Atul Kapur
akapur@rsmas.miami.edu
from a paper by
S. Manabe and Richard T. Wetherald
1966
No atmosphere
R 2
4


1

A
S


T
e
4R 2
Fixed emissivity and
absorptivity at a
given layer
Fixed distribution of
absorbers including
water vapor (or
Absolute humidity)
(Manabe and Srickler, 1964)
But in reality
Absolute Humidity
is a strong function
of temperature?
DJF
JJA
Why fixed Relative
Humidity?
Strong seasonal
variation in
Absolute Humidity
Zonal-mean Absolute humidity (g kg-1)
DJF
JJA
Weak seasonal
variation in
Relative Humidity
Zonal-mean Relative humidity (%)
(Peixoto and Oort, 1992)
No atmosphere
R 2
4


1

A
S


T
e
4R 2
Fixed emissivity and
absorptivity at each
layer
Fixed distribution of
absorbers including
water vapor (or
Absolute humidity)
(Manabe and Srickler, 1964)
But Absolute Humidity is
a strong function of
temperature?
(Telegadas
and London, 1954)
Fixed distribution of
Relative humidity
(Manabe and Wetherald, 1967)

Mixing ratio is now allowed to change with
change in temperature
w  RH  ws T 

Another degree of freedom PARTIALLY
released

Constrained by the condition of fixed Relative
Humidity

Mixing ratio of CO2 is
assumed to be constant (300
ppm by volume)
(Herring
and Borden, 1965)
(London, 1956)
Cloud characteristics
Ozone
Radiative
(Fixed abs. humidity)
Cooler
Atmospheric
Temperature
+
Fixed relative
humidity
Radiative
(Fixed relative
humidity)
Less
moisture
Less
greenhouse
effect
RadiativeConvective
(Fixed relative
humidity)
Further
temperature
drop at the
surface
Self Amplification effect
(Hergesell, 1919)
OLR  Tz
4
Fixed abs.
humidity (I)

L Fixed
w  RH with C dry (II)
C p  C p 1 

RH with effective C
 C p t Fixed
T 4

OLR  Tc
4
p
z
p (III)
Tc 4
Warmer
OLR lesser
Increase in
(than in case
Atmospheric
Increase
in of
Slower
Slower
moisture
in
a
fixed absolute
Increase in
Temperature
latent
energy
Approach
approach
humidity)
given
volume
height of
+
of air
towards
towards
of
air
effective
Lesser Radiative
Fixed relative
equilibrium
equilibrium
Increase
in
source of OLR
cooling
humidity
effective heat
Approach of mean temperature towards equilibrium
capacity
OLR  Tz
OLR  Tc
4
Tc 4
Tz 4
Higher value
of Solar
constant
+
Fixed relative
humidity
Increase in
temp.
+
But OLR
less than
expected
4
Further inc. in
temp. to
increase OLR at
top of
atmosphere
Higher
sensitivity of
temperature
upon Solar
constant
For fixed RH,
equilibrium temp. is
almost twice as
sensitive as for fixed
absolute humidity
 Difference in sensitivity
decreases with temp.

Fixed RH
Surf
Temp.
Solar constant
Fixed abs.
humidity
Mixing ratio of water
vapor is lower at lower
temperatures
Self-amplification
effect
More CO2 results
in warmer
troposphere and
warmer surface
 More CO2 results
Increase in
Inc. inin
COcolder
2
temp.
+
Increased
stratosphere
+
Fixed relative
sensitivity
 Stratospheric
OLR less
humidity
to CO2
thanmore
temp. much
sensitiveexpected
to CO2
than
troposphere.
Sensitivity
of temperature
upon
Doubling
of CO2 raises

COthe
double astemp.
compared
atmospheric
by
2 almost
to fixed absolute humidity


Larger albedo
colder the
temperature
Influence of
surface albedo
vanishes with
height
Sensitivity upon surface
albedo almost double as
compared to fixed
absolute humidity



Time required for radiation-condensation
relaxation is almost double than that required
for radiation relaxation.
For fixed RH, sensitivity of surface temp.
upon solar constant, cloudiness, surface
albedo, and CO2 content is almost twice as
compared to that for fixed absolute humidity
Doubling of CO2 with fixed relative humidity
increases surface temp. by about 2.3°C.