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

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)

Zero-Dimensional GEBM Incoming (absorbed) radiation: At photosphere surface, solar flux ~ 6.2.107 W-m-2 At Earth’s orbit, solar flux ~ 1360 W-m-2

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

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

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

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

Zero-Dimensional GEBM Suppose black-body emission: What then is TRAD?

Zero-Dimensional GEBM Observed, average surface temperature = Ts = 288 K Why is Ts ≠ TRAD?

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

Zero-Dimensional GEBM If CO2 doubles instantaneously, outgoing radiation drops 4 W-m-2 for the same Ts. What is the new ε? 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.)

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

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 = ?

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?

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 = ?

End - Class Exercise: Global Energy Balance & Planetary Temperature