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

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

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

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

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

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]

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