 2; Table 3), which is considerably
larger than in the AR4 ensemble. One might expect that an
ensemble based on a single model would be more tightly
constrained than the AR4 ensemble (for example through
the use of a single radiative transfer code in the case of the
CO2 forcing). This is not the case here however. This is
partly due to the experimental design of the PPE, which
aims to reflect the full range of sensitivities possible with
perturbations of HadSM3, while placing constraints on top-
of-atmosphere radiative balance which are relatively weak
Table 3 As Table 2 but for the
PPEModel Forcing, f (W m-2) Feedback,
K (W m-2K-1)
Effective climate
sensitivity DT (K)
adsea 2.75 (-0.62, 0.38) -0.40 (-0.06, 0.10) 6.87 (-0.14, 0.20)
adrye 2.72 (-0.27, 0.19) -0.49 (-0.04, 0.06) 5.53 (-0.18, 0.21)
adrhl 3.23 (-0.70, 0.42) -0.67 (-0.10, 0.16) 4.81 (-0.15, 0.20)
adrya 3.48 (-0.80, 0.41) -0.74 (-0.09, 0.18) 4.72 (-0.08, 0.13)
adsbh 3.27 (-0.34, 0.49) -0.70 (-0.11, 0.08) 4.68 (-0.14, 0.14)
adsbb 3.70 (-0.54, 0.38) -0.82 (-0.08, 0.13) 4.54 (-0.08, 0.10)
adsbd 2.93 (-0.45, 0.48) -0.65 (-0.12, 0.12) 4.48 (-0.16, 0.21)
adseb 3.20 (-0.35, 0.20) -0.72 (-0.06, 0.08) 4.44 (-0.13, 0.15)
adrhj 2.84 (-0.54, 0.33) -0.72 (-0.09, 0.17) 3.97 (-0.15, 0.23)
adseo 3.48 (-0.66, 0.30) -1.03 (-0.09, 0.21) 3.39 (-0.09, 0.11)
adumf 2.80 (-1.08, 1.02) -0.92 (-0.35, 0.38) 3.03 (-0.17, 0.25)
adumd 3.16 (-0.41, 0.93) -1.11 (-0.38, 0.18) 2.86 (-0.15, 0.19)
adtlg 2.86 (-0.71, 1.15) -1.11 (-0.49, 0.33) 2.58 (-0.21, 0.39)
adrea 2.15 (-0.68, 0.85) -0.86 (-0.39, 0.33) 2.52 (-0.18, 0.30)
aduvb 2.39 (-1.58, 1.53) -1.08 (-0.76, 0.80) 2.22 (-0.22, 0.51)
Ensemble mean 3.00 -0.80 4.04
Effective climate sensitivity
predicted by ��f=�K3.75
Ensemble range 1.55 0.71 4.65
Climate sensitivity, forcing and feedback in climate models 683
123
compared to those applied to the AR4 ensemble (Sexton
et al. 2012).
The ranges in climate sensitivity due to forcing differ-
ences alone and feedback differences alone are both larger
than in the AR4 ensemble, but the two ensembles are
qualitatively consistent in the sense that inter-model dif-
ferences in feedbacks contribute roughly twice as much as
differences in forcings to the range in effective climate
sensitivity (Tables 4, 5).
Cloud and clear-sky components of the forcing and
feedback terms are also calculated, as in GW08. Cloud
components of forcing and feedback are more than
capable of explaining the full range in climate sensitivity
in the AR4 ensemble, and cloud components of the global
feedback contribute more than four times as much as
cloud components of the global forcing (Table 4). In the
PPE however, cloud components of forcing and feedback
terms alone give a range less than half the size of the
total, and cloud components of the forcing contribute
more than the cloud components of the feedback
(Table 5).
4 Regional contributions to forcings and feedbacks
Here we decompose the global mean forcings and feed-
backs and their cloud components into contributions from
low latitude ocean regions (30�N/S), mid-latitude oceans
(30–55�N/S), low-mid latitude land (55�N/S) and high
latitude ocean/land (55–90�N/S), and look for relationships
between them and regional biases in the control simula-
tions compared to observed climatologies. The boundaries
between latitude bands were chosen as far as possible to lie
between the major features of the annual mean net CRE
climatology from ERBE (not shown), and to fit in with
regions used in previous studies (e.g. Bony and Dufresne
2005). The low latitude ocean is the largest region, cov-
ering 30 % of the globe, and includes the deep convection
associated with the ITCZ and warm pool, the persistent
stratocumulus decks in the Eastern basins of the subtropical
oceans in the vicinity of California, Peru, Namibia, Aus-
tralia and the Canaries, and the trade cumulus regions. We
define mid-latitude oceans as those between (30–55�N/S),
which contain most of the cloud associated with the mid-
latitude oceanic storm tracks. The 55� boundary was cho-
sen to exclude sea ice from the mid-latitude regions, and
was chosen by examining climatologies of clear-sky
reflected shortwave radiation from ERBE. We consider
high latitude land and ocean regions poleward of 55�N/S
together. We also consider the remaining low-mid latitude
land areas as a single region. Forcing and feedback con-
tributions from each region are calculated by regressing the
regional average quantities against the global near-surface
temperature response, following the regional feedback
decomposition of Boer and Yu (2003).
To compare the contributions of the different regions to
the range in climate sensitivity, we use a similar procedure
to that described above when comparing global forcing and
feedback values. For each model, we calculate the effective
climate sensitivity using the forcing and feedback values
from the region of interest, but using ensemble mean val-
ues elsewhere. This procedure includes area weighting, so
that for example a forcing value which is 1 W m-2
stronger than the ensemble mean value over the low lati-
tude oceans will contribute an extra 0.3 W m-2 to the
global forcing value, and an extra 0.3 K to the climate
sensitivity (the ensemble mean feedback parameter being
close to -1). Although we refer to these values as contri-
butions, it is important to note that they do not add up
exactly. This is because of the non-linearity of the effective
climate sensitivity equation, which has the feedback
parameter on its denominator. Still, this procedure provides
Table 4 Contributions to the effective climate sensitivity (K) range and variance from global forcing and feedback components in the AR4
ensemble
Total range, variance Net cloud Shortwave clear Longwave clear
Feedback and forcing 2.3, 0.55 3.5, 0.99 1.5, 0.21 2.0, 0.31
Feedback only 2.9, 0.70 4.3, 1.30 1.4, 0.20 1.7, 0.30
Forcing only 1.5, 0.31 0.9, 0.11 1.0, 0.09 1.0, 0.07
Table 5 As Table 4 but for the PPE
Total range, variance Net cloud Shortwave clear Longwave clear
Feedback and forcing 4.6, 1.64 2.2, 0.49 0.7, 0.05 1.5, 0.16
Feedback only 4.8, 1.73 1.5, 0.17 1.0, 0.08 2.4, 0.35
Forcing only 1.9, 0.28 2.1, 0.36 0.5, 0.01 0.7, 0.04
684 M. J. Webb et al.
123
an indication of the relative sizes of the contributions from
the different regions.
In the AR4 ensemble, differences in forcings and feed-
backs over the low latitude oceans alone can explain a
range in climate sensitivity two thirds the size of the total
range, almost twice as much as any of the other regions
(Fig. 3a). This is more than would be expected on the basis
of area alone; if the different feedbacks and forcings were
globally uniform in the models, then the low latitude
oceans would explain only 30 %. Feedback differences in
this region contribute about twice as much as forcing dif-
ferences (Fig. 3b, c). These can in turn be largely explained
by their cloud components (Fig. 4b, c). These results are
consistent with those of Bony et al. (2006), in that they
indicate that the ocean regions between 30�N/S show a
larger inter-model range in feedback spread than the
extratropics. Contributions from these other regions are
still substantial however, and are required to account fully
for the highest model climate sensitivities, none of which
can be explained entirely by the contributions from the low
latitude oceans. In the PPE, the low-latitude oceans also
make the largest contribution, but this is only a third of the
size of the global climate sensitivity range in this case, and
contributions from mid-latitude oceans and high latitudes
are relatively more important than in the AR4 ensemble,
being required to explain all of the higher model sensitiv-
ities (Fig. 5).
Non-cloud components also contribute in some models.
For example, the largest contribution to the higher-than-
average sensitivity of HadGEM1 comes from the feedback
term in the high latitude region (Fig. 3). However, the cloud
component of the feedback term is very close to the
ensemble mean in this region (Fig. 4). This feature of
HadGEM1 is explained by a stronger than average short-
wave clear-sky feedback term (not shown). The most likely
explanation for this is a stronger than average positive sur-
face albedo feedback associated with changes to surface
snow and sea ice. (This is discussed in more detail in Sect. 5.)
We also compare the net downward top-of-atmosphere
radiative flux and the net CRE from the control simulations
with observed equivalents from ERBE and ISCCP-FD. In
the AR4 ensemble, there is no obvious relationship
between the global mean biases in these quantities and the
climate sensitivity, or the contributions from global forc-
ings or feedbacks (Figs. 3, 4). This null result is not rep-
licated in the PPE however, where there is a distinct
tendency for higher sensitivity models in the PPE to be
associated with positive biases in net downward top-of-
atmosphere radiation and net CRE in the global mean, and
for lower sensitivity models to have negative biases
(Figs. 5, 6). The climate sensitivities in the PPE are posi-
tively correlated with the global net downward radiation in
the control simulations (r = 0.91, significant at the 95 %
level). This is mainly attributable to relationships between
the control values and the cloud components of the feed-
back terms in the mid-latitude ocean and high latitude
regions. These can in turn be attributed to the shortwave
cloud components in these regions (not shown).
Possible situations in which present-day biases in clouds
might affect cloud feedbacks have been suggested in a
number of studies. For example, Williams and Tselioudis
(2007) argued that excessive cloud fraction (or frequency
of occurrence) might possibly lead to a cloud feedback
which is too strong, for a given change in cloud optical
thickness. Similarly, excessive cloud optical thickness
might lead to a cloud feedback which is too strong for a
given change in cloud fraction. Another possibility was
raised by Trenberth and Fasullo (2010), who argued that
models which underpredict cloud fraction might have more
scope for increases in cloud fraction than would be possible
in the real world in locations which are nearly overcast in
reality (for example in over the Southern Oceans).
Yokohata et al. (2010) analysed the full set of experi-
ments from which our PPE is drawn, and showed that
model versions with a larger global mean low level cloud
cover and cloud albedo tend to have stronger negative
global mean shortwave cloud responses at equilibrium and
lower climate sensitivities (see their Fig. 11). Our results
indicate that this effect is mainly due to feedbacks oper-
ating in midlatitudes. Separating the contributions from the
Northern and Southern Hemisphere mid-latitude regions
(not shown) indicates that this is due the the contribution
from the southern midlatitudes, illustrating the importance
of feedbacks in this region as highlighted by Trenberth and
Fasullo (2010). It is possible that the potential for similar
relationships might be present in AR4 ensemble, but that
these are not apparent because many of the models have
been tuned to agree with observations.
5 Unusual behaviours in individual models
Here we highlight unusual forcings and feedbacks in
individual models, focusing on the global forcings and
feedbacks which have confidence intervals distinct from
the ensemble means in Figs. 1 and 2. We also highlight any
substantial control biases which coincide with them.
The higher-than-average sensitivity of IPSL CM4 is
entirely due to its global feedback parameter, as its global
forcing value is close the the ensemble mean (Fig. 1;
Table 2). This is primarily due to cloud feedback compo-
nents which are more positive than the ensemble mean over
low latitude ocean and low/mid-latitude land areas
(Figs. 3b, 4b) which are in turn all due to the corresponding
shortwave cloud feedback components (not shown). These
are the most strongly positive in the ensemble.
Climate sensitivity, forcing and feedback in climate models 685
123
(a) AR4 Ensemble Climate Sensitivity
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =2.3K
variance =0.55
Low Lat Ocean
1.5K
0.15
Mid Lat Ocean
0.7K
0.05
High LatLand/Ocean
0.8K
0.05
GISS-ERCCSM3GFDL 2.0 CCCMA-3MRI-2.3.2ACSIRO Mk3 ECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
Low/MidLat Land
0.8K
0.07
(b) AR4 Ensemble Contributions from Feedback
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =2.9K
variance =0.70
Low Lat Ocean
1.4K
0.17
Mid Lat Ocean
0.8K
0.09
High LatLand/Ocean
0.9K
0.06
Low/MidLat Land
1.3K
0.11
(c) AR4 Ensemble Contributions from Forcing
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =1.5K
variance =0.31
Low Lat Ocean
0.8K
0.07
Mid Lat Ocean
0.4K
0.02
High LatLand/Ocean
0.5K
0.02
Low/MidLat Land
0.6K
0.03
(d) AR4 Ensemble Control Net TOA Radiation Bias (W/m2)
-20
-15
-10
-5
0
5
10
Con
trol
GlobalLow Lat Ocean
Mid Lat Ocean
High LatLand/Ocean
Low/MidLat Land
Fig. 3 Climate sensitivities in the AR4 ensemble with regional contri-
butions (a). Climate sensitivities due to feedback (b) and forcing
differences (c). Net down TOA radiation biases relative to ERBE and
ISCCP FD (d). Regional values are area weighted so that inter-model
differences sum to global equivalents. Black lines denote observational
estimates on d and the climate sensitivity from the ensemble mean forcing
and feedback on a–c. Ranges (maximum–minimum) and variances are
annotated in black. Models are presented in order of climate sensitivity
686 M. J. Webb et al.
123
(a) AR4 Ensemble Cloud Component of Climate Sensitivity
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =3.5K
variance =0.99
Low Lat Ocean
1.9K
0.25
Mid Lat Ocean
1.0K
0.09
High LatLand/Ocean
0.7K
0.06
GISS-ERCCSM3GFDL 2.0 CCCMA-3MRI-2.3.2ACSIRO Mk3 ECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
Low/MidLat Land
1.0K
0.11
(b) AR4 Ensemble Contributions from Cloud Component of Feedback
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =4.3K
variance =1.30
Low Lat Ocean
1.6K
0.20
Mid Lat Ocean
1.5K
0.15
High LatLand/Ocean
0.8K
0.06
Low/MidLat Land
1.9K
0.27
(c) AR4 Ensemble Contributions from Cloud Component of Forcing
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =0.9K
variance =0.11
Low Lat Ocean
0.7K
0.05
Mid Lat Ocean
0.6K
0.03
High LatLand/Ocean
0.3K
0.01
Low/MidLat Land
0.8K
0.04
(d) AR4 Ensemble Control Net CRE Bias (W/m2)
-20
-15
-10
-5
0
5
10
Con
trol
GlobalLow Lat Ocean
Mid Lat Ocean
High LatLand/Ocean
Low/MidLat Land
Fig. 4 As previous figure, but for net CRE contributions only
Climate sensitivity, forcing and feedback in climate models 687
123
(a) PPE Climate Sensitivity
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =4.6K
variance =1.64
r =0.91
Low Lat Ocean
1.5K
0.20
Mid Lat Ocean
1.2K
0.16
0.96
High LatLand/Ocean
1.1K
0.12
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
Low/MidLat Land
0.5K
0.03
(b) PPE Contributions from Feedback
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =4.8K
variance =1.73
r =0.90
Low Lat Ocean
2.6K
0.37
Mid Lat Ocean
1.2K
0.14
0.87
High LatLand/Ocean
1.4K
0.17
Low/MidLat Land
0.7K
0.04
(c) PPE Contributions from Forcing
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =1.9K
variance =0.28
Low Lat Ocean
1.3K
0.10
Mid Lat Ocean
0.6K
0.03
High LatLand/Ocean
0.5K
0.02
Low/MidLat Land
0.4K
0.02
(d) PPE Control Net TOA Radiation Bias (W/m2)
-20
-15
-10
-5
0
5
10
Con
trol
GlobalLow Lat Ocean
Mid Lat Ocean
High LatLand/Ocean
Low/MidLat Land
Fig. 5 As Fig. 3 but for the PPE. Correlations with control biases which take values greater than r = 0.8 are annotated in black
688 M. J. Webb et al.
123
(a) PPE Cloud Component of Climate Sensitivity
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =2.2K
variance =0.49
r =0.83
Low Lat Ocean
2.3K
0.27
Mid Lat Ocean
1.4K
0.18
0.96
High LatLand/Ocean
1.1K
0.09
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
Low/MidLat Land
1.5K
0.13
(b) PPE Contributions from Cloud Component of Feedback
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =1.5K
variance =0.17
Low Lat Ocean
4.1K
0.95
Mid Lat Ocean
1.3K
0.16
0.90
High LatLand/Ocean
1.0K
0.08
0.86
Low/MidLat Land
2.4K
0.33
(c) PPE Contributions from Cloud Component of Forcing
2
3
4
5
6
7
Clim
ate
Sens
itivi
ty (
K)
Global
range =2.1K
variance =0.36
Low Lat Ocean
1.4K
0.15
Mid Lat Ocean
0.5K
0.02
High LatLand/Ocean
0.3K
0.01
Low/MidLat Land
0.8K
0.05
(d) PPE Control Net CRE Bias (W/m2)
-20
-15
-10
-5
0
5
10
Con
trol
GlobalLow Lat Ocean
Mid Lat Ocean
High LatLand/Ocean
Low/MidLat Land
Fig. 6 As Fig. 4 but for the PPE. Colours are as in Fig. 2
Climate sensitivity, forcing and feedback in climate models 689
123
The higher-than average sensitivity of HadGEM1 is also
due to its global feedback parameter (Fig. 1; Table 2). This
is partly due to positive cloud feedbacks over the mid-lat-
itude oceans (Figs. 3b, 4b) which are mainly explained by
their shortwave components (not shown). The largest con-
tribution is however from the high latitudes (Fig. 3b) and is
due to a stronger-than-average positive clear-sky shortwave
feedback, which coincides with a substantial negative bias
in the absorbed shortwave clear-sky radiation at high lati-
tudes in the control compared to observations, indicating
excessive clear-sky albedo (not shown). These results are
consistent with Johns et al. (2006), who note that sea ice
extents in the slab version of HadGEM1 are too extensive.
Sea ice extents are smaller in the fully coupled AOGCM
version of HadGEM1, and they attribute this difference to
the ice thickness distribution component of the sea ice
scheme in HadGEM1 being dependent on coupled ocean
effects which are not well represented in the slab model.
They also show that removing the ice thickness distribution
scheme from the slab model version of HadGEM1 reduces
the climate sensitivity by 1K. This brings the slab model
sensitivity much closer to that of the fully coupled version
of HadGEM1 estimated by Williams et al. (2008).
The higher-than-average sensitivity of MIROC 3.2
medres is mainly due to its strong forcing parameter
(Fig. 1; Table 2). This is largely due to the cloud compo-
nents of the forcing originating in the low and mid latitude
ocean and land regions (Figs. 3c, 4c) which are mainly
explained by their shortwave cloud components (not
shown). In this case the global cloud adjustment contrib-
utes more to the higher-than-average climate sensitivity of
MIROC3.2 than the cloud feedback component (in contrast
to IPSL CM4 where the reverse is true). This demonstrates
the fact that, although cloud components of the CO2 forc-
ing cannot explain as much of the sensitivity range as cloud
feedback components, they do have a substantial impact on
some models. Williams and Webb (2009) show evidence of
the net CRE in MIROC 3.2 medres becoming substantially
more positive at equilibrium after CO2 doubling in strato-
cumulus and trade cumulus/stratocumulus transition
regimes. Our results suggest that these are most likely due
to rapid cloud adjustments. A substantial negative net CRE
bias is present over the low latitude oceans, which is the
second largest in the ensemble, due to a shortwave CRE
bias which is the largest (not shown).
MPI ECHAM5 shows a large global forcing and
strongly negative feedback, the net effect of which is a mid-
range climate sensitivity. This cancellation is mainly due to
cloud components of forcing and feedback over the low and
mid-latitude oceans (again mainly shortwave, not shown).
CCCMA CGCM3.1 has a similar global compensation
arising in the same regions. However the feedback con-
tribution is mainly a clear-sky longwave effect, while the
forcing contribution is mainly due to the shortwave cloud
component (not shown).
The lower-than average sensitivity of GFDL AM2.0 is
mainly due to its global forcing parameter, which is the
smallest in the AR4 ensemble. This behaviour is unusually
uniform; all of the regions contribute a small amount.
However, no single forcing component dominates in any of
them.
The lower-than-average sensitivity of NCAR CCSM3.0
can also be explained mostly in terms of its small forcing
value. The largest contributions are in the mid and high-
latitude ocean regions, and are primarily due to cloud
effects (mainly the shortwave components, not shown). It is
also worth noting however that NCAR CCSM3.0 has the
strongest negative total and cloud feedback components in
the ensemble over the low latitude oceans (again mainly
due to the shortwave cloud component, not shown). A
substantial negative shortwave CRE bias (the largest in the
ensemble) is also present here (not shown). We analyse
cloud feedbacks over the low latitude oceans in more detail
in Sect. 6.
GISS-ER has the lowest sensitivity, mainly due to its
strongly negative global feedback parameter (Fig. 1;
Table 2). This is primarily due to a clear-sky feedback
component over the mid-latitude oceans and a shortwave
cloud effect over the low latitude oceans (not shown).
Regression uncertainties are larger in PPE than the AR4
ensemble, particularly at the low sensitivity end of the
range, and only two of the lower sensitivity models in the
PPE (adumd and adrea) have forcing or feedback values
whose confidence intervals are distinct from the ensemble
mean (Fig. 2; Table 3). We attribute this to the fact that
low sensitivity models reach equilibrium more quickly, and
so have fewer values which the linear regression can be
applied to, resulting in a smaller signal to noise ratio. The
problem is exacerbated in the PPE because the low sensi-
tivity model versions tend to have more interannual vari-
ability (not shown).
The two highest sensitivity models adsea and adrye are
similar in that both of their high sensitivities are due to
their global feedback parameters (Fig. 2; Table 3). In
adsea, low latitude ocean, mid-latitude ocean and high
latitude regions all make comparable contributions
(Fig. 5). The low-latitude contribution is mainly due to the
clear-sky longwave feedback component (not shown).
Stainforth et al. (2005) showed that versions of HadSM3
with low values of the convective entrainment parameter
tend to have high climate sensitivities. Joshi et al. (2010)
found a positive stratospheric water vapour feedback in an
experiment with the convective entrainment set to 0.6,
caused by a buildup of relative humidity below the tropo-
pause which provided a source for increased stratospheric
water vapour. adsea has an entrainment parameter which is
690 M. J. Webb et al.
123
near the lower end of the range explored in our PPE
(Table 6), which suggests a possible contribution from this
feedback mechanism. However, this value is not as low as
in Joshi et al. (2010), because model versions with very
low entrainment values were screened out in the selection
process for members of the PPE, which included an
assessment of present day performance using the index of
Murphy et al. (2004). adsea also has a quite small ice fall
speed parameter, which Rougier et al. (2009) showed has a
tendency to increase the climate sensitivity in HadSM3.
Reduced ice fall speeds might be expected to increase
upper tropospheric humidity and hence affect the water
vapour feedback. Over the mid-latitude oceans, the cloud
component dominates (Fig. 6), mainly due to the longwave
component (not shown). This may also be a consequence of
the reduced ice fall speeds. The high latitude component is
mainly due to a strongly positive clear-sky shortwave
feedback (not shown) which is the strongest in the
ensemble, and is presumably due to a surface albedo
feedback. The value of the ocean ice diffusion parameter in
adsea is at the upper end of the ensemble range, but
Rougier et al. (2009) show that high values of this
parameter generally tend to reduce the climate sensitivity
of HadSM3. Rougier et al. (2009) also showed that large
values of precipitation efficiency and small values of the
precipitation threshold parameters (both of which adsea
has) tend to increase climate sensitivity in HadSM3. So it
seems likely that these contribute also.
The feedback value for adrye can be attributed to the
same regions as adsea. Again, the low-latitude contribu-
tion is mainly due to the clear-sky longwave feedback
component (not shown). adrye has a relatively large
critical relative humidity threshold, which Rougier et al.
(2009) have shown tends to increase the climate
sensitivity of HadSM3. A larger critical relative humidity
would be expected to inhibit the formation of cloud and
subsequent fallout of ice at upper levels, leading to a
moister upper troposphere in the control simulation. This
could affect the water vapour feedback, as discussed
above. Over the mid-latitude oceans, the cloud component
dominates, but is mainly a shortwave effect in this case
(not shown). The high latitude component is due to a
combination of clear-sky shortwave and shortwave cloud
feedback components (not shown). These shortwave cloud
feedback components may well be due to the precipitation
efficiency value of adrye, which is near the upper end of
the range. Negative shortwave cloud feedbacks can occur
at mid-high latitudes in models, for example when low-
level ice clouds change into liquid water clouds with
smaller drops in the warmer climate (Senior and Mitchell
1993). It is possible that a larger precipitation efficiency
for warm clouds might reduce liquid water contents to
such an extent that this negative shortwave cloud feed-
back would become weaker or even positive. The clear-
sky shortwave feedback component may be caused by the
relatively large value of the sea ice albedo at 0�C in
adrye, which is shown by Rougier et al. (2009) to
increase the climate sensitivity in HadSM3.
adsbb has the strongest global forcing, the largest con-
tribution to which originates over the low latitude oceans
(mainly a shortwave cloud effect, not shown). This model
version has one of the largest precipitation efficiencies in
the ensemble, which would be expected to reduce the
liquid water contents of low clouds. It also has the largest
value of the CAPE timescale parameter in the convection
scheme, which clearly has the potential to affect the
response of shallow and deep convection to changes in
stability following a rapid doubling of CO2.
Table 6 Selected parameter values and switches used in the perturbed physics ensemble for high-mid sensitivity versions
adsea adrye adrhl adrya adsbh adsbb adsbd adseb
Entrainment rate 2.37726 4.51062 3.75359 3.61375 3.16226 3.83715 2.42950 2.16414
Ice fall speed 0.54306 0.64807 0.52716 0.99225 0.57054 0.87884 0.65138 0.53499
Flow dependent RHcrit On Off On On Off On Off Off
Critical rel. humidity Off 0.87689 Off Off 0.68958 Off 0.79788 0.67225
Sat. cloud fraction (BL) 0.51262 0.51606 0.50077 0.51981 0.62522 0.56161 0.50408 0.54746
Sat. CF (free trop.) 0.50631 0.50803 0.50038 0.50991 0.56261 0.53080 0.50204 0.52373
Precip. efficiency 3.50e-4 3.08e-4 1.97e-4 2.36e-4 2.50e-4 3.76e-4 9.90e-5 2.44e-4
Land precip. threshold 1.41e-4 3.23e-4 1.11e-4 1.91e-4 1.49e-4 1.67e-4 2.70e-4 1.04e-3
Ocean precip. threshold 3.23e-5 8.07e-5 2.33e-5 4.73e-5 3.47e-5 4.01e-5 6.75e-5 2.60e-4
Sea ice albedo at 0 �C 0.60104 0.64455 0.53872 0.64619 0.58361 0.58108 0.62855 0.63533
CAPE timescale Off 1.28 Off Off Off 2.43 1.39 Off
Ocean ice diffusion 3.73e-4 3.71e-4 3.62e-4 3.53e-4 3.59e-4 3.45e-4 3.54e-4 3.74e-4
Vertical gradient cloud area Off Off Off Off Off Off Off Off
Climate sensitivity, forcing and feedback in climate models 691
123
adumd has the most negative global feedback parameter
in the ensemble, the largest contribution to which arises
over the mid-latitude oceans (due to longwave cloud and
clear-sky components, not shown). This model version has
quite large values of saturated cloud fraction (Table 7), and
Rougier et al. (2009) show that this tends to result in lower
climate sensitivities in HadSM3.
adrea is the same model version analysed in GW08
(their ‘modified HadSM3’ experiment). Its low sensitivity
can be explained by its small global forcing value, which
originates mainly over the low latitude oceans (primarily
due to a negative shortwave cloud component, not shown).
Negative feedbacks in the mid-latitude ocean and high
latitude regions also contribute substantially. The mid-lat-
itude feedback is mainly a shortwave cloud effect, which
coincides with a strong negative shortwave CRE bias in the
control, the largest in the ensemble (not shown). adrea has
values of saturated cloud fraction which are very close the
the upper end of the range, and one of the smallest values
of precipitation efficiency. Both of these factors would be
expected to increase cloud amount and cloud water in the
control simulation, and have been shown by Rougier et al.
(2009) to reduce the climate sensitivity of HadSM3.
6 Cloud responses in stability regimes over low
latitude oceans
In this section we sort cloud components of the feedback
and forcing terms over the low latitude oceans into per-
centile ranges of LTS, following the approach of Wyant
et al. (2009). This is to see the extent to which the model
features described above originate from different stability
regimes of the tropics. If the conclusions of Williams and
Webb (2009) apply to this more diverse set of models, then
we would expect to see the largest differences in the stable
regions, where stratocumulus clouds are frequent.
Composite responses of LTS, EIS (Wood and Brether-
ton (2006) and pressure velocity at 500 hPa are also
examined to see if any relationships are present between
these large scale forcings and the cloud terms. EIS is
included because it is a slightly better predictor of observed
variations in low cloud amount, and because it makes an
allowance for the systematic increase in static stability due
to the warming free troposphere staying close to a moist
adiabat (Wood and Bretherton 2006). We also examine
composites from the control simulations and compare them
with observational estimates of the equivalent quantities
from ERBE, ISCCP FD, ERA40 and MERRA.
The G04 method is applied in the LTS composite
framework as follows. Ocean grid points between 30�N/S in
each monthly mean are sorted by LTS (defined as the dif-
ference between the potential temperature at the surface and
700 hPa). These are then divided into ten bins covering
equal areas. Ten area-weighted averages of the CRE are
then calculated across these bins for each monthly mean in
the control and CO2 integrations. These are annually aver-
aged, after which the G04 method is applied to estimate
forcing and feedback terms. Bin values are regressed
against global temperatures, to ensure that the forcing/
feedback components within the bins sum exactly to the
equivalents using the full domain average. A similar pro-
cedure is used to calculate the rapid responses of the LTS,
EIS and pressure velocity at 500 hPa, and their responses
with increasing global temperature. To highlight potential
relationships of interest we correlate the net cloud responses
with the other variables in each bin, showing correlations
with a magnitude greater than 0.8. This threshold is well
Table 7 Selected parameter values and switches used in the perturbed physics ensemble for mid-low sensitivity versions
adrhj adseo adumf adumd adtlg adrea aduvb
Entrainment rate 2.98215 4.85597 2.78167 4.35483 3.49381 2.91705 2.89934
Ice fall speed 0.50546 1.42575 1.12286 0.94015 1.04130 0.98441 0.93976
Flow dependent RHcrit Off On Off Off Off On Off
Critical rel. humidity 0.82018 Off 0.72846 0.78531 0.71434 Off 0.84077
Sat. cloud fraction (BL) 0.73756 0.59233 0.67577 0.73136 0.67342 0.79552 0.79598
Sat. CF (free trop.) 0.61878 0.54616 0.58789 0.61568 0.58671 0.64776 0.64799
Precip. efficiency 3.29e-4 3.80e-4 1.10e-4 2.35e-4 6.10e-5 6.30e-5 1.63e-4
Land precip. threshold 1.72e-3 6.78e-4 1.95e-4 1.45e-3 2.76e-4 1.40e-3 1.75e-4
Ocean precip. threshold 4.30e-4 1.69e-4 4.85e-5 3.62e-4 6.90e-5 3.50e-4 4.25e-5
Sea ice albedo at 0 �C 0.63406 0.52116 0.52653 0.53246 0.50429 0.59963 0.50666
CAPE timescale 1.40 Off 1.97 1.56 Off 1.02 Off
Ocean ice diffusion 3.59e-4 3.44e-4 3.63e-4 3.72e-4 3.72e-4 3.74e-4 3.67e-4
Vertical gradient cloud area Off Off Off Off Off Off On
692 M. J. Webb et al.
123
above the 95 % confidence limit, and correlations above 0.8
can account for approximately two thirds of the variance.
(CSIRO Mk3 is not included because pressure velocity at
500 hPa is not available.)
6.1 Cloud feedback components
Previous studies (e.g. Bony and Dufresne 2005; Webb
et al. 2006) have found that, in the AR4 generation of
models, areas where low clouds predominate contribute
more to the inter-model spread in cloud feedback than
those dominated by high-top clouds. This is confirmed by
Fig. 7a. Inter-model differences in the net CRE component
of the feedback are smallest at the low end of the stability
range, where high clouds might be expected to dominate,
becoming larger in the mid-stability range, where trade
cumulus is expected, and largest in upper stability range,
where stratocumulus and stratocumulus-trade cumulus
transition clouds might be expected. The PPE shows
qualitatively consistent results, although the differences in
the stable regions are larger (Fig. 8). Previous studies have
also noted a tendency for model differences in net cloud
feedback to be dominated by the contribution from the
shortwave. This is also clear from Fig. 7. In the 60–100 %
stability range, inter model differences in the shortwave are
much larger than the longwave, and are strongly correlated
with the net. This is also true in the PPE for the 80–100 %
LTS range. The differences in the longwave terms become
progressively larger with towards lower stability bins,
becoming comparable with the range in shortwave differ-
ences. The range in shortwave and longwave is larger than
the net, indicating cancellation in longwave and shortwave
terms, presumably due to changes in high clouds.
Medeiros et al. (2008) showed that differences in trop-
ical climate sensitivity in atmosphere only versions of
NCAR CCSM3.0 and GFDL AM2.0 (forced with globally
uniform SST perturbations) are dominated by different
responses in regions of weak subsidence which would be
expected to be dominated by trade cumulus. Figure 7 also
supports this conclusion for the slab versions of those two
models; their responses are more different in the interme-
diate range, where trade cumulus would be expected to
dominate, than in the stable end of the range, where per-
sistent stratocumulus decks would be expected. When all of
the models are considered however it is clear that the dif-
ferences are larger at the strongly stable end of the range
than the intermediate range, as would be expected from
Williams and Webb (2009). This is also consistent with the
finding of Soden and Vecchi (2011) that traditional
stratoculumus regions show the largest inter-model differ-
ences in cloud feedback in coupled models. This does not
necessarily mean however that the clouds in the stable bins
contribute more to the overall differences in feedback
across the low latitude oceans. As pointed out by previous
studies including Soden and Vecchi (2011), trade cumulus
clouds cover a larger fraction of the tropics than stratocu-
mulus clouds.
Here we attempt to quantify the relative contributions
from these two regimes. It is not immediately clear where
the dividing line should be drawn between these regimes.
Medeiros and Stevens (2011) separated clouds in subsi-
dence regimes into a stratocumulus and a cumulus regime
using an LTS threshold of 18.5 K, which was based on the
point at which stratus cloud fraction reaches 50 % in the
Klein–Hartmann relation. They found that applying this
criterion to ERA40 data over the tropical oceans (30�N/S)
predicted stratocumulus 5 % of the time and trade wind
cumulus 30 % of the time, but noted that this classification
might place transitional cloud types like cumulus topped by
stratiform cloud into the trade-wind cumulus regime.
Figures 1 and 2 of Klein and Hartmann (1993) show maps
of annual stratus cloud amount and net CRE from obser-
vations. Examining these indicates that the 30 and 40 %
contours of stratus cloud amount sit between the regions
classically associated with stratocumulus (with values of
net CRE values below -20 W m-2) and trade cumulus
(with net CRE values above -10 W m-2). Maps showing
the frequency of occurrence of the Williams and Webb
(2009) clusters for ISCCP and MODIS (see their Electronic
Supplementary Material) show that this division captures
the dividing line between the trade cumulus cluster and the
sum of the transition/stratocumulus clusters reasonably
well. According to the Klein–Hartmann relation, a 35 %
value of stratus cloud fraction corresponds to an LTS of
15.9 K. For the models and observations examined here,
the average value of the 80th LTS percentile is 15.8 K. For
this reason, we consider the 80th percentile of LTS to
represent a reasonable dividing line between stabilities
favouring trade cumulus and those favouring stratocumulus
and stratocumulus-cumulus transition clouds. The Wil-
liams and Webb (2009) clustering method gives a fre-
quency of occurrence of 5.7 and 10.4 % for stratocumulus
and transition clouds respectively over the 30�N/S oceans,
a total of 16.1 %, compared with a trade cumulus fre-
quency of occurrence of 42 %. This also supports the
choice of the 80th percentile.
Based on this we estimate that differences in net cloud
feedback components in the 30–80 % LTS range contrib-
ute 0.6 K to the range in climate sensitivity in the AR4
ensemble, while those in the 80–100 % range contribute
0.5 K. From this we conclude that the two regimes are
likely to be of comparable overall importance to the cloud
feedback differences over the low latitude oceans in the
AR4 ensemble. In the PPE, inter-model differences in the
80–100 % LTS range do contribute more than those in
the 30–80 % LTS range.
Climate sensitivity, forcing and feedback in climate models 693
123
The net and shortwave cloud feedback components are
positive in the strongly stable LTS range in eight of the
models in the AR4 ensemble, and very weakly negative in
three (Figs. 7a, b). This is in spite of the fact that LTS
increases in all models in all regimes (Fig. 7d). Klein and
Hartmann (1993) showed that larger amounts of stratus
cloud are observed when LTS is highest, for both seasonal
and interannual variations, but this relationship does not
correctly predict the cloud feedbacks seen here in stable
regions.
Net CRE feedback component (W/m2/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-2
0
2
4
6
8
Net
CR
E f
eedb
ack
com
pone
nt (
W/m
2 /K
)
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
(b) SW CRE feedback component (W/m2/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-2
0
2
4
6
8
SW C
RE
fee
dbac
k co
mpo
nent
(W
/m2 /
K)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
-1.0
0.0
0.2
0.4
corr
elat
ion
(c) LW CRE feedback component (W/m2/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-2
0
2
4
6
8
LW C
RE
fee
dbac
k co
mpo
nent
(W
/m2 /
K)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
corr
elat
ion
LTS response with global temperature (K/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
0.0
0.2
0.4
0.6
LTS
resp
onse
with
glo
bal t
empe
ratu
re (
K/K
)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
corr
elat
ion
(e) EIS response with global temperature (K/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-0.2
0.0
0.2
0.4
EIS
res
pons
e w
ith g
loba
l tem
pera
ture
(K
/K)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
corr
elat
ion
(f) w500 response with global temperature (hPa/day/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-4
-2
0
2
4
6
8
(hPa
/day
/K)
w50
0 re
spon
se w
ith g
loba
l tem
pera
ture
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
corr
elat
ion
(a) (d)Fig. 7 LTS composites of net,
shortwave and longwave cloud
components of feedback over
the low latitude oceans (30�N/S)
in the AR4 ensemble, and
responses per degree change in
global temperature of LTS, EIS
and 500 hPa vertical pressure
velocity. The dashed black linesshows the ensemble mean.
Diamonds indicate correlations
with the net CRE response
which are greater than 0.8
694 M. J. Webb et al.
123
An interesting question to consider at this point is how
much of the response in a given LTS bin can be attributed
to changes in LTS within that bin (assuming any rela-
tionship between LTS and CRE in the control climate
remains unchanged) and how much is due to a change in
such a relationship, or other factors. Figure 11 shows the
present-day CRE as a function of LTS, from the models
and from two sets of satellite observations and analyses. If
CRE was a pure function of LTS and nothing else, then the
CRE values in the warmer climate would simply move
(a) Net CRE feedback component (W/m2/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-2
0
2
4
6
8
Net
CR
E f
eedb
ack
com
pone
nt (
W/m
2 /K
)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
(b) SW CRE feedback component (W/m2/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-2
0
2
4
6
8
SW C
RE
fee
dbac
k co
mpo
nent
(W
/m2 /
K)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(c) LW CRE feedback component (W/m2/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-2
0
2
4
6
8
LW C
RE
fee
dbac
k co
mpo
nent
(W
/m2 /
K)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(d) LTS response with global temperature (K/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
0.0
0.2
0.4
0.6
LTS
resp
onse
with
glo
bal t
empe
ratu
re (
K/K
)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(e) EIS response with global temperature (K/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-0.2
0.0
0.2
0.4
EIS
res
pons
e w
ith g
loba
l tem
pera
ture
(K
/K)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(f) w500 response with global temperature (hPa/day/K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-4
-2
0
2
4
6
8
(hP
a/da
y/K
)
w50
0 re
spon
se w
ith g
loba
l tem
pera
ture
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
Fig. 8 As previous figure, but
for the PPE
Climate sensitivity, forcing and feedback in climate models 695
123
along the curves in the figure. Figure 11 also shows that the
gradients in the models in the 80–100th percentile range
vary from negative to weakly negative in the net CRE, and
negative to weakly positive in the SW CRE. If this rela-
tionship was unchanged in the warmer climate, the larger
LTS values would translate into mostly negative feedbacks
in the 80–100th percentile range. Since the cloud feedback
components are mostly positive here, this demonstrates that
they cannot be understood as simple responses to stability
increases, and that other factors must contribute.
The change in the EIS looks very similar in character to
that in LTS, but is approximately 0.2 K/K smaller on
average (Fig. 7e). This offset is expected because EIS is
formulated to be less sensitive than LTS to changes in lapse
rates in the free troposphere (Wood and Bretherton 2006).
No strong correlations are seen between the net cloud
feedback components and the LTS or EIS responses here,
making it unlikely that the differences between the cloud
feedbacks are caused primarily by differing stability
responses. This does not mean that stability changes are
irrelevant however. The range of stability responses seen in
the models is substantial, and any idealised studies which
aim to reproduce the range in model feedbacks should
explore this large scale forcing comprehensively.
There are of course a number of potential factors other
than stability and subsidence which could explain the
positive feedbacks seen here. Clement et al. (2009) argue
that a weakening of the circulation in the North East Pacific
could reduce low cloud fraction in the warmer climate in
spite of increasing LTS. Watanabe et al. (2011) argue that
increased surface evaporation driven by the strengthening
hydrological cycle might force clouds to break up follow-
ing the deepening warming mechanism which was pro-
posed by Bretherton and Wyant (1997) to explain the
observed transition between subtropical stratocumulus and
trade cumulus clouds in the current climate. Richter and
Xie (2008) do show evidence of increased surface evapo-
ration in the subtropics in the warmer climate in models,
consistent with this idea. Alternatively, Stevens and
Brenguier (2009) argued that increases in free tropospheric
clouds and/or humidity might encourage stratocumulus
breakup by suppressing longwave radiative cooling at
cloud top. Klein et al. (1995) found that observations of
stratocumulus from weather ship P showed small cloud
fractions on days with relatively moist free tropospheric
soundings. More recently, Brient and Bony (2012) have
argued that changes in the vertical gradient of moist static
energy in a warmer climate increase the amount of dry air
imported into the boundary layer in a new version of the
IPSL model, leading to a reduction in cloud and a positive
feedback.
It is also interesting to note that the strong negative low
cloud feedback diagnosed by Wyant et al. (2009) in stable
areas of the low latitude ocean in the ‘super parametrized’
SP-CAM in a uniform ?2K SST perturbation experiment is
not reproduced by any of the models. This difference may
be explained by Blossey et al. (2009), who conclude that
negative low cloud feedbacks in SP-CAM may be exag-
gerated by under-resolution of trade cumulus boundary
layers.
We see decreases in subsidence in most models in mid-
high stability regions (Fig. 7f), as expected given the
established weakening of the Walker Circulation with
increasing temperatures (Vecchi and Soden 2007). A
strong negative correlation between the 500 mb pressure
velocity and the net cloud feedback component is seen in
the 40–60 % percentile range. This seems to be at least in
part due to the unusual behaviour of MPI ECHAM5 and
NCAR CCSM3.0, which show strengthening subsidence
and negative net cloud feedback components in both of the
40–60 % LTS bins. The negative cloud feedback compo-
nent is mainly due to the longwave in NCAR CCSM3.0,
but due to negative shortwave and longwave components
in MPI ECHAM5. This suggests that strengthening subsi-
dence in the trades may be a factor in explaining negative
feedbacks in some models, in contrast to the positive cloud
feedbacks seen with weakening subsidence in the majority
of models. If this behaviour is present in the models par-
ticipating in CFMIP-2, it might be possible to constrain
these feedbacks via comparisons with Cloudsat data via
COSP—for instance if these cloud changes can be shown
to only occur if there is excessive and/or overly optically
thick cloud in these regions compared to observations.
It is also interesting to note that the models with
increasing subsidence in the mid-stability regions show
stronger ascent in the unstable regions, and that most of the
models in the PPE seem to exhibit this behaviour also. This
may be a consequence of the eastward shift of deep con-
vection in the Pacific noted by Vecchi and Soden (2007)
being stronger in some models than others. The correlation
mentioned above is not present in the PPE, which suggests
that it may be due to structural differences between the
members of the AR4 ensemble (e.g. different convective
parametrizations). Ringer and Ingram (submitted) show that
replacing the convective parametrization in HadSM3 with a
simple adjustment scheme substantially weakens the pattern
in the tropical cloud feedback and circulation change,
making it resemble the multi-model mean response.
6.2 Cloud components of CO2 forcing
In the AR4 ensemble, the spread in the net cloud compo-
nents of the forcing is largest at the stable end of the LTS
range, and this is mainly due to the shortwave components
(Fig. 9). This suggests that different rapid adjustments in
low clouds are a leading order cause of differences in the
696 M. J. Webb et al.
123
cloud components of the CO2 forcing over the low latitude
oceans. The same is true in the PPE (Fig. 10). Differences
in the net cloud components of the forcing in the mid-
stability range are however relatively small in both
ensembles. Opposing changes in shortwave and longwave
components cancel to some extent in the net, suggesting
changes in upper level clouds in some of the models.
The net and shortwave CRE components of the forcing
take a range of positive and negative values in all stability
bins in the AR4 ensemble. A strong anti-correlation is seen
(a) Net CRE forcing component (W/m2)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-10
-5
0
5
Net
CR
E f
orci
ng c
ompo
nent
(W
/m2 )
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
(b) SW CRE forcing component (W/m2)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-10
-5
0
5
SW C
RE
for
cing
com
pone
nt (
W/m
2 )
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(c) LW CRE forcing component (W/m2)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-10
-5
0
5
LW C
RE
for
cing
com
pone
nt (
W/m
2 )
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(d) LTS 2CO2 rapid response (K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-1.0
-0.5
0.0
0.5
1.0
LTS
2CO
2 rap
id r
espo
nse
(K)
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(e) EIS 2CO2 rapid response (K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-1.0
-0.5
0.0
0.5
1.0
EIS
2C
O2 r
apid
res
pons
e (K
)
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(f) w500 2CO2 rapid response (hPa/day)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-15
-10
-5
0
5
10
15
w50
0 2C
O2 r
apid
res
pons
e (h
Pa/d
ay)
GISS-ERCCSM3GFDL 2.0CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
Fig. 9 Lower tropospheric
stability (LTS) composites of
net, shortwave and longwave
CRE components of forcing
over the low latitude oceans
(30�N/S) in the AR4 ensemble,
and rapid responses of LTS,
estimated inversion strength
(EIS) and pressure velocity at
500 hPa
Climate sensitivity, forcing and feedback in climate models 697
123
between the EIS responses and the net cloud components in
the most stable bin. This highlights a tendency for models
with the largest positive cloud components (IPSL CM4 and
MIROC 3.2 medres) to show reductions in EIS, and those
with the most negative (HadSM3 and HadGEM1) to show
increases, and is fully consistent with what would be
(a) Net CRE forcing component (W/m2)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-10
-5
0
5
Net
CR
E f
orci
ng c
ompo
nent
(W
/m2 )
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
(b) SW CRE forcing component (W/m2)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-10
-5
0
5
SW C
RE
for
cing
com
pone
nt (
W/m
2 )
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0co
rrel
atio
n
(c) LW CRE forcing component (W/m2)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-10
-5
0
5
LW C
RE
for
cing
com
pone
nt (
W/m
2 )
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(d) LTS 2CO2 rapid response (K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-1.0
-0.5
0.0
0.5
1.0
LTS
2CO
2 r
apid
res
pons
e (K
)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(e) EIS 2CO2 rapid response (K)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-1.0
-0.5
0.0
0.5
1.0
EIS
2C
O2
rap
id r
espo
nse
(K)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
corr
elat
ion
(f) w500 2CO2 rapid response (hPa/day)Oceans [30S,30N]
0 20 40 60 80 100
Percentiles of LTS (%)
-15
-10
-5
0
5
10
15
w50
0 2C
O2
rap
id r
espo
nse
(hPa
/day
)
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0co
rrel
atio
n
Fig. 10 As previous figure, but for the PPE
698 M. J. Webb et al.
123
expected from the observed relationships in Wood and
Bretherton (2006). This suggests that stability changes are
relatively more important for the cloud adjustments than is
the case with the feedbacks.
The longwave components in the AR4 ensemble are
mostly negative, which is in part attributable to the cloud
masking component of the longwave CRE response
(Andrews and Forster 2008). The shortwave components
are positive slightly more often than negative, and modest
positive values are present in most bins for MPI ECHAM5
and CCCMA CGCM3.1, the models with compensating
forcing and feedback components highlighted above. The
relationship between EIS and cloud fraction seen in the
observations cannot explain the tendency of the shortwave
cloud components to be positive more often than negative,
as the EIS increases in most models.
Colman and McAvaney (2011) found that a positive
shortwave cloud adjustment in a version of the Australian
Bureau of Meteorology Research Centre (BMRC) climate
model was due to reductions in low-mid level cloud frac-
tion associated with enhanced heating rates and increased
temperatures from increased CO2, and reductions in rela-
tive humidity. Meanwhile, Wyant et al. (in press) and
Watanabe et al. (2011) have found positive adjustments in
the SP-CAM and MIROC models respectively, coincident
with a shallowing of the boundary layer in subtropical
regions. Wyant et al. (in press) argue that the shallowing of
the boundary layer seen in the SP-CAM is a local effect
caused by a reduction in entrainment, stemming from a
suppression of net longwave cooling in the cloud-topped
boundary layer with increased CO2. Meanwhile, Watanabe
et al. (2011) argue that the boundary layer in MIROC5
shallows because of reduced surface latent heat fluxes in
response to a reduction in the strength of the global
hydrological cycle with increased CO2. We have estimated
the boundary layer depth in the AR4 ensemble using the
difference between the surface pressure and the pressure
level at which the relative humidity drops below 50 %.
This difference reduces in magnitude in the mid-high sta-
bility range in all but a couple of the models examined here
(not shown). This finding is consistent with what would be
expected if boundary layer depth was reducing. However,
this result could equally be explained by a reduction in
relative humidity near top of the boundary layer, as seen in
Colman and McAvaney (2011).
It is also worth noting that the MIROC 3.2 medres is
quite unusual, in that it shows a substantial decrease in LTS
and EIS in all bins, the strongest value being the most
stable bin where the shortwave cloud term is the most
positive. This may be the key to understanding the global
forcing value for MIROC 3.2 medres, which is one of the
largest in the AR4 ensemble. Increasing CO2 would be
expected to warm the lower troposphere in the absence of
any other changes in local diabatic heating terms, leading
to an increase in stability. The decrease in LTS and EIS
suggests that the diabatic heating terms (from the radiation
code or other terms such as the convective heating) must be
acting to reduce temperatures at 700 hPa in response to
CO2 doubling. The MIROC group are currently examining
these terms in a fixed SST experiment with CO2 quadru-
pling and the results will be presented in a later study. A
smaller reduction in EIS is seen in IPSL CM4 in the most
stable bin, coincident with the largest net cloud component
of the CO2 forcing.
The PPE shows results which are similar to the AR4
ensemble in many respects, but it does not capture the
behaviour of MIROC 3.2 medres or IPSL CM4, tending to
favour strong negative shortwave cloud components in the
most stable bins (Fig. 10). Again there is a strong anti-
correlation suggesting a relationship between the adjust-
ments and the EIS at the stable end of the range. The
shortwave components show less of a tendency for positive
values than in the AR4 ensemble, and a slight tendency for
more strongly negative longwave cloud components results
in a tendency for most of the net terms to be negative.
These differences are probably due to the fact that the PPE
is based on HadSM3, which has the strongest negative
shortwave component in the AR4 ensemble, and negative
longwave components in all bins (Fig. 9). The relative
sizes of the spread in unstable, stable and intermediate bins
of stability are quite similar to the AR4 ensemble, however
the spread is larger overall, mainly because of the short-
wave term.
We also note a slight increase in subsidence on average
across the low latitude oceans in both ensembles. This is
expected given the increased transport of heat from land to
ocean with increased CO2, as the tropical atmosphere acts
to minimise zonal temperature gradients in the free tro-
posphere, reducing any rapid land warming due to CO2
increases (Lambert et al. 2011; Wyant et al. in press).
Dong et al. (2009) show evidence of a warming in the
free troposphere spreading out from land regions in a CO2
doubling experiment with the atmosphere component of
HadSM3, and Williams et al. (2008) show evidence of
rapid warming over land in the slab versions of HadSM3
and HadGEM1. Such behaviour might explain the rela-
tively large increase in stability in the stable bins in
HadSM3, some members of the PPE, and to a lesser extent
HadGEM1. All of these models exhibit a dependence of
stomatal conductance on CO2 which reduces evapotrans-
piration and low level cloud when CO2 is increased,
resulting in a positive cloud feedback over land and
enhanced warming (Joshi et al. 2008; Doutriaux-Boucher
et al. 2009). This might also explain why the largest neg-
ative cloud adjustments are seen in stable regions, which
tend to be coastal in the subtropics. It would not explain the
Climate sensitivity, forcing and feedback in climate models 699
123
(a) Net CRE (W/m2)Oceans [30S,30N]
10 15 20 25
LTS (K)
-100
-80
-60
-40
-20
0
Net
CR
E (
W/m
2 )xERBE /ERA40
+ISCCP FD /MERRA
GISS-ERCCSM3GFDL 2.0 CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
(b) SW CRE (W/m2)Oceans [30S,30N]
10 15 20 25
LTS (K)
-100
-80
-60
-40
-20
SW C
RE
(W
/m2 )
xERBE /ERA40
+ISCCP FD /MERRA
GISS-ERCCSM3GFDL 2.0 CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
(c) LW CRE (W/m2)Oceans [30S,30N]
10 15 20 25
LTS (K)
0
10
20
30
40
50
60
70
LW C
RE
(W
/m2 )
xERBE /ERA40
+ISCCP FD /MERRA
GISS-ERCCSM3GFDL 2.0 CCCMA-3MRI-2.3.2AECHAM5HadSM3CCCMA-4MIROC3.2HadGEM1IPSL-CM4
(d) Net CRE (W/m2)Oceans [30S,30N]
10 15 20 25
LTS (K)
-100
-80
-60
-40
-20
0
Net
CR
E (
W/m
2 )
xERBE /ERA40
+ISCCP FD /MERRA
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
(e) SW CRE (W/m2)Oceans [30S,30N]
10 15 20 25
LTS (K)
-100
-80
-60
-40
-20
SW C
RE
(W
/m2 )
xERBE /ERA40
+ISCCP FD /MERRA
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
(f) LW CRE (W/m2)Oceans [30S,30N]
10 15 20 25
LTS (K)
0
10
20
30
40
50
60
70
LW C
RE
(W
/m2 )
xERBE /ERA40
+ISCCP FD /MERRA
aduvbadreaadtlgadumdadumfadseoadrhjadsebadsbdadsbbadsbhadryaadrhladryeadsea
Fig. 11 Lower tropospheric
stability (LTS) composites of
net, shortwave and longwave
CRE over the low latitude
oceans (30�N/S) in the AR4
ensemble, PPE and observations
700 M. J. Webb et al.
123
decreases in EIS seen in MIROC 3.2 medres and IPSL
CM4 however. It is also possible that the relationship
between cloud adjustment and EIS is partly a coupled
effect, as local SST’s adjust to changes in surface radiation
caused by rapid cloud adjustments. As pointed out by
GW08, the rapid adjustment to CO2 in a transient experi-
ment diagnosed by regressing on global near-surface tem-
perature may include the effects of changes in local surface
temperatures as well as in the troposphere. A fixed-SST
experiment might therefore be somewhat different because
sea surface temperatures are held fixed everywhere. If local
SST adjustments play an important role in the relationship
we see here, then it will not be present in the fixed
SST experiments being performed for CMIP5/CFMIP-2.
Aquaplanet experiments will be also performed with fixed
SSTs and quadrupled CO2. If cloud adjustments are mainly
driven by land warming, then such experiments will show
no evidence of them.
6.3 Performance compared to observations
We now return to Fig. 11 and consider the present-day
performance of the models in the LTS composite frame-
work. The distribution of the LTS values from the analyses
are captured quite well by most models in the AR4
ensemble and the PPE. NCAR CCSM3.0 has a tendency to
be more slightly more stable than either MERRA or
ERA40, which is indicative of a warm bias at 700 mb.
Equivalent plots with EIS on the x-axis are qualitatively
very similar (not shown).
It is clear that many of the models fail to capture the
variation of the net and shortwave CRE seen across LTS
regimes in the observational estimates. Many of the models
exhibit net CRE values which are too negative in the
intermediate stability range, which presumably reflects the
difficulty that models have in representing the stratocumu-
lus to trade cumulus transition in the subtropics. The PPE
shows larger biases than the AR4 ensemble, particularly at
higher LTS values, which may be the result of model tuning
in the AR4 ensemble. The longwave CRE is generally better
simulated than in the shortwave in both ensembles.
As discussed above, the model feedbacks in the stable
bins are not generally negative as would be the case if the
Klein–Hartmann relationship was maintained under cli-
mate change. This could be due to an inability of the
models to reproduce the Klein–Hartmann relationship even
for the current climate. If so, there would no reason to
expect them to do so for a climate change. Clement et al.
(2009) showed that many coupled models do not capture
the observed relationships between cloud fraction and LTS
on decadal timescales on the subtropical East Pacific,
which does not give us much confidence in the ability of
models to reproduce such relationships for seasonal
variations in within stratus cloud regions as identified by
Klein and Hartmann (1993)
We are not in a position to evaluate the present day Klein–
Hartmann relationship directly in our models because low
level stratus cloud fractions are not available. We can
however assess the ability of the models to reproduce the
negative gradient in net CRE in the 80–100 % percentile
range in our observational spatio-temporal composites in
Fig. 11. This will be due to the combined effect of interan-
nual, seasonal and spatial covariations in CRE and LTS, and
might be consistent with the Klein–Hartmann relation. Klein
and Hartmann (1993) showed that observed stratus cloud
fraction varies by 5.7 % per K increase in LTS. They also
showed that observed net CRE varies by -1.2 W m-2 per
one percent increase in stratus cloud amount. Combining the
two gives a variation of -6.8 W m-2 per degree K increase
in LTS. Our spatio-temporal composites have a gradient in
the 80–100th LTS precentile range of -7.0 W m-2 for
ISCCP FD/MERRA and -6.4 W m-2 for ERBE/ERA40
and so agree very well with what would be expected from the
Klein-Hartmann relation.
Figure 11 shows that most of the models fail to repro-
duce this relationship. HadGEM1 (which performed well in
Clement et al. 2009) is the only model to lie within the
envelope of the observations in the 80–100th LTS per-
centile range. NCAR CCSM3.0 also has a strongly nega-
tive slope, but not as strong as that observed. These two
models produce very different cloud feedbacks however
(positive in HadGEM1 and weakly negative in NCAR
CCSM3.0). This suggests again that other factors other
than LTS must be contributing to differences between
model cloud feedback components. None of the members
of the PPE fall within the envelope of the observed esti-
mates for net or shortwave CRE in the 80–100th LTS
percentile range.
7 Conclusions
We have diagnosed CO2 forcings and feedbacks in Atmo-
sphere/ Ocean Mixed Layer ‘slab’ climate models from
CMIP3/CFMIP1 (the AR4 ensemble) and from a parameter
perturbed ensemble of HadSM3 experiments (the PPE)
using the method of Gregory and Webb (2008). This
diagnoses an effective CO2 forcing, considering the radia-
tive effects of rapid cloud adjustments in response to CO2
forcing as a component of radiative forcing for analysis
purposes. These adjustments operate on short atmosphere/
land response timescales, in contrast to conventional cli-
mate feedbacks, which operate on longer ocean surface
temperature response timescales (Gregory and Webb 2008).
Differences in feedbacks contribute approximately twice
as much to the range in effective climate sensitivity as
Climate sensitivity, forcing and feedback in climate models 701
123
differences in effective CO2 forcings, qualitatively consis-
tent with the findings of earlier studies which did not allow
for the effects of rapid cloud adjustments on radiative
forcing (e.g. Webb et al. 2006; Dufresne and Bony 2008).
However, the inclusion of adjustment effects means that the
forcing differences contribute more than in Webb et al.
(2006).
In the AR4 ensemble, cloud effects are capable of
explaining the full range in climate sensitivity. Cloud
feedback components contribute four times as much as
cloud components of CO2 forcing to this range, relatively
more than indicated by Gregory and Webb (2008). This is
in part due to the inclusion of additional models, for which
the necessary outputs were not available at the time of
Gregory and Webb (2008) and Andrews and Forster
(2008). These include IPSL CM4, which has the highest
sensitivity in the AR4 ensemble, due to a strong positive
cloud feedback component.
Differences in low latitude oceans regions (30�N/S)
contribute more to the range than in mid-latitude oceans
(30–55�N/S), low/mid latitude land (55�N/S) or high lati-
tude ocean/land (55–90�N/S). Contributions from these
other regions are still substantial however, and are required
to account fully for the higher model sensitivities. Exam-
ples include contributions from mid-latitude oceans and
low/mid latitude land in IPSL CM4, and from mid-latitude
oceans and high latitudes in HadGEM1, the two highest
sensitivity models in the AR4 ensemble.
The models with the highest sensitivities are those
which have strong feedbacks operating in two or more
large scale regions. This suggests that the highest sensi-
tivity models are not so much the ones which have the
strongest local feedbacks, but more the ones which happen
to have positive feedbacks over larger areas. This idea is
also supported by the analysis of Webb et al. (2006), which
showed that inter-model differences in feedbacks from
regions dominated by shortwave cloud feedbacks were
almost entirely due to these regions covering larger areas in
the higher sensitivity models, rather than differences in the
strength of the feedbacks within the regions.
Although many studies have (quite justifiably) focused
on low latitude feedbacks, it will be necessary to scrutinise
other regions as well if the causes of the highest model
sensitivities are to be fully understood. Although it is well
established that inter-model differences in cloud responses
explain more of the inter-model spread than non-cloud
forcings and feedbacks, it does not necessarily follow that
the high or low sensitivities of individual models are pri-
marily attributable to cloud effects. Non-cloud feedbacks
contribute substantially to the high sensitivities of some
models. For example, the largest contribution to the high
sensitivity of HadGEM1 is from a high-latitude clear-sky
shortwave feedback, and clear-sky longwave feedbacks
contribute substantially to the highest sensitivity members
of the PPE. This fact is relevant to studies that consider the
impact of cloud feedback on climate sensitivity—e.g.
Clement et al. (2009).
We identify a number of cases where individual models
show unusually strong forcings and feedbacks compared to
other members of their respective ensembles. This should
not in itself give us reason to doubt the credibility of these
models, as such models may include some key physical
mechanism which is present in the real world and not the
other models. We would like to encourage the modelling
groups to investigate these unusual features in more detail,
performing sensitivity experiments to see what aspects of
the model formulations are responsible.
Effective climate sensitivities in the PPE are strongly
correlated with the global net radiation balance, as in
Yokohata et al. (2010). This is mainly due to relationships
between the biases in the present day shortwave CRE
compared to observations and the strength of the shortwave
cloud feedback arising in the Southern mid-latitude ocean
regions.
We do not find any clear relationships between present
day biases and forcings or feedbacks across the AR4
ensemble (a null result, in contrast with the PPE). We think
that even in the absence of such relationships, it is useful to
highlight unusual values in individual models for further
investigation. We do find a few cases where unusually
strong forcings or feedbacks coincide with unusually large
present day biases in the AR4 ensemble. For these cases we
encourage the modelling groups to perform sensitivity tests
to establish whether or not climate forcings and feedbacks
in these regions are sensitive to local present-day biases.
The observational measures we are using here are crude,
and we would not wish to see any models discounted
purely on the basis of this analysis. More detailed diag-
nostics will be available from the CMIP5 models to pro-
mote better evaluation with observations. For example, the
daily cloud regime analysis of Williams and Webb (2009)
should be possible for all models in CMIP5 using cloud
diagnostics produced by the ISCCP simulator (Klein and
Jakob 1999; Webb et al. 2001). The ISCCP simulator, as
well as new simulators for CloudSat (Bodas-Salcedo et al.
2008) and CALIPSO (Chepfer et al. 2008) will be applied
to the CMIP5 models as part of a programme of activities
coordinated under the Cloud Feedback Model Intercom-
parison Project (CFMIP) using the CFMIP Observation
Simulator Package (COSP, Bodas-Salcedo et al. 2011).
Net cloud feedback components across the low latitude
oceans sorted into percentile ranges of LTS show largest
differences in stable regions, mainly due to their shortwave
components. Although smaller, differences in the mid-
stability range are still substantial, and cover a larger area.
The two regimes contribute comparable amounts to the
702 M. J. Webb et al.
123
overall differences in cloud feedback components over the
low latitude oceans in the AR4 ensemble, but the stable
regions dominate in the PPE.
The net and shortwave cloud feedback components
range from weakly negative to substantially positive in the
strongly stable LTS range in both ensembles. This is in
spite of the fact that LTS and EIS increase in almost all
cases; the observed relationships between LTS, EIS and
low cloud would predict mostly negative feedbacks in this
scenario (Klein and Hartmann 1993; Wood and Bretherton
2006). The range of stability responses seen in the models
is substantial however, and we recommend that future
idealised studies that aim to reproduce the range in model
feedbacks in a single column modelling (SCM) framework
should explore a range of LTS of at least 0.2–0.6 K per
degree global warming.
We see decreases in subsidence in most models in mid-
high stability regions, as expected given the established
weakening of the Walker Circulation with increasing tem-
peratures (Vecchi and Soden 2007). A strong negative cor-
relation between the pressure velocity at 500 hPa and the net
cloud feedback is seen here, suggesting that strengthening
subsidence in the trades may be a factor in explaining nega-
tive feedbacks in some models, in contrast to the positive
cloud feedbacks seen with weakening subsidence in the
majority of models. We recommend that future single column
model studies that aim to reproduce the range in model
feedbacks should explore a range of subsidence forcing of up
to ±2 hPa/day per degree global warming at 500 hPa.
Cloud components of CO2 forcing have the largest dif-
ferences in stable regions, and take a range of positive and
negative values, mainly due to their shortwave compo-
nents. A strong anti-correlation is seen between the EIS
responses and the net cloud components in the most stable
bin. This is qualitatively consistent with what would be
expected from the observed relationships in Wood and
Bretherton (2006). The ability of models to reproduce the
observed relationship between EIS and low level cloud
fraction in the present day (both qualitatively and quanti-
tatively) will be very relevant to their ability to their ability
simulate cloud adjustments correctly, and this could be the
basis for a useful model performance metric. We recom-
mend that future single column studies that aim to repro-
duce the range in model cloud adjustments should explore
a range of stability changes which yield a range of at least
±0.5 K in EIS for CO2 doubling.
The shortwave components are positive slightly more
often than negative, and many of the models in the AR4
ensemble show a reduction in the height of the 50 % rel-
ative humidity level, which might be explained by reduc-
tions in the depth of the boundary layer (Wyant et al.,
in press; Watanabe et al., 2011) or reduced relative
humidity (Colman and McAvaney 2011).
The models struggle to reproduce the observed negative
gradient in net CRE with increasing LTS in the stable
regions of the subtropics, which is consistent with the
observed relationship between LTS and low cloud from
Klein and Hartmann (1993). Clearly this area should
remain a priority for model improvement activities for the
foreseeable future.
One of the main limitations of the Gregory et al. (2004)
method applied to slab models subject to CO2 doubling is
the difficulty of dealing with substantial regression uncer-
tainties in CO2 doubling experiments, a problem which is
particularly acute for low sensitivity models. This problem
is addressed in CMIP5 in three ways. Firstly, the slab
model experiments have been replaced by fully coupled
experiments subject to a sudden quadrupling of CO2, which
we have proposed to enable the Gregory and Webb (2008)
method to be applied with improved signal to noise ratios
(although time dependence of feedbacks will be more of an
issue). Second, we proposed an additional ensemble of
eleven CO2 quadrupling experiments of five years in
length, starting from consecutive months, which can be
used to reduce uncertainty in the diagnosis of the CO2
forcing further, as in Doutriaux-Boucher et al. (2009). Low
signal-to-noise estimates of the effective forcing will also
be available from 30 year experiments with fixed SSTs and
quadrupled CO2 diagnosed using the Hansen et al. (2002)
method. The availability of these experiments for multiple
models will allow the first systematic comparison of the
different methods for diagnosing effective CO2 forcing,
and will be the subject of a follow on study (Andrews
et al., in preparation).
Equilibrium 2CO2 change experiments and the resulting
climate sensitivities are to some extent artificial. However,
they do provide a framework in which CO2 forcing and
atmospheric feedbacks can be consistently diagnosed and
compared. These values are useful because they can be
used to predict transient global temperature responses
under more realistic scenarios. CO2 forcings and feedbacks
diagnosed from slab models subject to instantaneous CO2
doubling are routinely used to calibrate simple energy
balance climate models such as MAGIC6 (Meinhausen
et al. 2011), which can be used to explore a range of cli-
mate change scenarios for which full climate models have
not been run. For example, Rogelj et al. (2011) use the
MAGIC6 model to explore emission pathways consistent
with a 2 K global temperature increase, an exercise which
would be prohibitively expensive with full GCMs. We
have shown that cloud adjustments can contribute much as
0.9 K to climate sensitivity differences between models. A
simple model such as MAGIC6 will inevitably have diffi-
culty predicting the transient response of a full climate
model if it has been calibrated with values which incor-
rectly partition forcing and feedback. Hence we think that
Climate sensitivity, forcing and feedback in climate models 703
123
these effects should be in included in estimates of CO2
forcing so that simple models such as MAGIC6 can be
calibrated using the most accurate forcing and feedback
estimates available.
Instantaneous CO2 doubling is also artificial in the sense
that it is not applied so rapidly in the real world. However,
CO2 concentrations are expected to double by the end of
the 21st century in most climate change scenarios.
Applying the forcing rapidly is simply a diagnostic device
which allows the CO2 forcing to be separated from the
feedback which operates on a longer timescale. It is not
necessarily the case that cloud adjustments diagnosed fol-
lowing an abrupt CO2 doubling are good predictors of the
responses that would be seen with more gradual increases
in CO2. However, Good et al. (2011) show that a simple
model based on results from a 2CO2 step experiment per-
forms well when reconstructing global temperature
responses in a range of emission scenarios with HadCM3,
and Good et al. (submitted) shows that this approach works
well when predicting global temperature responses for a
number of CMIP5 models forced with various RCP sce-
narios. This would not be the case if cloud adjustments
diagnosed following step forcings were inconsistent with
those which occur in response to more gradual increases of
CO2.
Separating the effects of forcing and feedback is also a
necessary step on the road to understanding why some
models have high sensitivities and others have low sensi-
tivities. CFMIP-2 will diagnose forcings and feedbacks in
the next generation of models in a hierarchy of atmosphere
only experiments based on AMIP experiments, aquaplanets
and single column models, to which CO2 forcings and sea
surface temperature perturbations will be applied. These
experiments will include additional diagnostics including
high frequency outputs at fixed sites, radiative fluxes
internal to the atmosphere and temperature, humidity and
cloud physics tendency terms. Single column versions of
these models will also be compared with LES (large eddy
simulation) models with equivalent large scale climate
forcings. Given the failure of observationally based sta-
bility relationships to explain the cloud feedbacks seen in
the models, it will be necessary to develop and test alter-
native physical hypotheses. We have discussed a number of
possibilities, and encourage the modelling groups to test
these in the experimental framework proposed by CFMIP-
2. In this way we hope to gain a better understanding of the
mechanisms controlling climate sensitivity, CO2 forcings
and feedbacks in climate models.
Acknowledgments We would like to acknowledge Rob Wood for
providing code to calculate the EIS, and Tim Andrews, Alejandro
Bodas-Salcedo, Ben Booth, Chris Bretherton, Philip Brohan, Leo
Donner, William Ingram, Manoj Joshi, Adrian Lock, Tomoo Ogura,
Mark Ringer, David Sexton, Yoko Tsushima, Keith Williams, Tokuta
Yokohata and the anonymous reviewers for their helpful comments
and suggestions. We acknowledge the modelling groups, the Program
for Climate Model Diagnosis and Intercomparison (PCMDI) and the
WCRP’s Working Group on Coupled Modelling (WGCM) for their
roles in making available the WCRP CMIP3 and CFMIP multi-model
datasets. Support of these datasets is provided by the Office of Sci-
ence, US Department of Energy. This work was supported by the
Joint DECC/Defra Met Office Hadley Centre Climate Programme
(GA01101).
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