Operational Calibration of the Imagers and Sounders
on the GOES-8 and -9 Satellites, Page 19

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

APPENDIX A: INTERPRETATION OF INFRARED DATA IN GVAR

In the GVAR data stream, the data from the infrared channels of the imagers and sounders are scaled radiances packaged in 10-bit and 16-bit words, respectively. The conversion of the raw data from the instruments to scaled radiances is carried out in real time in the Sensor Processing System computers at the Command and Data Acquisition facility at Wallops, VA, and is described in the body of this paper. This appendix describes how users may convert the ten-bit GVAR count values (0-1023) in channels 2 - 5 of the imagers and the 16-bit GVAR count values (0-65535) in channels 1-18 of the sounders back to scene radiances, brightness temperatures, and eight-bit mode-A counts¹⁵.

The first step is to convert GVAR counts to radiances with the following equation:

R = (X_G - B)/ M ,

where R is radiance in mW/(m²-sr-cm-1) and X_G is the GVAR count value. The coefficients M and B are the "scaling" slope and intercept, respectively, and appear in Tables A1 and A2. The units of M are counts/(mW/[m²-sr-cm^-1]). Their values depend only on channel, not detector, and for a given channel we expect them to be constant for all time and to be the same for each satellite of the series.

Table A1. GOES imagers scaling coefficients

Table A2. GOES sounders scaling coefficients

To convert radiance to temperature, one first uses the following formula (the inverse of the Planck function) to derive "effective" temperature:

T_eff = (c₂n)/ln(1 + [c₁n³]/R) ,

where T_eff is effective temperature (K), "ln" stands for natural logarithm, and R is radiance. The coefficients c1 and c2 are the two radiation constants, given by

c₁ = 1.191066x10-5 mW/(m²-sr-cm^-4)

c₂ = 1.438833 K/cm^-1

The quantity n is the central wavenumber of the channel. For a given channel it may vary slightly among detectors, and it will vary from instrument to instrument. The values of appear in tables A3-A6.

To convert effective temperature T_eff to actual temperature T (K), one uses the following formula:

T = bT_eff + a,

The constants n, a, and b and depend on channel, detector, and instrument and appear in Tables A3-A6.

The use of T_eff accounts for the variation of the Planck function across the spectral passband of the channel. The differences between the values of T and T_eff increase with decreasing temperature. They are usually of the order of 0.1K. In the worst case, near 180K, they are approximately 0.3K.

The mode - A count value X_a is derived from the temperature with the following equations¹⁵:

For 163K <= T <= 242K,    X_a = 418 - T.
For 242K <= T <= 330K,    X_a = 660 - 2T.

Mode-A count values are on an eight-bit scale and range in value from 0 to 255, with high counts representative of low temperatures. Beyond the difference in precision, there is a fundamental difference between GVAR counts and mode-A counts--their units. GVAR counts are scaled radiances, whereas mode-A counts are temperatures.

Tables of GVAR counts, radiances, temperatures, and mode-A counts will be provided by the first author on request.

Table A3. Constants for GOES-8 imager

Table A4. Constants for GOES-9 imager

Table A5. Constants for GOES-8 sounder

Table A6. Constants for GOES-9 sounder

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