WorldView-3

WorldView-3 L1B panchromatic and multispectral EO data products are calibrated using the Optical Products Calibration (OPT-Calib) service.

Figure 1 - True Color composite derived from Worldview-3 L1B calibrated data acquired on 23/06/2023 over Spera District, Khost Province, Afghanistan. Credits: DigitalGlobe, USGS.

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

Input

The input is an ingested WorldView-3, find details here.

DN to Radiance

The WorldView-3 product handbook¹ provides the formula below to convert the DN into radiance:

L_{(b)} = g a i n_{(b)} \times D N_{(b)} \times \frac{a b s c a l f a c t o r}{e f f e c t i v e b a n d w i t h} + o f f s e t_{(b)}

Where:

$g a i n_{(b)}$ and $o f f s e t_{(b)}$ are values taken from Table 1:

Common band name	Gain	Offset
pan	0.950	-3.629
coastal	0.905	-8.604
blue	0.940	-5.809
green	0.938	-4.996
yellow	0.962	-3.649
red	0.964	-3.021
rededge	1.000	-4.521
nir08	0.961	-5.522
nir09	0.978	-2.992

Table 1 - Gain and offset for the Worldview-3 DN to radiance conversion.

And $a b s c a l f a c t o r$ and $e f f e c t i v e b a n d w i t h$ are extracted from the acquisition metadata.

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

L_{λ} = g a i n \times D N + o f f s e t

As such, the calibration uses:

g a i n = g a i n_{(b)} \times \frac{a b s c a l f a c t o r}{e f f e c t i v e b a n d w i t h}

and

o f f s e t = o f f s e t_{(b)}

$L$ in $W / m^{2} / s t e r a d i a n s / m i c r o m e t e r s$ with $b$ being a band ID.

Radiance to Reflectance

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

R (b) = \frac{π \times L (b) \times d \times d}{E S U N (b) \times c o s (θ)}

where :

$L (b)$ is the spectral radiance for band b
$p i$ is the famous mathematical constant
$d$ is the earth-sun distance (in astronomical units) and depends on the acquisition’s day and month
$E S U N (b)$ is the mean TOA solar irradiance (or solar illumination) in $W / m^{2} / m i c r o m e t e r s$
$θ$ is the solar zenith angle in degrees.

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

θ = 90 - e l e v a t i o n_{a} n g l e

The values for the $E S U N (b)$ are provided in Table 2:

Common band name	Thuillier 2003
pan	1574.41
coastal	1757.89
blue	2004.61
green	1830.18
yellow	1712.07
red	1535.33
rededge	1348.08
nir08	1055.94
nir09	858.77

Table 2 - ESUN value employed in the conversion of radiance to reflectance for Worldview-3 products.

Output

The output is a STAC item GeoJSON² including the assets shown below

  "assets": {
    "coastal": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/coastal.tif",
      "eo:bands": [
        {
          "name": "coastal",
          "common_name": "coastal",
          "center_wavelength": 0.4274,
          "solar_illumination": 1757.89,
          "full_width_half_max": 0.02025
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000147646949405,
          "statistics": {
            "minimum": "0",
            "maximum": "6347",
            "mean": "854.39426479578",
            "stddev": "551.85802604088",
            "valid_percent": "100"
          },
      "file:size": 91755870
    },
    "red": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/red.tif",
      "eo:bands": [
        {
          "name": "red",
          "common_name": "red",
          "center_wavelength": 0.6601,
          "solar_illumination": 1535.33,
          "full_width_half_max": 0.02925
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000147646949405,
          "statistics": {
            "minimum": "0",
            "maximum": "9597",
            "mean": "781.44649721892",
            "stddev": "601.396273167",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -18.81764705882353,
            "max": 9615.817647058824,
          }
        }
      ],
      "file:size": 120220176
    },
    "blue": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/blue.tif",
      "eo:bands": [
        {
          "name": "blue",
          "common_name": "blue",
          "center_wavelength": 0.4819,
          "solar_illumination": 2004.61,
          "full_width_half_max": 0.027
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000147646949405,
          "statistics": {
            "minimum": "0",
            "maximum": "7645",
            "mean": "787.38125030186",
            "stddev": "537.64898625588",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -14.990196078431373,
            "max": 7659.990196078431,
          }
        }
      ],
      "file:size": 103085046
    },
    "yellow": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
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      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/yellow.tif",
      "eo:bands": [
        {
          "name": "yellow",
          "common_name": "yellow",
          "center_wavelength": 0.6043,
          "solar_illumination": 1712.07,
          "full_width_half_max": 0.01905
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000147646949405,
          "statistics": {
            "minimum": "0",
            "maximum": "6683",
            "mean": "739.05154238735",
            "stddev": "552.66287363469",
            "valid_percent": "100"
          },
          "histogram": {
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            "min": -13.10392156862745,
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          }
        }
      ],
      "file:size": 118063652
    },
    "rededge": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
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        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/rededge.tif",
      "eo:bands": [
        {
          "name": "rededge",
          "common_name": "rededge",
          "center_wavelength": 0.7227,
          "solar_illumination": 1348.08,
          "full_width_half_max": 0.01935
        }
      ],
      "raster:bands": [
        {
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          "statistics": {
            "minimum": "0",
            "maximum": "7853",
            "mean": "887.91057425555",
            "stddev": "627.02772123954",
            "valid_percent": "100"
          },
          "histogram": {
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          }
        }
      ],
      "file:size": 124186124
    },
    "green": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/green.tif",
      "eo:bands": [
        {
          "name": "green",
          "common_name": "green",
          "center_wavelength": 0.5471,
          "solar_illumination": 1830.18,
          "full_width_half_max": 0.0309
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000147646949405,
          "statistics": {
            "minimum": "0",
            "maximum": "7279",
            "mean": "744.49282038834",
            "stddev": "537.28707470685",
            "valid_percent": "100"
          },
          "histogram": {
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            "min": -14.272549019607844,
            "max": 7293.272549019608,
          }
        }
      ],
      "file:size": 119246699
    },
    "nir09": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
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        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/nir09.tif",
      "eo:bands": [
        {
          "name": "nir09",
          "common_name": "nir09",
          "center_wavelength": 0.9136,
          "solar_illumination": 858.77,
          "full_width_half_max": 0.04445
        }
      ],
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            "stddev": "653.75464762957",
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      ],
      "file:size": 125324505
    },
    "nir08": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/nir08.tif",
      "eo:bands": [
        {
          "name": "nir08",
          "common_name": "nir08",
          "center_wavelength": 0.824,
          "solar_illumination": 1055.94,
          "full_width_half_max": 0.0502
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000147646949405,
          "statistics": {
            "minimum": "0",
            "maximum": "9543",
            "mean": "1135.7010306127",
            "stddev": "787.44611040581",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -18.711764705882352,
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      ],
      "file:size": 127019973
    },
    "overview-trc": {
      "type": "image/tiff; application=geotiff",
      "roles": [
        "composite",
        "reflectance",
        "visual"
      ],
      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/overview-trc.tif",
      "raster:bands": [
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    "overview-wad": {
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      "roles": [
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        "visual"
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      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/overview-wad.tif",
      "raster:bands": [
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            "stddev": "111.96667166902",
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      "roles": [
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      "href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/overview-trc-low-res.tif",
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  }

Kuester, M. Absolute Radiometric Calibration: 2016v0; updated on 6/6/2017 GE01 and CAVIS, DigitalGlobe: Westminster, CO, USA, 2017; pp. 1–8. ↩
Radiant Earth Foundation, STAC item specifications, a single spatiotemporal asset as a GeoJSON feature plus datetime and links, available at:https://github.com ↩