1. Atmospheric Radiation &
EARTH: The operators’ manual
The Whole Earth Course
Atmospheric Radiation &
Convection
Instructor: Dr. Steven M. Lazarus
Oct 15, 2015
"No branch of atmospheric physics is more difficult than that dealing with radiation. This is not because we do not know the laws of radiation, but because of the difficulty of applying them to gases." — G.C. Simpson

2. S What is the earth’s radiative equilibrium temperature? IN = OUT
See Fig. 2.4 pg 37 BP
IN = OUT
(1-a)Spr2 = 4pr2sT4
(1-a)Spr2 = 4pr2sT4
(1-a)Spr2 = 4pr2sT4
(1-a)Spr2 = 4pr2sT4
e=? ?
Volume of sphere?
Area of sphere?
Area of circle?
Albedo:
earth
Earth S f n dA
dAe
Bring flashlight and inflatable earth!
The effective temperature of a planet is the temperature that would exist near its surface under radiative balance with the incoming solar radiation if the planet had no atmosphere. The only change in the radiation from the Sun considered in this case is reflection (i.e., albedo). Reflection reduces the amount of heat the planet has to come to equilibrium with.
Over a period of one planetary rotation around its axis, the entire surface of the planet is exposed to the incoming radiation and warms up to a absolute temperature, T. Averaged over the length of a full number of rotation period the entire plant's surface (equal to 4πR2) emits energy, which according to the Stefan-Boltzman law is proportional to the fourth power of its temperature.
Albedo of one (zero) means all radiation coming in is being reflected (absorbed)!

3. Actual average surface temperature is 15 oC! What is going on?
(1-a)Spr2 = 4pr2sT4
S = ?
a = ?
r = ?
s = ?
1367 Wm-2
0.14 bare rock
6374 km
5.67 x 10-8 Wm-2/K4
Actual average surface temperature is 15 oC! What is going on?
‘Bare Rock’ Model

4. THIS IS NOT SO FOR THE ATMOSPHERE!
Most solids and liquids absorb much of the radiation they intercept, and they also emit radiation rather easily
THIS IS NOT SO FOR THE ATMOSPHERE!
Atmosphere is composed of almost entirely of O2 and N2. Neither of which interact much with SW or LW radiation.
If this were all there was to the atmosphere – the radiative balance problem would be much easier (as previously shown)!
Earth’s average temperature would have to be warm enough to emit enough energy to balance the absorbed solar/SW energy. This is what is referred to as a “radiative equilibrium” condition:
IN = OUT (no change in temperature).

5. Earth’s annual global mean energy balance
IN = OUT?
IPCC FAQ 1.1
ap =107/342~0.30
What are the units?
Also, why is there only 342 W m-2 instead of 1370? LW SW
GHE!!!
( )Wm-2 –
( )Wm-2 = 0
168/342 ~50% absorbed at sfc (daytime only!)
> TOA solar!!!

6. Terrestrial vs. Solar Spectrum
LONG (LW)
solar
SHORT (SW)
1 mm = ?? m
% ABSORRBED RADIATOIN
TOTAL!!!
SHORT (SW)
LONG (LW)
little direct absorption of
shortwave (solar) radiation
by atmosphere
little overlap between solar and
terrestrial radiation
‘atm window’
Note CO2 LW absorption where H20 is not radiatively active!
Fig. B11.1 page 330 BP

7. Atmosphere vs. No Atmosphere
shortwave (solar)
atm longwave
surface longwave
input ~ constant
Add an atmosphere
(Pane in the Glass)
Iin,solar = (1-a)S/4
268 K
Atmosphere
NO ATMOSPHERE
absorb/re-emit (LW)
OUT IN
Earth’s sfc must warm up!!!
Earth’s surface
Earth’s surface
What happens if we add gasses that absorb in the infrared where the earth’s radiation peaks? Assume Thermodynamic Equilibrium.

8. Another perspective: Glass half empty?
Equilibrium in
out
old level
initial undisturbed
increase flow in
out
new level in
out
GHG OR
slow exit (GHG)
What does the “in” represent?
What does the water level represent?
What does the “out” represent?
Will the bucket fill infinitely – or will it stop at some point?
When will it stop?

9. Convection in a liquid (Global Warming: Understanding the forecast, D
Convection in a liquid (Global Warming: Understanding the forecast, D. Archer)
AKA why isn’t the greenhouse truly a greenhouse?
Occurs when a fluid is heated from below and/or cooled from above. Consider an incompressible fluid:
convectively unstable
warm
initial well mixed
(neutral stability)
COSMOSPHERE!
2 possible scenarios…
Which one is the atmosphere most like?
warm
mixing
no mixing
stably stratified
neutral stability
temperature

10. What is a lapse rate (pp. 337-338)?
boxes grow in size?
Change in temperature w.r.t. height
Fig
Atmosphere is compressible (gas):
Rising air expands/cools
Sinking air compresses/warms
‘parcel’ (box of air) lapse rates:
dry adiabatic (if unsaturated, RH<100%)
moist adiabatic (if saturated, RH>100%)
So why do we care?
Fig. B11.4
Fig. 11.8
WELL-MIXED LIQUID (OCEAN)

11. radiative equilibrium with atmosphere/no convection
If the atmosphere were a true greenhouse, it would not be able to convect the heat away from the surface! This is sometimes referred to as “pure” greenhouse warming (e.g., Lindzen, Bulletin of the American Meteorological Society 1991). The temperature in this case would approach 72 oC!
Fig. 11.8
100 C
50 C
-5 C
72 C
15 C
temperature
radiative equilibrium with atmosphere/no convection
radiative/convective equilibrium with atmosphere
radiative equilibrium no atmosphere (i.e., no GH!)
Observed surface temperature is much closer to the atmosphere without
GHG! This is due to 1.) convection and 2.) north/south heat transport.

12. Key Points and Issues Radiation Basics: heat transfer blackbody
characteristics of thermal radiation (electromagnetic spectrum)
radiatively active gases
global energy balance
radiative equilibrium
simple radiative models:
no atmosphere
slab atmosphere
Convection
lapse rates
radiative/convective equilibrium