# Operational Calibration of the Imagers and Sounders

on the GOES-8 and -9 Satellites, Page 13

Michael Weinreb, Michael Jamieson, Nancy Fulton, Yen Chen, Joy Xie Johnson,

James Bremer, Carl Smith, and Jeanette Baucom

## 6.3 Calibration

Although the visible detector-channels are not calibrated in orbit,
calibration coefficients measured by ITT before launch^{6} are
transmitted to users in the GVAR data stream. A factor that converts radiance to
reflectance factor, or effective albedo, is included as well. Since detector
responsivities can vary unpredictably, the pre-launch calibration may not be
valid after launch.

The calibration equation is either

**Equation 10**

or

**Equation 11**

where X is the instrument output in counts, the subscript sp refers to the view of
space, and m and b are the calibration coefficients measured before launch^{6}.
For each visible-channel detector, the radiance R is the average of the spectral
(monochromatic) radiance over the spectral response function for that detector, i.e.,

where l is wavelength in µm, F the spectral response
function, and R(l) the spectral radiance of the target. Units of R are
W/(m^{2}-sr-µm).

The value of b in Eq. (10) depends on the electronic zero level. As was
discussed in the preceding section, this level varies with a standard deviation of approximately one count
for the imagers and tens of counts for the sounder. Therefore, when the satellite is in orbit, the value
of b determined in the laboratory (or at any other earlier time) may not be valid. Equation (11) is
preferred.

Furthermore, relativization and normalization affect the calibration. Currently, visible-channel data from the
imagers, but not the sounders, are being normalized. Since normalization makes the responses from all
eight imager detectors the same as that of the reference detector, users of the pre-launch calibration of
the imagers should apply the calibration coefficients for the reference detector (identified in Table 5)
to the data from all detectors.

With relativization enabled, an instrument's output at the view of space is modified
slightly, and the value of b in the calibration equation (Eq. [10]) needs to
be modified accordingly. For this reason also, the
best approach is to use Eq. (11). If Eq. (10) must be used, then the value of
b should be determined from
the equation: b = -mM_{0}

in which, for the imagers, m is the slope for the reference detector. For the sounders, it is the slope for
an individual detector. Values of b determined in this way, as well as the values of m (from Ref. 6)
and X_{0}, appear in Tables 5 and 6.

The reflectance factor (or effective albedo) is
obtained^{6} from the radiance by

where

and where H is the solar spectral irradiance H(l) averaged over the spectral
response function of the visible detector, i.e.,

Values of H were computed^{6} by ITT from tables of solar irradiance vs wavelength provided by Rossow et
al.^{13}, whose values are based on measurements by Neckel and Labs^{14}.
The values of A lie between 0 and 1. When A has the value of 1, it corresponds to the radiance of a perfectly
reflecting diffuse surface illuminated at normal incidence when the sun is at its annual-average distance
from the Earth. Values of k appear in Tables 5 and 6.

### Table 5. Visible-channel calibration coefficients for imagers

Satellite |
GOES-8 |
GOES-9 |

Identity of reference detector
(number in physical array) |
2 |
3 |

m
(reference detector)
(W/(m^{2}-sr-m-count)) |
0.5501873 |
0.5492361 |

X_{0} |
29 |
29 |

b
(W/(m^{2}-sr-µm)) |
-15.955 |
-15.928 |

k
((m^{2}-sr-µm)/W) |
1.92979 x 10^{-3} |
1.94180 x 10^{-3} |

### Table 6. Visible-channel calibration coefficients for sounders

Satellite |
Detector
No. |
m
(W/(m^{2}-sr-µm-count)) |
X_{0} |
b
(W/(m^{2}-sr-µm)) |
k
((m^{2}-sr-µm)/W) |

GOES-8 |
1 |
6.482527
x 10^{-2} |
920 |
-59.64 |
2.2008 x 10^{-3} |

2 |
6.522216
x 10^{-2} |
-60.00 |

3 |
6.560241
x 10^{-2} |
-60.35 |

4 |
6.642020
x 10^{-2} |
-61.11 |

GOES-9 |
1 |
6.416324
x 10^{-2} |
920 |
-59.03 |
2.2919 x 10^{-3} |

2 |
6.427129
x 10^{-2} |
-59.13 |

3 |
6.523361
x 10^{-2} |
-60.01 |

4 |
6.489786
x 10^{-2} |
-59.71 |

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**Contact Michael P. Weinreb at michael.weinreb@noaa.gov**

*Latest Revision: July 9, 1997*