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WorldView-2

WorldView-2 L1B panchromatic and multispectral EO data products are calibrated using the Optical Products Calibration (OPT-Calib) service.

Image-001

Figure 1 - True Color composite derived from Worldview-2 L1B calibrated data acquired on 05/01/2023 over the Saint Brandon archipelago, Mauritius. Credits: DigitalGlobe, USGS.

The process applied is the same for PAN and MS acquisitions.

Input

The input is an ingested WorldView-2, find details here.

DN to Radiance

The WorldView-2 product handbook1 provides the formula below to convert the DN into radiance:

\[ L_{(b)} = gain_{(b)} \times DN_{(b)} \times { abscalfactor \over effectivebandwith } + offset_{(b)} \]

Where:

\(gain_{(b)}\) and \(offset_{(b)}\) are values taken from Table 1:

Common band name Gain Offset
pan 0.942 -2.704
coastal 1.151 -7.478
blue 0.988 -5.736
green 0.936 -3.546
yellow 0.949 -3.564
red 0.952 -2.512
rededge 0.974 -4.120
nir08 0.961 -3.300
nir09 1.002 -2.891
Table 1 - Gain and offset for the Worldview-2 DN to radiance conversion.

And \(abscalfactor\) and \(effectivebandwith\) are extracted from the acquisition metadata.

The conversion from \(DN\) (for Digital Numbers) to spectral radiance (or ‘TOA radiance’) \(L \) is done with the formula below:

\[ L_\lambda = gain \times DN + offset \]

As such, the calibration uses:

\[ gain = gain_{(b)} \times { abscalfactor \over effectivebandwith } \]

and

\[ offset = offset_{(b)} \]

\(L \) in \(W/m^2/steradians/micrometers\) with \(b\) being a band ID.

Radiance to Reflectance

To convert TOA radiance to TOA reflectance, the following formula is used :

\[ R(b) = { {\pi \times L(b) \times d \times d} \over {ESUN(b) \times cos(θ)} } \]

where :

  • \(L(b)\) is the spectral radiance for band b

  • \(pi\) is the famous mathematical constant

  • \(d\) is the earth-sun distance (in astronomical units) and depends on the acquisition’s day and month

  • \(ESUN(b)\) is the mean TOA solar irradiance (or solar illumination) in \(W/m^2/micrometers\)

  • \(θ\) is the solar zenith angle in degrees.

The conversion from elevation angle to solar zenith angle \(θ\) (in degrees) is:

\[ θ = { 90 - elevation_angle } \]

The values for the \(ESUN(b)\) are provided in Table 2:

Common band name Thuillier 2003
pan 1571.36
coastal 1773.81
blue 2007.27
green 1829.62
yellow 1701.85
red 1538.85
rededge 1346.09
nir08 1053.21
nir09 856.599
Table 2 - ESUN value employed in the conversion of radiance to reflectance for Worldview-2 products.

Output

The output is a STAC item GeoJSON2 having a similar structure to the Worldview-3 one available here.

  1. Kuester, M. Absolute Radiometric Calibration: 2016v0; updated on 6/6/2017 GE01 and CAVIS, DigitalGlobe: Westminster, CO, USA, 2017; pp. 1–8. ↩

  2. Radiant Earth Foundation, STAC item specifications, a single spatiotemporal asset as a GeoJSON feature plus datetime and links, available at:https://github.com ↩