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# Operational Calibration of the Imagers and Sounders on the GOES-8 and -9 Satellites, Page 5

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/(m2-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 launch6. 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 temperature7. 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 Rbb 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 ai were derived before launch6 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 c1 and c2 are the two radiation constants, given by

c1 = 1.191066x10-5mW/(m2-sr-cm-4);

c2 = 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 Xsp and Xbb require elaboration. For the sounder, Xsp is the average of the 40 samples at the space look preceding the blackbody look. For the imager, Xsp 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 sequence5. The values of Xbb 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 Xsp 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.

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