1' Electromagnetic Radiation:

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1. Electromagnetic Radiation How we describe
it the EM spectrum
Simple wave properties Energy
Doppler effect -
heterodyne detection
Polarization How we create it Blackbodies
brightness temperature

The energy carried is proportional to ??o?2
Basic quantity is the radiance
4 Stokes parameters, IQUV
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Molecular Absorption how why quantum
transitions, electronic,
vibrational and rotation -
dipole Absorption Spectrum Absorption
coefficient and pressure broadening Transmissi
on optical depth, gas path length Beers law,
Langley plots etc
k? S f(?-?o)
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Applications bases for estimating column CO2 and
O2 (surface pressure) Spectrometer systems
prism (Dobson), grating and interferometers
(contrast to filter radiometers)
3. Optimal estimation and the Bayesian retrieval
approach
Gaussian statistics??
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Bayes Theorem
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Bayes Theorem
This represents an updating to our prior
knowledge P(x) given the measurement y
is the knowledge of y given x pdf of forward
model
The most likely value of x derived from this
posterior pdf therefore represents our inverse
solution. Our knowledge contained in
is explicitly expressed in terms of the forward
model and the statistical description of both
the error of this model and the error of the
measurement. The factor P(y) will be ignored as
it in practice is a normalizing factor.
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Optimal Estimation Inversion

Maximize
Minimize

• Rodgers , C.D, 2000 Inverse methods for
  Atmospheric sounding Theory
• and Practice, World Scientific, 238pp

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The general transfer equation (absorption/emission
only)
dI dI(extinction) dI (emission)
Insert fig. 4.3
Here, we change vertical co-ordinate systems
Main point is that the radiative transfer
equation is merely a (simple) statement of
energy conservation
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The (general) integral solution
You need to be able to derive both the equations
of transfer as introduced previously and its
general integral solution given here.
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SST
UTH
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Weighting functions
With lorenz line shape
Nadir sounding
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