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 -X_sp),       (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.,

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 (2) 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]. Visible-channel data from the GOES-8 and -9 imagers (but not GOES-10 through GOES-15, 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 X_o,     (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 = pi / H,     (6)

and (pi = 3.1416...) 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 imager

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 imager
(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 imager
(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
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 imager
(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 imager
(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

Table 6. Visible-channel calibration coefficients for GOES-14 imager
(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	5.874693 x 10-1	29	-17.037	1.88772 x 10-3
2	5.865367 x 10-1		-17.010
3	5.862807 x 10-1		-17.002
4	5.864086 x 10-1		-17.006
5	5.857146 x 10-1		-16.986
6	5.852004 x 10-1		-16.971
7	5.860814 x 10-1		-16.996
8	5.841697 x 10-1		-16.941

Table 7. Visible-channel calibration coefficients for GOES-15 imager
(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	5.851966 x 10-1	29	-16.9707	1.88852 x 10-3
2	5.879772 x 10-1		-17.0513
3	5.856793 x 10-1		-16.9847
4	5.854250 x 10-1		-16.9773
5	5.866992 x 10-1		-17.0143
6	5.836241 x 10-1		-16.9251
7	5.846555 x 10-1		-16.9550
8	5.843753 x 10-1		-16.9469

Table 8. 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
GOES-14	1	7. 269366 x 10-2	920	-66.878	2.18573 x 10-3
	2	7. 230454 x 10-2		-66.520
	3	7. 172957 x 10-2		-65.991
	4	7. 241027 x 10-2		-66.617
GOES-15	1	6. 752245 x 10-2	920	-62.121	2.20768 x 10-3
	2	789340 x 10-2		-62.462
	3	6. 753861 x 10-2		-62.136
	4	6. 738188 x 10-2		-61.991

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).