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
averaged 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 ~ W-m-2
At Earth’s 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. What about other planets?
How does Trad change with orbit?

11. Two Spheres Surrounding Sun
Total energy flux the same through each sphere
R2 = 2 x R1 R2 R1
Consider 2 spheres surrounding the sun. Both intercept all the energy emitted by the sun. The larger sphere covers 4 x the surface area of the innner sphere. Thus the same amount of energy is spread over 4 times greater area.
The same area at R2 intercepts only 1/4 of energy it intercepts at R1
 Flux decreases as R-2

12. What about other planets?
How does Trad change with orbit?
Planet Distance Albedo Outgoing IR Trad from sun
[A.U.] [W-m2] [K]
Venus
Earth
Mars
Sources give a range of Ts for Mars, from about 210 K – 225 K.
Venus: Ts = 755 K
Mars: Ts = 216 K

13. End - Class Exercise: Global Energy Balance & Planetary Temperature