Conversion of GVAR Infrared Data to Scene Radiance or Temperature
Michael P. Weinreb, Joy X. Johnson, and Dejiang Han
NOAA NESDIS Office of Satellite Operations
(Revised, June 2006)
Infrared image data in GVAR (GOES VARiable Format) from the imagers are scaled radiances
packaged in 10-bit words. The conversion of the raw data from the instruments to 10-bit 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 10-bit GVAR count value (0-1023)
to a scene radiance or temperature for channels 2-5 of the GOES-8 through -13 imagers. The
method for imagers given here is also applicable to sounders.
Contents
I. Conversion of Imager GVAR Count to Scene Radiance
II. Conversion of Imager GVAR Count to Temperature
III.
Precision of the conversion of Imager GVAR Count to Temperature
IV.
Conversion Sounder GVAR Count to Scene Radiance or Temperature
V. Look-Up Tables of GOES radiance, Brightness Temperatures vs. GVAR Counts
I. Conversion of Imager GVAR Count to Scene Radiance
A 10-bit GVAR count value (0-1023) can be converted to a scene radiance according to the
following equation:
R = (X - b)/m,
(1)
where R is radiance (mW/[m 2-sr-cm-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.
Table 1-1. GOES-8 through -11 Imager Scaling Coefficients
Channel
m
b
2
227.3889
68.2167
3
38.8383
29.1287
4
5.2285
15.6854
5
5.0273
15.3332
Table 1-2. GOES-12 and -13 Imager Scaling Coefficients
Channel
2
3
4
6
m
227.3889
38.8383
5.2285
5.5297
b
68.2167
29.1287
15.6854
16.5892
II. Conversion of Imager GVAR count to Temperature
There are three steps to convert a 10-bit GVAR count value (0-1023) 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:
(c2 *  )
_____________________________
ln [1 + (c1 *  3) / R]
Teff =
(2)
c1 = 1.191066 x 10-5 [mW/(m2-sr-cm-4)]
c2 = 1.438833 (K/cm-1)
where Teff is effective temperature (K), ln stands for natural logarithm, and R is radiance. The
coefficients , c1, and c2 are the central wavenumber of the channel and the two radiation
constants, respectively. The constants c1 and c2 are invariant, but  depends on the spectral
characteristics of the channel and will vary from instrument to instrument.
Step 3: Convert effective temperature Teff to actual temperature T (K) using the following
equation:
T =  +  * Teff
(3)
where  and  are two conversion coefficients.
Note in the conversions that:


The values of  (cm-1) in step 2 and constants  and  in step 3 depend on channel and
instrument. Their values are listed below in Tables 2-1 through 2-5.
The term side 1 or side 2 in the table headings indicates the operation of one of the two
redundant sets of detectors and electronics on each imager. The coefficients , , and 
depend on the choice of side. The GOES-8, -9, -11, and -12 imagers have always

operated on side 1. The GOES-10 imager is operating on side 2. The GOES-13 imager is
expect to operate on side 1 after launch in May, 2006.
We will provide the coefficients for other electronics sides when they are needed.
Table 2-1. GOES-8 Imager (Side 1) Coefficients
Channel/Detector



2/a
2/b
3
4/a
4/b
5/a
5/b
2556.71
2558.62
1481.91
934.30
935.38
837.06
837.00
-0.578526
-0.581853
-0.593903
-0.322585
-0.351889
-0.422571
-0.466954
1.001512
1.001532
1.001418
1.001271
1.001293
1.001170
1.001257
Table 2-2. GOES-9 Imager (Side 1) Coefficients
Channel/Detector



2/a
2/b
3
4/a
4/b
5/a
5/b
2555.18
2555.18
1481.82
934.59
934.28
834.02
834.09
-0.579908
-0.579908
-0.493016
-0.384798
-0.363703
-0.302995
-0.306838
1.000942
1.000942
1.001076
1.001293
1.001272
1.000941
1.000948
Table 2-3. GOES-10 Imager (Side 2) Coefficients
Channel/Detector



2/a
2/b
3
4/a
4/b
5/a
5/b
2552.9845
2552.9845
1486.2212
936.10260
935.98981
830.88473
830.89691
-0.60584483
-0.60584483
-0.61653805
-0.27128884
-0.27064036
-0.26505411
-0.26056452
1.0011017
1.0011017
1.0014011
1.0009674
1.0009687
1.0009087
1.0008962
Table 2-4. GOES-11 Imager (Side 1) Coefficients
Channel/Detector



2/a
2/b
3
2562.07
2562.07
1481.53
-0.644790
-0.644790
-0.543401
1.000775
1.000775
1.001495
4/a
4/b
5/a
5/b
931.76
931.76
833.67
833.04
-0.306809
-0.306809
-0.333216
-0.315110
1.001274
1.001274
1.001000
1.000967
Table 2-5. GOES-12 Imager (Side 1) Coefficients
Channel/Detector



2/a
2/b
3/a
3/b
4/a
4/b
6
2562.45
2562.45
1536.43
1536.94
933.21
933.21
751.91
-0.650731
-0.650731
-4.764728
-4.775517
-0.360331
-0.360331
-0.253449
1.001520
1.001520
1.012420
1.012403
1.001306
1.001306
1.000743
Table 2-6. GOES-13 Imager (Side 1) Coefficients
Channel/Detector



2/a
2/b
3/a
3/b
4/a
4/b
6
2561.74
2561.74
1522.52
1521.66
937.23
937.27
753.15
-1.437204
-1.437204
-3.625663
-3.607841
-0.386043
-0.380113
-0.195055
1.002562
1.002562
1.010018
1.010010
1.001298
1.001285
1.000610
III. Precision of the Conversion of Imager GVAR Count to Temperature
The use of Teff accounts for the variation of the Planck function across the spectral passband of
the channel. The differences between the values of T and Teff 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 second-order polynomial is adopted:
T =  +  * Teff +  * Teff2
(4)
This yields errors under 0.001 K, even at temperatures above 310 K or under 210 K. The , ,
and  coefficients and centroid wavenumber  for all detectors are listed in the tables 3-1a
through 3-5a below:






Table 3-1: GOES-8 imager
Table 3-2: GOES-9 imager
Table 3-3: GOES-10 imager
Table 3-4: GOES-11 imager
Table 3-5: GOES-12 imager
Table 3-6: GOES-13 imager
IV. Conversion of Sounder GVAR Count to Scene Radiance or Temperature
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 above-mentioned NOAA
Technical Memorandum - Operational Calibration of the Imagers and Sounders on
the GOES-8 and -9 Satellites.. As described in the memorandum, infrared sounder data in
GVAR are scaled radiances packaged in 16-bit words. The conversion of the raw data from the
instruments to 16-bit scaled radiances is carried out in real time in the SPS at the CDA facility at
Wallops, VA. The related coefficients (, , , and ) of GOES sounders for the first- and secondorder polynomials (Equations [3] and [4]) - are included in the following tables:
Coefficients (,  and ) for the first-order polynomial:






Table 4-1a: GOES-8 sounder
Table 4-2a: GOES-9 sounder
Table 4-3a: GOES-10 sounder
Table 4-4a: GOES-11 sounder
Table 4-5a: GOES-12 sounder
Table 4-6a: GOES-13 sounder
Coefficients (, , , and ) for the second-order polynomial:






Table 4-1b: GOES-8 sounder
Table 4-2b: GOES-9 sounder
Table 4-3b: GOES-10 sounder
Table 4-4b: GOES-11 sounder
Table 4-5b: GOES-12 sounder
Table 4-6b: GOES-13 sounder
V. Look-Up Tables of GOES radiances, Brightness Temperatures vs. GVAR Counts
The GOES-8, GOES-9, GOES-10 GOES-11 and GOES-M Imager and Sounder look-up tables of
radiances, brightness temperatures vs. GVAR counts are listed below. The look-up tables for the
Imagers cover all the detectors, while the look-up 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 look-up tables are arranged according to their channels
and are also compressed.
Imagers:






Table 5-1a: GOES-8 Imager look-up table
Table 5-2a: GOES-9 Imager look-up table
Table 5-3a: GOES-10 Imager look-up table
Table 5-4a: GOES-11 Imager look-up table
Table 5-5a: GOES-12 Imager look-up table
Table 5-6a: GOES-13 Imager look-up table
Sounders:






Table 5-1b: GOES-8 Sounder look-up table
Table 5-2b: GOES-9 Sounder look-up table
Table 5-3b: GOES-10 Sounder look-up table
Table 5-4b: GOES-11 Sounder look-up table
Table 5-5b: GOES-12 Sounder look-up table
Table 5-6b: GOES-13 Sounder look-up table
The mode - A count value Xa is derived from the temperature with the following equations3:
For 163K <= T <= 242K,
Xa = 418 - T.
For 242K <= T <= 330K,
Xa = 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.
REFERENCES
[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 Satellite-8 and -9
imagers and sounders," Applied Optics, 36, pp. 6895-6904, 1997.
[2] Johnson, J.X., GOES-8 radiance to brightness-temperature 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)