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

A simple 2-box model

T1

t 1

rT1 Te1 1

dT1 T2

T2

t 1

rT2 Te2 1

dT1 T2

•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

radiation

A simple 2-box model

T1

t 1

rT1 Te1 1

dT1 T2

T2

t 1

rT2 Te2 1

dT1 T2

•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

dynamics

A simple 2-box model

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 .

•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

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

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

Equilibria of 2-box model

Equilibria of 2-box model

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

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

ice-free

Equilibria of 2-box model

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

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

ice-free

Ice-albedo feedback ➙ multiple equilibrium states

Equilibria of 2-box model

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