12.003
Introduction to Atmosphere, Ocean, and
Climate Dynamics
Topic 4
Greenhouse Effect
Topic 4 Outline
1. The greenhouse effect
2. A simple greenhouse model
3. A layered greenhouse model
Atmosphere and Earth’s Radiation Budget
The Earth’s atmosphere is relatively:
• transparent to shortwave incoming solar radiation
• opaque to longwave outgoing infrared radiation
Absorption (%)
from surface to
top of
atmosphere
Sun
Earth
Normalizaiton is
by lambda T-4
Shortwave radiation
Longwave radiation
Atmospheric Greenhouse effect
Simplest explanation considering radiation only:
Surface receives downwelling radiation emitted by
atmosphere in addition to solar radiation Raises surface temperature above emission temperature
Land/Sea
No atmosphere
With atmosphere
SW
SW
LW
LW
Atmospheric Greenhouse effect
Convection and other non-radiative processes also
transport energy vertically in the atmosphere • Key point is that atmosphere emits radiation to space
at a different (lower) temperature than the surface
(draw sketch)
• No greenhouse effect if atmosphere is isothermal and
at same temperature as surface
Atmospheric Greenhouse effect
Different in mechanism from domestic greenhouse for
growing plants! • Domestic greenhouse primarily works by preventing
movement of air into and out of the greenhouse while
absorbing sunlight
• Similar effect causes interior of car to become very
hot when in direct sunlight
Average solar radiation =
Absorbed incoming r
Earth’s surface a
Simplest greenhouse
1model:
A ⇥= (1
p )S0 ,
4
One-layer Atmosphere
1
A ⇥= (1
4
1
S ⇥= A ⇤ + (1
4
⇤ Ts4
p )S0 ,
1
= (1
4
⇤ Ta4
p )S0 ,
p )S0 ,
1
S ⇥= A ⇤ + (1
4
⇤ Ta4
1
=
4
= ⇤ Ta4 +
1
4
⇤ Ts4 = ⇤ Ta4 +
Ta = Te = 255 K
Ta = Te = 255 K
Ts = 21/4 Ta = 21/4 255 K = 28
Ts = 21/4 Ta = 288 K
(30C or 86F)
Emission and Surface Temperatures
• Surface temperature is too large for Earth and Mars
• Surface temperature is too low for Venus and Jupiter
Te
Ts
Theory Measured Theory Measured
Ts
K
270
303
251
122
Tsm
K
760
288
230
134
a S ⇥= A ⇤ + (1
⇤ Ts = ⇤ Ta + (1
(
p )S0 ,
p )S0 = 2⇤ Ta
4
4
1
2
4
4
4incoming
4 radiation
4 S0
Absorbed
S=
0 ⇥a
)S
,
⇤
T
=
⇤
T
+
(1
)S
2⇤
T
(3)
1
1
p
0
p
0
s
a
a
4
4
4
ation =
=
=
(1)
4
S
⇥=
A
⇤
+
(1
)S
,
⇤
T
=
⇤
T
+
(1
)S
=
2⇤
T
2
p
0
p
0
s
a
a
1
1
Earth’s surface
4
1area S ⇥= A ⇤44⇥a
1
4
4 + (1 (4)p )S0 = 2⇤ T 4
4
+
(1
)S
,
⇤
T
=
⇤
T
T
=
T
=
255
K
p
0
)S
,
⇤
T
=
(1
)S
(2)
= (1
a
e
s
a
a
p 0
p 0
a
4
4
4
4
1
4
4
T4 = Te =(3)
255 K
(
)S
,
⇤
T
=
⇤
T
+
(1
p 0
p )S0 = 2⇤ Taa
s
a
4
composed of
three layers of
1
1 Consider
Ta = Te =an
255atmosphere
K
(4)
4
Ta = T
e = 255 K
⇤ Ta = (1
(2)
= (1
p )S0 ,
p )S0 1/4
Ts = 2 Ta = 288 K T = T = 255 K
(5)
4 different 4temperature
a
e
4 41
4
⇤ Ts = ⇤ Ta + (1
(3)
p )S0 ,
p )S0 = 2⇤ Ta
1/4
T
=
2
T
(
4
s
a = 288 K
Ta = Te = 255 K increases towards the
(4) surface
• temperature
1/4
T
=
2
Ta = 288 K
Ts = 21/4 Ta4 = 2884K 1
(5)
s
4
I
=
(1
)S
/4
(6)
⇤ Ts = ⇤ Ta + (1
(3)
1/4
p )S0 ,
p )S0 = 2⇤pTa 0
Ts = 2 Ta = 288 K
4
Ta = Te = 255 K
(4)
I = (1
(
p )S0 /4
1/4
Ts = 2 Ta = 288 K
(5)
(1T p )S0 /4
I = ⇤ T14 =⌅ IT=
(7)
I = (1
1 = (6)
e
p )S0 /4
Ta = Te = 255 K
(4)
4
1/4
I
=
p )S0 /4
2
I
=
⇤
T
=⌅
T
=
2
Te(1
(8)
2
4
2
1/4
Layer 1 (
I
=
⇤
T
=⌅
T
=
T
1
e
Ts = 2 Ta = 288 K
(5)
1
(9)
4
1/4
2 I = ⇤ T2 =⌅(6)
T =2 T
(
I = (1
p )S0 /4
I = ⇤ T 4 2=⌅ T e= T
p
0
p
0
Multilayered Greenhouse Model
1/4
Ts = 2 Ta = 288 K
I = (1
p )S0 /4
3I=⇤
2I
4I=⇤
3I
4I
I = (1
p )S0 /4
1
e
=⌅ T24 = 3 Te1/4
T2I4 = (5)
=⌅
2 = 2 T1Te= Te
⇤
T1 T=⌅
1/4
=⌅
T
=
3
Te1/4 1/4
4
4
4
T
=⌅
T
=
(6)
2 I = 2⇤ T2 =⌅ 2 T23 = 2Te Te
4
1/4
4=⌅
=
⇤
T
T
=
4
4
4
3 I = ⇤ T2 =⌅ T2 = 3Te1/4 Te
4
4 I = ⇤ T(6)
=⌅ Ts = 41/4 Te
s
T24
=⇤
T44
=⇤
1
1/4
Layer 2
(
(1
Layer 2(1
Layer 3
Layer 3
Land/Sea
Land/Sea