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Twentieth century climate model response and climate sensitivity
Jeffrey T. Kiehl
Received 19 July 2007; revised 30 August 2007; accepted 13 September 2007; published 28 November 2007.
 Climate forcing and climate sensitivity are two key
factors in understanding Earth’s climate. There is
considerable interest in decreasing our uncertainty in
climate sensitivity. This study explores the role of these
two factors in climate simulations of the 20th century. It is
found that the total anthropogenic forcing for a wide range
of climate models differs by a factor of two and that the total
forcing is inversely correlated to climate sensitivity. Much
of the uncertainty in total anthropogenic forcing derives
from a threefold range of uncertainty in the aerosol forcing
used in the simulations. Citation: Kiehl, J. T. (2007),
Twentieth century climate model response and climate
sensitivity, Geophys. Res. Lett.,34, L22710, doi:10.1029/
 Understanding the climate of the past is an important
aspect to our ability to predict Earth’s future climate. Three
dimensional global climate models are the most compre-
hensive tools available to simulate Earth’s past, present and
future climates. Methods of testing these models with
observations form an important part of model development
and application. Over the past decade one such test is our
ability to simulate the global anomaly in surface air tem-
perature for the 20th century. A number of observational
reconstructions of the temporal evolution of this climatically
important quantity have been created [Jones et al., 1999].
Climate model simulations of the 20th century can be
compared in terms of their ability to reproduce this temper-
ature record. This is now an established necessary test for
global climate models. Of course this is not a sufficient test
of these models and other metrics should be used to test
models, for example the ability to simulate the evolution of
ocean heat uptake over the later part of the 20th century
[Levitus et al., 2001; Barnett et al., 2001], or a models
ability to simulate trends in various modes of variability. All
of these can be viewed as necessary test for climate models.
 A review of the published literature on climate
simulations of the 20th century indicates that a large number
of fully coupled three dimensional climate models are able
to simulate the global surface air temperature anomaly with
a good degree of accuracy [Houghton et al., 2001]. For
example all models simulate a global warming of 0.5 to
0.7°C over this time period to within 25% accuracy. This is
viewed as a reassuring confirmation that models to first
order capture the behavior of the physical climate system
and lends credence to applying the models to projecting
 One curious aspect of this result is that it is also well
known [Houghton et al., 2001] that the same models that
agree in simulating the anomaly in surface air temperature
differ significantly in their predicted climate sensitivity. The
cited range in climate sensitivity from a wide collection of
models is usually 1.5 to 4.5°C for a doubling of CO
most global climate models used for climate change studies
vary by at least a factor of two in equilibrium sensitivity.
 The question is: if climate models differ by a factor of
2 to 3 in their climate sensitivity, how can they all simulate
the global temperature record with a reasonable degree of
accuracy. Kerr  and S. E. Schwartz et al. (Quantifying
climate change –too rosy a picture?, available at www.
nature.com/reports/climatechange, 2007) recently pointed
out the importance of understanding the answer to this
question. Indeed, Kerr  referred to the present work,
and the current paper provides the ‘‘widely circulated
analysis’’ referred to by Kerr . This report investi-
gates the most probable explanation for such an agreement.
It uses published results from a wide variety of model
simulations to understand this apparent paradox between
model climate responses for the 20th century, but diverse
climate model sensitivity.
 The application of simple climate models has eluci-
dated the most important factors that, to first order, deter-
mine Earth’s global mean surface temperature. A number of
studies [Raper et al., 2001; Forest et al., 2002; Knutti et al.,
2002] have shown that there are three fundamental climate
factors, namely: the climate forcing, the climate sensitivity
and the efficiency of ocean heat uptake. Given these three
factors one can calculate the evolution of the global mean
surface temperature. All of the models applied to simulating
the 20th century climate represent these factors in varying
degrees of sophistication. The focus of the present work is
on two of these factors: climate forcing and climate sensi-
tivity. The role of the efficiency of ocean heat uptake will be
discussed later. In the simpler energy balance models these
three factors are specified, while in the more comprehensive
three dimensional climate models the climate sensitivity and
efficiency of ocean heat uptake are predicted.
 The climate forcing of the 20th century is calculated
by assuming time evolving growth curves for greenhouse
gas concentrations, aerosol concentrations and natural forc-
ing factors that include solar variability and volcanic aero-
sols. It is important to note that the change in radiative flux
is calculated and not prescribed in the fully coupled climate
models. In the simpler energy balance models the actual
radiative forcing is prescribed. The temporal evolution of
the well-mixed greenhouse gases is more constrained by
GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L22710, doi:10.1029/2007GL031383, 2007
Climate Change Research Section, National Center for Atmospheric
Research, Boulder, Colorado, USA.
Copyright 2007 by the American Geophysical Union.
observations compared to changes in tropospheric aerosols
[Houghton et al., 2001]. Given the evolution of these
forcing agents a temporal evolution of climate forcing is
applied to the climate system, which then responds to the
forcing. The magnitude of the surface temperature response
for a given forcing is determined by the climate sensitivity.
Uncertainties in climate forcing will be reflected in uncer-
tainties in a models ability to replicate the observed climate
 The climate sensitivity is determined by a myriad of
feedback processes in the climate system, which includes
water vapor, clouds, sea ice and other processes. It is
believed that much of the range in model climate sensitivity
is due to uncertainties in cloud feedback processes [Cess et
al., 1996]. The reason for the 2 to 3 fold spread in climate
sensitivity has been of great concern to the climate com-
munity [Kerr, 2004]. Although much focus has been on
uncertainties in climate sensitivity, the question arises as to
how important are uncertainties in forcing and the implica-
tions of these uncertainties in the ability to simulate the
climate of the 20th century [Hansen and Sato, 2001].
 A large number of climate modeling groups have
carried out simulations of the 20th century. These simula-
tions employed a number of forcing agents in the simula-
tions. Although there are established data for the time
evolution of well-mixed greenhouse gases, there are no
established standard datasets for ozone, aerosols or natural
forcing factors. Results from nine fully coupled climate
models [Dai et al., 2001; Boer et al., 2000; Roeckner et al.,
1999; Haywood et al., 1997; Mitchell et al., 1995; Tett et al.,
2002; Meehl et al., 2004; Meehl et al., 2000] and two
energy balance models [Crowley and Kim, 1999;
Andronova and Schlesinger, 2000] have been used to
consider the relationship between total anthropogenic cli-
mate forcing and climate sensitivity. All of these simula-
tions show very good agreement between the simulated
anomaly in global mean surface temperature and the obser-
vational record. Many of these studies document the models
equilibrium climate sensitivity and the aerosol and total
forcing over the 20th century time period.
 The total climate forcings used in the present anal-
ysis were taken from the above cited references. When only
total climate forcings were available from the studies, the
total greenhouse forcing was used from Houghton et al.
 to back out the net aerosol forcing. Since the
uncertainty in total greenhouse forcing (20% or less) is
much smaller than that due to aerosols, this approach
introduces only small uncertainty in the present analysis.
 The theoretical relationship between climate forcing
and climate sensitivity is obtained by considering Earth’s
global energy budget [e.g., Andreae et al., 2005],
which states that the forcing of the climate system, DQ, is
balanced by energy escaping to space, lDT, and energy
stored in the oceans, H. Note that the total forcing of the
system, DQ, is defined as the change in total radiative
forcing between the end of the 20th century and the time
period of the late 1800s. lis the climate feedback parameter
and is determined by the various feedback processes in the
system. The climate sensitivity, DT
, is defined as the
change in equilibrium global surface-air temperature due to
a doubling of carbon dioxide, where at equilibrium, H = 0,
and (1) implies,
Using (2), l=DQ
, which means (1) can be written
The forcing due to a doubling of carbon dioxide is
[Andreae et al., 2005], while the observed
change in surface-air temperature is taken to be 0.6°C. The
change in ocean energy storage is 0.7 Wm
Substituting these values into (3) yields,
This expression indicates an inverse relationship between
total forcing and climate sensitivity. With regards to the
change in ocean heat storage, Hansen et al.  estimate
an uncertainty in H of ±0.15 Wm
. An analysis of coupled
model simulations forced with a 1% per year increase in
carbon dioxide indicates a spread in ocean energy storage,
at the point of doubling, of 0.4 Wm
. Based on these
estimate, the present analysis will assume an uncertainty of
 The model results for total anthropogenic forcing,
DQ, and equilibrium climate sensitivity, DT
, are shown
in Figure 1, while the solid line is based on (4), and the
dashed lines above and below this central line arise from the
uncertainty in H. It is assumed that the natural
forcing is much smaller than the anthropogenic forcing.
These results clearly illustrate a strong inverse correlation
between total anthropogenic forcing used for the 20th
century and the model’s climate sensitivity. Indicating that
models with low climate sensitivity require a relatively
higher total anthropogenic forcing than models with higher
 It may be argued that it would be more accurate to
use a measure of the transient climate sensitivity in this
analysis, since the simulation of the 20th century is a
transient phenomenon. However, the transient climate re-
sponse as defined as the change in global mean surface air
temperature at the time of doubling in models assuming 1%
per year increase in CO
show a similar range as the
equilibrium sensitivity (1.4 to 3.8°C, see Table 9.1 by
Houghton et al. ). So whether equilibrium or transient
sensitivity is used the results in Figure 1 will be unchanged.
 Note that the range in total anthropogenic forcing is
slightly over a factor of 2, which is the same order as the
uncertainty in climate sensitivity. These results explain to a
large degree why models with such diverse climate sensi-
tivities can all simulate the global anomaly in surface
temperature. The magnitude of applied anthropogenic total
forcing compensates for the model sensitivity.
 Although there is a clear inverse correlation between
the forcing and the climate sensitivity there is some spread
in the data points. Note that all the model results, except for
one, fall close to or within the theoretical curves based on
L22710 KIEHL: CLIMATE MODEL RESPONSE AND SENSITIVITY L22710
the estimated uncertainty in H. This strongly suggests that
the scatter among the models is mostly due to the range in
modeled change in ocean heat storage.
 What is the major reason for the large uncertainty in
total anthropogenic forcing? Figure 2 shows the correlation
between total anthropogenic forcing and forcing due to
tropospheric aerosols. There is a strong positive correlation
between these two quantities with a near 3-fold range in the
magnitude of aerosol forcing applied over the 20th century.
This large uncertainty in aerosol forcing has recently been
noted [Anderson et al., 2003; Schwartz, 2004] as a signif-
icant challenge to the climate modeling community. Thus,
the large uncertainty in aerosols over the past leads to a
wide range in total anthropogenic forcing. Some of the
models used in these simulations employed only the direct
effect, while others used both direct and indirect effects of
aerosols, which makes a more detailed comparison of
simulated aerosol forcing difficult.
 These results indicate that the range of uncertainty in
anthropogenic forcing of the past century is as large as the
uncertainty in climate sensitivity and that much of forcing
uncertainty is due to aerosols. In many models aerosol
forcing is not applied as an external forcing, but is calcu-
lated as an integral component of the system. Many current
models predict aerosol concentrations interactively within
the climate model and this concentration is then used to
predict the direct and indirect forcing effects on the climate
system. Thus, it may be difficult to arrive at a standard
approach that all models could employ for use in compar-
ison of simulations forced in the same manner. However, a
first step would be for models to employ standard emissions
for aerosol gas precursors and particulate emissions.
 It is important to note that in spite of the threefold
uncertainty in aerosol forcing, all of the models do predict a
warming of the climate system over the later part of the 20th
century. The warming is in essence bounded by the fact that
climate sensitivity is a positive quantity and the total
forcings used by modelers are also positive. This implies
that the total forcing of the 20th century cannot be negative,
i.e. the negative aerosol forcing cannot be larger than the
positive greenhouse forcing, which bounds the magnitude
of the total aerosol forcing.
 It could also be argued that these results do not
invalidate the application of climate models to projecting
future climate for, at least, two reasons. First, within the
range of uncertainty in aerosol forcing models have been
benchmarked against the 20th century as a way of establish-
ing a reasonable initial state for future predictions. The
analogy would be to weather forecasting where models
assimilate information to constrain the present state for
improved prediction purposes. Climate models are forced
within a range of uncertainty and yield a reasonable present
state, which improves the models predictive capabilities.
Second, many of the emission scenarios for the next 50 to
100 years indicate a substantial increase in greenhouse
gases with associated large increase in greenhouse forcing.
Given that the lifetime of these gases is orders of magnitude
larger than that of aerosols, future anthropogenic forcing is
dominated by greenhouse gases. Thus, the relative uncer-
tainty in aerosol forcing may be less important for projec-
ting future climate change.
Figure 1. Total Anthropogenic Forcing (Wm
equilibrium climate sensitivity (°C) from nine coupled
climate models and two energy balance models that were
used to simulate the climate of the 20th century. Solid line is
theoretical relationship from equation (4). Dashed lines arise
from assuming a ±0.2 Wm
uncertainty in ocean energy
storage in equation (4).
Figure 2. Total anthropogenic forcing (Wm
aerosol forcing (Wm
) from nine fully coupled climate
models and two energy balance models used to simulate the
L22710 KIEHL: CLIMATE MODEL RESPONSE AND SENSITIVITY L22710
 Finally, the focus of this study has been on anthro-
pogenic forcing. There is also a range of uncertainty in
natural forcing factors such as solar irradiance and volcanic
aerosol amount. It would of value to reduce uncertainties in
these forcing factors as well. It would also be of great value
to investigate the robustness of these results relative to the
latest versions of coupled climate system models. However,
given the fundamental physical relationship among climate
response, climate forcing and sensitivity, i.e. (3), it is hard to
imagine that these results do not apply to the latest coupled
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search is sponsored by the National Science Foundation. This work was
supported in part by the Department of Energy Office of Science Climate
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L22710 KIEHL: CLIMATE MODEL RESPONSE AND SENSITIVITY L22710