1.IP  01-05-95  NOAA-7-9-11 CALIBRATION INFORMATION
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Calibration formulae for the Visible and Near-Infrared Channels
of the Advanced Very High Resolution Radiometer on Board the
NOAA-7, -9, and -11 Spacecraft: An Update

C.R. Nagaraja Rao
NOAA/NESDIS Satellite Research Laboratory
Washington, D.C. 20233
U.S.A

1.   Background

     The performance of the visible(channel 1: 0.58-0.68m) and
near-infrared(channel 2: 0.72-1.1m) channels of the Advanced
Very High Resolution Radiometer is observed to degrade in orbit,
initially because of the outgassing(e.g., water vapor from the
filter interstices) and launch associated contamination(e.g.,
rocket exhaust and outgassing), and subsequently because of the
continued exposure to the harsh space environment(e.g., Brest and
Rossow 1992; Kaufman and Holben 1993).  It is therefore necessary
to correct the measured signals in these two channels for the in
orbit degradation to obtain correct values of the upwelling
radiance at the top of the atmosphere(e.g., Kaufman and Holben
1993; Che and Price 1992; Teillet and Holben 1994; Rao et al.,
1993).  Use of the pre-launch calibration coefficients would lead
to erroneous values of the upwelling radiances, and hence, of
geophysical products derived from these radiances such as
Normalized Difference Vegetation Index, upwelling visible and
near-infrared radiances at the top of the atmosphere, Earth's
radiation budget, and the columnar aerosol burden over the global
oceans.  The absence of on board calibration devices renders the
task of post-launch characterization of the performance of the
two AVHRR channels rather difficult.

     The work presented here was motivated by the NOAA/NASA
AVHRR Pathfinder program which has for its main objective the
reprocessing and rehabilitation of the long-term records of
AVHRR-derived geophysical products for the Pathfinder period,
1981 - present.  As part of this program, considerable effort has
been expended, under the AVHRR Pathfinder Calibration Activity,
on the determination of the in-orbit degradation of the AVHRR
visible and near-infrared channels (Rao et al. 1993).  We
summarize here the results of this effort in the form of formulae
for the calculation of radiances and albedos(AVHRR usage)
measured in the two channels, after the in-orbit degradation has
been duly accounted for.  Several applications of these formulae
to date indicate that they do minimize, if not remove, spurious
trends in the long term records of AVHRR-derived geophysical
products, and do serve to establish linkages among the segments
of records of the same(geophysical products) obtained with AVHRRs
on the NOAA-7, -9, and -11 spacecraft.

2.   Relative degradation rates

     The relative degradation rates, which essentially
characterize the response of the given AVHRR channel when viewing
an Earth scene on any given day in orbit in reference to its
response on the day of launch of the spacecraft, all other
conditions remaining unaltered, were determined using statistical
procedures on the International Satellite Cloud
Climatology(ISCCP) B3 data for the southeastern part of the
Libyan desert(21-23oN latitude; 28-29oE longitude).  It was
assumed that the desert site was a radiometrically stable target,
and that the decay of the sensors was exponential in time.  The
interested reader is referred to Staylor(1990) and Rao et
al.(1994) for greater details of the statistical techniques used
to obtain the relative degradation rates.

     The relative annual degradation rates, given by
100[1 - exp(-365k)] in per cent, for the two channels are
respectively: 3.6 and 4.3 for the NOAA-7 AVHRR; 5.9 and 3.5 for
the NOAA-9 AVHRR; and 1.2 and 2.0 for the NOAA-11 AVHRR.

3.   Inter-satellite calibration linkages

     In view of the length of records of the geophysical
products derived from radiances measured with the AVHRRs on
different spacecraft, it becomes necessary to establish linkages
between the calibrations of the different AVHRRs to ensure the
quality and continuity of the long-term records.  We have used
the AVHRR on NOAA-9 as the standard of comparison to establish
inter-satellite linkages since its post-launch performance has
been studied extensively and since its effective operational life
covered multi-agency, multi-platform experiments such as the
First International Satellite Cloud Climatology Regional
Experiment(FIRE), and the First International Land Surface
Climatology Project Field Experiment(FIFE).  

     The relative degradation rates for the visible and near-
infrared channels of the AVHRR on NOAA-9 were rendered absolute
by comparison with absolute calibrations based on congruent path
aircraft/satellite radiance measurements made over White Sands,
New Mexico, U.S.A. during October/November 1986(Smith et al.,
1988).  The absolute calibrations are based on establishing
correspondence between simultaneous measurements of upwelling
radiance by a well-calibrated spectrometer on board a high flying
U-2 aircraft, and the signal issuing from the AVHRR when both
instruments are looking at the same White Sands target under
identical conditions of illumination and observation.

     A matched data set was established consisting of
measurements made over the Libyan desert calibration target site
by the AVHRRs on NOAA-7 and -11 and by the reference AVHRR on
NOAA-9 with the requirements that the solar and satellite zenith
angles for measurements made with the AVHRR on NOAA-7(-11) should
be within one degree of the corresponding angles for the
measurements made with the AVHRR on NOAA-9, and that the
measurements should have been made in the same month of the year. 
It is thus likely that measurements made in any month, say March,
during the ith year of operation of NOAA-7(-11) could be matched
with measurements made by the AVHRR on NOAA-9 in March during the
jth year of operation of NOAA-9.  The signals(counts) issuing from
the AVHRR on either NOAA-7 or NOAA-11 were then corrected for
sensor degradation using the relative degradation rates
determined earlier, and  regressed against the radiances measured
by the AVHRR on NOAA-9 to obtain the "slopes"(AVHRR usage),
expressed in units of Watts/(m2 m sr ct), on the day of launch
of the respective sensors.  The "slope"(i.e., the reciprocal of
the gain of the instrument) essentially gives the amount of
radiant energy required to generate unit response from the AVHRR
and increases in time because of the deterioration of the
sensors. 

4.   Radiance and Albedo Formulae
     
     We give in Table 1 the formulae for the calculation of the
upwelling radiances in AVHRR channels 1 and 2 from the measured
10-bit counts on any given day in orbit, with elapsed time
expressed in days d reckoned from the day of launch of the
spacecraft; the dates of launch are shown in parentheses after
the spacecraft identification in the table.  The corresponding
formulae for the calculation of the albedos(AVHRR usage) are
found in Table 2; the albedo, A, in either channel is given by
A = 100(Ib/Fb) where Ib and Fb are the in-band upwelling radiance
and the extraterrestrial solar irradiance respectively(e.g., Rao
1987; Price 1987).  The in-band radiance is obtained by
multiplying the radiances given by the formulae in Table 1 by w,
the  equivalent width of the channel.  Thus, the formulae for the
calculation of the AVHRR albedo, given in Table 2, were obtained
by scaling the radiance formulae of Table 1 by the factor
100(w/Fb).  We use the Neckel and Labs(1984) extraterrestrial
solar irradiance values in the calculation of Fb; values of w and
Fb are listed in Table 3.

     5.   Concluding Remarks

     It will be appreciated if the users will convey their views
on the information provided here--its usefulness and relevance,
the format and contents--to the author either on e-mail
(nrao@orbit.nesdis.noaa.gov), or by phone(301-763 8136) or
FAX(301 763 8108).

References:

Brest, C. and W.R. Rossow, 1992: Radiometric calibration and 
     monitoring of NOAA AVHRR data for ISCCP. Int. J. Remote
     Sensing, 13, 235-273.
Che, N. and J.C. Price, 1992: Survey of radiometric calibration 
     results and methods for visible and near-infrared channels
     of NOAA-7, -9, and -11 AVHRRS, Remote Sensing of Environ.,
     41, 19-27.
Kaufman, Y.J. and B.J. Holben, 1993: Calibration of AVHRR visible
     and near-IR bands by atmospheric scattering, ocean glint,
     and desert reflection, Int. J. Remote Sensing, 14, 21-52.
Neckel, H. and D. Labs, 1984: The solar radiation between 3300 
     and 12500A, Solar Physics, 90, 205-258.
Price, J.B., 1987: Calibration of satellite radiometers and
     comparison of vegetation indices.  Remote Sens. Environ.,
     21, 15-27.
Rao, C.R.N., 1987: Prelaunch calibration of channels 1 and 2 of 
     the Advanced Very High Resolution Radiometer, NOAA Technical
     Report NESDIS 36, Department of Commerce, Washington, D.C.
Rao, C.R.N., J. Chen, F.W. Staylor, P. Abel, Y.J. Kaufman, E. 
     Vermote, W.R. Rossow, and C. Brest, 1993: Degradation of the
     visible and near-infrared channels of the Advanced Very High
     Resolution Radiometer on the NOAA-9 spacecraft: Assessment
     and recommendations for corrections, NOAA Technical Report
     NESDIS 70, U.S. Department of Commerce, Washington, D.C.
Rao, C.R.N., M.P. Weinreb, and J. Chen, 1994: Recalibration of 
     the Advanced Very High Resolution Radiometer for climate
     research, Adv. Spa. Res., 14, 117-120.
Rao, C.R.N., and J. Chen, 1994: Post-launch calibration of the 
     visible and near-infrared channels of the Advanced Very High
     Resolution Radiometer on NOAA-7, -9, and -11 spacecraft(NOAA
     Technical Report NESDIS 78, U.S. Department of Commerce,
     Washington, D.C.)
Smith, G.R., R.H. Levin, P. Abel, and H. Jacobowitz, 1988:
     Calibration of the solar channels of the AVHRR on using high
     altitude aircraft measurements. J. Atmos. Ocean. Tech., 5,
     631-639.
Staylor, W.F., 1990: Degradation rates of the AVHRR visible 
     channel for the NOAA 6, 7, and 9 spacecraft, J. Atmos.
     Ocean. Tech., 7, 411-423. 
Teillet, P.M. and B.J. Holben, 1994: Towards operational
     radiometric calibration of NOAA AVHRR imagery in the visible
     and near-infrared channels, Canadian Journal of Remote
     Sensing, 20, 1-10.


Table 1.  Formulae for the calculation of calibrated radiances

=================================================================
Spacecraft                     Radiance(W/m2 sr m)
=================================================================

NOAA-7(6-23-1981)
Channel 1      (C10 - 36) x 0.5753 x exp(1.01 x 10-4 x d) 
Channel 2      (C10 - 37) x 0.3914 x exp(1.20 x 10-4 x d)  

NOAA-9(12-12-1984)
Channel 1      (C10 - 37) x 0.5465 x exp[1.66 x 10-4 x (d - 65)]  
Channel 2      (C10 - 39.6) x 0.3832 x exp[0.98 x 10-4 x (d - 65)] 
               
NOAA-11(9-24-1988)
Channel 1      (C10 - 40) x 0.5496 x exp(0.33 x 10-4 x d) 
Channel 2      (C10 - 40) x 0.3680 x exp(0.55 x 10-4 x d)  
 
=================================================================

Table 2.  Formulae for the calculation of calibrated AVHRR
          albedos

=================================================================
Spacecraft                   Albedo(per cent) 
=================================================================

NOAA-7(6-23-1981)
Channel 1      (C10 - 36) x 0.1100 x exp(1.01 x 10-4 x d) 
Channel 2      (C10 - 37) x 0.1169 x exp(1.20 x 10-4 x d)  

NOAA-9(12-12-1984)
Channel 1      (C10 - 37) x 0.1050 x exp[1.66 x 10-4 x (d - 65)]  
Channel 2      (C10 - 39.6) x 0.1143 x exp[0.98 x 10-4 x (d - 65)] 
               
NOAA-11(9-24-1988)
Channel 1      (C10 - 40) x 0.1060 x exp(0.33 x 10-4 x d)  
Channel 2      (C10 - 40) x 0.1098 x exp(0.55 x 10-4 x d)  
 
=================================================================

Note:     In the formulae in Tables 1 and 2, the effective counts
          (C10 - C0) are normalized to mean Earth-Sun distance; C10
          and C0 are the AVHRR measured signal and offset
          respectively on the 10-bit scale; C0 has been given
          appropriate numerical values in the formulae.

Table 3.  Equivalent widths and in-band solar irradiances

=================================================================
Spacecraft    Launch         w(m)              Fb(Wm-2)
               Date      Ch.1   Ch. 2     Ch.1          Ch.2
                                         
=================================================================

NOAA-7     6-23-1981     0.108  0.249     177.5         261.9
 
NOAA-9     12-12-1984    0.117  0.239     191.3         251.8

NOAA-11    9-24-1988     0.113  0.229     184.1         241.1

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