# Stefan-Boltzmann Law

```What happens to solar energy ?
1.
Absorption (absorptivity=ζ)
Results in conduction, convection
and long-wave emission
2.
Transmission (transmissivity=ϕ)
3.
Reflection (reflectivity=α)
ζλ + ϕλ + αλ = 1
GEOGRAPHY 2015
Response varies with the surface type
Energy due to rapid oscillations of electromagnetic
fields, transferred by photons
Snow reflects 40 to 95% of solar energy and
requires a phase change to increase above 0&deg;C
The energy of a photon is equal to
Planck’s constant, multiplied by
the speed of light, divided by the
wavelength
Forests and oceans absorb more than dry lands
Then why do dry lands still “heat up” more?
Oceans transmit solar energy and have a high
heat capacity
Stefan-Boltzmann Law
As the temperature of an object increases, more
E = hv
λ
All bodies above 0 K emit radiation
Black body emits maximum possible radiation per unit area.
Emissivity, ε = 1.0
All bodies have an emissivity between 0 and 1
Temperature determines E, λ emitted
Consists of electrical field
(E) and magnetic field (M)
Travels at speed of light (C)
The shorter the wavelength,
the higher the frequency
This is important for
understanding information
obtained in remote sensing
Wien’s Displacement Law
Higher frequencies (shorter wavelengths) are
emitted from bodies at a higher temperature
As the temperature of a body increases, so does the
total energy and the proportion of shorter wavelengths
Max Planck determined a characteristic
emission curve whose shape is retained for
radiation at 6000 K (Sun) and 300 K (Earth)
λmax = (2.88 x 10-3)/(T0)
Energy emitted = ε⋅σ(T
ε⋅σ 0)4
Radiant flux or flux density refers to the rate of flow
of radiation per unit area (eg., W⋅m-2)
Emittance =
*wavelength in metres
Sun’s λmax = 0.48 &micro;m
Ultraviolet to infrared - 99% short-wave (0.15 to 3.0 &micro;m)
Earth’s λmax = 10 &micro;m
Infrared - 99% longwave (3.0 to 100 &micro;m)
Terrestrial
Microwaves are longest
wavelengths used in
remote sensing
Solar
We are blind to
everything except
this narrow band
UV are shortest
wavelengths practical
for remote sensing
Transmission through the Atmosphere
ALBEDO: April, 2002
Some wavelengths of
E-M energy are
absorbed and scattered
more efficiently than
others
H2 O, CO 2, and ozone
have the strongest
absorption spectra
Transmission
Light moves through a
surface (eg. on a natural
surface)
8-11 &micro;m window
Wavelength dependent
(eg. leaves)
white and red
are high albedo,
green and yellow
are low albedo
Radiation emitted from Earth is of
a much longer wavelength and is of
much lesser energy
•white snow
•old snow
•vegetation
•light colour soil
•dark colour soil
•clouds
•calm water surface
Characteristic spectral responses of different surface types. Bands are those
of the SPOT remote sensing satellite.
0.80-0.95
0.40-0.60
0.15-0.30
0.25-0.40
0.10
0.50-0.90
0.10 (midday)
http://profhorn.aos.wisc.edu/wxwise/AckermanKnox/Earth's Albedochap2/Albedo.html
```