1. Radiation  = 1 for blackbody (emissivity) Qr = T4
All matter at a temperature above absolute zero radiates energy, the rate of which is given by the Stefan-Boltzmann law:
Qr is rate of emission per unit surface area, W m-2
 = 1 for blackbody (emissivity)
= 5.67  10-8 W m-2 K-4
A blackbody is a surface that emits maximum radiation at all wavelengths in all directions & absorbs all incident radiation
Qr = T4

2. Radiation
The (peak) wavelength of energy emitted by a radiating surface decreases as the temperature of the surface increases, according to Wien’s law:
max T = 2897 m K

3. Energy balance - no atmosphere
Incoming SW radiation = Reflected SW radiation + Outgoing longwave

4. Energy balance - no atmosphere
apR2 S
pR2 S
4pR2 sT4
Incoming SW radiation = Reflected SW radiation + Outgoing longwave
R = Earth’s radius
S = 1370 Wm-2
a = 0.3
s = 5.67 x10-8 Wm-2

5. Energy balance - no atmosphere
apR2 S
pR2 S
4pR2 sT4
Incoming SW radiation = Reflected SW radiation + Outgoing longwave
pR2 S =
apR2 S +
4pR2 sT4
R = Earth’s radius
S = 1370 Wm-2
a = 0.3
= 5.67 x10-8 Wm-2
T = 255oK
S (1 - a) = 4Tp4

6. Radiation max T = 2897 m K Q = 8hc-5[exp(hc/ kT)-1]
The (peak) wavelength of energy emitted by a radiating surface decreases as the temperature of the surface increases, according to Wien’s law:
Planck’s law gives the spectral shape of radiation as a function of temperature:
h = Planck’s constant
C = speed of light
K = Boltzmann constant
max T = 2897 m K
Q = 8hc-5[exp(hc/ kT)-1]

7. Blackbody radiation 255K 5780K
Normalized blackbody spectra representative of the sun (left) and the earth (right).
Wallace and Hobbs, p. 288