# 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 relationship^{9}

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*