1. Atmospheric Radiation &
EARTH: The operators’ manual
The Whole Earth Course
Atmospheric Radiation &
Convection
Instructor: Dr. Steven M. Lazarus
October 8, 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. ROADMAP: Radiative/Convective equilibrium 1 m 100 km 105 m
IPCC AR4 FAQ #1
100 km
105 m
1 m

3. Why should we care about atmospheric composition?
Fig , page 326 BP

4. TOOLS… See text pages 36-37, Chapter 2 BP depends on mass
depends on motion

5. TOOLS…
A black body is a theoretical object that absorbs 100% of the radiation that hits it (at all wavelengths). Therefore it reflects no radiation and appears perfectly black.
It is also a perfect emitter of radiation. At a particular temperature the black body would emit the maximum amount of energy possible for that temperature.
Hence, a black body curve represents an upper limit, that is, the theoretical maximum amount of emitted radiation for a given temperature (or wavelength).
Planck’s Law
El~1/l5
Can we see this radiation?
frequency (n) = speed of light (c)/wavelength = c/l
wave number = 1/l

6. Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object's temperature only.
Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation. For a perfect blackbody, the radiative flux (E) is given by the Stefan-Boltzman Law:
COOLER
WARMER
Fig. B2.2, page 38 BP
‘perfect’ BB e = 1
even though peaks at a single temperature, occurs at a wide range of
frequencies.
peak value for each curve moves to the left as the temperature increases
LOW ENERGY
HIGH ENERGY
total amount of radiation, of all frequencies, goes up very fast as the
temperature rises LW SW

7. shortwave and longwave! A + R + S + T = 1 r
What does radiation do?
absorption
reflection
scatter
transmission
If the quantities above increase then… ? ?
shortwave and longwave!
A + R + S + T = 1 r
(for non-opaque layer)

8. asymmetric stretch vertical bend symmetric stretch horizontal bend
Molecular Calisthenics
There are several modes of vibration for a CO2 molecule that are IR ‘active’
asymmetric stretch
vertical bend
symmetric stretch
horizontal bend

9. 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)!

10. 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

11. 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).
Well…what is going on is…Imagine you have an object and place it under a heat lamp – what happens?