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Spectral Sources used for R2009

Hyperspectral models and data sources are integrated with the satellite sensor relative spectral response functions (RSR) to account for the relatively wide spectral bands and any out-of-band response on various absorption and scattering processes. This band averaging is used to produce the Rayleigh optical thicknesses for each spectral band, which are then utilized in the generation of Rayleigh-scattering-coefficient look-up tables and Rayleigh pressure corrections. The approach is also applied to the absorption coefficients for atmospheric gases (O3 and NO2) and the absorption and scattering coefficients for pure sea water.

Integration method

The band-averaged quantity X is derived by integrating the spectral values x(L) at each wavelength L over the full wavelength range of the RSR for each sensor band. i.e.:

X = integral{ x(L)*RSR(L)*W(L)*dL } / integral{ RSR(L)*W(L)*dL }

Where W(L) is an additional weighting value (typically 1 or the solar irradiance, F0). The reference solar spectrum is taken from Thuillier 2002. The interpolated solar spectrum at 1-nm increments is available here.

Relative spectral response functions

The relative spectral response (RSR) functions, or spectral band-passes, for CZCS, OCTS, SeaWiFS, and MODIS were measured in laboratory conditions prior to launch. They are assumed to be stable on-orbit. The RSRs used for band-pass integrations are listed by sensor below.

  • MODIS/Aqua
  • MODIS/Terra
  • SeaWiFS
  • OCTS
  • CZCS

    Rayleigh optical thicknesses

    The spectral model for Rayleigh optical thickness is derived from the work of Bodaine et al. 1999, assuming standard pressure of 1013.25mb, temperature of 288.15K, and CO2 concentration of 360ppm. The resulting model of Rayleigh optical depth and depolarization factor at 1-nm increments over the spectral range from 200 to 2450-nm is available here.

    In computing the band averages, the Rayleigh optical thickness model was integrated with the sensor RSRs with weighting by the solar spectrum. Band-averaged depolarization factors were also computed for use in the radiative transfer computations.

    Ozone aborption coefficients

    The ozone absorption cross-sections were computed at 220.15K using software provided by E.P.Shettle based on the work of S.Anderson (1990,1991,1992,1993) and Burkholder & Talukdar, 1994. This is a departure from previous processing where Nicolet, 1981 was used. The new ozone absoprption spectrum, expressed as an attenuation coefficient (cm^-1) at 1-nm increments over the 200 - 2550nm spectral range is here.

    In computing the band averages, the ozone attenuation coefficients were integrated with the sensor RSRs with weighting by the solar spectrum.

    NO2 absorption coefficients

    The NO2 absorption cross-sections were taken from Bogumil et al. 2003 and Schneider et al. 1987. The NO2 absorption cross-sections, expressed as cm^2/molecule at 1-nm increments over the 200 - 2450nm spectral range are here.

    In computing the band averages, the NO2 absorption cross-sections were integrated with the sensor RSRs with weighting by the solar spectrum.

    Pure seawater absorption and scattering coefficients

    To cover the range from ultra-violet to short-wave infrared, the pure seawater water absorption spectrum was derived by combination of Smith and Baker, 1981, Pope and Fry, 1997, and Kou et al. 1993. The pure seawater scattering spectrum was taken from Smith and Baker, 1981. Interpolated spectra at 1-nm increments over the 200-2450nm range are available here.

    In computing the band averages, the water absorption and scattering coefficients were integrated with the sensor RSRs with no additional weighting. The scattering coefficients were converted to backscattering coefficients by applying a multiplicative factor of 0.5.

    Results

    Results of the band-pass integrations are presented for each sensor below. The band-averaged solar irradiances and center wavelength values are also shown. Wave center is the bisection of the RSR width at half maximum response. Wave average is the integrated band wavelength, and wave peak is the location of maximum response.

    MODIS/Aqua

    Quantity Band1 Band2 Band3 Band4 Band5 Band6 Band7 Band8 Band9 Band10 Band11 Band12 Band13 Band14 Band15 Band16
    Wave Center 412.123 442.260 466.122 487.508 530.220 547.353 554.026 644.898 665.970 677.665 746.938 857.323 867.050 1241.597 1627.972 2113.124
    Wave Average 416.324 442.617 466.073 487.505 530.183 547.159 553.919 645.832 667.183 678.527 745.324 856.871 866.861 1241.489 1628.069 2113.957
    Wave Peak 416.000 442.000 461.000 489.000 530.000 547.000 551.000 657.000 665.000 677.000 747.000 848.000 865.000 1243.000 1623.000 2105.000
    Wave Width (fwhm) 14.481 9.691 18.894 10.677 12.039 10.389 19.753 47.493 10.048 11.382 9.830 38.252 15.562 23.356 27.593 53.079
    F0 (Thuillier) 172.912 187.622 205.878 194.933 185.747 186.539 183.869 157.811 152.255 148.052 128.065 97.174 95.824 45.467 23.977 9.885
    Taur (Rayleigh) 3.099E-01 2.367E-01 1.914E-01 1.592E-01 1.126E-01 9.906E-02 9.432E-02 5.082E-02 4.443E-02 4.146E-02 2.849E-02 1.613E-02 1.540E-02 3.617E-03 1.219E-03 4.286E-04
    Dpol (Depolarization) 2.945E-02 2.910E-02 2.887E-02 2.869E-02 2.841E-02 2.832E-02 2.829E-02 2.794E-02 2.789E-02 2.786E-02 2.772E-02 2.756E-02 2.755E-02 2.732E-02 2.723E-02 2.719E-02
    k_oz (Ozone) 1.987E-03 3.189E-03 8.745E-03 2.032E-02 6.838E-02 8.622E-02 9.553E-02 7.382E-02 4.890E-02 3.787E-02 1.235E-02 2.347E-03 1.936E-03 0.000E+00 0.000E+00 0.000E+00
    k_no2 (NO2) 5.814E-19 4.985E-19 3.938E-19 2.878E-19 1.525E-19 1.194E-19 9.445E-20 1.382E-20 7.065E-21 8.304E-21 2.157E-21 6.212E-23 7.872E-23 0.000E+00 0.000E+00 0.000E+00
    aw (water) 2.030E-02 1.110E-02 1.034E-02 1.676E-02 4.494E-02 5.491E-02 5.839E-02 3.458E-01 4.923E-01 5.116E-01 2.800E+00 4.396E+00 4.727E+00 1.147E+02 6.689E+02 2.810E+03
    bbw (water) 3.245E-03 2.453E-03 1.964E-03 1.621E-03 1.131E-03 9.887E-04 9.386E-04 4.903E-04 4.265E-04 3.967E-04 2.670E-04 1.474E-04 1.404E-04 2.852E-05 8.840E-06 2.862E-06

    MODIS/Terra

    SeaWiFS

    Quantity Band1 Band2 Band3 Band4 Band5 Band6 Band7 Band8
    Wave Center 413.306 443.944 491.123 510.071 554.631 668.236 764.876 866.353
    Wave Average 413.972 443.968 491.599 510.056 555.661 668.112 766.962 863.467
    Wave Peak 418.000 446.000 487.000 514.000 558.000 671.000 775.000 858.000
    Wave Width (fwhm) 20.124 19.608 20.576 22.376 18.293 19.845 40.284 41.366
    F0 (Thuillier) 172.998 190.154 196.438 188.164 182.997 151.139 122.330 96.264
    Taur (Rayleigh) 3.128E-01 2.329E-01 1.542E-01 1.326E-01 9.444E-02 4.444E-02 2.553E-02 1.690E-02
    Dpol (Depolarization) 2.946E-02 2.908E-02 2.866E-02 2.854E-02 2.828E-02 2.788E-02 2.769E-02 2.757E-02
    k_oz (Ozone) 4.114E-04 3.162E-03 2.346E-02 4.094E-02 9.568E-02 4.649E-02 8.141E-03 3.331E-03
    k_no2 (NO2) 6.004E-19 4.963E-19 2.746E-19 2.081E-19 9.411E-20 9.234E-21 1.078E-21 1.942E-21
    aw (water) 4.994E-03 7.512E-03 2.501E-02 4.002E-02 7.708E-02 4.456E-01 2.944E+00 4.865E+00
    bbw (water) 3.271E-03 2.421E-03 1.568E-03 1.339E-03 9.393E-04 4.261E-04 2.376E-04 1.489E-04

    OCTS

    CZCS

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    Authorized by: gene carl feldman

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    Updated: 10 October 2009