12.003 introduction to atmosphere, ocean, and climate...
TRANSCRIPT
12.003 Introduction to Atmosphere, Ocean, and Climate Dynamics
Topic 5 Greenhouse Effect (continued)
and Climate Sensitivity
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
Radiative transfer in the atmosphere
• Shortwave Absorption: clouds, H20, O3, O2
• Shortwave Reflection: clouds, surface
• Longwave Absorption: clouds, H20, CO2, CH4, N2O
Absorption and Emission in a Gas Vibrational and rotational transitions that dominate infrared absorption are associated with H2O and C02
(major greenhouse gases)
Principal Atmospheric Absorbers
David Archer website
Model spectrum of upwelling longwave radiation at TOA(surface 270K, coldest point 215K)
David Archer textbook
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
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
Radiative Equilibrium Vertical Profile • Equilibrium state of atmosphere and surface with only radiative fluxes • Radiative heating drives actual state toward state of radiative equilibrium
Fig 6a, Manabe and Strickler, 1964
Radiative Equilibrium: Contributions
Problems with Radiative Equilibrium• Too hot at and near surface• Lapse rate of temperature too large below 10 km• Missing ingredient: circulations in atmosphere
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)
Radiative forcing • Radiative forcing due to human activity is estimated at roughly 1.5 W/m2
(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
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
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?)
Observed temperature changes • Reconstruction of global surface temperature record suggests increase of about 1K