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NASA-TH-111634 



) , j - 



INT. J. RUMOTK SHNSING, 1995, VOL. 16, NO. 11, 1931-1942 //^ / "' V /K 



Inter-satellite calibration linkages for the visible and near-infared 
channels of the Advanced Very High Resolution Radiometer on the 
NOAA-7, -9, and -11 spacecraft 



C. R. NAGARAJA RAO 

NOAA/NESDIS Satellite Research Laboratory, Washington, D.C. 20233, 

U.S.A. 

and J. CHEN 

SM Systems and Research Corporation, Bowie, Maryland 20716, U.S.A. 

{Received 29 December 1994; in fatal form 16 January 1995) 

Abstract. The post-launch degradation of the visible (channel I: 
«0-58 0-68/jm) and near-infrared (channel 2: ^0-72 M/<m) channels of the 
Advanced Very High Resolution Radiometer (AVHRR) on the NOAA-7. -9, and 
-11 Polar-orbiting Operational Environmental Satellites (POES) was estimated 
using the south-eastern part ol" the Libyan desert as a radiometrically stable 
calibration target. The relative annual degradation rates, in per cent, for the two 
channels are, respectively: 3-6 and 4-3 (NOAA-7); 5-9 and 3-5 (NOAA-9); and 1-2 
and 2-0 (NOAA-11). Using the relative degradation rates thus determined, in 
conjunction with absolute calibrations based on congruent path aircraft/satellite 
radiance measurements over White Sands. New Mexico (U.S.A.), the variation in 
time of the absolute gain or 'slope' of the AVHRR on NOAA-9 was evaluated. 
Inter-satellite calibration linkages were established, using the AVHRR on 
NOAA-9 as a normalization standard. Formulae for the calculation of calibrated 
radiances and albedos (AVHRR usage), based on these interlinkages, are given 
for the three AVHRRs. 

1. Introduction 

One of the main objectives of the National Oceanographic and Atmospheric 
Administration (NOAA)/National Aeronautics and Space Administration (NASA) 
Advanced Very High Resolution Radiometer (AVHRR) Pathfinder program is the 
establishment of long-term, accurate records of environmental products such as 
vegetation cover, cloud morphology, aerosols, and sea surface temperature gener- 
ated from broad-band spectral measurements made by the AVHRRs on board the 
NOAA Polar-orbiting Operational Environmental Satellites (POES) (Ohring and 
Dodge 1992). There is evidence (e.g., Brest and Rossow 1992) that the visible 
(channel 1: %0-58 0-68 jun) and near-infrared (channel 2: a 0-72 11 fim) channels, 
which have no on board calibration devices, degrade in orbit, initially because of 
outgassing (e.g., water vapour from filter interstices) and launch associated contami- 
nation (e.g., rocket exhaust and outgassing), and subsequently because of the 
continued exposure to the harsh space environment. It is therefore necessary, in 
order to ensure the quality and continuity of the long-term records of AVHRR- 
derived environmental products, to evaluate the in-orbit degradation of the two 
channels, and develop correction algorithms; and to establish inter-satellite calib- 
ration linkages. Accordingly, we wish to present here the work done at the NOAA 

( 1W5 U.S. (invernnicnl 



1932 C. R. Naaaraja Rao and J. Chen 

Satellite Research Laboratory to characterize the post-launch performance of the 
AVHRR visible and near-infrared channels as part of the AVHRR Pathfinder 
Calibration activity (Rao el al. 1993). We have confined our attention to the 
AVHRRs on NOAA-7, -9, and -1 1 spacecraft for programmatic reasons. It should 
be mentioned that the AVHRR Pathfinder Calibration activity is an integral part of 
the operational satellite calibration program presently underway at the Satellite 
Research Laboratory, Office of Research and Applications, National Environmental 
Satellite, Data, and Information Service, NOAA. 

2. Degradation rates 

2.1. General 

Relative changes in the gains of the three AVHRRs, expressed in units of 
Counts/(W m " 2 sr " ' /mi '), or equivalently, the relative changes in the 'slope', the 
reciprocal of gain, expressed in units of W/(m 2 sr/<m count), were determined using 
the south-eastern part of the Libyan desert (21 23" N latitude; 28 29 "E longitude) 
as a radiometrically stable calibration target. It is assumed that the isotropic albedo, 
defined as (7t/,/F, cos () () ), does not vary in time; here /, and F iu are, respectively the 
in-band upwelling radiance and the extraterrestrial solar irradiance in the /' lh 
channel; and o is the solar zenith angle. This is a reasonable assumption since the 
highly variable atmospheric contribution to the upwelling radiance at the top of the 
atmosphere is small compared to the contribution of the radiation reflected by the 
bright desert surface (e.g., Brest and Rossow 1992, Kaufman and Holben 1993). The 
recent work of Cosnefroy el al. (1993) on the radiometric stability of desert targets 
also lends support to this assumption; based on an analysis of Meteosat images for a 
100 by 100 km area in the general vicinity of the calibration site, they found the 
reflectance of the region to be very uniform, with the ratio of the standard deviation 
to the mean value of the reflectance of the 2-5 km resolution pixels to be of the order 
of 3 per cent; temporal stability was found to be of the same order after the seasonal 
trends in reflectance had been removed. 

The International Satellite Cloud Climatology Project (ISCCP) B3 data (Schiffer 
and Rossow 1983) for the region of the calibration target were used in the present 
study; the data comprised the measured counts in the visible, near-infrared, and 
thermal infrared channels of the AVHRR; the satellite and solar zenith angles, and 
the azimuth angle of observation; the latitude and longitude of the ISCCP B3 pixel; 
and the date of measurement. A variant of Minnaert's reflection law (Barkstrom 
1972) was used to characterize the dependence of the upwelling radiance on the solar 
and satellite zenith angles. Following a scheme suggested by Staylor (1990) where it 
is assumed that the degradation of the radiometer in time is exponential in its nature, 
the degradation rates are estimated from solutions of the following equation: 

Y=AX"exp(-kd) (1) 

where Y: p 2 (C w -C\ ) )cosO; C i0 : measured signal in 10-bit counts; C„: offset in 
10-bit counts; p: Earth Sun distance in astronomical units for the date of measure- 
ment; X: {cosOcosO n )/(cos() + cos() ), and o being the satellite and solar zenith 
angles, respectively; k: daily rate of the degradation of the gain of the radiometer, 
assuming it to be exponential in time; d: days after launch of the spacecraft; and A, 
B: regression parameters. Standard numerical techniques were used to determine the 
value of the daily degradation rate, k. We have confined our attention to the B3 data 
corresponding to satellite zenith angles sg 14 to minimize the effects, if any, of the 



Inter-satellite calibration linkages 



1933 



azimuthal dependence of the upwelling radiation at the top of the atmosphere; also, 
only data corresponding to solar zenith angles ^60 have been included in the 
analysis. Greater details of the method of determination of the degradation rates, of 
the quality control criteria adopted to detect the presence of clouds, and of the 
ISCCP B3 data used are found in Rao and Chen (1993). 

2.2. The AVliRRs on NOAA-7, -9, and -11 spacecraft 

The degradation rates k for the two channels of the three AVHRRs. determined 
using the method outlined in the previous section, and the relevant ancillary data are 
shown in table 1; the k values yield the daily rate at which the AVHRR signal 
associated with an Earth scene, set equal to unity (1) on the day of launch, would 
apparently decrease in time, all other conditions remaining unaltered, because of the 
degradation of the radiometer. Thus, the corrected AVHRR signal can be obtained 
from the uncorrected signal on day d after launch by multiplying the latter 
(uncorrected signal) by exp (kd). 

We have compared in table 2 the annual rates of degradation in per cent, 100 [( 1- 
exp (-365/c))], based on the daily degradation rates listed in table 1 with results 
reported by researchers elsewhere; this comparison is only representative and not 
complete. The choice of the data for comparison was mainly governed by our desire 
to compare our results with those obtained over desert calibration targets (Staylor 
1990, Kaufman and Holben 1993, Wu and Zhong 1994); with the results of 
statistical analysis of a large body of global reflectance data (Brest and Rossow 
1992); with results based on composite calibration data (Che and Price 1992); and 
with those based on measurements made over a variety of targets, and on model 
simulations (R. Santer, 1993, personal communication). Staylor (1990) used the 
monthly means of AVHRR channel 1 albedos extracted from the Heat Budget 
Parameter (HBP) data (Gruber and Winston 1978) for a broad region (% 10" km 2 ) 
of the Libyan desert in his work. Kaufman and Holben (1993) used the AVHRR 
GAC data (nominal spatial resolution: *4km; daily and monthly means) for several 
sites located in the Libyan desert to establish the rate at which the ratio of the pre- 



Table 1. Relative degradation rates for the visible and near-infrared channels of the 
AVHRRs on NOAA-7, -9, and -11 spacecraft. 





Launch 
date 


Dates of 

data 

availability 


Number of 

data 

points 

84 
86 
83 


Degra 
rate (k) 


.dalion 
per day 


Spacecraft 


Channel 1 
0-000101 

0000166 

0000033 


Channel 2 


NOAA-7 
NOAA-9 
NOAA-11 


23 June 1981 
12 December 1984 
24 September 1988 


August 1981 
December 1984 

January 1985 
November 1988 

January 1989 
December 1991 


0000120 
0000098 
0-000055 



Note: Each data point is the average of measurements made over approximately 35 pixels 
in the 1" (longitude) x 2° (latitude) area of the calibration target in the course of the day; the 
entries in the 'Number of data points* column give the number of days of appropriate data 
availability. 



1934 C. R. Nagarqja Rao and J. Chen 

Table 2. Comparison of annual relative degradation rates (in per cent) reported by different 

authors. 



NOAA-7 NOAA-9 NOAA-11 



Source Channel 1 Channel 2 Channel 1 Channel 2 Channel 1 Channel 2 



Present work 


3-6 


Staylor (1990) 


3-5 


Kaufman and Holben 




(1993) 


4-2 


Brest and Rossow 




(1992) 





Che and Price (1992) 


4-4 


Santer (1993. personal 




communication) 


4-7 


Wu and Zhong (1994) 





43 5-9 3-5 1-2 2-0 
6-0 

5-6 5-7 31 1-3 2-9 

4-6 

46 50 6-7 6-7 3-9 

4-7 7-5 4-5 

5-8 46 



Note: It is assumed in Brest and Rossow (1992) that there was no degradation of channel 1 
of the AVHRR on NOAA-7 over the period July 1983 January 1985. 



launch value of the 'slope' to its actual value varied in time. Brest and Rossow (1992) 
based their findings on statistical analysis of a large body of ISCCP global 
reflectance data, assuming that 'the global aggregate of regional variations of surface 
visible reflectance is not changing with time'; their results indicate that the visible 
channel of the AVHRR on NOAA-7 did not exhibit any perceptible in-orbit 
degradation over the period July 1983 to January 1985. Che and Price (1992) used a 
composite of post-launch calibration results given by several authors, using different 
techniques, and established linear regression relationships between the published 
values of gains (or "slopes"), and elapsed time since launch (in months) of the 
spacecraft, assuming similarity in the degradation of different AVHRRs. Santer 
(1993, personal communication) has used measurements of upwelling radiances over 
desert surfaces, stratus cloud decks, ocean targets, and model simulations to derive 
the degradation rates. Wu and Zhong (1994) used two sets of measurements made 
over desert sites in China, approximately 3 years apart, to derive the degradation 
rates for the visible and near-infrared channels of the AVHRR on NOAA-9; a 
bidirectional reflection model, appropriate for deserts, was used to account for the 
dependence of the reflected radiation on the solar and satellite zenith angles, and the 
azimuth angle of observation. 

The range of values of the degradation rates is an indication of the complexity of 
post-launch calibration of sensors like the AVHRR in the absence of on-board 
calibration, and is also traceable to the differences in the techniques employed. 

2.3. Absolute calibration of the AVHRR on NOAA-9 spacecraft 

The in-orbit degradation of the visible and near-infrared channels of the 
AVHRR on NOAA-9 spacecraft has been studied very extensively (e.g., Whitlock 
et al. 1990) by researchers employing a variety of techniques since its effective 
operational life (% 1985-1988) encompassed important, international, multi-agency, 
multi-platform experiments such as the First ISCCP Regional Experiment (FIRE), 
and the First International Satellite Land Surface Climatology Project (ISLSCP) 
Field Experiment (FIFE). Also, the availability of the results of several aircraft/ 



Inter-satellite calibration linkages 1935 

satellite congruent path radiance measurements over White Sands, New Mexico 
(U.S.A.) during October/November 1986 (Smith el al. 1988), employing a well 
calibrated spectrometer on board a U-2 aircraft, made it possible to translate the 
relative degradation rates into variations in time of the gain or 'slope'. Accordingly, 
using the aircraft-based absolute calibrations as anchors, and employing the relative 
degradation rates (table 1), the rate of variation of the 'slope' in time over the 
operational life of the spacecraft was determined. The resulting expressions for the 
calculation of radiances /,, (in units of W m 2 sr ' /mi ' ) on day d after launch, are: 



Channel 1: 
Channel 2: 



/ d = 0-5465xexp[l-66x 10 4 x (J-65)](C, -C ) (2) 

/,, = 0-3832 xexp [0-98 x 10 4 x(r/-65)](C l0 -C„) (3) 



C n has been given values of 370 and 39-6 in channels 1 and 2, respectively, and d is 
taken to be zero on the day of launch. Also, the effective counts (C [0 — C ) have 
been normalized to mean Earth Sun distance in the above formulae. The formulae 
have been recommended to the user community by the NOA A/NASA AVHRR 
Pathfinder Calibration Working Group (Rao et al. 1993); it was also the aim of the 
Working Group that the AVHRR on NOAA-9 should be used as the reference or 
normalization standard in the post-launch calibration of the AVHRRs on NOAA-7 
and -11. 

3. Inter-satellite calibration linkages 

We have used the AVHRR on NOAA-9 as the normalization standard to 
establish interrelationships among the visible and near-infrared radiances measured 
by the three AVHRRs. The method is based on the use of matched data sets 
consisting of the measured counts, satellite zenith and solar zenith angles, and the 
dales of measurements over the south-eastern part of the Libyan desert, which was 
used as the calibration target in the present study. The following selection criteria 
were used to generate two sets of matched data, one for the NOAA-7/NOAA-9 
combination, and the other for the NOAA-9/NOAA-1 1 combination: 

(a) The solar zenith angle, () a , and the satellite zenith angle, 0, for the 
measurements made by the AVHRRs on NOAA-7 and NOAA-1 1 should be 
within 1 of the corresponding angles for measurements by the AVHRR on 
NOAA-9; 

{b) The two measurements should have been made in the same calendar month, 
with the days of the month being as close to one another as was practicable, 
to allow for seasonal variations, if any, in the radiometric characteristics of 
the target. It is thus likely that measurements made by the AVHRR on either 
NOAA-7 or -II in a given calendar month in the ith year in orbit of the 
relevant spacecraft could be matched with measurements made in the same 
calendar month, but in a different year (y'th) in orbit of NOAA-9. 

These selection criteria resulted in 1 1 sets of matched data for the NOAA-7/ 
NOAA-9 combination, and 10 sets of matched data for the NOAA-ll/NOAA-9 
combination. 

The method of normalization of the AVHRRs on NOAA-7 and NOAA-1 1 to the 
AVHRR on NOAA-9 is illustrated below, using the NOAA-7/NOAA-9 matched 
data set as an example: 



1936 C. R. Nauuraju Rao and J. Chen 

(a) For either channel, the effective counts (C 1() -C ) were corrected for the 
NOAA-7 AVHRR degradation, using the k values listed in table 1; the 
elapsed time in days, d, since launch was calculated from the known dates of 
launch and of the measurements in the matched data set. 

(b) The matched, calibrated radiance measured by the AVHRR on NOAA-9 was 
calculated, using either (2) or (3) as was appropriate. 

(c) A linear regression relationship was established between the NOAA-9 
radiances from (b), and the corrected effective counts for the NOAA-7 
AVHRR from (a). 

The regression relationship established in (c) above links the AVHRR on NOAA-7 
to the AVHRR on NOAA-9, and yields the 'slope', in units of W/m 2 sr/im count), 
for the given channel on the day of launch of NOAA-7. The AVHRR on NOAA-1 1 
was linked to the AVHRR on NOAA-9 in a similar manner. The regressions had 
correlation coefficients in excess of 0-9. The resulting formulae for the calculation of 
radiances are given in table 3. The reflectance factor (Rao 1987) (or albedo (AVHRR 
usage) or scaled radiance (Brest and Rossow (1992)), given by (100n/,/F, ), is also 
used in different applications of AVHRR data; to facilitate this activity, we have 
listed in table 4 the formulae for the calculation of the albedos; the extra-terrestrial 
solar spectral irradiance values given by Neckel and Labs (1984) were used in the 
conversion of the radiance formulae (table 3) to the albedo representation; the 
conversions are effected by multiplying the radiances by ( \00nw : /F U) ), vv, being the 
equivalent width of the /th channel. We have given in table 5 the values of w, and F io 
used in the conversion of the radiance formulae given in table 3 to the albedo 
(AVHRR usage) representation (table 4). 

It is felt that the attainable accuracies in the radiance or albedo calculated using 
the formulae we have given (tables 3 or 4) are at best comparable to the estimated 



Table 3. Formulae for the calculation of calibrated radiances. 

Spacecraft Radiance (Wm 2 sr '/(in ') 

NOAA-7 

Channel I 0-5753 exp (1-01 x 10 4 ,/) (C 10 36) 

Channel 2 0-3914 exp (1-20 x 10 4 d) (C ]( , -37) 

NOAA-9 (Set A) 

Channel 1 0-5465 exp [l-66x 10 4 (d- 65)] (C,„-37) 

Channel 2 0-3832 exp [0-98 x 10 4 (J- 65)] (C,„-39-6) 

NOAA-9 (Set B) 

Channel 1 0-5406 exp (1-66 x 10 4 d) (C 1() --37) 

Channel 2 0-3808 exp (0-98 x 10 4 d) (C',,,-39-6) 

NOAA-1 1 

Channel 1 0-5496 exp (0-33 x 10 4 d) (C 10 -40) 

Channel 2 0-3680 exp (0-55 x 10 4 d) (C,„-40) 

Note: The two sets of formulae given for NOAA-9 yield the same radiances; the quantity 
exp (-65A) occurring in Set A has been incorporated into the numerical coefficient appearing 
at the beginning of the formulae in Set B to render their format the same as that of the 
formulae for the AVHRRs on NOAA-7 and NOAA-1 1. 



Inter-satellite calibration linkages 1937 

Table 4. Formulae Tor the calculation of calibrated AVHRR albedos. 

Spacecraft Albedo (per cent) 

NOAA-7 

Channel I 01 100 exp ( 101 x 10 4 d) (C 1() -36) 

Channel 2 0-1 169 exp ( 1-20 x 10 4 rf)(C 10 -37) 

NOAA-9 (Set A) 

Channel 1 01050 exp [1-66 x 10 4 (J-65)] (C 1() -37) 

Channel 2 01 143 exp [0-98 x 10 4 (J-65)] (C l(l -39-6) 

NOAA-9 (Set B) 

Channel 1 01 039 exp (l-66x 10 4 d) (C 10 -37) 

Channel 2 01 136 exp [0-98 x 10 4 d) (C 10 -39-6) 

NOAA-11 

Channel 1 0-1060 exp (0-33 x 10~ 4 d) (C,„-40) 

Channel 2 01098 exp (0-556 x 10 4 d) (C lo -40) 

Note: The two sets of formulae given for NOAA-9 yeild the same albedos; the quantity 
exp ( — 65/c ) occurring in Set A has been incorporated into the numerical coefficient appearing 
at the beginning of the formulae in Set B to render their format the same as that of the 
formulae for the AVHRRs on NOAA-7 and NOAA-1 1. 



accuracies of the order of a few per cent (G. Smith, 1993, personal communication) 
of the Fall 1986 aircraft-based absolute calibrations of the AVHRR on NOAA-9 
which we have used as the normalization standard in the present work. 

Staylor (1990) has established linkages among the visible channels (channel 1) of 
the AVHRRs on NOAA-6, -7 and -9, using the instrument on NOAA-7 as the 
normalization standard. Starting with the regions of overlap in the X variable in the 
plots of Von X (1), he determined adjustment factors (multipliers) for Y that would 
force the regression plots for the radiometers on NOAA-6 and -9 to coalesce with 
the regression plot for the AVHRR on NOAA-7. The ratio of the adjustment factors 
he has given for the AVHRRs on NOAA-7 and NOAA-9 is 1 07 which is very close 
to the ratio (1064) of the channel 1 slopes for the day of launch (d = 0) listed in table 
3 for the two AVHRRs. Brest and Rossow (1992) have also established a linkage 
between the visible channels of the AVHRRs on NOAA-7 and -9, using reflectance 
data from the two satellites, obtained over a 3-week overlap period from 18 January 
to 8 February 1985; it should however be noted that they have assumed that there 
was no perceptible degradation in the performance of NOAA-7 AVHRR channel 1 
over the period from the middle of 1983 to early 1985. 



Table 5. Equivalent widths and in-band extraterrestrial solar irradiances. 







Wfl/rni) 


i 


F i0 


(Wm 


2 ) 


Spacecraft 


Channel 


1 


Channel 2 


Channel 1 




Channel 2 


NOAA-7 
NOAA-9 

NOAA-11 


0-108 
0-117 
0-113 




0-249 
0-239 
0-229 


177-5 
191-3 
184-1 




261-9 
251-8 
241-1 



1938 C. R. Nagaraja Rao and J. Chen 

4. Validation 

To evaluate the reasonableness of the inter-satellite calibration linkages we have 
established using the AVHRR on NOAA-9 as a normalization standard we shall 
first compare the variation in time of the 'slopes' of channels 1 and 2 of the AVHRR 
on NOAA-11, derived from these formulae, with the absolute calibrations based on 
congruent path aircraft/satellite radiance measurements over the White Sands area, 
New Mexico, U.S.A. (Abel et al. 1993). The results are shown in figure 1; we have 
also included results of several other investigators for purposes of comparison. It 
should be mentioned that Mitchell et al. (1992) obtained their results using the split- 
pass imagery technique and model simulations of the upwelling radiation over an 
oceanic target in the Southern Ocean off the north-west coast of Tasmania. 

The noticeable feature is that the variation in time of the 'slope', expressed in 
units of W/(m 2 sr/nn count), is within one standard deviation of the mean values of 
the majority of aircraft-based absolute calibrations in both channels. This behaviour 
can be taken as an indicator of the viability of the method we have used to develop 
interrelationships among the three radiometers, using the AVHRR on NOAA-9 as a 
normalization standard. The differences, practically systematic, between the trends 
in 'slope' in the present study, and those reported in Kaufman and Holben (1993) 
may perhaps be due to differences in the absolute calibration anchors used. 

We used about 15 per cent of the ISSCP B3 (table 1) data for the south-eastern 
Libyan desert calibration site in the establishment of the matched data set; we thus 
felt it may be scientifically meaningful to apply the inter-satellite calibration linkages 
to the entire set of data to determine the impact of in-orbit degradation on the 
calculated albedos. Accordingly, the time series (1981 1991) of albedos 
\0OnlJ(F i0 cos0 o ) in channels 1 and 2 of the calibration target site obtained using 
the pre- and post-launch calibrations are shown in figure 2; we have included the 
albedo values calculated using the post-launch calibrations reported by Kaufman 
and Holben (1993) and by Che and Price (1992) for purposes of comparison. The 
noticeable feature is that the calibrated radiance formulae given here (table 3) 
establish continuity of record of the isotropic albedo among the three satellites, and 
also remove the spurious downward trends in the albedos obtained with the pre- 
launch coefficients. The mean and standard deviation (in parentheses) of the 
corrected albedos (in per cent) in AVHRR channels 1 and 2 are found to be, 
respectively 37-8 (0-7) and 42-6 (1-5). It has been observed that channel 2 data are 
generally noisier than those for channel 1; this may be due to the uncertainties 
introduced by the variations in the atmospheric precipitable water, which exhibits 
absorption in the spectral region of channel 2. 

It may rightfully be argued that the time seris of the albedos of the calibration 
target site should not be used to validate our results. However, the calibrated 
radiance/albedo formulae we have given here have been implemented in the 
reprocessing of the Normalized Difference Vegetation Index (NDVI) global climat- 
ology at NOAA (Gutman et al. 1995); in the NOAA experimental clouds from 
AVHRR (CLAVR) product (L. Stowe and P. Davis, 1994, personal communica- 
tion); in the validation of the NOAA aerosol product using shipboard aerosol 
optical thickness measurements (Ignatov et al. 1994); and in the generation of the 
NOAA/NASA Pathfinder AVHRR Land Data Set (Agbu and James 1994, James et 
al. 1994). Results to date of the above application are very encouraging (personal 
communications from different users) in terms of establishment of continuity 



Inter-satellite calibration linkages 



1939 



0.68 



c 0.64 



Channel 1 



0.6 



S 



•g 0.56 



a. 0.52 

o 



0.48 4-- 





200 400 

Days after launch 



600 



800 



c 

a 
o 



a. 

I** 

"a 



a. 

o 



0.44 



0.4 



0.36 



0.32 



Channel 2 




200 400 

Days after launch 



600 



800 



Figure 1. Comparison of the predicted variation in time of the 'slopes' of channels 1 (lop) 
and 2 (bottom) of the AVHRR on NOAA-1 1 (launch date: 24 September 1988) with 
aircraft-based absolute calibrations. • Abel el al. (1993), — present work, 
Kaufman and Holben (1992), Che and Price (1992), ■ Mitchell el al. (1992). 



1940 



C. R. Nagaraja Rao and J. Chen 




August 
1981 


March 
1984 


December 
1986 

Date 


September 
1989 


June 
1992 




August 


March 


December 


September 


June 


1981 


1984 


1986 


1989 


1992 



Date 



Figure 2. Time series of the isotropic albedo of the Libvan desert calibration target. 

present work, Kaufman and Holben (1993). • Che and Price (1992), 

Pre-launch. 



Inter-satellite calibration linkages 1941 

amongst the three AVHRRs and in terms of removal of spurious trends in the 
different products. 

5. Conclusion 

The validity and usefulness of the inter-satellite calibration linkages we have 
established, and of the radiance and albedo formulae we have given can be evaluated 
only after they have been applied to the reprocessing of long-term records of 
different AVHRR-derived geophysical products by a large community of users. 
Several activities along these lines, some of which have been mentioned earlier, are 
presently underway both within NOAA, and at other institutions elsewhere. It 
should also be recognized that the improvements in the products brought about by 
the use of the radiance and albedo formulae we have given are also determined by 
the nature of the data (e.g.. skewness or bias, composite nature) to which they are 
applied, and the approximations and assumptions made in the product-generation 
algorithms. Also, in continuation of the present investigation, a sensitivity analysis 
of the post-launch calibration of the AVHRR visible and near-infrared channels 
using desert calibration targets is presently underway to evaluate the impact, if any, 
of uncertainties or changes in the various physical parameters used in the derivation 
of the degradation rates (§2.1); results of this investigation will be published in a 
forthcoming paper. 

Acknowledgments 

The work reported here was supported by the Information Management 
component (NOAA Pathfinder Program Manager: Dr Arthur Booth) of the Climate 
and Global Change Program, NOAA Office of Global Programs. Useful discussions 
with Dr Sullivan and Dr Gutman, NOAA Satellite Research Laboratory, Wash- 
ington, D.C., and with Dr Staylor, NASA Langley Research Center, Hampton, are 
herewith acknowledged. 

References 

Abi-l, P., Gin nihir, B., Gai.imori:, R. N., and C<x)1>i:r. J. W., 1993, Calibration results for 
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