Atmospheric Radiation – Lecture 8
PHY2505 - Lecture 8
Radiative Transfer
Band Models
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Atmospheric Radiation – Lecture 8
Outline
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Equivalent width
Weak line/strong line approximations
Band models
Curtis-Godson approximation
MODTRAN
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Atmospheric Radiation – Lecture 8
Equivalent width
Consider a homogenous atmospheric
layer. Here the spectral absorption
coefficient does not depend on path
length.
The spectral transmittance T
for a band of width Dv is
And spectral absorptance, A
Equivalent width, W [cm-1]:
a measure of absorptance, A,
over the spectral interval Dv
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Atmospheric Radiation – Lecture 8
Equivalent width of a Lorentz line
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Atmospheric Radiation – Lecture 8
Equivalent width of a Lorentz line
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Atmospheric Radiation – Lecture 8
“Weak line” limit
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Atmospheric Radiation – Lecture 8
“Strong line” limit
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Atmospheric Radiation – Lecture 8
Strong/weak line: limits of validity
Can find experimentally from
“curves of growth”
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Atmospheric Radiation – Lecture 8
Band models
A band is a spectral interval of a width Dv small enough to use a mean value of the
Planck function Bv(T) but large enough to contain several absorption lines
Band models are introduced to simplify computation of spectral transmittance
Now we have found out how to calculate the equivalent width of a single line, need
to consider how we deal with a band of many lines
Two main cases:
1)Lines with regular positions
2)Lines with random positions
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Atmospheric Radiation – Lecture 8
Regular Elasser band model
This gives
See Liou p139-141 for derivation
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Atmospheric Radiation – Lecture 8
Principle of statistical band models
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Atmospheric Radiation – Lecture 8
Principle of statistical band models
where d is the mean spacing
For multiple lines, transmission is exponential in W
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Atmospheric Radiation – Lecture 8
Goody statistical model
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Atmospheric Radiation – Lecture 8
Goody statistical model: weak and strong line limits
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Atmospheric Radiation – Lecture 8
Correlated k distribution
Here, the spectral lines are
rearranged over a given spectral
interval and a histogram produced
Absoprtion coefficient for
representative lines is multiplied by a
weighting function representing
frequency of occurance of this type
of line
Typically useful to use 4 divisions per
decade on log scale …
See Liou section 4.3 for a
discussion of the limits of validity for
this approximation
Liou, FIG 4.5
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Atmospheric Radiation – Lecture 8
Curtis – Godson approximation
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Atmospheric Radiation – Lecture 8
Curtis – Godson approximation
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Atmospheric Radiation – Lecture 8
Curtis – Godson approximation
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Atmospheric Radiation – Lecture 8
Curtis – Godson approximation
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Atmospheric Radiation – Lecture 8
MODTRAN4
A. Berk *, G.P. Anderson #, P.K. Acharya *,
J.H. Chetwynd #, M.L. Hoke #,L.S. Bernstein
*, E.P. Shettle ^, M.W. Matthew *, and S.M.
Adler-Golden
#
US Air Force Research Laboratory
*Naval research Laboratory
2cm-1 resolution
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Atmosphere: gas profiles, temperature, pressure profiles, aerosol/cloud type &
vertical distribution
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Surface type & measurement geometry
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Select calculation methods: eg. correlated K method, scattering (DISTORT
Atmospheric Radiation – Lecture 8
Who still uses band models (MODTRAN)?
UV/VIS atmospheric instruments where scattering important
Eg. SCISAT-1 MAESTRO McElroy, C.T. , A spectroradiometer for the
measurement of direct and scattered solar spectral irradiance from on-board the
NASA ER-2 high-altitude research aircraft, Geophys. Res. Lett., 22, 1361-1364
(1995).
Multispectral imagers cloud, ozone, water vapour retrieval
Eg. MODIS Justice, C.et al, The Moderate Resolution Imaging
Spectroradiometer (MODIS): Land remote sensing for global change research, IEEE
Trans. Geosci. Remote Sens., 36, 1228-1249 (1998).
Hyperspectral imagers for atmospheric corrections
Eg. AVIRIS Berk, A, et al, MODTRAN Cloud and Multiple Scattering Upgrades
with Application to AVIRIS, Remote Sens. Environ., 65, 367-375 (1998).
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Atmospheric Radiation – Lecture 8
MODTRAN dialogue windows
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