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Implementation of the post-launch vicarious calibration of the GOES imager visible channel

C.R. Nagaraja Rao
NOAA/NESDIS Office of Research and Applications
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* (πω /F)*I       (1)

where ω is the equivalent width of the GOES-8 imager visible channel = 0.193 μm; F is the in-band extraterrestrial solar irradiance = 314.5 w/m2; and I is the average radiance (w/m2 μm sr) over the visible channel. When the pre-launch calibration is used, the radiance I is given by

I = mρ2 (C10 - C0);       (2)

where 'm' is the pre-launch calibration coefficient, and is equal to 0.5502(w/m2 μm sr count), and ρ 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 (πω/F) has a numerical value of 0.001927. Thus,

A(pre) = 100*(0.001927)*(0.5502)* ρ2 ( 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 ρ2( C10 - C0) for that day by the appropriate S(d) values. Thus,

Radiance (d) = 0.6556 (1 + 0.0001688 * d)* ρ2( C10 - C0)       (6)

and

Albedo (d) = 0.1264 (1 + 0.0001688 * d)* ρ2( 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)* ρ2( 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 2126 and 2491, respectively.

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

ρ2( 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 ω(μm) F(w/m2) πω /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 (πω /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)* ρ2( 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)* ρ2( C10 - C0)
GOES-10 Imager Launch date: 25 April 1997
Albedo (per cent) Albedo (d; post) = 0.1165 (1 + 0.0001022*d)* ρ2( 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)* ρ2 ( 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.