# Conversion of GVAR Infrared Data to Scene Radiance or Temperature

Michael Weinreb
NOAA/NESDIS/STAR

Dejiang Han
Integral Systems, Inc.
Revised, August, 2011

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 GOES-8 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 2-6 of the GOES-8 through GOES-15 imagers. The method for imagers given here is also applicable to sounders.

## 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/[m2-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:

 (c2 * n ) Teff = _____________________________ ln [1 + (c1 * n 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 n, c1, and c2 are the central wavenumber of the channel and the two radiation constants, respectively. The constants c1 and c2 are invariant, but n 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 = a + b * Teff (3)

where a and b are two conversion coefficients.

Note in the conversions that:

• The values of central wavenumbers, n (cm-1), in step 2 and constants a and b in step 3 depend on channel and instrument. Their values are listed below in Tables 2-1 through 2-8.

Central wavenumber for a detector is defined on this website to be that wavenumber which splits the area under the spectral response function (SRF) associated with that detector into two equal halves, i.e. there are equal areas under the SRF curve to shorter and to longer wavenumbers at the central wavenumber. The values of the coefficients *alpha* and *beta* (and *gamma* in the following sections) appearing in the tables depend on this definition. (Note that other definitions of central wavenumber would produce different values for these coefficients, but should be able to produce the same actual temperature from the same GVAR count as the current definition.)
• 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 n, a, and b depend on the choice of side. The GOES-8, -9, -11, -12 ,-13, -14 and -15 imagers have always operated on side 1. The GOES-10 imager was operated on side 2.
• We will provide the coefficients for other electronics sides when they are needed.

### Table 2-1. GOES-8 Imager (Side 1) Coefficients

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

### Table 2-2. GOES-9 Imager (Side 1) Coefficients

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

### Table 2-3. GOES-10 Imager (Side 2) Coefficients

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

### Table 2-4. GOES-11 Imager (Side 1) Coefficients

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

### Table 2-5a. GOES-12 Imager (Side 1) Coefficients

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

### Table 2-5b. GOES-12 Imager (Side 2) Coefficients

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

### Table 2-6. GOES-13 Imager (Side 1) Coefficients

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

### Table 2-7a. GOES-14 Imager (Side 1) Coefficients (Release Rev D, 2005)

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

### Table 2-7b. GOES-14 Imager (Side 1) Coefficients (Release Rev E, 2008; Operational Nov. 23, 2009)

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

### Table 2-7c. GOES-14 Imager (Side 1) Coefficients (ITT Release RevH plus STAR correction)

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

### Table 2-8a. GOES-15 Imager (Side 1) Coefficients (Release Rev E, 2008)

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

### Table 2-8b. GOES-15 Imager (Side 1) Coefficients (ITT Release RevH plus STAR correction)

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

## 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 = a + b * Teff + g * Teff2 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 3-1 through 3-8 below (see comments about central wavenumber definition under Step 3 in Section II):

## 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 Table A2 of the above-mentioned NOAA Technical Memorandum - Operational Calibration of the Imagers and Sounders on the GOES-8 and -9 Satellites 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 (n, a, b, and g) of GOES sounders for the first- and second-order 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 first-order polynomial:

Coefficients (n, a, b, and g) for the second-order polynomial:

## V. Look-Up Tables of GOES radiances, Brightness Temperatures vs. GVAR Counts

The GOES-8 through GOES-15 Imager and Sounder look-up tables of radiances, brightness temperatures vs. GVAR counts are listed below for the currently operational spectral response functions. 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 look-up tables might have occupied. Sounder look-up tables are arranged according to their channels and are also compressed.

Imagers:

Sounders:

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)