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Atmospheric Radiation – Lecture 8

PHY2505 - Lecture 8

Radiative Transfer

Band Models

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Atmospheric Radiation – Lecture 8

Outline

• 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 widthv is

And spectral absorptance, A

Equivalent width, W [cm-1]:a measure of absorptance, A, over the spectral interval v

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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 positions2)Lines with random positions

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Atmospheric Radiation – Lecture 8

Regular Elasser band model

See Liou p139-141 for derivation

This gives

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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 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 forrepresentative 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

• Atmosphere: gas profiles, temperature, pressure profiles, aerosol/cloud type & vertical distribution

• Surface type & measurement geometry

• Select calculation methods: eg. correlated K method, scattering (DISTORT)

2cm-1 resolution

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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