AOSC 621


The total amount of solar radiation intercepted by the Earth is where R e is the radius of the earth. This energy will be spread over the entire area of the Earth - 4

R e
2
. Hence the average solar flux

R e
2
, that reaches the top of the atmosphere (TOA) is given by :
F
S
 
R e
2
S / 4

R e
2

S / 4
Where S is the solar constant. The earth reflects some of this radiation . Let the albedo be ρ, then the energy absorbed by the earth is (1ρ) F s
.
The thermal energy emitted by the earth is σ
B
T e
4
Hence we get
T e

 

( 1


B
) F s


1 / 4

• The spherical albedo of the earth is about 30%. This gives an effective temperature of 255 K. This is considerably lower than the measured average temperature at the surface T s of about 288 K.
• The fact that T s
>T e is seen in all of the terrestrial planets with substantial atmospheres. It is due to the fact that whereas the planets are relatively transparent in the visible part of the spectrum, they are relatively opaque in the infra-red.
• A portion of the IR emitted by the surface and atmosphere is absorbed by polyatomic gases and reemitted in all directions – including back to the earth.

Greenhouse effect - one atmospheric layer model
•
 is the fraction of the IR radiation absorbed by the atmosphere


Greenhouse effect
Consider the radiative equlibrium in the atmosphere.
The amount of energy absorbed is emitted is 2
 b
T
E
4
and the amount
 b
T
A
4
. Hence in equilibrium :
T
A
4 
T
E
4
/2
Now consider the energy balance at the surface :
(1
 
) S
4
  b
T
A
4   b
T
E
4 substituting for T
A
we get
(1

4

) S

 b
T
E
4
2 which gives
  b
T
E
4
T
E


 4

(1
 b

(1

)

S
/2)


1/ 4

Greenhouse effect
• An examination of the previous equation shows that as e increases the ground temperature increases.
• This is what is referred to as greenhouse warming.
• As we shall show later, not all of the additional energy trapped by the additional absorption goes inot heating the surface. Some , for example goes into evaporation of water - which stores energy in the atmosphere as additional latent heat.
• So one should view the inference of the equation with some caution.
• This issue will be discussed later when climate feedback is addressed.

• First Law of Thermodynamics - the time rate of change of the column energy is

E
 t

N

( 1
 
) F s

F
TOA
• Where N is called the radiative forcing
• and F
TOA
  eff

B
T
S
4
Where Teff is the effective transmission of the atmosphere to thermal radiation ( (1-e) in the simple model)

• What happens if N(T
S
) is changed by Δ N(T
S
)
• Assume that the atmosphere moves to a new equilibrium temperature , then we can write

N


N

T s

T s

0
We define the climate sensitivity α as

T s d   
N

  
(

N /

T s
)

1 



F
TOA

T s


( 1
 

T s
)

F s



2
• The calculated radiative forcing from doubling
CO
2 is ~4 Wm -2
• Assuming that the solar flux is constant we get
 

(

B
T s
4 T eff

T s
)

1


4

B
T s
3
T eff


1 
T s
4 F
TOA
• F
TOA
= 240 Wm -2 and T s
= 288 K, hence α=0.3 Wm -2 K -1
• Hence the increase in surface temperature is 1.2 K

• Suppose the solar constant were to decrease by 1%
• Assume no feedbacks other than the reduced thermal emission. If there is no albedo change due to the decreased solar flux then the second term in the climate sensitivity is zero. Hence we get:
 

N

T
S


F
TOA
/

T s



( 1



( 1

)

F
S

)

F
S

• Substituting for F
TOA
 

( T eff


T s
B
T s
4

T s d 
T s

1




4
T s

F
S
4 F
S
F
TOA




1
• Change in temperature is -0.72 K

• Consider a parameter Q ( such as albedo) that depends on the surface temperature
• The direct forcing Δ N is augmented by a term

N

Q

Q
.

T s
.

T s
• Solving for the climate sensitivity we find



{ 4 F
TOA
/ T s

(

N /

Q )(

Q /

T s
)}

1

• If we have an arbitrary number of forcings Q then one can derive a general expression for the climate sensitivity
 

4 F
TAO
/ T s
 
(

N /

Q ) /(

Q /

T s
)


1
It should be noted that the above equation assumes that the individual forcings are independent of one another

• ·POSITIVE AND NEGATIVE FEEDBACKS
• ·WATER VAPOR - POSITIVE
• ·ICE COVER - POSITIVE
• .CLOUDS - POSITIVE AND NEGATIVE -
MAINLY NEGATIVE

Positions of the jet streams
Fig. 7-27, p. 191

Relation between jet stream and high and low pressure systems
Fig. 8-30, p. 231

Using Total Ozone measurements
• Contributions to the column ozone amount
(total ozone) come mainly from the lower stratosphere. In this altitude region ozone has a long chemical lifetime compared to its dynamic lifetime. Hence one can treat Total
Ozone acts as a dynamic tracer.
• The subtropical and polar fronts correspond to a rapid change in the tropopause height, and total ozone shows abrupt changes.
• Hudson et. al, 2003, 2006 developed a method to determine the position of the fronts
(jet streams) from satellite total ozone data.

Jet Streams on March 11, 1990
Sub-tropical = Blue, Polar = Red

Mean latitude of the Sub-tropical front
Shift from 1980 to 2004 is 1.7 degrees

Mean Latitude of the Polar Front
Shift from 1980 to 2004 is 3.1 degrees

• Zonal mean stream function study gives values from 2.5 to 3.1 degrees
• Tropopause analysis gives values of 5-8 degrees
• OLR study gives values from 2.3 to 4.5
• Ozone gives value for the Northern Hemisphere only of
1.7 degrees
• All over the period 1979 to 2005

21 st Century Predicted Widening
Ensemble mean ~2 deg. latitude Lu et al. (2007)
Southern
Edge south Hadley Cell north
Northern
Edge

• Observed: ~2-5°latitude 1979-2005
• Modeled (A2 scenario): ~2°lat over 21 st century
• Modeled 25-yr trends during 21 st century
– 40 100-yr projections →
– Mean 0.5°
– >2.0° in only 3% of cases
– Max 2.75°
– (Celeste Johanson, Univ. of Washington)

Temperature deviation (GISS) versus latitude

Number of tropical pixels versus time for longitude -80 to -60
28 to 32 latitude
38 to 42 latitude
48 to 52 latitude
58 to 62 latitude

Number of tropical pixels for 58 to 62 latitude vs longitude