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Climate Sensitivity: Analysis of Feedback Mechanisms

Authors:

Abstract

We study climate sensitivity and feedback processes in three independent ways: (1) by using a three dimensional (3-D) global climate model for experiments in which solar irradiance S0 is increased 2 percent or CO2 is doubled, (2) by using the CLIMAP climate boundary conditions to analyze the contributions of different physical processes to the cooling of the last ice age (18K years ago), and (3) by using estimated changes in global temperature and the abundance of atmospheric greenhouse gases to deduce an empirical climate sensitivity for the period 1850–1980.
Reprinted From
Climate Procqses iindClimate Sensitivity
Geophysical Monograph
29,
Maurice
Ewing
Volume
5
Copyright
1984
by
the
American Geophysical
Union.
CLIMATE SENSITIVITY: ANALYSIS OF
FEEDBACK
MECHANISMS
J.
Hansen,
A.
Cacis,
D.
Rind.
G.
Russell
NASAlGoddard Space Flight Center, Institute for Space Studies
2880 Broadway,
New
York.
NY
10025
P.
Stone
Center for Meteorology and Physical Oceanography
Massachusetts Institute of Technology, Cambridge,
MA
02139
I.
Fung
Lamont-Dohe rty Geological Ob se
r
vat0 ry of Columbia University
/
Palisades,
NY
10964
R.
Ruedy.
J.
Lerner
MIA
COM
Sigma Data, Inc.
2880 Broadway, New York.
NY
10025
Abstract. We study climate sensitivity and
feedback processes in three independent ways
:
(1)
by using a three dimensional (3-D) global cli-
mate model for experiments in which solar irra-
diance
So
is
increased
2
percent
or
C02
is
doubled,
(2)
by
using the
CLIMAP
climate boun-
dary conditions to analyze the contributions of
different physical processes to the cooling of the
last ice age (18K years ago), and
(3)
by using
estimated changes in global temperature and the
abundance of atmospheric greenhouse gases to
deduce an empirical climate sensitivity for the
period 1850-1980.
Our 3-D global climate model yields a warming
of
-4OC
for either a
2
percent increase of
So
or
doubled
C02.
This indicates a net feedback fac-
tor of
f =
3-4, because either of these forcings
would cause the earth's surface temperature to
warm 1.2-1.3OC to restore radiative balance with
space,
if
other factors remained unchanged.
Principal positive feedback processes in the
model are changes in atmospheric water vapor,
clouds and snow lice cover. Feedback factors
calculated for these processes, with atmospheric
dynamical feedbacks implicitly incorporated, are
respectively fwater va
or
-
1.6.
fclouds
-
1.3
and fsnqw/ice
-
1.1,
wiph the latter mainly caused
by sea ice changes.
A
number of potential feed-
backs, such
as
land ice cover, vegetation cover
and ocean heat transport were held fixed
in
these
experiments.
We calculate land ice, sea ice and vegetation
feedback
1.2-1.3,
1.05-1
1
.s
for the 18K climate to be fland
ice
-
fsea ice
N
1.2,
and fye etation
from their effect on the radiagon budget
at the top
of
the atmosphere. This sea ice feed-
back at 18K
is
consistent with the smaller
fsnow/ice
1.1
in
the
So
and
C02
experiments,
which applied to a warmer earth with
less
sea
ice.
We
also
obtain an empirical estimate of
f
=
2-4
for the fast feedback processes (water
vapor, clouds, sea ice) operating on
10-100
year
time scales by comparing the cooling due to slow
or
specified changes (land
ice,
C02,
vegetation)
to the total cooling at 18K.
The temperature increase believed to have
occurred in the past 130 years (approximately
0.5OC)
is
also
found to imply a climate sensitivity
of 2.5-5OC for doubled
C02
(f
=
2-41.
if
(1)
the
temperature increase
is
due to the added
greenhouse gases,
(2)
the 1850
C02
abundance
was
270210
ppm, and
(3)
the heat perturbation
is
mixed like a passive tracer in the ocean with ver-
tical mixing coefficient k
-
1
cm2
s-1.
These analyses indicate that
f
is
substantially
greater than unity on all
time
scales. Our best
estimate for the current climate due to processes
operating on the
10-100
year time scale
is
f
=
2-4,
corresponding to a climate sensitivity of
2.5-5OC for doubled
C02.
The physical process
contributing the greatest uncertainty to
f
on this
time scale appears to be the cloud feedback.
We show that the ocean's thermal relaxation
time depends strongly on
f.
The e-folding time
constant for response of the isolated ocean mixed
layer
is
about
15
years, for the estimated value
of
f.
This time
is
sufficiently long to allow
substantial heat exchange between the mixed layer
and deeper layers.
For
f
=
3-4
the response time
of the surface temperature to a heating pertur-
bation
is
of order
100
years,
if
the perturbation
is
sufficiently small that it does not alter the
rate of heat exchange with the deeper ocean.
The climate sensitivity we have inferred
is
larger than that stated in the Carbon Dioxide
Assessment Committee report
(CDAC.
1983).
Their result
is
based on the empirical tem-
perature increase
in
the past 130 years, but their
analysis did not account for the dependence of
-
the ocean response timnon climate sensitivity.
Their choice of a fixed
15
year response time
biased their result to low sensitivities.
We infer that, because of recent increases in
atmospheric
C02
and trace gases, there
is
a
large, rapidly growing gap between current cli-
mate and the equilibrium climate for current
atmospheric composition. Based on the climate
sensitivity
we
have estimated, the amount of
greenhouse gases presently in the atmosphere will
cause an eventual global mean warming of about
l0C,
making the global temperature at least com-
parable to that
of
the Altithermal, the warmest
period in the past 100,000 years. Projection of
future climate trends on the
10-100
year time
scale depends crucially upon improved under-
standing of ocean dynamics, particularly upon how
ocean mixing will respond to climate change at the
ocean surface.
Introduction
Over a sufficient length of time, discussed
below, thermal radiation from the earth must
balance absorbed solar radiation. This energy
balance requirement defines the effective
radiating temperature of the earth, Te, from
or
where
R
is
the earth radius,
A
the earth albedo,
So
the solar irradiance,
s
the mean flux of
absorbed solar radiation per unit area and
IJ
the
Stefan-Boltzmann constant. Since
A
-
0.3
and
So
-
1367
W
m-2,
s
-
239
W
m-2
and
this require-
ment of energy balance yields Te
-
255K. The
effective radiating temperature
is
also
the physi-
cal temperature at
an
appropriately defined mean
level of emission to space. In the earth's
atmosphere this mean level of emission to space
is
at altitude
tl
-
6
km. Since the mean tro-
pospheric temperature gradient
is
-5.5OC
km-1,
the surface temperature
is
T
-
288K.
-33K
warmer
than Tee
It
is
apparent
from
(3)
that for changes of
solar irradiance
(3)
Thus
if
So
increases by a small percentage
6,
Te increases by
614.
For example,
a
2
percent
change in solar irradiance would change Te by
about
0.5
percent,
or
1.2-1.3OC.
If
the atmo-
spheric temperature structure and all other fac-
tors remained fixed, the surface temperature
would increase
by
the same amount
as
Te.
Of
course all factors are not fixed, and we there-
fore define the net feedback factor,
f,
by
ATeq
=
f
ATo
(4
1
where ATeq
is
the equilibrium change
of
global
mean surface air temperature and ATo
is
the
change of surface temperature that would be
required to restore radiative equilibrium
if
no
feedbacks occurred.
We use procedures and terminology of feedback
studies in electronics (Bode. 1945) to help ana-
lyze the contributions of different feedback pro-
cesses. We define the system gain as the ratio
of the net feedback portion
of
the temperature
change to the total temperature change
Since
ATeq
=
ATo
+
ATf
eedbacks
*
(6)
it follows that the relation between the feedback
factor and gain
is
1
f
=--
1-g
(7)
In general a number of physical processes
contribute to
f.
and it
is
common to associate a
feedback factor
fi
with a given process
i,
where
fi
is
the feedback factor which would exist
if
all
other feedbacks were inoperative.
If
it
is
assumed that the feedbacks are independent, feed-
back contributions to the temperature change can
be separated into portions identifiable with indi-
vidual feedbacks,
with
HANSEN
ET
AL.
131
and
(10)
-1
ATeq
---
AT^
-
1-cgi
i
It follows that two feedback gains combine
linearly as
g =g1+ g2
s
but the feedback factors combine as
(11)
f=
flf2
(12)
Thus even when feedback processes are linear
and independent the feedback factors are not
multiplicative.
For
example, a feedback process
with gain gi
=
1/3
operating by itself would cause
a 50 percent increase in ATeq.compared to the no
feedback radiative response, 1.e..
fi
=
1.5.
If
a
second feedback process of the same strength
is
also operating, the net feedback
is
f
=
3
(not
2.25).
One implication
is
that,
if
strong positive
feedback exists, a moderate additional positive
feedback
may
cause a large increase in the net
feedback factor and thus
in
climate sensitivity.
The feedback factor
f
provides an intuitive
quantification of the strength of feedbacks and a
convenient way to describe the effect of feed-
backs on the transient climate response. The
gain g allows clear comparison of the contribu-
tions of different mechanisms to total climate
change. The above formalism relates
f
and g and
provides a framework for analyzing feedback
interactions and climate sensitivity.
A
number of physical mechanisms have been
identified as causing significant climate feedback
(Kellogg and Schneider,
1974).
As
examples, we
mention two of these mechanisms here. Water
vapor feedback arises from the ability of the
atmosphere to hold more water vapor as tem-
perature increases. The added water vapor
increases the infrared opacity of the atmosphere,
raising the mean level of infrared emission to
space to greater altitude, where it
is
colder.
Because the planetary radiation to space temporar-
ily does not balance absorbed solar energy, the
planet must warm to restore energy balance; thus
fw
>
1
and gw
>
0.
a condition described as a
positive feedback. Ice/snow feedback
is
also
positive; it operates by increasing the amount of
solar energy absorbed by the planet as ice melts.
Feedback analyses will be most useful
if
the
feedback factors are independent to
first
order
of the nature of the radiative forcing (at the top
of the atmosphere). The si-milar model responses
we obtain in our
So
and
C02
experiments tend to
corroborate this possibility, although there are
some significant differences in the feedbacks for
solar and
C02
forcings. We expect the strength
of feedbacks to have some dependence on the ini-
tial climate state and thus on the magnitude of the
climate forcing; for example, the icelsnow albedo
feedback
is
expected to change with climate as
the cryospheric region grows
or
shrinks.
We examine feedback processes quantitatively
in the following sections by means of
3-D
climate
model simulations and analysis of conditions
during the last ice age (18K years
ago).
The
3-D
experiments include doubling
C02
and increasing
So
by
2
percent, forcings of roughly equal
magnitude which have also been employed by
Manabe and Wetherald
(1975)
and Wetherald and
Manabe
(1975).
18K
simulations with a
3-D
general circulation model have previously been
performed
by
Williams et al.
(1974).
Gates
(1976)
and Manabe and Hahn
(1977).
Three-Dimensional Climate Model
The global climate model we employ
is
described and its abilities and limitations for
simulating today's climate are documented as
model
I1
(Hansen et al., 1983b, hereafter
referred to as paper
1).
We note here only that
the model solves the simultaneous equations for
conservation of energy, momentum, mass and
water and the equation of state on a coarse grid
with horizontal resolution
8O
latitude by
loo
longitude and with
9
atmospheric layers. The
radiation includes the radiatively significant
atmospheric gases, aerosols and cloud particles.
Cloud cover and height are computed. The diur-
nal and seasonal cycles are included. The ground
hydrology and surface albedo depend upon the
local vegetation. Snow depth is computed and
snow albedo includes effects of snow age and
masking
by
vegetation.
Ocean temperatures and ice cover are spe-
cified climatologically in the documented model
11.
In the experiments described here, ocean tem-
peratures and ice cover are computed based on
energy exchange with the atmosphere, ocean heat
transport, and
the
ocean mixed layer heat capa-
city. The latter two are specified, but vary
seasonally at each gridpoint. Monthly mixed layer
depths are climatological, compiled from
NODC
mechanical bathythermograph data
(NOAA,
1974)
and from temperature and salinity profiles in the
southern Ocean (Gordon, 1982). The resulting
global-mean seasonal-maximum mixed layer depth
is
110m. In our
3-D
experiments a
65m
maximum
is
imposed on the mixed layer depth to minimize
computer time
;
this yields a global-mean seasonal-
maximum mixed layer depth of
63m.
The
65m
maximum depth
is
sufficient to make the mixed
layer thermal response time much greater than
one year and provide a realistic representation of
seasonal temperature variations,
so
the mixed
layer depth limitation should not significantly
affect the modeled equilibrium climate.
The ocean heat transport was obtained from
the divergence of heat implied
by
energy conser-
vation at each ocean gridpoint in the documented
132
HANSEN
ET
AL.
I
1 1
I
I
I
-180 -120
-
60
0
60
I20
I80
Longitude (degrees)
eat
FIUX
into
Ocean
(
w
m-')
Control
Run
I
i
Month
Fig.
1.
Specified heat flux into the ocean
sur-
face in the
3-D
climate model experiments,
obtained from the model
I1
run of paper
1
which
had specified climatological seasonally-varying
ocean surface temperature and ocean ice cover.
(a)
is
the geographical distribution of the annual-
mean flux.
(b)
is
the latitudelseason distribution
of the zonal-mean flux.
model
I1
(paper
l),
using the specified mixed
layer depths. The geographical distribution of
the resulting annual mean heat flux into and out
of the ocean surface
is
shown in Fig. la;
averaged over the entire hemispheres,
it
yields
2.4
W
m-2
into the Southern Hemisphere surface
and an equal amount out of the Northern
Hemisphere. The
gross
characteristics of the
ocean surface heating and implied ocean heat
transport appear to be realistic, with heat input
at low latitudes. especially in regions of
upwelling cold water, and release at high lati-
tudes, especially in regions of poleward
currents. Fig.
15
of paper
1
shows that the
longitude-integrated heat transport
is
consistent
with available knowledge of actual transports.
A
more co mpre hens
i
ve comparison with observations
has been made by Miller et al.
(1983).
who show
that the implied annual northward heat flux at the
equator
is
6.2
x
1014
W.
With the ocean heat
transport specified in this manner, the control
run with computed ocean temperature has a simu-
lated climate nearly the same as the documented
model
11.
It
is
not identical, as a result of
changes in the sea ice coverage which arise when
the sea ice
is
a computed quantity. There
is
15
percent less sea ice
in
the standard control run
with computed ocean temperature than in the docu-
mented model
11,
as discussed below. This has
local effects, mainly around Antarctica, but
otherwise simulated quantities are practically
identical to the documented model
I1
climatology.
In our experiments with changed solar irra-
diance and atmospheric
C02
we keep the ocean
heat transport identical to that in the control
run. Thus
no
ocean transport feedback
is
per-
mitted in these experiments. Our rationale for
this approach as a first step
is
its simplicity for
analysis, and the fact that it permits a realistic
atmospheric simulation.
Ocean ice cover
is
also computed in the
experiments described here on the basis of the
local heat balance. When the ocean surface loses
heat, the mixed layer temperature decreases as
far as the freezing point of ocean water,
-1.6OC.
Further heat loss from the open ocean causes ice
to grow horizontally with thickness
lm
until the
gridbox
is
covered up to the limit set by the pre-
scription for leads (open water). Still further
heat loss causes the ice to thicken. Leads are
crudely represented by requiring the fraction of
open water in a gridbox to be greater than
or
equal to O.l/zice, where
zice
is
the ice thickness
in meters (paper
1).
Heat exchange between ocean ice and the mixed
layer occurs by conduction in the climate model.
A
two-slab model
is
used for ice, with the tem-
perature profile parabolic in each slab. This
conduction is inefficient, and,
if
it were the only
mechanism for heat exchange between the mixed
layer and the ice, it would at times result in
ocean ice coexisting with ocean water far above
the freezing point; since this does not occur in
nature, other mechanisms (such as lateral heat
exchange) must contribute to the heat exchange.
Therefore in our standard control run and
So
and
C02
experiments we impose the condition that the
mixed layer temperature, which represents a mean
for
an
8O
x
loo
gridbox, not
be
allowed to exceed
OOC
until all the ice in the gridbox
is
melted;
i.e.,
if
the mixed layer temperature reaches
O°C
additional heat input
is
used to meltice, decreas-
ing its horizontal extent within the gridbox.
The annual mean sea ice cover in out standard
control run
is
shown in Fig.
2b.
Evidently there
is
too little sea ice in the model
(15
percent less
than the observations of Fig. 2a). especially at
longitudes
-1OOOW
and
-50°E
in the Southern
Hemisphere. Thus we also produced an alternate
control run by removing the condition that all
heat added
to
the mixed layer be used to melt ice
HANSEN
ET
AL.
133
if
the mixed layer temperature reaches
OOC.
This
alternate control run has about
23
percent
greater ocean ice cover (Fig. 2c) than observed,
and thus the standard and alternate control runs
bracket observations. We use the alternate
control run for a second doubled
COP
experiment,
as one means of assessing the role of ocean ice
in climate sensitivity.
In the following we first describe our standard
So
and
C02
experiments.
So
and
CO2
Experiments
So
was increased
2
percent and
CO2
was
doubled (from
315
ppm to
630
ppm) instantaneously
on January
1
of year
1.
Both experiments were
run for
35
years. In this section we study the
equilibrium response of the climate model to the
So
and
CO2
forcings. The time dependence of the
surface air temperature and the heat flux into the
planetary surface are briefly noted, but only
to
verify that equilibrium has been achieved. The
time dependence of these experiments
is
discussed in greater detail in a subsequent sec-
tion concerned with the transient response of the
climate system.
Global Mean Heat Balance and Temperature
_____________I
Model
I1
(paper
1)
has a global annual mean
net heat flux into the top of the atmosphere of
7.5
W
m-2
(-2
percent of the insolation).
2.5
W
m-2
of this imbalance
is
due to conversion of
potential energy to kinetic energy (which
is
not
reconverted to heat in the model) and computer
truncation. The other global
5
W
m-2
is
absorbed
by the ocean and ocean ice, at a rate of
7.1
W
me2
for the ocean surface area. This portion of
the imbalance must be due to inaccuracies such as
in the cloud properties, surface albedo, thermal
emission calculations, etc.
In
our control
run
and experiments with computed ocean temperature
we multiply the solar radiation absorbed at the
ocean surface by the factor 0.96, which cancels
the entire energy imbalance. The radiation
correction factor has no appreciable direct effect
on model sensitivity since all results are dif-
ferenced against a control run; however, it does
enable physical processes, such as condensation
and ice melting, to operate at temperatures
as
realistic as possible. Together with the spe-
cified ocean transports, this allows the control
run with computed ocean temperature to have
essentially the same ocean temperature and cli-
mate as the model
I1
run with fixed climatological
ocean temperatures (paper
1).
The global mean heat flux into the planetary
surface and surface air temperature are shown in
Fig.
3
for the
So
and
CO2
experiments. The heat
flux peaks at
-3
w
m-2
for both experiments; the
radiative imbalance at the top
of
the atmosphere
is
essentially the same as this flux into the pla-
netary surface, since the heat capacity of
the
atmosphere
is
small. Similar fluxes are expected
Observations
Sea Ice Cover (Dercent)
I
1
I I I
1
Longitude
a
-180
-120
-
60
0
60
I20
I
BO
-
60
-
90
-180 -120
-
60
0
60
I20
Longitude
90
60
30
Sea
Ice
Cover (~ercentl
Model
It
(alternate control run)
30
-
60
-90
1
I
1
I
I
1
-180
-120
-
60
0
60
I20
I80
Fig.
2.
Annual-mean sea ice cover. (a) obser-
vational climatology
of
Walsh and Johnson (1979)
for the northern hemisphere and Alexander and
Mobley
(1976)
for the southern hemisphere.
(b)
our standard control run of the
3-D
climate
model.
(c)
alternate control run, as described in
the text.
Longitude
C
134
HANSEN
ET
AL.
Year
of
Experiment
Run
a
Fig.
3.
Global net heat flux into planetary
sur-
face (a) and global surface air temperature (b).
On April
1
of year
2
in the
So
experiment the
computer was hit
by
a cosmic ray
or
some other
disturbance which caused improper numbers to be
stored in the ground temperature array. This
affected the temporal development of that run,
but should not influence its equilibrium results.
In order to determine the maximum heat flux into
the ocean, the
So
experiment was rerun for years
2
and
3
froin
March
31
year
2
thus eliminating the
computer error for that period.
in the two experiments because of the similar
magnitudes of the radiative forcings. The
2
per-
cent
So
change corresponds to a forcing of
4.8
W
The initial radiative imbalance at the top of
the atmosphere due
to
doubling
C02
is
only
-2.5
W
m-2, but after
C02
cools the stratosphere
(within a few months) the global mean radiative
forcing
is
about
4
W
m-2
(Fig.
4,
Hansen et
al.,
1981).
Over the ocean fraction of the globe we
find a peak flux into the surface of
4-5
W
m-2
in
both experiments, of order
10
percent greater
than the global mean forcing
for
an
all-ocean pla-
net. Thus heating of the air over land with sub-
sequent mixing by the atmosphere increases the
net heat flux into the ocean, but not by the ratio
of global area to ocean area as assumed by
Hanscn et al.
(1981).
Apparently heating over
continental areas
is
balanced substantially by
increased cooling to space.
A
chief implication
is
that the time constant for the ocean to respond
to global heating
is
longer than obtained from the
common practice of averaging the ocean heat
capacity over the entire globe (rather than over
the ocean area).
The equilibrium global mean warming of the
surface air
is
about
4OC
in both the
So
and
C02
experiments. This corresponds to a feed-
back factor
f
=
3-4,
since the no-feedback tem-
perature change required to restore radiative
equilibrium with space
i.s
ATo
= 1.2-1.3OC.
The
heat flux and temperature approach their new
equilibria with an e-folding time of almost a
decade. We show in the section on transient cli-
mate response that the e-folding time is propor-
tional to f, and that the value inferred from Fig.
3
is
consistent with
f
=
3-4.
The mechanisms causing the global warmings
in
these experiments are investigated below,
including presentation of the global distribution of
key changes. These results are the means for
years 26-35 of the control and experiment runs.
Fig.
3
indicates that this should provide essen-
tially the equilibrium response, since by that time
the heat flux into the ocean
is
near zero and
the
temperature trend has flattened out.
Global Temperature Changes
--
The temperature changes in the
So
and
C02
ex-
periments are shown in Fig.
4
for the annual mean
surface
air
temperature as a function of latitude
and longitude, the zonal mean surface
air
tem-
perature as a function of latitude and month, and
the annual and zonal mean temperature as a func-
tion
of
altitude and latitude. We discuss the
nature and causes of the temperature changes,
and then make a more quantitative analysis below
using
1-D
calculations and the alternate
CO2
ex-
periment with changed sea ice prescription.
The surface air warming
is
enhanced at high
latitudes (Fig.
4,
upper panel) partly due to the
greater atmospheric stability there which tends to
confine the warming to the lower troposphere,
as
shown by the radiation changes discussed below
and the experiment with altered sea ice.
There
is
a very strong seasonal variation of
the surface warming at high latitudes (Fig.
4,
middle panel), due to the seasonal change of
atmospheric stability and the influence of melting
sea ice in the summer which limits the ocean tem-
perature rise. At low latitudes the temperature
increase
is
greatest in the upper troposphere
(Fig.
4,
lower panel), because the added heating
at the surface primarily causes increased eva-
poration and moist convection, with deposition of
HANSEN
ET
AL.
135
Doubled
COz
9o
A
Surface Air Temperature
("C)
Longitude
(degrees)
JFMAMJJASONDJ
Month
Longitude
(degrees)
ASurface Air Temperature
("C)
cn
e,
~
5=
%---
JFMAMJJASONDJ
I_
Month
Latitude
(degrees)
Latitude
(degrees)
Fig.
4.
Air
temperature change in the climate model for a two percent increase of solar irra-
diance (left) and for doubled atmospheric
CO2
(right). The upper graphs show the geographical
distribution of annual mean surface
air
warming, the middle graphs show the seasonal variation of
the surface
air
warming averaged over longitude, and the lower graphs show the altitude distri-
bution of the temperature change averaged over season and longitude.
136
HANSEN
ET
AL.
Longitude (degrees)
Control
Run
9o
u
Surface
Air
Ternperoture
("C)
60
-
v)
a,
30
?
0
a,
7J
W
3
-0
-
0
1
-
-30
_I
Month
u
Ternperoture
("C)
Control
Run
Latitude (degrees
)
Longitude (degrees)
90A
Surface
Air
Temperoture/u
Fig.
5.
Right side:
standard deviation of temperature in the control run.
Left side: standard deviation of temperature for the last
10
years in the control run.
ratio of temperature change for years
26-35
of the doubled
CO2
experiment to the
latent heat and water vapor at high levels. the ratio of the change
of
the quantity in the
The statistical significance of these results doubled
C02
experiment to the standard deviation.
can be verified from Fig.
5,
which shows the The standard deviation
is
computed routinely for
standard deviation
for
the last
10
years of the all of the quantities output from our
3-D
model.
control run for all the quantities in Fig.
4,
and We only discuss changes in the experiment runs
HANSEN
ET
AL.
137
which are far above the level of model fluc-
tuations
or
'noise' in the control run.
The patterns of temperature change are re-
markably similar in the
So
and
C02
experiments,
suggesting that the climate response
is
to first
order a function of the magnitude of the radiative
forcing. The only major difference
is
in
the tem-
perature change as a function of altitude; in-
creased
C02
causes substantial stratospheric
cooling. This similarity suggests that, to first
order, the climate effect due to several forcings
including various tropospheric trace gases may
be
a simple function of the total forcing.
The global mean warming of surface
air
that
we obtain for doubled
C02
is
similar to that
obtained by Manabe and Stouffer (1980)
for
quadrupled
C02.
This large difference in sen-
sitivity of the two models appears to be asso-
ciated mainly with the feedback mechanisms in the
models, as discussed below. The patterns of the
temperature changes in the two models
show
gross similarities, but also significant differen-
ces. We defer detailed comparison of the model
results until after discussion of the feedback
mechanisms.
1-D
Analysis of Feedbacks in 3-D Experiments
The processes chiefly responsible for the tem-
perature rise in the
3-D
model can be investi-
gated with
a
1-D
radiative convective
(RC)
climate model. We use the
1-D
model of Lacis et
al. (1981) to evaluate the effect of changes in
radiative forcing that take place in the
3-D
model
experiments.
As
part of the 3-D model
diagnostics,
we
have available global average
changes in surface and planetary albedo, and
changes in amount and vertical distribution of
clouds, water vapor and atmospheric lapse rate.
We insert these changes one-by-one,
or
in
com-
bination, into the
1-D
model and compute the
change in global surface temperature.
We
employ
the usual 'convective adjustment' procedure in
our
1-D
calculations, but with the global mean
temperature profile of the 3-D model as the cri-
tical lapse rate in the troposphere. Contrary to
usual practice, we allow no feedbacks to operate
in the
1-D
calculations, making it possible to
associate surface temperature changes with indi-
vidual feedback processes.
There is no a priori guarantee that the net
effect of these changes will yield the same
warming in the
1-D
model as in the
3-D
model,
because simple global and annual averages of the
changes do not account for the nonlinear nature
of the physical processes and their
2-D
and
3-D
interactions. Also, changes in horizontal dynarni-
cal transports of heat and moisture are not
entered explicitly into the
1-D
model; the effects
of dynamical feedbacks are included in the
radiative factors which they influence, such as
the cloud cover and moisture profile, but the
dynamical contributions are not identified.
Nevertheless, this exercise provides substantial
138
HANSEN
ET
AL.
information on climate feedbacks. Determination
of how well the
1-D
and 3-D results correspond
also
is
a useful test for establishing the value of
1-D
global climate models.
The procedure we use to quantify the feed-
backs
is
as follows. The increase of total water
vapor in the
3-D
model (33 percent in the
So
experiment)
is
put in the
1-D
model by
multiplying the water vapor amount at all levels
by the same factor (1.33); the resulting change in
the equilibrium surface temperature of the
1-D
model defines the second bars in Fig.
6.
Next
the water vapor at each level in the
1-D
model
is
increased by the amount found in the 3-D experi-
ment; the temperature change obtained in the
first
(total
H20
amount) test
is
subtracted from
the temperature change obtained in this test to
obtain the temperature change credited to the
change in water vapor vertical distribution. The
change of temperature gradient (lapse rate) be-
tween each pair of levels in the
3-D
model
is
inserted in the control
1-D
model to estimate the
effect of lapse rate change on surface tem-
perature, shown by the fourth bars in Fig.
6.
Since the lapse rate changes are due mainly to
changes of water vapor,
we
take the net of these
three temperature changes in the
1-D
model as
our estimate of the water vapor contribution to
the total temperature change. The global mean
ground albedo change in the
3-D
model (defined as
the ratio of the global mean upward and downward
solar radiation fluxes at the ground)
is
inserted
into the
1-D
control run to obtain our estimate of
the icelsnow albedo contribution to the tem-
perature change.
Cloud contributions are more difficult to ana-
lyze accurately because of the variety of cloud
changes that occur in the 3-D model (see below),
including changes in cloud overlap, and the fact
that the changes do not combine linearly. We
first estimate the total cloud impact by changing
the cloud amounts at all levels in the
1-D
model
in proportion to changes obtained in the 3-D
model. The total cloud effect on the temperature
obtained in this way
is
subdivided by defining a
portion to be due to the cloud cover change (by
running the
1-D
model with a uniform change of
all clouds
so
as to match the total cloud cover
change in the 3-D model) and by assigning the
remainder of the total cloud effect to cloud
height changes. These assumptions involve some
arbitrariness. Nevertheless, the resulting total
temperature changes in the
1-D
model are found
to be within
0.2OC
of the global mean temperature
changes in the 3-D experiments, providing cir-
cums tantial evidence that the procedure takes into
account the essential radiative aspects of cloud
cover change.
The temperature changes in the
1-D
model are
shown in Fig.
6
for the standard
So
and
C02
experiments, and the
C02
experiment with alter-
nate sea ice computation. Resulting gains and
feedback factors are given in Table
1.
Water vapor feedback. Water vapor provides
-I
i
I
-
V
;0
a
-I
Fig.
6.
(-02KlkmI
CO,
H,O
H,O
Ground
Cloud Cloud
1x21
(~1.371
Vertical Albedo
Height
Cover
Distribution
I-
I. I
%I
Contributions to the global mean tem-
-
perature rise in the
So
and
C02
experiments as
estimated by inserting changes obtained in the
3-D
experiments into
l-D
radiative convective model.
(a)
+2
percent
So
experiment,
(b)
doubled
C02
experiment, md (c) doubled
C02
experiment for
alternate control run with greater sea ice.
the largest feedback, with most of it caused by
the increase of water vapor amount. Additional
positive feedback results from the water vapor
distribution becoming weighted more to higher
altitudes, but for the global and hemispheric
means this
is
approximately cancelled by the nega-
tive feedback produced by the changes in lapse
rate, also due mainly to the added
H2O.
The
near cancellation
of
these two cffects
is
not
sur-
prising, since the amount of water the atmosphere
holds
is
largely dependent on the mean tem-
perature, and the temperature at which the
infrared opacity occurs determines the infrared
radiation. This tendency for cancellation
suggests that the difficulty in modeling moist con-
vection and the vertical distribution of water
vapor may not have a great impact on estimates of
global climate sensitivity (excluding the indirect
effect on cloud distributions).
The net water vapor gain thus deduced from
the 3-D model
is
gw
-
0.4,
or a feedback factor
fw
-
1.6.
The same sensitivity for water vapor
is
obtained in
l-D
models by using fixed relative
humidity and fixed critical lapse rate (Manabe and
Wetherald.
1967),
thus providing some support for
that set of assumptions
in
simple climate models.
Relative humidity changed only slightly i