Radiative Transfer Radiative transfer equation (RTE) - IAP ...

Radiative transfer equation
Schwarzschild equation
Interpretation:
I (0) = I (τ)e −τ +
∫ τ
0
Be −τ ′ dτ ′
◮ I (τ) emission at level τ, e.g. by surface of the Earth, or
any other level where opacity is τ when looking down
from sensor
◮ but reduced by the absorption along the path to the
sensor by e −τ , i.e. the transmissivity
◮ plus emission of atmospheric layers Bdτ ′
◮ Note: Planck function depends on T , B = B(T (τ))
◮ taking into account attenuation on the way to the
sensor e −τ ′
☞ Almost all radiative transfer problems involving
emission and absorption, without scattering, can be solved
with this equation
RTE
Beer’s law
Abs. cross section
Opacity &
Transmission
Mean free path
Scattering
Schwarzschild eq.