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?

What about other planets? How does Trad change with orbit?

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

What about other planets? How does Trad change with orbit? Planet Distance Albedo Outgoing IR Trad from sun [A.U.] [W-m2] [K] Venus 0.72 0.76 Earth 1.00 0.30 238 255 Mars 1.52 0.16 Sources give a range of Ts for Mars, from about 210 K – 225 K. Venus: Ts = 755 K Mars: Ts = 216 K

End - Class Exercise: Global Energy Balance & Planetary Temperature