Radiation in the Earth's Atmosphere Part 1: Absorption and … · 2014. 1. 28. · Electromagnetic...
Transcript of Radiation in the Earth's Atmosphere Part 1: Absorption and … · 2014. 1. 28. · Electromagnetic...
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Radiation in the Earth's Atmosphere
Part 1:
Absorption and Emission by Atmospheric Gases
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Electromagnetic Waves
● Electromagnetic waves are transversal.
● Electric and magnetic fields are perpendicular.
● In the quantum mechanic context EM waves are travelling photons.
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Refraction
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Scattering
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Absorption
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Blackbody Radiation
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What is a Black Body?
● 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”.
Source: http://web.mit.edu
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Blackbody Radiation
● A black body also emits radiation in a characteristic way.
● The emitted radiation only depends on temperature, not on material or other properties.
Source: http://en.wikipedia.org
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● The wavelength of the maximum of the radiation is inversely proportional to the absolute temperature:
Wien's Displacement Law
Source: http://en.wikipedia.org
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Classical Explanation:Rayleigh-Jeans Law
● For each wavelength/frequency only a certain number of waves fit into the cavity.
Source: http://hyperphysics.phy-astr.gsu.edu
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The Ultraviolet Catastrophe
● The classical Rayleigh-Jeans law would produce infinite radiation at short wavelengths.
Source: http://hyperphysics.phy-astr.gsu.edu
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● 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.
Planck's Law
Source: http://en.wikipedia.org
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Absorption and Emission
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Absorption Coefficient
I=I 0 e− l
● The incoming radiation with intensity I
0 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:
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Kirchhoff's Law for Thermal Radiation
● A blackbody emits radiation with the source term
● The emission coefficient ε ds=1 for a blackbody andε 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.
S=νB νT
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Optical Depth
● We define the optical depth τ as
● Transmission: T = exp(-τ)● τ<<1: optically thin case
● τ>>1: optically thick case
s =∫0
sds' s'
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Radiative Transfer Equation
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Radiative Transfer
● 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.
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Radiative Transfer Equation
I ν0 =I ν s0e−s0∫0
s0
ds Bν T e−s
● Intensity at observer's position s=0
● Background radiation at s=s0
● Source (emission) term: B● Units: W/(m2 Hz sterad)
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Discrete Radiative Transfer
● 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.
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Molecular Absorption
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Atomic and Molecular Spectra● 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.
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Rotational Molecular Spectra
● 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.
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Vibrational Molecular Spectra
● 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.
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Vibrational-Rotational Spectra● P branch: ΔJ= -1● Q branch: ΔJ= 0
(often forbidden)● R branch: ΔJ= +1
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Pressure (Collision) Broadening● 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 collision-broadened line is roughly proportional to pressure.
● Pressure-broadening adds altitude information that can be used for profile retrievals.
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Effect of Pressure-Broadening Observed at Ground Level
● The observer sees the integral over all emitted lines from all altitudes.
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Lorentz- and Doppler Broadening
● Lorentz: natural broadening due to limited lifetime of excited state.
● Doppler: broadening due to the relative thermal speed of the emitting molecules.
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Altitude Effect (emission)
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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
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Fine Structure (absorption)
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Line-by-line vs. Band Spectra
● 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. CO
2)
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Solar and Earth Spectra
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Solar and Atmospheric Radiation
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Solar and Earth Emission
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Absorption Bands by Atmospheric Trace Gases
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Vertical Range of Solar Radiation
Source: http://amazing-space.stsci.edu
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Solar Constant and Incoming Solar Radiation (Insolation)
● Solar constant at top of atmosphere:1364 W/m2
● Incoming solar radiation: 341 W/m2
● Why the factor of 4?
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Radiative Energy Budget