1. Global Change: Class Exercise Global Energy Balance & Planetary Temperature Mteor/Agron/Envsci/Envst 404/504

2. 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) Zero-Dimensional, Global Energy Balance Model

3. At photosphere surface, solar flux ~ 6.2. 10 7 W-m -2 Incoming (absorbed) radiation: At Earth’s orbit, solar flux ~ 1360 W-m -2 Zero-Dimensional GEBM

4. Scattering: air molecules, aerosols Reflection: clouds Surface albedo Planetary Albedo Zero-Dimensional GEBM

5. Incoming (absorbed) radiation: Incoming = (1-albedo) x (area facing sun) x S = (1-  )  R 2 S R Emitted radiation: Outgoing = I x (4  R 2 ) R Zero-Dimensional GEBM

6. Global energy balance: Radiative equilibrium (in = out) Zero-Dimensional GEBM

7. Global energy balance: Radiative equilibrium (in = out) Zero-Dimensional GEBM Temperature ??

8. Suppose black-body emission: Zero-Dimensional GEBM What then is T RAD ?

9. Observed, average surface temperature = T s = 288 K Zero-Dimensional GEBM Why is T s ≠ T RAD ?

10. Alternative – imperfect emission: black-body emission × emissivity Zero-Dimensional GEBM What then is the emissivity ε?

11. If CO 2 doubles instantaneously, outgoing radiation drops 4 W-m -2 for the same T s. What is the new ε? Zero-Dimensional GEBM What is the new T s 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. 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 … Zero-D GEBM: Empirical I I = A + BT s (˚C), where A = 214 W-m -2, B = 1.6 W-m -2 -˚C -1

13. If instantaneous CO 2 doubling reduces I by 4 W-m -2, and the change leads to A new = 210 W-m -2, then if there is no albedo change (no change in mean snow/ice cover) … Zero-D GEBM: Empirical I T s,new = ? T s,new – T s,old = ?

14. 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 T s Zero-D GEBM: Albedo Feedback What now is the energy balance equation?

15. What then is T s =? (what equation?) Zero-D GEBM: Albedo Feedback We have S/4 = 340 W-m -2, and B = 1.6 W-m -2 -˚C -1. For current CO 2 levels, A = 214 W-m -2, and for doubled CO 2 levels, A = 210 W-m -2. T s,new = ? T s,new – T s,old = ?

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