Global Change: Class ExerciseGlobal Change: Class Exercise

Global Energy Balance Global Energy Balance & &

Planetary TemperaturePlanetary Temperature

Mteor/Agron/Envsci/Envst 404/504Mteor/Agron/Envsci/Envst 404/504

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 Zero-Dimensional, Global Energy Balance ModelEnergy Balance Model

At photosphere surface, At photosphere surface, solar flux ~ 6.2solar flux ~ 6.2..101077 W-m W-m-2-2

Incoming (absorbed) radiation:

At EarthAt Earth’’s orbit, solar flux ~ 1360 W-ms orbit, solar flux ~ 1360 W-m-2-2

Zero-Dimensional GEBMZero-Dimensional GEBM

Scattering: air molecules, aerosols Reflection: clouds

Surface albedo

Planetary Albedo

Zero-Dimensional GEBMZero-Dimensional GEBM

Incoming (absorbed) radiation:

Incoming = (1-albedo) x (area facing sun) x S = (1-)R2S

R

Emitted radiation:

Outgoing = I x (4R2)R

Zero-Dimensional GEBMZero-Dimensional GEBM

Global energy balance: Radiative equilibrium (in = out)

Zero-Dimensional GEBMZero-Dimensional GEBM

Global energy balance: Radiative equilibrium (in = out)

Zero-Dimensional GEBMZero-Dimensional GEBM

Temperature ??

Suppose black-body emission:

Zero-Dimensional GEBMZero-Dimensional GEBM

What then is TRAD?

Observed, average surface temperature = Ts = 288 K

Zero-Dimensional GEBMZero-Dimensional GEBM

Why is Ts ≠ TRAD?

Alternative – imperfect emission:

black-body emission × emissivity

Zero-Dimensional GEBMZero-Dimensional GEBM

What then is the emissivity ε?

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

Zero-Dimensional GEBMZero-Dimensional GEBM

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.)

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 IZero-D GEBM: Empirical I

I = A + BTs(˚C) , where

A = 214 W-m-2 , B = 1.6 W-m-2-˚C-1

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) …

Zero-D GEBM: Empirical IZero-D GEBM: Empirical I

Ts,new = ?

Ts,new – Ts,old = ?

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

Zero-D GEBM: Albedo FeedbackZero-D GEBM: Albedo Feedback

What now is the energy balance equation?

What then is Ts=? (what equation?)

Zero-D GEBM: Albedo FeedbackZero-D GEBM: Albedo Feedback

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 - End - Class ExerciseClass Exercise::

Global Energy Balance Global Energy Balance & &

Planetary TemperaturePlanetary Temperature