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 |
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