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GeoEye-1

GeoEye-1 panchromatic and multispectral EO data products are calibrated using the Optical Products Calibration (OPT-Calib) service. The process applied is the same for PAN and MS acquisitions.

Image-001

DN to Radiance

The GeoEye-1 product handbook1,2 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:

Band Gain Offset
pan 0.970 -1.926
blue 1.053 -4.537
green 0.994 -4.175
red 0.998 -3.754
nir 0.994 -3.870

Table 1 - Gain and offset for the Geoeye-1 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 Bandwidth Thuillier 2003
pan 0.3074 1610.73
blue 0.0584 1993.18
green 0.0646 1828.83
red 0.0316 1491.49
nir 0.1012 1022.58

Table 2 - ESUN values employed in the conversion of radiance to reflectance for Geoeye-1 products.

Input

The input is an ingested GeoEye-1, see details here.

Output

The output is a STAC item GeoJSON3 including the assets shown below

  "assets": {
    "green": {
      "type": "image/tiff; profile=cloud-optimized; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../green.tif",
      "eo:bands": [
        {
          "name": "green",
          "common_name": "green",
          "center_wavelength": 0.545,
          "solar_illumination": 1828.83,
          "full_width_half_max": 0.03
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "6489",
            "mean": "863.56089417308",
            "stddev": "886.24396805544",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -12.723529411764705,
            "max": 6501.7235294117645,
          }
        }
      ],
      "file:size": 21813124
    },
    "nir08": {
      "type": "image/tiff; profile=cloud-optimized; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../nir08.tif",
      "eo:bands": [
        {
          "name": "nir08",
          "common_name": "nir08",
          "center_wavelength": 0.85,
          "solar_illumination": 1022.58,
          "full_width_half_max": 0.03
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "6427",
            "mean": "1886.247575313",
            "stddev": "1620.4647902937",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -12.601960784313725,
            "max": 6439.601960784314,
          }
        }
      ],
      "file:size": 27161474
    },
    "blue": {
      "type": "image/tiff; profile=cloud-optimized; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../blue.tif",
      "eo:bands": [
        {
          "name": "blue",
          "common_name": "blue",
          "center_wavelength": 0.48,
          "solar_illumination": 1993.18,
          "full_width_half_max": 0.03
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "5444",
            "mean": "882.13915505924",
            "stddev": "878.21414854936",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -10.674509803921568,
            "max": 5454.674509803922,
          }
        }
      ],
      "file:size": 20748394
    },
    "red": {
      "type": "image/tiff; profile=cloud-optimized; application=geotiff",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../red.tif",
      "eo:bands": [
        {
          "name": "red",
          "common_name": "red",
          "center_wavelength": 0.673,
          "solar_illumination": 1491.49,
          "full_width_half_max": 0.03
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "7533",
            "mean": "669.12548358611",
            "stddev": "833.3870434736",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -14.770588235294118,
            "max": 7547.770588235294,
          }
        }
      ],
      "file:size": 21817073
    },
    "overview-trc": {
      "type": "image/tiff; profile=cloud-optimized; application=geotiff",
      "roles": [
        "composite",
        "reflectance",
        "visual"
      ],
      "href": "https://.../overview-trc.tif",
      "raster:bands": [
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "253",
            "mean": "44.113735557357",
            "stddev": "53.367084044392",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        },
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "252",
            "mean": "59.218777275141",
            "stddev": "58.264231030447",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        },
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "248",
            "mean": "60.933859268563",
            "stddev": "58.460926022744",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        },
        {
          "spatial_resolution": 0.0000141800457472,
          "statistics": {
            "minimum": "0",
            "maximum": "255",
            "mean": "156.34194277981",
            "stddev": "124.19497709926",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        }
      ],
      "file:size": 33974844
    },
    "overview-trc-low-res": {
      "type": "image/tiff; profile=cloud-optimized; application=geotiff",
      "roles": [
        "composite",
        "overview",
        "reflectance"
      ],
      "href": "https://.../overview-trc-low-res.tif",
      "raster:bands": [
        {
          "spatial_resolution": 0.0001445976930592,
          "statistics": {
            "minimum": "0",
            "maximum": "253",
            "mean": "44.10063457489",
            "stddev": "53.378320324808",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        },
        {
          "spatial_resolution": 0.0001445976930592,
          "statistics": {
            "minimum": "0",
            "maximum": "252",
            "mean": "59.193407058716",
            "stddev": "58.26799239793",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        },
        {
          "spatial_resolution": 0.0001445976930592,
          "statistics": {
            "minimum": "0",
            "maximum": "248",
            "mean": "60.905345916748",
            "stddev": "58.462711737198",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        },
        {
          "spatial_resolution": 0.0001445976930592,
          "statistics": {
            "minimum": "0",
            "maximum": "255",
            "mean": "156.28141880035",
            "stddev": "124.20901711164",
            "valid_percent": "100"
          },
          "histogram": {
            "count": 256,
            "min": -0.5,
            "max": 255.5,
          }
        }
      ],
      "file:size": 4197770
    }
  }

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

  2. Podger, N.E., Colwell, W.B. and Taylor, M.H. (2011) GeoEye-1 Radiance at Aperture and Planetary Reflectance. 

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