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, 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.
Contents
- Conversion of Imager GVAR Count to
Scene Radiance
- Conversion of Imager GVAR Count to
Temperature
- Precision of the conversion of Imager
GVAR Count to Temperature
- Conversion Sounder GVAR Count to Scene
Radiance or Temperature
- 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:
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:
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 (Currently operational,
STAR updated) |
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 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 (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:
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)
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