the atmosphere: part 8: climate change: sensitivity and feedbacks composition / structure radiative...

The Atmosphere:Part 8: Climate Change:

Sensitivity and Feedbacks

• Composition / Structure

• Radiative transfer• Vertical and latitudinal heat transport• Atmospheric circulation

• Climate modeling

Suggested further reading:

Hartmann, Global Physical Climatology (Academic Press, 1994)

A simple 2-box model

•Two equal mass boxes, temperatures T1 and T2

•Radiatively relaxed to temperatures Te1 and Te2 with time constant τr

•Temperatures mixed with time constant τd


T1

t 1

rT1 Te1 1

dT1 T2

T2

t 1

rT2 Te2 1

dT1 T2




radiation


T1

t 1

rT1 Te1 1

dT1 T2

T2

t 1

rT2 Te2 1

dT1 T2




dynamics


T1

t 1

rT1 Te1 1

dT1 T2

T2

t 1

rT2 Te2 1

dT1 T2

steady state solutions

1 r

T1 Te1 1 d

T1 T2 0

1 r

T2 Te2 1 d

T1 T2 0

T1 Te1 Te1 Te2 1 2

T2 Te2 Te1 Te2 1 2

{

where .




r/ d

with polar ice

0.0 0.5 1.0 1.5 2.0 2.5

240

260

280

300 T1

T2

Te1 300K

Te2 240K

Assumes ice in high latitude box (T2 < 263K)

Equilibria of 2-box model

Fix Te, vary γ

with polar ice

0.0 0.5 1.0 1.5 2.0 2.5

240

260

280

300 T1

T2

Te1 300K

Te2 240K




with polar ice

Te1 300K

Te2 240K

Assumes high latitude box is ice-free (T2 > 263K)

0.0 0.5 1.0 1.5 2.0 2.5

240

260

280

300 T1

T2

Te1 300K

Te2 250K


ice-free


with polar ice

Te1 300K

Te2 240K

Assumes high latitude box is ice-free (T2 > 263K)

0.0 0.5 1.0 1.5 2.0 2.5

240

260

280

300 T1

T2

multiple equilibria

Te1 300K

Te2 250K


ice-free

Ice-albedo feedback ➙ multiple equilibrium states


Fix γ, vary Te

Te1 300K

Te2 250K ice-free

240K ice

0.5

T1

T2

ice-free

with polar ice

0.95 1.00 1.05240

260

280

300

T

A 1-D model (Budyko/Sellers)(T, ice edge, vary with latitude)

Climate forcings and sensitivity

Function of solar constant, albedo (ice cover, cloudiness, vegetation, …)

Function of temperature, water vapor, clouds, CO2 and other greenhouse gases …

RTOA RTOATs,x 1 ,x 2 , . . . . . . .x N

RTOA RTOA

TsTs

i 1

NRTOA

x ix i

in equilibrium, net incoming flux is

Climate forcing due to ith process (all else held fixed) = δQ

(e.g., [CO2] doubling to 600ppm ➙

δQ = 4 Wm-2)

}

RTOA Fsolar F IR 0

Climate forcings and sensitivity

Function of solar constant, albedo (ice cover, cloudiness, vegetation, …)

Function of temperature, water vapor, clouds, CO2 and other greenhouse gases …

RTOA RTOATs,x 1 ,x 2 , . . . . . . .x N

RTOA RTOA

TsTs

i 1

NRTOA

x ix i

in equilibrium, net incoming flux is

Climate forcing due to ith process (all else held fixed) = δQ

(e.g., [CO2] doubling to 600ppm ➙

δQ = 4 Wm-2)

}

RTOA RTOA

TsTs

i 1

N 1RTOA

x ix i Q 0

RTOA

Ts

i 1

N 1RTOA

x i

x i

TsTs Q

➙ climate sensitivity

feedbacks

RTOA Fsolar F IR 0

Ts

Q R

RTOA

Ts

i 1

N 1RTOA

x i

x i

Ts

1

Radiative response only(no feedbacks)

Suppose Te = Ts - constant

(Te = 255 K)

➙ (Need doubling of CO2 or 1.6% increase of solar constant to produce 1K warming)

RTOA

Ts

Ts Te

4 3 Ts3

3.8Wm 2

K 1

R RTOA

Ts

1 0.26K Wm

2 1

Water vapor feedback

q ep ,

mvmair

0.622

d lnes

dT L

RT2

es exp LRT

q s

q s es

es L

RTTT

U 80%

R |FRH RTOA

Ts FRH

1

0.5 K Wm 2 1

RTOA

Ts FRH 2 Wm

2K

1

RTOA

Ts RTOA

qqTs

-4 Wm-2K-1 +2Wm-2K-1

w.v. feedback

Ice albedo feedback

TT/ ice_edge

RTOA

Ts ice S 0

4cos ice_edge

Ts/ ice_edge

2 Wm 2

K 1

(overestimate — have neglected clouds)

0.4

R RTOA

Ts RTOA

ice_edge

ice_edge

Ts

1

-4 Wm-2K-1 +2 Wm-2K-1

Cloud feedback dRTOA

dTs cloud RTOA

A cloud

A cloud

Ts

Current climate: cloud amount ~ 50%

RTOA

A cloud 40 Wm

2

A cloud

Ts ?

10% increase in Ac

RTOA 4 Wm 2

➙ would offset CO2 doubling

RTOA 20 Wm 2

Past T trend simulated by 3D coupled atmosphere-ocean models

Predicted ΔT for doubled CO2 from 3 different coupled 3D atmosphere-ocean models

the atmosphere: part 8: climate change: sensitivity and feedbacks composition / structure radiative...

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