Climate Sensitivity & Climate Feedback

Instructor: Prof. Johnny Luohttp://www.sci.ccny.cuny.edu/~luo

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Te =(S0 /4)(1−α )

σ4

=(1367 /4)(1−0.3)

5.67 ×10−84

= 255K ≅ −180C

Ts = 15 0C > -18 0C

Considering the Greenhouse Effect

€

Te =(S0 /4)(1−α )

σ4

=(1367 /4)(1−0.3)

5.67 ×10−84

= 255K ≅ −180C

Part I: Fundamentals of Climate Science

1.Introduction to the climate system2.The Earth’s energy balance3.Atmospheric radiation and climate4.Surface energy balance5.Atmosphere general circulation6.Ocean general circulation

Part II: Climate Change

1.Climate sensitivity & climate feedback2.Natural & anthropogenic climate change3.IPCC assessment of past & future climate change

Energy budget (global balance & local imbalance)

Fluid movement (due to local energy imbalance)

What will happen if energy imbalance occurs at a global level?

EAS 488/B8800 Climate & Climate Change

Outlines

1. Basic concepts: climate forcing, response, sensitivity and feedbacks

2. Climate sensitivity w/o feedback

3. Water vapor feedback

4. Ice albedo feedback

5. Cloud feedback

6. Tropical SST regulatory mechanism

7. Daisy world

Global energy balance: the starting point

This chapter deals with:

1) what may break this balance?

2) what will happen when this balance is violated?

First, we will look at a few fundamental concepts:

1)climate forcing, 2)climate response,3)climate sensitivity4)climate feedback

€

S04(1−α ) =σTe

4

Climate Forcing: change in external factors that breaks the aforementioned energy balance (usually measured in changes in energy flux density in W m-2 at TOA).

Climate Response: adjustment of the climate system in response to the external forcings (usually measured as change in surface temperature, Ts).

Forcing & Response

Example:

Forcing: When CO2 is doubled, OLR will change from 240 W m-2 to 236 W m-2 (is this a warming or cooling for the climate system?).

Response: For planet A: Ts increases by 1 K; for planet B: Ts increases by 10 K.

Sensitivity: λ(A) = 1K/(4 W m -2) = 0.25 K/(W m -2). λ(B) = 10K/(4 W m -2) = 2.5 K/(W m -2).

Climate Sensitivity: climate response (Ts) over climate forcing (Q).

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λ ≡dTsdQ

€

Q =S04(1−α ) −σT 4

Outlines

• Basic concepts: climate forcing, response, sensitivity and feedbacks

• Climate sensitivity w/o feedback

• Water vapor feedback

• Ice albedo feedback

• Cloud feedback

• Tropical SST regulatory mechanism

• Daisy world

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dRTOAdQ

=∂RTOA∂Q

+∂RTOA∂Ts

dTsdQ= 0

Suppose a forcing dQ is imposed on RTOA. Let’s calculate the climate sensitivity dTs/dQ.

=1€

λ =dTsdQ= −

1

∂RTOA /∂Ts€

RTOA = RTOA (Q,Ts(Q))

equilibrium

New equilibrium: RTOA = 0

Sensitivity parameter

Sensitivity of the Earth’s climate

€

RTOA =S04(1−α ) −σTe

4 = 0

Suppose a forcing dQ is imposed on RTOA. Let’s calculate the climate sensitivity dTs/dQ.

€

RTOA = RTOA (Q,Ts(Q))

equilibrium

Sensitivity of the Earth’s climate

dQ: forcing; dTs: response

€

RTOA =S04(1−α ) −σTe

4 = 0

€

dRTOAdQ

=∂RTOA∂Q

+∂RTOA∂Ts

dTsdQ= 0

Suppose a forcing dQ is imposed on RTOA. Let’s calculate the climate sensitivity dTs/dQ.

= 1 (b/c instantaneous changes in RTOA & dQ are the same)

€

RTOA = RTOA (Q,Ts(Q))

equilibrium

New equilibrium at the TOA

Sensitivity of the Earth’s climate

dQ: forcing; dTs: response

€

RTOA =S04(1−α ) −σTe

4 = 0

€

RTOA =S04(1−α ) −σTe

4 = 0

€

dRTOAdQ

=∂RTOA∂Q

+∂RTOA∂Ts

dTsdQ= 0

Suppose a forcing dQ is imposed on RTOA. Let’s calculate the climate sensitivity dTs/dQ.

= 1 (b/c instantaneous changes in RTOA & dQ are the same)

€

dTsdQ= −

1

∂RTOA /∂Ts≡ λ

€

RTOA = RTOA (Q,Ts(Q))

equilibrium

New equilibrium at the TOA

Sensitivity parameter

Sensitivity of the Earth’s climate

dQ: forcing; dTs: response

€

RTOA =S04(1−α ) −σTe

4

∂RTOA∂Ts

=∂(−σTe

4 )

∂Ts= −4σTe

3

Now we calculate:

€

∂RTOA /∂Ts

Assuming: 1) solar constant is unchanging, and 2) Te and Ts change at the same rate

€

RTOA =S04(1−α ) −σTe

4

∂RTOA∂Ts

=∂(−σTe

4 )

∂Ts= −4σTe

3

Now we calculate:

Estimating the sensitivity parameter (Te = 255 K for current climate)

€

dTsdQ= −

1

∂RTOA /∂Ts=

1

4σTe3= 0.26 K(W m−2)−1

What this means is: for every 1 W m-2 of energy we add to or subtract from the climate system, change of effective temperature (or surface temperature) will be 0.26 K.

This is dictated by the Stefan-Boltzmann relation. Note that other factors (e.g., albedo, water vapor) are held unchanged at this point.

€

∂RTOA /∂Ts

Assuming: 1) solar constant is unchanging, and 2) Te and Ts change at the same rate

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λ ≡dTsdQ= 0.26 K(W m−2)−1

Think-Pair-Share Questions:

1)For this kind of climate system, i.e., λ=0.26 K (W m-2)-1, what dQ is needed to warm up the Earth’s surface by 1K (i.e., dTs=1K) ?

2)How many W m-2 does the Solar Constant (S) have to increase to achieve dTs=1 K? Assume the albedo is 0.3

This is the climate sensitivity that is built-in of the σTe4 relationship.

€

RTOA =S04(1−α ) −σTe

4

1 W m-2 -> 0.26 K about 4 W m-2 is needed for 1 K.

€

ΔS04(1−0.3) = 4 W m−2 →ΔS0 ≈ 22 W m−2

€

S0 ≈1370 W m−2

€

S04(1−α )To achieve 4 W m-2 thru changing the

Solar Constant (S0)

Think-Pair-Share Questions:

1)For this kind of climate system, i.e., λ=0.26 K (W m-2)-1, what dQ is needed to warm up the Earth’s surface by 1K (i.e., dTs=1K) ?

2)How many W m-2 does the Solar Constant (S) have to increase to achieve dTs=1 K? Assume the albedo is 0.3

Observations show that S0 varies in magnitude of 1 W m-2 (historical data dated back to 1870 can also support this estimate; however, over a longer history such as millions of years, there are larger variations).

So, ΔS0(1-0.3)/4 = 0.175 W m-

2. With this climate forcing, the response will be 0.175 × 0.26 = 0.0455 K.

Conclusion: the σTe4 type of climate

system is a rather stable one because of the fundamental way energy balance is achieved.

€

λ ≡dTsdQ= 0.26 K(W m−2)−1

Outlines

• Basic concepts: climate forcing, response, sensitivity and feedbacks

• Climate sensitivity w/o feedback

• Water vapor feedback

• Ice albedo feedback

• Cloud feedback

• Tropical SST regulatory mechanism

• Daisy world

Feedback mechanism:

Sensitivity = Output/Input. With feedback, the sensitivity parameter will be different.

T-P-S: How will water vapor affect the intrinsic climate sensitivity parameter? In other words, given the same forcing, how will water vapor changes the Ts response?

€

λ ≡dTsdQ= 0.26 K(W m−2)−1

Temperature

Feedback mechanism:

H2O

Water vapor: a strong positive feedback in global warming scenario

Increasing CO2

dQ dTs

Much of the infrared absorption (greenhouse effect) comes from the contribution of H2O

IR absorption spectra (0 means no absorption; 100 means total absorption)

€

deses= (

L

RvT)dT

T

Clausius-Clapeyron relationship (C-C): saturation vapor pressure increases with temperature

For current terrestrial conditions, for every 1 K increase in temperature, es increases by ~ 6%.

Calculate OLR as a function of surface temperature (holding RH constant so vapor pressure increases with Ts).

This will need a radiative transfer model. For each Ts, we calculate I (OLR), so we have dTs/d(OLR)

OLR increases with increasing Ts, but at a SLOWER rate than what the stefan-Boltzmann relationship gives: σ(Ts-30)4.

Conclusion: because of the water vapor feedback, climate sensitivity is HIGHER than a sigma-T-to-the-4th relationship. T* is the surface temperature (Ts). T* - 10, T* - 20,

…, T* - 50 are attempts to estimate the effective temperature (Te) from the surface temperature.

For global average, T* = 288 K, Te = 255 K, so T* -30 is a good approximation for global average curve.

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λ =(dOLR

dTs)−1

Red: assume clear skyGreen: average cloudiness

Climate sensitivity has doubled with water vapor feedback.

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With water feedback λ ≡dTsdQ= 0.5 K(W m−2)−1

€

dTsdQ=∂Ts∂Q+∂Ts∂H2O

dH2O

dQ= 0.5 K(Wm−2)−1

0.26 K (Wm-2)-1

€

Ts = Ts(Q,H2O)

Sensitivity = response / forcing.

Climate sensitivity w/o feedback:

Double CO2 forcing:

4 W m-2 -> 4×0.26 ≈ 1 K

€

RTOA =S04(1−α ) −σT 4 = 0

Climate Forcing: change in external factors that breaks the energy balance of the climate system (usually measured in changes in energy flux density in W m-2 at TOA).

Climate Response: adjustment of the climate system in response to the external forcings (usually measured as change in surface temperature, Ts).

€

λ ≡dTsdQ

= −1

∂RTOA /∂Ts=

1

4σTe3 = 0.26 K(W m−2)−1

Summary

Temperature goes up

Feedback mechanism:

H2O goes up

Water vapor: a strong positive feedback, doubling the climate sensitivity

Increasing CO2

(or whatever causes the warming)

dQ dTs

€

λ ≡dTsdQ

= −1

∂RTOA /∂Ts= 0.5 K(W m−2)−1

dQ dTs

Summary