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Calculating Spectral Radiance or Top-of-Atmosphere Reflectance from QuickBird2 DN values for GRASS-GIS (Python script)
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i.quickbird.toar is a GRASS-GIS add-on module converting QuickBird2 DN values (Digital Numbers, that is relatively readiometrically corrected detector data) to Spectral Radiance or Reflectance.

Conversion to top-of-atmosphere spectral radiance is a simple two step process that involves multiplying radiometrically corrected image pixels by the appropriate absolute radiometric calibration factor (also referred to as a K factor) to get band-integrated radiance [W-m-2-sr-1] and then dividing the result by the appropriate effective bandwidth to get spectral radiance [W-m-2-sr-1-μm-1]. (Taylor, 2005)

For the moment, the module requires as an input the acquisition's date and time formatted as a UTC string, the (mean) Sun Elevation Angle and the Panchromatic band's TDI level. These are required to calculate the Earth-Sun distance parameter for the modules' internal computations and can be retrieved from the imagery's metadata files. The UTC string can be overriden by using the optional parameter doy, given the day of year (Julian Day) has been correctly estimated for the acquisition that is to be processed.

Optionally, the module may operate on the current computational region, instead of a bands whole extent.

ToAdd: More details about retrieving the acquisition's metada.

Source: Krause, 2005

Spectral Radiance

Planetary Reflectance

ρ(p) = π x L(λ) x d^2 / ESUN(λ) x cos(θ(S))


  • ρ: Unitless Planetary Reflectance
  • π: Mathematical constant
  • L(λ): Spectral Radiance from equation (1)
  • d: Earth-Sun distance in astronomical units [calculated using AcquisitionTime class]


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