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PHY2505 - Lecture 8

PHY2505 - Lecture 8. Radiative Transfer Band Models. Outline. Equivalent width Weak line/strong line approximations Band models Curtis-Godson approximation MODTRAN. Equivalent width.

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PHY2505 - Lecture 8

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  1. PHY2505 - Lecture 8 Radiative Transfer Band Models

  2. Outline Equivalent width Weak line/strong line approximations Band models Curtis-Godson approximation MODTRAN

  3. 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 intervalDv

  4. Equivalent width of a Lorentz line

  5. Equivalent width of a Lorentz line

  6. “Weak line” limit

  7. “Strong line” limit

  8. Can find experimentally from “curves of growth” Strong/weak line: limits of validity

  9. 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: • Lines with regular positions • Lines with random positions

  10. Regular Elasser band model This gives See Liou p139-141 for derivation

  11. Principle of statistical band models

  12. Principle of statistical band models where d is the mean spacing For multiple lines, transmission is exponential in W

  13. Goody statistical model

  14. Goody statistical model: weak and strong line limits

  15. 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 Liousection 4.3for a discussion of the limits of validity for this approximation Correlated k distribution Liou, FIG 4.5

  16. Curtis – Godson approximation

  17. Curtis – Godson approximation

  18. Curtis – Godson approximation

  19. Curtis – Godson approximation

  20. 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 • Atmosphere: gas profiles, temperature, pressure profiles, aerosol/cloud type & vertical distribution • Surface type & measurement geometry • Select calculation methods: eg. correlated K method, scattering (DISTORT)

  21. 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).

  22. MODTRAN dialogue windows

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