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Calibration of Visible Channels
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Calibration of the Visible
Channels of the GOES Imagers and Sounders
Michael
Weinreb and Dejiang Han
(Revised, June 2006)
Although the visible detector-channels are not calibrated in
orbit, calibration coefficients measured by ITT before launch[1]
are transmitted to users in the GVAR data stream. A factor that
converts radiance to reflectance factor, or effective albedo,
is included as well. Since detector responsivities can vary
unpredictably, the pre-launch calibration may not be valid after
launch. The calibration equation is either Equation (1)
R = m X + b (1)
or Equation (2)
R = m (X -Xsp), (2)
where X is the instrument
output in counts, the subscript sp refers to the
view of space, and m and b are the calibration
coefficients measured before launch[1]. For each
visible-channel detector, the radiance R is the average
of the spectral (monochromatic) radiance over the spectral
response function for that detector, i.e.,
 (3)
where l is wavelength in µm, f the spectral response function,
and R(l ) the spectral radiance of the target. Units
of R are W/(m2-sr-µm).
The value of b in Equation (1) depends on the electronic
zero level. This level varies with a standard deviation of approximately
one count for the imagers and tens of counts for the sounders.
Therefore, when the satellite is in orbit, the value of b
determined in the laboratory (or at any other earlier time)
may not be valid. Equation (1) is preferred[2]. Currently,
visible-channel data from the GOES-8 and -9 imagers (but not
GOES-10 and GOES-11, nor any sounder) are being normalized.
Since normalization makes the responses from all eight imager
detectors the same as that of the reference detector, users
of the pre-launch calibration of the GOES-8 and -9 imagers should
apply the calibration coefficients for the reference detector
(identified in Table 1) to the data from all detectors. With
relativization enabled, an instrument's output at the view of
space is modified slightly, and the value of b in the
calibration equation (1) needs to be modified accordingly. For
this reason also, the best approach is to use Equation (2).
If Equation (1) must be used, then the value of b should
be determined from the equation
b = - m Xo, (4)
in which, for the imagers, m is the slope for the
reference detector. For the sounders, it is the slope for
an individual detector. Values of b determined in
this way, as well as the values of m and X0,
appear in Tables 1 - 3.
The reflectance factor (or effective albedo) is obtained from
the radiance by
A = k R, (5) where
k = p / H, (6)
and where H is the solar spectral irradiance H(l
) averaged over the spectral response function of the
visible detector, i.e.,
(7)
Values of H were computed by ITT[1] from
tables of solar irradiance vs wavelength provided by Rossow
et al.[3], whose values are based on measurements
by Neckel and Labs[4]. The values of A
lie between 0 and 1. The value of 1 corresponds to the radiance
of a perfectly reflecting diffuse surface illuminated at normal
incidence when the sun is at its annual-average distance from
the Earth. Values of k appear in Tables 1 - 3.
Table 1. Visible-channel calibration
coefficients for GOES-8 and -9 imagers
| Satellite |
GOES-8 |
GOES-9 |
|
Identity
of reference detector
(number in physical array)
|
2
|
3
|
|
m (reference
detector)
(W/(m2-sr-m-count))
|
0.5501873
|
0.5492361
|
|
X0
|
29
|
29
|
|
b
(W/(m2-sr-µm))
|
-15.955
|
-15.928
|
|
k
((m2-sr-µm)/W)
|
1.92979
x 10-3
|
1.94180
x 10-3
|
Table 2. Visible-channel calibration
coefficients for GOES-10 imagers
(normalization not enabled; no reference detector chosen)
Detector
number
(in physical array) |
m
(reference detector)
(W/(m2-sr-µm-count)) |
X0 |
b
(W/(m2-sr-µm)) |
k
(m2-sr-µm)/W) |
|
1
|
5.605602
x 10-1
|
29
|
-16.256
|
1.98808 x 10-3
|
|
2
|
5.563529
x 10-1
|
-16.134
|
|
3
|
5.566574
x 10-1
|
-16.143
|
|
4
|
5.582154
x 10-1
|
-16.188
|
|
5
|
5.583361
x 10-1
|
-16.192
|
|
6
|
5.571736
x 10-1
|
-16.158
|
|
7
|
5.563135
x 10-1
|
-16.133
|
|
8
|
5.613536
x 10-1
|
-16.279
|
Table 3. Visible-channel calibration
coefficients for GOES-11 imagers
(normalization not enabled; no reference detector
chosen)
Detector
number
(in physical array) |
m
(reference detector)
(W/(m2-sr-µm-count)) |
X0 |
b
(W/(m2-sr-µm)) |
k
(m2-sr-µm)/W) |
|
1
|
5.561568
x 10-1
|
29
|
-16.129
|
2.01524 x 10-3
|
|
2
|
5.552979
x 10-1
|
-16.104
|
|
3
|
5.558981
x 10-1
|
-16.121
|
|
4
|
5.577627
x 10-1
|
-16.175
|
|
5
|
5.557238
x 10-1
|
-16.116
|
|
6
|
5.587978
x 10-1
|
-16.205
|
|
7
|
5.586530
x 10-1
|
-16.201
|
|
8
|
5.528971
x 10-1
|
-16.034
|
Table 4. Visible-channel calibration
coefficients for GOES-12 imagers
(normalization not enabled; no reference detector
chosen)
Detector
number
(in physical array) |
m
(reference detector)
(W/(m2-sr-µm-count)) |
X0 |
b
(W/(m2-sr-µm)) |
k
(m2-sr-µm)/W) |
|
1
|
5.771030
x 10-1
|
29
|
-16.736
|
1.97658 x 10-3
|
|
2
|
5.761764
x 10-1
|
-16.709
|
|
3
|
5.775825
x 10-1
|
-16.750
|
|
4
|
5.790699
x 10-1
|
-16.793
|
|
5
|
5.787051
x 10-1
|
-16.782
|
|
6
|
5.755969
x 10-1
|
-16.692
|
|
7
|
5.753973
x 10-1
|
-16.687
|
|
8
|
5.752099
x 10-1
|
-16.681
|
Table 5. Visible-channel calibration
coefficients for GOES-13 imagers
(normalization not enabled; no reference detector
chosen)
Detector
number
(in physical array) |
m
(reference detector)
(W/(m2-sr-µm-count)) |
X0 |
b
(W/(m2-sr-µm)) |
k
(m2-sr-µm)/W) |
|
1
|
6.120196
x 10-1
|
29
|
-17.749
|
1.89544 x 10-3
|
|
2
|
6.118504
x 10-1
|
-17.744
|
|
3
|
6.096360
x 10-1
|
-17.769
|
|
4
|
6.087055
x 10-1
|
-17.653
|
|
5
|
6.132860
x 10-1
|
-17.785
|
|
6
|
6.118208
x 10-1
|
-17.743
|
|
7
|
6.122307
x 10-1
|
-17.755
|
|
8
|
6.066968
x 10-1
|
-17.594
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Table 6. Visible-channel calibration
coefficients for sounders
| Satellite |
Detector
No. |
m
(W/(m2-sr-µm-count)) |
X0 |
b
(W/(m2-sr-µm)) |
k
((m2-sr-µm)/W) |
|
GOES-8
|
1
|
6.482527
x 10-2
|
920
|
-59.64
|
2.2008 x 10-3
|
|
2
|
6.522216
x 10-2
|
-60.00
|
|
3
|
6.560241
x 10-2
|
-60.35
|
|
4
|
6.642020
x 10-2
|
-61.11
|
|
GOES-9
|
1
|
6.416324
x 10-2
|
920
|
-59.03
|
2.2919 x 10-3
|
|
2
|
6.427129
x 10-2
|
-59.13
|
|
3
|
6.523361
x 10-2
|
-60.01
|
|
4
|
6.489786
x 10-2
|
-59.71
|
|
GOES-10
|
1
|
6.987580
x 10-2
|
920
|
-64.29
|
2.16966 x 10-3
|
|
2
|
7.064522
x 10-2
|
-64.99
|
|
3
|
7.039932
x 10-2
|
-64.77
|
|
4
|
7.196864
x 10-2
|
-66.21
|
|
GOES-11
|
1
|
6.820695
x 10-2
|
920
|
-62.75
|
2.15268 x 10-3
|
|
2
|
6.961050
x 10-2
|
-64.04
|
|
3
|
7.214539
x 10-2
|
-66.37
|
|
4
|
7.367121
x 10-2
|
-67.78
|
|
GOES-12
|
1
|
7.087293
x 10-2
|
920
|
-65.20
|
2.1530 x 10-3
|
|
2
|
7.006026
x 10-2
|
-64.46
|
|
3
|
7.494441
x 10-2
|
-68.95
|
|
4
|
7.496490
x 10-2
|
-68.97
|
|
GOES-13
|
1
|
7.192174
x 10-2
|
920
|
-66.168
|
2.18293 x 10-3
|
|
2
|
7.189435
x 10-2
|
-66.143
|
|
3
|
7.199156
x 10-2
|
-66.232
|
|
4
|
7.137384
x 10-2
|
-65.664
|
References
[1a] ITT Aerospace/Communications Div. (Ft. Wayne, IN), "GOES-IJ/KLM
SN03 Imager data and calibration handbook," submitted by Space
Systems/Loral, Palo Alto, CA, and prepared for NASA, Greenbelt,
MD, 15 Jan. 1994.
[1b] ITT Aerospace/Communications Div. (Ft. Wayne, IN), "GOES-IJ/KLM
SN03 Sounder data and calibration handbook," submitted by Space
Systems/Loral, Palo Alto, CA, and prepared for NASA, Greenbelt,
MD, 15 Jan. 1994.
[1c] ITT Aerospace/Communications Div. (Ft. Wayne, IN), "GOES
calibration and alignment handbook for the Imager SN04 instrument,"
submitted by Space Systems/Loral, Palo Alto, CA, and prepared
for NASA, Greenbelt, MD, Sept. 1994.
[1d] ITT Aerospace/Communications Div. (Ft. Wayne, IN), "GOES
SN04 Sounder calibration and alignment handbook," submitted
by Space Systems/Loral, Palo Alto, CA, and prepared for NASA,
Greenbelt, MD, Dec. 1994.
[2] 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.
[3] Rossow, W.R., E. Kinsella, A. Wolf, and L. Gardner, "Description
of reduced radiance data," International Satellite Cloud
Climatology Project (ISCCP), WMO/TD-No. 58 (1985).
[4] Neckel, H. and D. Labs, "The solar radiation between 3300
and 12500 A," Solar Physics 90, 205 (1984).
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