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 -O Imager Scaling Coefficients
Channel
m
b
2
227.3889
68.2167
3
38.8383
29.1287
4
5.2285
15.6854
6
5.5297
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:

Teff =
(c2 * )
_____________________________
ln [1 + (c1 *  3) / R]
(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, -12 and -13 imagers have always
operated on side 1. The GOES-10 imager is operating on side 2. The GOES-O imager is
expect to operate on side 1 after launch on April 28, 2009.
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
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
Table 2-2. GOES-9 Imager (Side 1) Coefficients
Channel/Detector



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
Table 2-3. GOES-10 Imager (Side 2) Coefficients
Channel/Detector



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
Table 2-4. GOES-11 Imager (Side 1) Coefficients
Channel/Detector



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
Table 2-5. GOES-12 Imager (Side 1) Coefficients
Channel/Detector



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
Table 2-6. GOES-13 Imager (Side 1) Coefficients

Channel/Detector


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
(Currently operational, STAR updated)
Table 2-7a. GOES-14 Imager (Side 1) Coefficients
(Release Rev D, 2005)
Channel/Detector



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
Table 2-7b. GOES-14 Imager (Side 1) Coefficients
(Release Rev E, 2008; Operational Nov. 23, 2009)
Channel/Detector



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
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 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
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
Table 3-7: GOES-14 imager