12.003 Introduction to Atmosphere, Ocean, and Climate...
Transcript of 12.003 Introduction to Atmosphere, Ocean, and Climate...
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12.003 Introduction to Atmosphere, Ocean, and Climate Dynamics
Topic 5 Greenhouse Effect (continued)
and Climate Sensitivity
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Topic 5 Outline
1. Radiative transfer in the atmosphere2. A leaky greenhouse model that accounts for fact that atmosphere not opaque to longwave radiation3. Climate sensitivity to radiative forcing
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Radiative transfer in the atmosphere
• Shortwave Absorption: clouds, H20, O3, O2
• Shortwave Reflection: clouds, surface
• Longwave Absorption: clouds, H20, CO2, CH4, N2O
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Absorption and Emission in a Gas Vibrational and rotational transitions that dominate infrared absorption are associated with H2O and C02
(major greenhouse gases)
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Principal Atmospheric Absorbers
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David Archer website
Model spectrum of upwelling longwave radiation at TOA(surface 270K, coldest point 215K)
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David Archer textbook
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Leaky Greenhouse Model
Average solar radiation =Absorbed incoming radiation
Earth’s surface area=
S0⇤a2
4⇤a2 =S0
4(1)
A ⇥= 14(1��p)S0, ⌅T 4
a =14(1��p)S0 (2)
A ⇥= 14(1��p)S0 +(1� ⇥)S ⇥, ⌅T 4
a =14(1��p)S0 (3)
S ⇥= A ⇤+14(1��p)S0, ⌅T 4
s = ⌅T 4a +
14(1��p)S0 = 2⌅T 4
a (4)
S ⇥= A ⇤+14(1��p)S0 = A ⇤+
14(1��p)S0 =
24(1��p)S0 +(1� ⇥)S ⇥, (5)
Ta = Te = 255 K (6)
Ta =�
12� ⇥
⇥1/4
Te (7)
Ts = 21/4Ta = 288 K (8)
Ts =�
22� ⇥
⇥1/4
Te (9)
I = (1��p)S0/4 (10)
I = ⌅ T 41 =⌅ T1 = Te (11)
2 I = ⌅ T 42 =⌅ T2 = 21/4Te (12)
3 I = ⌅ T 42 =⌅ T2 = 31/4Te (13)
4 I = ⌅ T 4s =⌅ Ts = 41/4Te (14)
(15)
Etotal = Eatomic +Evibrational +Erotational +Etranslational (16)
1
Average solar radiation =Absorbed incoming radiation
Earth’s surface area=
S0⇤a2
4⇤a2 =S0
4(1)
A ⇥= 14(1��p)S0, ⌅T 4
a =14(1��p)S0 (2)
A ⇥= 14(1��p)S0 +(1� ⇥)S ⇥, ⌅T 4
a =14(1��p)S0 (3)
S ⇥= A ⇤+14(1��p)S0, ⌅T 4
s = ⌅T 4a +
14(1��p)S0 = 2⌅T 4
a (4)
S ⇥= A ⇤+14(1��p)S0 = A ⇤+
14(1��p)S0 =
24(1��p)S0 +(1� ⇥)S ⇥, (5)
Ta = Te = 255 K (6)
Ta =�
12� ⇥
⇥1/4
Te (7)
Ts = 21/4Ta = 288 K (8)
Ts =�
22� ⇥
⇥1/4
Te (9)
I = (1��p)S0/4 (10)
I = ⌅ T 41 =⌅ T1 = Te (11)
2 I = ⌅ T 42 =⌅ T2 = 21/4Te (12)
3 I = ⌅ T 42 =⌅ T2 = 31/4Te (13)
4 I = ⌅ T 4s =⌅ Ts = 41/4Te (14)
(15)
Etotal = Eatomic +Evibrational +Erotational +Etranslational (16)
1
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Emission and Surface Temperatures
• Earth’s atmospheric emissivity in the infrared is 70-85% (very roughly!)
Ts = 21/4Ta = 288 K (12)
Ts =�
22� ⇤
⇥1/4
Te (13)
I = (1��p)S0/4 (14)
I = ⇧ T 41 =⇤ T1 = Te (15)
2 I = ⇧ T 42 =⇤ T2 = 21/4Te (16)
3 I = ⇧ T 42 =⇤ T2 = 31/4Te (17)
4 I = ⇧ T 4s =⇤ Ts = 41/4Te (18)
(19)
Etotal = Eatomic +Evibrational +Erotational +Etranslational (20)
⇥Ts = ⌅ ⇥Q =⇤ ⌅ =⌃Ts
⌃Q
⇤K
Wm�2
⌅(21)
⇥QBB = ⇥ (⇧T 4e ) = 4T 3
e ⇥Te = 4T 3e ⇥Ts =⇤ ⌅ =
14⇧T 3
e= 0.26
KWm�2 (22)
⇥QBB = ⇥ (⇧T 4e ) = 4T 3
e ⇥Te =4
21/4 T 3e ⇥Ts =⇤ ⌅ =
21/4
4⇧T 3e
= 0.31K
Wm�2 (23)
⌅ =⌃Ts
⌃QBB and H2O= 0.5
KWm�2 (24)
Te =�
12� ⇤
⇥1/4 ⇤(1��p)S0
4⇧
⌅1/4
⇥ (238�246)K (25)
Ts =�
22� ⇤
⇥1/4 ⇤(1��p)S0
4⇧
⌅1/4
⇥ (283�293)K (26)
2
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Radiative Equilibrium Vertical Profile • Equilibrium state of atmosphere and surface with only radiative fluxes • Radiative heating drives actual state toward state of radiative equilibrium
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Fig 6a, Manabe and Strickler, 1964
Radiative Equilibrium: Contributions
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Problems with Radiative Equilibrium• Too hot at and near surface• Lapse rate of temperature too large below 10 km• Missing ingredient: circulations in atmosphere
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Radiative Forcing and Climate Sensitivity Net radiation at top of atmosphere: R = S-OLRS = net absorbed shortwave OLR = outgoing longwave radiation
At equilibrium: R = 0
Introduce perturbation of �Rf E.g., �Rf = 3.7W/m2 for doubling of CO2(radiative forcing: hold temperature and other gases fixed)
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Radiative forcing • Radiative forcing due to human activity is estimated at roughly 1.5 W/m2
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(Equilibrium) Climate Sensitivity
• Temperature change needed to re-attain equilibrium given the radiative forcing:
• Climate sensitivity � [K/(W/m2)] is ratio of change in global surface temperature �T to radiative forcing �Rf
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Climate sensitivity for blackbody
• Climate sensitivity without atmosphere:
•Climate sensitivity with opaque isothermal atmosphere
Ts = 21/4Ta = 288 K (12)
Ts =�
22� ⇤
⇥1/4
Te (13)
I = (1��p)S0/4 (14)
I = ⇧ T 41 =⇥ T1 = Te (15)
2 I = ⇧ T 42 =⇥ T2 = 21/4Te (16)
3 I = ⇧ T 42 =⇥ T2 = 31/4Te (17)
4 I = ⇧ T 4s =⇥ Ts = 41/4Te (18)
(19)
Etotal = Eatomic +Evibrational +Erotational +Etranslational (20)
⇥Ts = ⌅ ⇥Q =⇥ ⌅ =⌃Ts
⌃Q
⇤K
Wm�2
⌅(21)
⇥QBB = ⇥ (⇧T 4e ) = 4T 3
e ⇥Te = 4T 3e ⇥Ts =⇥ ⌅ =
14⇧T 3
e= 0.26
KWm�2 (22)
⇥QBB = ⇥ (⇧T 4e ) = 4T 3
e ⇥Te =4
21/4 T 3e ⇥Ts =⇥ ⌅ =
21/4
4⇧T 3e
= 0.31K
Wm�2 (23)
⌅ =⌃Ts
⌃QBB and H2O= 0.5
KWm�2 (24)
2
Ts = 21/4Ta = 288 K (12)
Ts =�
22� ⇤
⇥1/4
Te (13)
I = (1��p)S0/4 (14)
I = ⇧ T 41 =⇥ T1 = Te (15)
2 I = ⇧ T 42 =⇥ T2 = 21/4Te (16)
3 I = ⇧ T 42 =⇥ T2 = 31/4Te (17)
4 I = ⇧ T 4s =⇥ Ts = 41/4Te (18)
(19)
Etotal = Eatomic +Evibrational +Erotational +Etranslational (20)
⇥Ts = ⌅ ⇥Q =⇥ ⌅ =⌃Ts
⌃Q
⇤K
Wm�2
⌅(21)
⇥QBB = ⇥ (⇧T 4e ) = 4T 3
e ⇥Te = 4T 3e ⇥Ts =⇥ ⌅ =
14⇧T 3
e= 0.26
KWm�2 (22)
⇥QBB = ⇥ (⇧T 4e ) = 4T 3
e ⇥Te =4
21/4 T 3e ⇥Ts =⇥ ⌅ =
21/4
4⇧T 3e
= 0.31K
Wm�2 (23)
⌅ =⌃Ts
⌃QBB and H2O= 0.5
KWm�2 (24)
2
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Climate feedbacks are important
• Climate sensitivities in Atmosphere-Ocean General Circulation Models (GCMs) range from 0.5 to 1.2 K W-1 m2
• Include feedbacks (relative to blackbody) from:- water vapor (+ve: why?)- albedo (+ve: why?)- cloud (+ve: why?)- lapse rate (-ve: why?)
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Observed temperature changes • Reconstruction of global surface temperature record suggests increase of about 1K