Hyper-spectral 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.
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.
An example using Python...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.
The spectral model for Rayleigh optical thickness is derived from the work of Bodhaine 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.
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.
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.
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 of the band-pass intergrations are presented here. 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.
