12.003 introduction to atmosphere, ocean, and climate...

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