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# 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 RM 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, rbb is not simply the radiance of the blackbody Rbb, but is related to it by

Equation 8 where RM,bb is the radiance of the scan mirror computed from its temperature at the time of the blackbody sequence. The quantity e is the scan mirror's emissivity when it is at the blackbody position, for which the angle of incidence of the incoming radiation is 45o. Similarly, e [sp] is the emissivity at the space look position, which will have an incidence angle of either 40o or 50o, depending upon which side of the Earth the space look occurs. (For the imager, 40o 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 RM,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 be, 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.

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