Please Note:   To view imagery from the operational GOES East (GOES-16) and GOES West (GOES-17) satellites, users may visit https://www.star.nesdis.noaa.gov/goes/.

# 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 = (XG - B)/ M ,

where R is radiance in mW/(m2-sr-cm-1) and XG 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

Channel M B
2 227.3889 68.2167
3 38.8383 29.1287
4 5.2285 15.6854
5 5.0273 15.3332

### Table A2. GOES sounders scaling coefficients

Channel M B
1 528.9773 1745.625
2 540.0049 1566.014
3 485.6243 1311.186
4 394.5752 887.7943
5 357.8019 787.1643
6 334.1747 417.7184
7 311.5226 249.2180
8 314.6032 251.6826
9 434.3518 716.6805
10 1126.224 900.9795
11 1899.565 1139.739
12 2874.342 2155.757
13 9642.747 626.7785
14 14105.38 916.8496
15 26221.34 1704.387
16 10720.60 428.8239
17 12136.11 497.5806
18 19358.13 348.4463

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

Teff = (c2n)/ln(1 + [c1n3]/R) ,

where Teff 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 Teff to actual temperature T (K), one uses the following formula:

T = bTeff + a,

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

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 0.1K. In the worst case, near 180K, they are approximately 0.3K.

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

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.

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

Channel Detector n(cm-1) a(K) b
2 1 2556.71 -0.578526 1.001512
2 2 2558.62 -0.581853 1.001532
3 1 1481.91 -0.593903 1.001418
4 1 934.30 -0.322585 1.001271
4 2 935.38 -0.351889 1.001293
5 1 837.06 -0.422571 1.001170
5 2 837.00 -0.466954 1.001257

### Table A4. Constants for GOES-9 imager

Channel Detector n(cm-1) a(K) b
2 1 2555.18 -0.579908 1.000942
2 2 2555.18 -0.579908 1.000942
3 1 1481.82 -0.493016 1.001076
4 1 934.59 -0.384798 1.001293
4 2 934.28 -0.363703 1.001272
5 1 834.02 -0.302995 1.000941
5 2 834.09 -0.306838 1.000948

### Table A5. Constants for GOES-8 sounder

Channel Detector n(cm-1) a(K) b
1 1 680.59705 0.0011541479 1.0000183
1 2 680.51139 0.0047380732 1.0000086
1 3 680.81462 0.0014610959 1.000018
1 4 680.73182 -0.00042293612 1.0000216
2 1 695.92447 -0.067530673 1.0001987
2 2 695.93168 -0.069026616 1.0002026
2 3 696.1214 -0.073060464 1.0002117
2 4 695.8373 -0.056595405 1.0001696
3 1 711.80216 -0.010171243 1.0000582
3 2 711.8637 -0.015032924 1.0000701
3 3 711.96416 -0.011705031 1.0000615
3 4 711.80891 -0.011002261 1.0000614
4 1 732.48438 -0.0042959367 1.0000392
4 2 732.39916 -0.0040822167 1.0000379
4 3 732.46298 -0.0051373478 1.0000106
4 4 732.46931 -0.0049827181 1.0000101
5 1 747.75312 -0.037536733 1.0001166
5 2 747.53399 -0.031523095 1.0001032
5 3 747.59143 -0.031117282 1.0001025
5 4 747.48321 -0.022986702 1.0000855
6 1 790.5998 -0.09722985 1.0002888
6 2 790.39692 -0.093920988 1.0002841
6 3 790.35717 -0.089752097 1.0002749
6 4 791.35802 -0.13292141 1.0003539
7 1 827.63841 -0.0232754 1.0003278
7 2 830.40346 -0.19918135 1.0006315
7 3 829.32451 -0.13434617 1.0005204
7 4 827.61148 0.017236714 1.0002605
8 1 906.81053 -0.15212177 1.0004685
8 2 906.20913 -0.15912377 1.0004923
8 3 906.91478 -0.18977748 1.0005115
8 4 907.56109 -0.2034948 1.0005222
9 1 1029.7209 -0.045072033 1.0001371
9 2 1029.6963 -0.043802031 1.000135
9 3 1029.2687 -0.033910527 1.0001365
9 4 1029.3769 -0.035802096 1.0001361
10 1 1339.7687 -0.15379456 1.0003742
10 2 1339.2473 -0.14469896 1.0003929
10 3 1339.5185 -0.14680066 1.0003878
10 4 1339.5473 -0.14827852 1.0003824
11 1 1421.09 -0.23363311 1.0007483
11 2 1421.8586 -0.24877913 1.0006982
11 3 1420.6829 -0.21459881 1.0007938
11 4 1422.4471 -0.26186387 1.0006938
12 1 1536.2837 -0.16825513 1.000216
12 2 1535.3069 -014374678 1.0002864
12 3 1537.5272 -0.23662459 1.0000769
12 4 1535.0548 -0.16469406 1.0002578
13 1 2184.7961 -0.01849728 1.0000665
13 2 2184.7961 -0.01849728 1.0000665
13 3 2184.7961 -0.01849728 1.0000665
13 4 2184.7961 -0.01849728 1.0000665
14 1 2207.5585 -0.023929612 1.0000191
14 2 2207.5585 -0.023929612 1.0000191
14 3 2207.5585 -0.023929612 1.0000191
14 4 2207.5585 -0.023929612 1.0000191
15 1 2247.5698 -0.034093166 0.99993075
15 2 2247.5698 -0.034093166 0.99993075
15 3 2247.5698 -0.034093166 0.99993075
15 4 2247.5698 -0.034093166 0.99993075
16 1 2422.0784 -0.066306989 1.000011
16 2 2422.0784 -0.066306989 1.000011
16 3 2422.0784 -0.066306989 1.000011
16 4 2422.0784 -0.066306989 1.000011
17 1 2509.4001 -0.060780208 1.0001174
17 2 2509.4001 -0.060780208 1.0001174
17 3 2509.4001 -0.060780208 1.0001174
17 4 2509.4001 -0.060780208 1.0001174
18 1 2664.7035 -0.34148389 1.0009243
18 2 2664.7035 -0.34148389 1.0009243
18 3 2664.7035 -0.34148389 1.0009243
18 4 2664.7035 -0.34148389 1.0009243

### Table A6. Constants for GOES-9 sounder

Channel Detector n(cm-1) a(K) b
1 1 681.53264 -0.061569679 1.0001824
1 2 681.40135 -0.053410761 1.0001603
1 3 681.52794 -0.090823775 1.0002626
1 4 681.23907 -0.049632175 1.0001508
2 1 694.26673 -0.035721417 1.0001135
2 2 694.09261 -0.026237608 1.0000894
2 3 693.93184 -0.014017787 1.0000574
2 4 694.11597 -0.026341654 1.0000893
3 1 711.39629 -0.043973934 1.0001314
3 2 711.25223 -0.035778771 1.0001112
3 3 711.00519 -0.026554312 1.0000877
3 4 711.07759 -0.025028536 1.0000841
4 1 732.56429 -0.031778653 1.0000973
4 2 732.50229 -0.028546325 1.0000897
4 3 732.50527 -0.032654323 1.0000997
4 4 732.33055 -0.025780988 1.0000829
5 1 747.19713 -0.043470631 1.0001236
5 2 747.1825 -0.04211854 1.0001205
5 3 746.83467 -0.020193021 1.0000714
5 4 746.91053 -0.03125795 1.0000972
6 1 789.55684 -0.065385221 1.0002199
6 2 789.72841 -0.072530803 1.0002344
6 3 789.84766 -0.080716615 1.0002493
6 4 789.35098 -0.056105065 1.0001998
7 1 826.87703 0.041396369 1.000228
7 2 827.22901 0.0274577 1.0002501
7 3 828.27187 -0.087133142 1.000445
7 4 828.67767 -0.069590619 1.0004218
8 1 911.22294 -0.30550413 1.0006317
8 2 910.73052 -0.28258246 1.0006113
8 3 909.80214 -0.23979418 1.0005719
8 4 909.70281 -0.22061492 1.0005457
9 1 1028.9077 -0.058287786 1.0001362
9 2 1028.8798 -0.054285716 1.0001341
9 3 1028.7845 -0.055189391 1.000134
9 4 1028.8579 -0.055101679 1.0001342
10 1 1335.2658 -0.1131839 1.0004206
10 2 1335.8313 -0.13015363 1.0003907
10 3 1336.0503 -0.13414168 1.0003834
10 4 1335.8627 -0.1304702 1.0003901
11 1 1420.8469 -0.2383551 1.0007496
11 2 1421.0338 -0.24007956 1.0007414
11 3 1420.6599 -0.23051649 1.0007729
11 4 1420.7697 -0.23480823 1.000752
12 1 1529.1783 -0.18721929 1.000148
12 2 1529.4056 -0.19578939 1.0001144
12 3 1529.2363 -0.17817533 1.0001506
12 4 1529.6935 -0.20017465 1.0001009
13 1 2183.9199 -0.019638376 1.0000246
13 2 2183.9199 -0.019638376 1.0000246
13 3 2183.9199 -0.019638376 1.0000246
13 4 2183.9199 -0.019638376 1.0000246
14 1 2207.0082 -0.024176572 0.99999895
14 2 2207.0082 -0.024176572 0.99999895
14 3 2207.0082 -0.024176572 0.99999895
14 4 2207.0082 -0.024176572 0.99999895
15 1 2245.837 -0.029091526 0.99994699
15 2 2245.837 -0.029091526 0.99994699
15 3 2245.837 -0.029091526 0.99994699
15 4 2245.837 -0.029091526 0.99994699
16 1 2415.1642 -0.051874656 1.000095
16 2 2415.1642 -0.051874656 1.000095
16 3 2415.1642 -0.051874656 1.000095
16 4 2415.1642 -0.051874656 1.000095
17 1 2512.0862 -0.063295056 1.0000751
17 2 2512.0862 -0.063295056 1.0000751
17 3 2512.0862 -0.063295056 1.0000751
17 4 2512.0862 -0.063295056 1.0000751
18 1 2665.3491 -0.28151318 1.0007142
18 2 2665.3491 -0.28151318 1.0007142
18 3 2665.3491 -0.28151318 1.0007142
18 4 2665.3491 -0.28151318 1.0007142

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