Operational Calibration of the Imagers and Sounders
on the GOES-8 and -9 Satellites, Page 7

Michael Weinreb, Michael Jamieson, Nancy Fulton, Yen Chen, Joy Xie Johnson,
James Bremer, Carl Smith, and Jeanette Baucom

4.1 Generalized infrared calibration equations

The processing change invokes a generalization of the calibration equation to include the emission and reflection of the scan mirror. The generalized calibration equation is

Equation 6

where R, X, q, m, and b are defined as in Eq. (1). The quantity e is the emissivity of the scan mirror, and it is a function of scan angle q. The procedure for determining e[q] is described in the next section. The parameter R_M is the radiance of the scan mirror. This radiance is computed via Eq. (4) from the temperature of the scan mirror, which is monitored by a thermistor embedded in its structure. The validity of Eq. (6) depends on the relationship⁹

in which r is the reflectance and e the emissivity in a particular direction of an opaque, specularly-reflecting surface.

Equation (6) differs from Eq. (1) on the left hand side, where now the scene radiance R is multiplied by (1 - e) instead of 1; this represents the reduction in the radiation received from the scene as the reflectance of the scan mirror is reduced from 1 to 1 - e. Also, there is a second term, which represents the radiation emitted by the scan mirror.

In orbit, the processing goes as follows: At each blackbody look, m is determined from

Equation 7

where the variables are defined as in Eq. (3). However, r_bb is not simply the radiance of the blackbody R_bb, but is related to it by

Equation 8

where R_M,bb is the radiance of the scan mirror computed from its temperature at the time of the blackbody sequence. The quantity e[45] is the scan mirror's emissivity when it is at the blackbody position, for which the angle of incidence of the incoming radiation is 45^o. Similarly, e [sp] is the emissivity at the space look position, which will have an incidence angle of either 40^o or 50^o, depending upon which side of the Earth the space look occurs. (For the imager, 40^o is on the west, while for the sounder it is on the east.)

From Eqs. (7) and (8), it would appear that m depends on the side of Earth on which the space view occurs. Nevertheless, it is, in fact, a property only of the instrument--it is essentially the reciprocal of the responsivity of the radiometer downstream of the scan mirror--and it does not depend on space-view side.

At each space look, b is determined from the equation

where R_M,sp is the mirror radiance at the time of the space look. The value of b may depend on space-clamp side.

It is convenient to define the quantity b_e, as

Equation 9

Then, for each pixel, the radiances are computed from

where m is from Eq. (7), and e(q) is e evaluated at the scan angle (pixel position) q.

For the imager, the interpolation of space-look counts within the blackbody sequences, and the interpolation of the intercepts between space looks, are still carried out, as described previously.

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Contact Michael P. Weinreb at michael.weinreb@noaa.gov
Latest Revision: July 9, 1997