Global Change: Class Exercise

1
Global Change Class Exercise

• Global Energy Balance
• Planetary Temperature

Mteor/Agron/Envsci/Envst 404/504
2
Zero-Dimensional, Global Energy Balance Model
Zero-dimensional steady, time-average averag
ed over all spatial directions Global average
is over the entire planet Energy
balance balance of incoming and outgoing energy
flux
Global energy balance Radiative equilibrium (in
out)
3
Zero-Dimensional GEBM
Incoming (absorbed) radiation
At photosphere surface, solar flux 6.2.107 W-m-2
At Earths orbit, solar flux 1360 W-m-2
4
Zero-Dimensional GEBM
Scattering air molecules, aerosols
Reflection clouds
Planetary Albedo
Surface albedo
5
Zero-Dimensional GEBM
Incoming (absorbed) radiation
R
Incoming (1-albedo) x (area facing sun) x S
(1-?)pR2S
Emitted radiation
Outgoing I x (4pR2)
R
6
Zero-Dimensional GEBM
Global energy balance Radiative equilibrium (in
out)
7
Zero-Dimensional GEBM
Global energy balance Radiative equilibrium (in
out)
Temperature ??
8
Zero-Dimensional GEBM
Suppose black-body emission
What then is TRAD?
9
Zero-Dimensional GEBM
Observed, average surface temperature Ts 288 K
Why is Ts ? TRAD?
10
Zero-Dimensional GEBM

Alternative imperfect emission black-body
emission emissivity
What then is the emissivity e?
11
Zero-Dimensional GEBM
If CO2 doubles instantaneously, outgoing
radiation drops 4 W-m-2 for the same Ts. What is
the new e?
What is the new Ts that restores balance? How
much warming occurs? (Note that this computation
does not include any changes in atmospheric water
vapor or snow/ice cover under warming.)
12
Zero-D GEBM Empirical I
The previous computation does not include any
changes in atmospheric water vapor or snow/ice
cover under warming. An empirical alternative
that includes effects of water vapor changes with
temperature is
I A BTs(C) , where A 214 W-m-2 , B 1.6
W-m-2-C-1
13
Zero-D GEBM Empirical I
If instantaneous CO2 doubling reduces I by 4
W-m-2 , and the change leads to Anew 210 W-m-2
, then if there is no albedo change (no change in
mean snow/ice cover)
Ts,new ? Ts,new Ts,old ?
14
Zero-D GEBM Albedo Feedback
For global temperature changes of no more than a
few degrees, observational evidence suggests that
the albedo (the portion of sunlight reflected)
varies approximately with temperature as ? 0.32
1.33x10-3 Ts
What now is the energy balance equation?
15
Zero-D GEBM Albedo Feedback
What then is Ts? (what equation?)
We have S/4 340 W-m-2, and B 1.6 W-m-2-C-1.
For current CO2 levels, A 214 W-m-2, and for
doubled CO2 levels, A 210 W-m-2.
Ts,new ? Ts,new Ts,old ?
16
End - Class Exercise Global Energy Balance
Planetary Temperature