Implementation
of the post-launch vicarious calibration
of the GOES imager visible channel
C.R. Nagaraja Rao
NOAA/NESDIS Office of Research and Applications
Camp Springs, MD 20746
(May 4, 2001)
1. General
This brief note describes a simple procedure to implement the
post-launch calibration of the visible channel ( ~ 0.52 -0.72 µm)
of the imagers on the GOES-8 and -10 spacecraft. Application of
the post-launch calibration will compensate for the in-orbit
degradation of the imager visible channel.
2. Pre-launch calibration of the visible channel of the GOES-8
imager
We will illustrate the post-launch calibration procedure using
the GOES-8 imager. Let A(pre) be the albedo calculated using the
pre-launch calibration coefficient, and A(post) the albedo
calculated using the post-launch calibration coefficient which
accounts for instrument degradation in orbit. A(pre) and A(post)
are expressed in per cent.
A(pre) = 100* (p w /F)*I
(1)
where
w: equivalent width of the GOES-8 imager visible channel =
0.193 µm;
F: In-band extraterrestrial solar irradiance = 314.5 w/m2;
and
I: average radiance (w/m2 µm sr) over the visible
channel. When the pre-launch calibration is used, the radiance I
is given by
I = m r2( C10 - C0) ;
(2)
where 'm' is the pre-launch calibration coefficient, and is
equal to 0.5502(w/m2 µm sr count ), and r is the
Earth-Sun distance expressed in astronomical units. C10
and C0 are respectively the scene and offset signals
in 10-bit counts. The quantity (p
w /F) has a numerical value of
0.001927. Thus,
A(pre) = 100 * (0.001927)*(0.5502)* r2 ( C10
- C0) (3)
3. Post-launch calibration
It is observed that the visible channel of the imager degrades
in orbit. Since the sensor has no onboard calibration device, it
is necessary to develop post-launch calibration coefficients (or
slopes) which take into account the in-orbit degradation of the
sensor so that the derived products are rendered accurate.
Therefore, the post-launch calibration of the imager visible
channel has been determined using a vicarious technique that has
been developed at the NOAA/NESDIS Office of Research and
Applications for the calibration of broad band sensors in the
visible, and near infrared. We determine the relative degradation
of the imager visible channel in orbit, using a radiometrically
stable calibration site located in the Sonoran desert (34.0 deg
N; 114.1 deg W); here radiometric stability implies that the
long-term mean value of the top-of-the-atmosphere (TOA) albedo
remains uniform in time for all practical purposes, and the small
but finite variations of the same in the course of a year are
reproduced from one year to the next. We render the relative
degradation absolute by transferring the calibration of channel 1 ( ~ 0.58 - 0.68 µm) of the Advanced Very High Resolution Radiometer
(AVHRR) on the NOAA-14 spacecraft by way of modeled
inter-relationship between the TOA albedos that would be measured
by the two instruments. Greater details of the vicarious
techniques are found in Rao and Zhang (1999; 2001).
The post-launch calibration formulae for the calculation of
radiance or albedo are given below; the calibration coefficient
S(d) is generally referred to as the 'slope.'
Radiance representation:
S(d) = 0.6556 (1 + 0.0001688 * d)
(4)
Albedo representation:
S(d) = 0.1264 (1 +0.0001688 * d)
(5)
where 'd' is the elapsed time in orbit, expressed in days
after launch; 'd' is set equal to zero on the day of launch (13
April 1994 for GOES-8). Thus, S(0), corresponding to the day of
launch has values of 0.6556 and 0.1264 in the radiance and albedo
representations respectively. It is apparent that as the
instrument degrades in orbit, the S(d) values increase to offset
the impact of instrument degradation. Equations (4) and (5) yield
a value of 6.1 per cent for the annual degradation rate of the
visible channel of the GOES-8 imager.
The radiance or albedo measured in the visible channel of the
GOES -8 imager on day 'd' after launch is obtained by multiplying r2( C10 - C0) for that day by the
appropriate S(d) values. Thus,
Radiance (d) = 0.6556 (1 + 0.0001688 * d)* r2( C10
- C0) (6)
and
Albedo (d) = 0.1264 (1 + 0.0001688 * d)*
r2( C10 -
C0)
(7)
We see from equation (6) that the post-launch calibration
coefficient on the day of launch (d = 0) 0.6556 which is
different from the pre-launch calibration coefficient of 0.5502.
This discrepancy is due to the degradation of the instrument
immediately after launch (e.g., Rao and Chen 1995).
It is likely that an appreciable number of viewers have the
albedo records calculated using the pre-launch calibration
coefficients. We show below how these albedo values can be
corrected for instrument degradation in orbit. Let A(d; post) be
the albedo on day 'd' after launch, calculated using the
post-launch calibration coefficient. Since the pre-launch
calibration coefficient 'm' is in the radiance representation, it
follows from equation (3) that
A(d; post) = 100*(0.001927)*0.6556* (1 + 0.0001688 * d)* r2(
C10 - C0) (8)
Therefore
[A(d;post)/A(pre)] = (0.6556/0.5502)*(1 + 0.0001688 * d)
(9)
Thus
A (d;post) = 1.192 * A(pre) * (1 + 0.0001688 * d)
(10)
Thus, the TOA albedo calculated using the pre-launch
calibration coefficient can be corrected for the in-orbit
degradation of the imager using equation (10)
4. Examples
We give below an example of the application of equation (10)
using GOES-8 imager visible channel measurements made over a site
in Florida, centered on 30.33N; 81.80W. We use a single pixel ( ~ 4
km on the side) data. However, post-launch calibration is not
affected if the Earth scene is larger the one pixel. The single
pixel data are listed in Table 1 below.
Table 1.
GOES-8 imager single pixel data
|
Date |
Time |
Solar zenith angle |
Pre-launch albedo A(pre)
|
7 February 2000 |
16:32 UTC
|
48.50
deg
|
6.7
|
7
February 2001
|
16:15 UTC
|
50.33
deg
|
5.6
|
The values for 'd' on 7 February 2000 and 7 February 2001 are
respectively 2126 and 2491.
Thus, from equation (10)
A(d; post) on 7 February 2000 = 1.192*(6.7)*(1 +
0.0001688*2126) = 10.85 (per cent)
and
A (d; post) on 7 February 2001 = 1.192*(5.6)*(1 +
0.0001688*2491) = 9.48(per cent)
Note that the above values of albedo are obtained under the
assumption that the sun is directly overhead (solar zenith angle
= 0) . If we normalize A (d; post) values to Cos (solar zenith
angle), and call the result A'(d; post), then
A'(d; post) on 7 February 2000 = 10.85/Cos (48.5) = 16.37 (per
cent) (11) A'(d; post) on 7 February 2001 = 9.44/Cos (50.33) = 14.79 (per
cent) (12)
It is generally the practice to use A'(d; post) in
meteorological work. The differences in albedo values on the two
dates may be attributed to changes in the atmospheric and surface
conditions over the pixel-size site of measurement on the two
dates.
We shall now calculate the post-launch albedo, starting with
the measured GOES-8 imager visible channel signal, to establish
that the result would be the same as we obtained in the previous
paragraph. Starting with equations (3), and the data for 7
February 2000, we get
r2( C10 - C0) = 6.7 / [100 *
(0.001927)*(0.5502) ] = 63.19 counts (13)
On substitution of this count value in equation (7), we get
A(d; post) = 63.19*0.1264)*(1+ 0.0001688*2126) = 10.85
(14)
On normalization of A(d; post) to Cos 48.50, we get
A'(d; post) = 10.85/Cos 48.50 = 16.37 (per cent).
The procedures to calculate the radiance or albedo in the
visible channel of the GOES-10 imager are the same as those for
the imager on GOES-8.
Summary
We list in Tables 2 and 3 below the characteristics of the
visible channels of the imager on GOES-8 and -10 , and the
relevant post-launch calibration formulae respectively.
Table 2.
Sensor Characteristics
|
Sensor |
w(µm) |
F(w/m2) |
p w/F (sr µm m2 w-1)
|
GOES-8 Imager |
0.193 |
314.5 |
0.001927 |
GOES-10 Imager |
0.220 |
347.2 |
0.001990 |
Note 1.There are very minor differences between the (p w /F)
values listed here and those reported by investigators elsewhere;
this will not affect in any discernible manner the values of any
radiance or albedo calculated using the formulae in Table 3.
Table 3. Formulae for the
calculation of radiance and albedo |
Goes-8 Imager |
Launch date: 13 April 1994 |
Albedo (per cent) |
Albedo (d; post)) = 0.1264 (1 +
0.0001688 * d)* r2( C10 - C0)
|
Albedo (per cent)+ |
Albedo (d;post) = 1.192 * A(pre) * (1 +
0.0001688 * d) |
Radiance (w/m2 µm
sr) |
Radiance (d; post) = 0.6556 (1 +
0.0001688 * d)* r2( C10 - C0) |
GOES-10 Imager |
Launch date: 25 April 1997 |
Albedo (per cent) |
Albedo (d; post) = 0.1165 (1 +
0.0001022*d)*r2( C10 - C0) |
Albedo (per cent)+ |
Albedo (d; post) = 1.049* A(pre)*(1 +
0.0001022*d) |
Radiance (w/m2 µm
sr) |
Radiance (d; post) = 0.5856*(1 +
0.0001022)*r2 ( C10 - C0) |
Note 1. The value of 'd' for the launch date is zero.
Note 2. The symbol + denotes the formulae to be used when the
pre-launch albedos are already available.
Note 3. The quantity ( C10 - C0) is
equal to [GVAR - 29].
Acknowledgment
The GOES-8 imager visible channel data were furnished by
Mamoudu Ba, University of Maryland, College Park, Maryland
(U.S.A.)
References
1. Rao, C.R.N., and J. Chen, 1995: Inter-satellite calibration
linkages for the visible and near-infrared channels of the
Advanced Very High Resolution Radiometer on the NOAA-7, -9, and
-11 spacecraft. International Journal of Remote Sensing, 16,
1931 - 1942.
2. Rao, C.R.N., and N. Zhang, 1999: Calibration of the visible
channel of the GOES imager using the Advanced Very High
Resolution Radiometer. Pre-print volume, 10th
Atmospheric Radiation Conference( Madison, Wisconsin , June
1999), 560 - 563.
3. Rao, C.R.N., and N. Zhang, 2001: Post-launch calibration of
the visible channel of the imager on GOES-8 and -10 using the
Advanced Very High Resolution Radiometer (AVHRR), in
preparation
4. Weinreb, M.P. et al. 1997: Operational Calibration of
GOES-8 and -9 Imagers and Sounders. Applied Optics, 36,
6895. Also see Weinreb, M.P. and Dejiang Han, 2000: Calibration
of the visible channels of the GOES Imagers and Sounders
(http://www.oso.noaa.gov/goes)
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