Geoscience Reference
In-Depth Information
Appendix A
Radiation
This appendix summarizes (without much commentary) basic equations related to
radiation in the atmosphere.
A.1 Radiation Laws
Planck's law: monochromatic hemispherical emissive power of a black body (in
W m
-2
μm
-1
)
−
5
c
λ
M
=
1
(A.1)
bλ
c
2
λ
T
e
−
1
in which
c
1
= 3.74 ·10
8
W μm
-4
m
-2
and
c
2
= 1.439 ·10
4
μm K;
T
is the absolute tem-
perature of the black body and
λ
is the wavelength in μm.
Direct consequences of Eq. (
A.1
) are Stefan-Boltzmann's law and Wien's dis-
placement law:
MT
b
=σ
4
(A.2)
λ
T
=28
89
m K
µ
(A.3)
m
where
σ
is the constant of Stefan-Boltzmann (5.67 · 10
-8
W m
-2
K
-4
) and
λ
m
is the
wavelength at which maximum emission takes place.
Hemispherical monochromatic emissive power of a general (non-black) body is
given by:
MM
λ
=
ε
(A.4)
λ λ
b
where
ε
λ
is the monochromatic emissivity. The total hemispherical emissive power of
a non-black body is given by:
∞
∫
ε λ
MM
=
λ b
d
(A.5)
0
345
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