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Radiation in the Earth's Atmosphere
Part 1:
Absorption and Emission by
Atmospheric Gases
Electromagnetic Waves
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Electromagnetic
waves are
transversal.
Electric and
magnetic fields are
perpendicular.
In the quantum
mechanic context
EM waves are
travelling photons.
Refraction
Scattering
Absorption
Blackbody Radiation
What is a Black Body?
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Source: http://web.mit.edu
An ideal black body
absorbs radiation at all
frequencies/wavelengts
completely.
A cavity is a good
approximation of a
black body.
No real body can
absorb more than a
black body.
If a body only absorbs
radiation partially, it is
called “gray”.
Blackbody Radiation
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Source: http://en.wikipedia.org
A black body also emits
radiation in a
characteristic way.
The emitted radiation
only depends on
temperature, not on
material or other
properties.
Wien's Displacement Law
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Source: http://en.wikipedia.org
The wavelength of
the maximum of
the radiation is
inversely
proportional to the
absolute
temperature:
Classical Explanation:
Rayleigh-Jeans Law
Source: http://hyperphysics.phy-astr.gsu.edu
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For each wavelength/frequency only a certain
number of waves fit into the cavity.
The Ultraviolet Catastrophe
Source: http://hyperphysics.phy-astr.gsu.edu
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The classical Rayleigh-Jeans law would
produce infinite radiation at short wavelengths.
Planck's Law
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Source: http://en.wikipedia.org
Planck assumed
that radiation could
only be absorbed
or emitted in
discrete packets of
h=6.626*10-34 J s.
Planck's law
correctly describes
the black body
radiation between
the classical
Rayligh-Jeans and
Wien
approximation.
Absorption and Emission
Absorption Coefficient
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The incoming radiation
with intensity I0 is
attenuated by the
medium.
The absorption
coefficient α is a
measure for the
absorption by path
length.
α depends on the
wavelength.
Beer-Lambert-Law:
− l
I =I 0 e
Kirchhoff's Law for Thermal
Radiation
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A blackbody emits radiation with the source term
S =ν B ν T 
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The emission coefficient ε ds=1 for a blackbody and
ε ds<1 for a real body.
To fulfill the 2nd law of thermodynamics, the emission
coefficient ε must be equal to the absorption coefficient
α.
Optical Depth
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We define the optical depth τ as
s
'
'
s =∫0 ds   s 
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Transmission: T = exp(-τ)
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τ<<1: optically thin case
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τ>>1: optically thick case
Radiative Transfer Equation
Radiative Transfer
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Electromagnetic radiation
traveling through a medium may
be absorbed.
The absorption is proportional to
the intensity I. It is characterised
by the absorption coefficient α.
The medium may also emit
electromagnetic radiation. This
is the source term S.
Radiative Transfer Equation
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Intensity at observer's position s=0
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Background radiation at s=s0
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Source (emission) term: B
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Units: W/(m2 Hz sterad)
−s 0 
I ν 0 =I ν  s 0 e
s0
∫0 ds B ν T  e
− s

Discrete Radiative Transfer
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The integral form of the radiative transfer
equation can be solved numerically.
Discretize radiative transfer equation into
optically thin layers with constant absorption
coefficient and convert integral into sum.
Alternative: calculate radiative transfer
iteratively for optically thin layers. Use previous
layer as background term.
Molecular Absorption
Atomic and Molecular Spectra
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Atoms and molecules may change
between different internal energetic
states.
According to quantum mechanics,
only distinct changes are allowed.
A change from one state to another
results in the emission or
absorption of a photon of distinct
frequency according to Planck's
law E=hν.
There are distinct classes of
changes that result in
emission/absorption in distinct
bands of the electromagnetic
spectrum.
Rotational Molecular Spectra
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Molecules rotate around their center of mass
They emit electromagnetic waves if the charges inside the molecule are not
symmetric with respect to the center of mass (permanent dipole moment).
Typical spectra are in the microwave region.
Vibrational Molecular Spectra
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Molecules vibrate by changing distances between atoms.
They emit electromagnetic waves if the vibration results in an asymmetric
charge distribution (induced dipole moment).
Typical spectra are in the infrared region.
Vibrational-Rotational Spectra
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P branch: ΔJ= -1
Q branch: ΔJ= 0
(often forbidden)
R branch: ΔJ= +1
Pressure (Collision) Broadening
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Spectral lines are
broadened by collisions with
other molecules.
A collision interrupts the
emission of a continuous
elecromagnetic wave. This
results in a wider frequency
distribution.
The width of the collisionbroadened line is roughly
proportional to pressure.
Pressure-broadening adds
altitude information that can
be used for profile retrievals.
Effect of Pressure-Broadening
Observed at Ground Level
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The observer sees the integral over all emitted
lines from all altitudes.
Lorentz- and Doppler Broadening
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Lorentz: natural
broadening due
to limited lifetime
of excited state.
Doppler:
broadening due
to the relative
thermal speed of
the emitting
molecules.
Altitude Effect (emission)
Real-World Spectra (absorption)
H2O: 27035 lines
 CO2: 10757 lines
 CH4: 7240 lines
 O2: 1087 lines
 N2O: 1569 lines
 CO: 2564 lines
 +12 additional species

Fine Structure (absorption)
Line-by-line vs. Band Spectra
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Because of the large number of spectral lines,
calculationg radiative transfer line-by-line is
very costly
For climate models, average absorption for a
larger band is calculated for each species.
The net absorption is then calculated by scaling
the average absorption with temperature and
mixing ratio of the trace gases (e.g. CO2)
Solar and Earth Spectra
Solar and Atmospheric Radiation
Solar and Earth Emission
Absorption Bands by Atmospheric
Trace Gases
Vertical Range of Solar Radiation
Source: http://amazing-space.stsci.edu
Solar Constant and Incoming Solar
Radiation (Insolation)
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Solar constant at top of atmosphere:
1364 W/m2
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Incoming solar radiation: 341 W/m
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Why the factor of 4?
2
Radiative Energy Budget