Infrared image data in GVAR(GOES Variable Format) from the imagers are scaled radiances packaged in 10bit words. The conversion of the raw data from the instruments to 10bit scaled radiances is carried out in real time in the Sensor Processing System (SPS) at the Command and Data Acquisition (CDA) facility at Wallops, VA, and is described in a NOAA Technical Memorandum  Operational Calibration of the Imagers and Sounders on the GOES8 and 9 Satellites. This memo describes how to convert a 10bit GVAR count value (01023) to a scene radiance or temperature for channels 26 of the GOES8 through GOES15 imagers. The method for imagers given here is also applicable to sounders.
A 10bit GVAR count value (01023) can be converted to a scene radiance according to the following equation:
R = (X  b)/m, 
(1) 
where R is radiance(mW/[m^{2}srcm^{1}]) and X is the GVAR count value. The coefficients m and b are the scaling slope and intercept, respectively. The values of m and b are listed in Table 1. They depend on the channel selected, but for a given channel they are constant for all time and are the same for all satellites of the series.
Channel  m  b 

2  227.3889  68.2167 
3  38.8383  29.1287 
4  5.2285  15.6854 
5  5.0273  15.3332 
Channel  m  b 

2  227.3889  68.2167 
3  38.8383  29.1287 
4  5.2285  15.6854 
6  5.5297  16.5892 
There are three steps to convert a 10bit GVAR count value (01023) to temperature.
Step 1: Convert the GVAR count value to a radiance using the way described in part I.
Step 2: Convert radiance to effective temperature using the inverse of the Planck function as follows:

(2)  
c_{1} = 1.191066 x 10^{5} [mW/(m^{2}srcm^{4})]  
c_{2} = 1.438833 (K/cm^{1}) 
where T_{eff} is effective temperature (K), ln stands for natural logarithm, and R is radiance. The coefficients n, c_{1}, and c_{2} are the central wavenumber of the channel and the two radiation constants, respectively. The constants c_{1} and c_{2} are invariant, but n depends on the spectral characteristics of the channel and will vary from instrument to instrument.
Step 3: Convert effective temperature T_{eff} to actual temperature T (K) using the following equation:
T = a + b * T_{eff} 
(3) 
where a and b are two conversion coefficients.
Note in the conversions that:
Channel/Detector  n  a  b 

2/a  2556.71  0.578526  1.001512 
2/b  2558.62  0.581853  1.001532 
3  1481.91  0.593903  1.001418 
4/a  934.30  0.322585  1.001271 
4/b  935.38  0.351889  1.001293 
5/a  837.06  0.422571  1.001170 
5/b  837.00  0.466954  1.001257 
Channel/Detector  n  a  b 

2/a  2555.18  0.579908  1.000942 
2/b  2555.18  0.579908  1.000942 
3  1481.82  0.493016  1.001076 
4/a  934.59  0.384798  1.001293 
4/b  934.28  0.363703  1.001272 
5/a  834.02  0.302995  1.000941 
5/b  834.09  0.306838  1.000948 
Channel/Detector  n  a  b 

2/a  2552.9845  0.60584483  1.0011017 
2/b  2552.9845  0.60584483  1.0011017 
3  1486.2212  0.61653805  1.0014011 
4/a  936.10260  0.27128884  1.0009674 
4/b  935.98981  0.27064036  1.0009687 
5/a  830.88473  0.26505411  1.0009087 
5/b  830.89691  0.26056452  1.0008962 
Channel/Detector  n  a  b 

2/a  2562.07  0.644790  1.000775 
2/b  2562.07  0.644790  1.000775 
3  1481.53  0.543401  1.001495 
4/a  931.76  0.306809  1.001274 
4/b  931.76  0.306809  1.001274 
5/a  833.67  0.333216  1.001000 
5/b  833.04  0.315110  1.000967 
Channel/Detector  n  a  b 

2/a  2562.45  0.650731  1.001520 
2/b  2562.45  0.650731  1.001520 
3/a  1536.43  4.764728  1.012420 
3/b  1536.94  4.775517  1.012403 
4/a  933.21  0.360331  1.001306 
4/b  933.21  0.360331  1.001306 
6  751.91  0.253449  1.000743 
Channel/Detector  n  a  b 

2/a  2562.45  0.650563  1.001519 
2/b  2562.45  0.650563  1.001519 
3/a  1536.43  4.764832  1.012421 
3/b  1536.27  4.760714  1.012385 
4/a  933.21  0.360250  1.001306 
4/b  933.21  0.360250  1.001306 
6  751.77  0.252130  1.000742 
Channel/Detector  n  a  b 

2/a  2561.74  1.437204  1.002562 
2/b  2561.74  1.437204  1.002562 
3/a  1522.52  3.625663  1.010018 
3/b  1521.66  3.607841  1.010010 
4/a  937.23  0.386043  1.001298 
4/b  937.27  0.380113  1.001285 
6 (ITT original)  753.15  0.195055  1.000610 
6 (ITT updated)  751.93  0.134688  1.000481 
6  749.83  0.134801  1.000482 
Channel/Detector  n  a  b 

2/a  2572.47  1.530285  1.002507 
2/b  2572.47  1.530285  1.002507 
3/a  1529.33  3.561161  1.009501 
3/b  1530.10  3.577037  1.009444 
4/a  934.04  0.263369  1.001176 
4/b  933.94  0.260576  1.001179 
6/a  753.38  0.199338  1.000616 
6/b  753.91  0.234004  1.000692 
Channel/Detector  n  a  b 

2/a  2577.98  1.596954  1.002631 
2/b  2577.98  1.5969544  1.002631 
3/a  1529.35  3.580129  1.009547 
3/b  1530.13  3.595987  1.009490 
4/a  936.20  0.2875616  1.001258 
4/b  936.14  0.2888648  1.001265 
6/a  753.30  0.1938129  1.000605 
6/b  753.84  0.2296604  1.000684 
Channel/Detector  n  a  b 

2/a  2577.3518  1.5297091  1.0025608 
2/b  2577.3518  1.5297091  1.0025608 
3/a  1519.3488  3.4647892  1.0093656 
3/b  1518.5610  3.4390527  1.0094427 
4/a  933.98541  0.29201763  1.0012018 
4/b  934.19579  0.31824779  1.0012303 
6/a  752.88143  0.22508805  1.0006686 
6/b  752.82392  0.21700982  1.0006503 
Channel/Detector  n  a  b 

2/a  2560.75  1.633214  1.002639 
2/b  2560.75  1.633214  1.002639 
3/a  1538.62  3.193019  1.008531 
3/b  1538.66  3.191726  1.008510 
4/a  935.09  0.3433922  1.001259 
4/b  934.89  0.3246338  1.001239 
6/a  752.91  0.2157592  1.000648 
6/b  752.76  0.2044856  1.000623 
Channel/Detector  n  a  b 

2/a  2562.7905  1.5693377  1.0025034 
2/b  2562.7905  1.5693377  1.0025034 
3/a  1521.1988  3.4706545  1.0093296 
3/b  1521.5277  3.4755568  1.0092838 
4/a  935.89417  0.36151367  1.0012715 
4/b  935.78158  0.35316361  1.0012570 
6/a  753.72229  0.21475817  1.0006485 
6/b  753.93403  0.24630068  1.0007178 
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 0.1 K. In the worst case, near 180 K, they are approximately 0.3 K.
A change of one GVAR count is equivalent to a temperature change of approximately 0.11 K in channels 2,4,5, and 6 for a scene at 300K, and a change of approximately 0.04 K in channel 3 for a scene at 290 K.
The errors resulting from the above approximations can be reduced by a factor of 10 if the following secondorder polynomial is adopted:
T = a + b * T_{eff} + g * T_{eff}^{2} 
4) 
This yields errors under 0.001 K, even at temperatures above 310 K or under 210 K. The a, b, and g coefficients and centroid wavenumber n for all detectors are listed in the tables 31 through 38 below (see comments about central wavenumber definition under Step 3 in Section II):
As mentioned at the beginning of this memorandum, the methods described here to convert imager GVAR data to scene radiance or temperature are also applicable to GOES sounders. The GOES sounder scaling coefficients are listed in Table A2 of the abovementioned NOAA Technical Memorandum  Operational Calibration of the Imagers and Sounders on the GOES8 and 9 Satellites. As described in the memorandum, infrared sounder data in GVAR are scaled radiances packaged in 16bit words. The conversion of the raw data from the instruments to 16bit scaled radiances is carried out in real time in the SPS at the CDA facility at Wallops, VA. The related coefficients (n, a, b, and g) of GOES sounders for the first and secondorder polynomials (Equations [3] and [4])  are included in the following tables (see comments about central wavenumber definition under Step 3 in Section II):
Coefficients (n, a and b) for the firstorder polynomial:
Coefficients (n, a, b, and g) for the secondorder polynomial:
The GOES8 through GOES15 Imager and Sounder lookup tables of radiances, brightness temperatures vs. GVAR counts are listed below for the currently operational spectral response functions. The lookup tables for the Imagers cover all the detectors, while the lookup tables for the Sounders only cover detector 1 for each infrared channel. This arrangement intends to avoid huge disk space the Sounder lookup tables might have occupied. Sounder lookup tables are arranged according to their channels and are also compressed.
Imagers:
Sounders:
The mode  A count value X_{a} is derived from the temperature with the following equations^{3}:
For 163K <= T <= 242K, X_{a} = 418  T.
For 242K <= T <= 330K, X_{a} = 660  2T.
Mode  A count values are on an eightbit 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 modeA countstheir units. GVAR counts are scaled radiances, whereas modeA counts are temperatures.
[1] Weinreb, M.P., M. Jamieson, N. Fulton, Y. Chen, J.X. Johnson, J. Bremer, C. Smith, and J. Baucom, "Operational calibration of Geostationary Operational Environmental Satellite8 and 9 imagers and sounders," Applied Optics, 36, pp. 68956904, 1997.
[2] Johnson, J.X., GOES8 radiance to brightnesstemperature conversions, internal memorandum, Sept. 20, 1996.
[3] Bristor, C.L. (ed.), "Central processing and analysis of geostationary satellite data," NOAA Tech. Memo. NESS 64, U.S. Dep't. Commerce, National Oceanic and Atmospheric Administration, Washington, DC, 155 pp. (1975)