# Operational Calibration of the Imagers and Sounders

on the GOES-8 and -9 Satellites

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

James Bremer, Carl Smith, and Jeanette Baucom

## 3. INFRARED CALIBRATION EQUATIONS AT LAUNCH

The calibration equation relates the radiance R from the scene to the output X of
the instrument, which is in ten-bit counts for the imager and 13-bit counts
for the sounder. There is a specific calibration equation for each detector of
each channel. The calibration equation that was in use at the time of the
launches of both GOES-8 and GOES-9 (but was modified several months later, as
will be described below) is

**Equation 1**

where q, m, and b are the coefficients and will be described below. The equation is
quadratic to allow for possible non-linearities in sensor response, which affect
primarily the longwave and midwave channels. For a particular channel and
detector, the radiance R is the average of the spectral (monochromatic) radiance
over the spectral response function for that channel and detector, i.e.,

**Equation 2**

in which n is the wavenumber (in cm^{-1}), F the spectral response function,
and R(n) the spectral radiance. The integrals are carried out over the range of n
for which F is non-zero. Units of R are mW/(m^{2}-sr-cm^{-1}).

The value of q, the coefficient of the quadratic term, was (and is) known a
*priori*, having been determined from measurements made by ITT before
launch^{6}. Values of q were determined in each channel as a function of
instrument operating temperature and detector temperature. The statistical
precision of each measurement of q was usually between 5 and 10%. Provision was
made in the in-orbit processing to allow q to depend on the actual instrument
and detector temperatures. However, analyses of the pre-launch data indicated
that, in most cases, q seemed to vary randomly with instrument temperature and
to be only weakly correlated with detector temperature^{7}. As a result,
for in-orbit calibrations we use a single value of q in each channel. It is the
unweighted mean over all instrument and detector temperatures.

The coefficients m and b, termed the slope and intercept, respectively, are
determined during in-orbit operations as follows: From the data in each
blackbody sequence, m is given by

**Equation 3**

where subscripts bb and sp refer to data taken from views of the blackbody and space,
respectively. The radiance R_{bb} of the blackbody is computed from its
temperature, which, for both the sounder and the imager, is indicated by eight
thermistors. In the computations, we average nine samples from each thermistor
and average over the eight thermistors. For efficiency in the real-time computation,
the radiance values are computed not by Eq. (2) but from cubic polynomials in temperature T,

**Equation 4**

The coefficients a_{i} were derived before launch^{6} from a fit
of a cubic to a table of temperatures vs blackbody radiances at every 0.1K between
270K and 310K. This range includes every temperature the blackbodies are expected to
assume in normal operations in orbit. The blackbody radiances were computed with Eq.
(2) in which R(n) is the Planck function B(n,T), given by

where the coefficients c_{1} and c_{2} are the two radiation constants, given by

c_{1} = 1.191066x10^{-5}mW/(m^{2}-sr-cm^{-4});

c_{2} = 1.438833 K/cm^{-1}.

The errors of the polynomial approximation are at least an order of magnitude less than the expected
noise in each channel

The values of X_{sp} and X_{bb} require elaboration. For the
sounder, X_{sp} is the average of the 40 samples at the space look
preceding the blackbody look. For the imager, X_{sp} is determined from
the 400-sample averages for the space looks preceding and following the
blackbody look. The value at the time of the blackbody look is estimated by
interpolation on time between the two space looks. The interpolation reduces the
effect of drifts over the period of the blackbody sequence^{5}. The
values of X_{bb} are the averages of the 40 samples (sounder) or 1000
samples (imager) acquired during the blackbody view.

From data collected at each space look, b is determined from

**Equation 5**

The value of X_{sp} is the average of the 40 samples (sounder) or 400 samples
(imager) acquired at the space view. For the imager, the intercepts are computed
and saved for both the pre- and post-clamp views. As space looks occur more
frequently than the blackbody looks, intercepts are updated more often than are
the slopes.

For each pixel, the radiances were computed from Eq. (1) with the values of m
and b from Eqs. (3) and (5). For the imager, to remove the effects of drift
between the space looks, we update the value of b at each pixel by interpolating
between the post-clamp view at the preceding space look and the pre-clamp view
at the following space look, as was described previously.

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

*Latest Revision: July 9, 1997*