The Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership (SNPP) satellite uses its 14 reflective solar bands to passively collect solar radiant energy reflected off the Earth. The Level 1 product is the geolocated and radiometrically calibrated top-of- the-atmosphere solar reflectance. The absolute radiometric uncertainty associated with this product includes contributions from the noise associated with measured detector digital counts and the radiometric calibration bias. Here, we provide a detailed algorithm for calculating the estimated standard deviation of the retrieved top-of-the-atmosphere spectral solar radiation reflectance

Lei, Ning

McIntire, Jeff

Twedt, Kevin

Xiong, Xiaoxiong

NASA Technical Reports Server

SNPP VIIRS RSB EARTH VIEW REFLECTANCE UNCERTAINTY  
 
Ning Lei1, Kevin Twedt1, Jeff McIntire1, and Xiaoxiong Xiong2 
 
1. Science Systems and Applications, Inc., 10210 Greenbelt Road, Suite 600, Lanham, MD 20706 USA 
2. Sciences and Exploration Directorate, NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA 
ABSTRACT 
The Visible Infrared Imaging Radiometer Suite (VIIRS) on 
the Suomi National Polar-orbiting Partnership (SNPP) 
satellite uses its 14 reflective solar bands to passively collect 
solar radiant energy reflected off the Earth. The Level 1 
product is the geolocated and radiometrically calibrated top-
of-the-atmosphere solar reflectance. The absolute 
radiometric uncertainty associated with this product includes 
contributions from the noise associated with measured 
detector digital counts and the radiometric calibration bias. 
Here, we provide a detailed algorithm for calculating the 
estimated standard deviation of the retrieved top-of-the-
atmosphere spectral solar radiation reflectance.  
Index Terms— SNPP, VIIRS, radiometric, calibration, 
uncertainty 
1. INTRODUCTION 
One of the five remote sensing instruments onboard the 
Suomi National Polar-orbiting Partnership (SNPP) satellite 
is the Visible Infrared Imaging Radiometer Suite (VIIRS). 
The Level 1 data product for the reflective solar bands 
(RSBs) of the VIIRS, with design band wavelengths from 
0.412 to 2.25 m, is the geolocated and radiometrically 
calibrated top-of-the-atmosphere (TOA) spectral solar 
radiation reflectance. It is important to estimate the absolute 
accuracy of the retrieved reflectance to compare with the 
2.0% uncertainty requirement [1]. Here, we show the 
algorithms for the retrieved reflectance uncertainty, 
measured by the estimated relative standard deviation. 
 
2. METHODOLOGY 
To calculate the standard deviation for the reflectance, we 
start with the equation [2] 
     
       
 

 


dtt
tRdtL
sunsunearth
ap
t,RSR,cos
4t,RSR,
2
 ,           (1) 
where  tL ap ,  is the retrieved scene TOA spectral 
radiance, RSR is the relative spectral response, sunearth   is 
the angle between the solar vector and the scene surface 
normal, sun  is the solar spectral power, and R is the 
distance between the VIIRS and the Sun. The RSR is 
averaged over all detectors in a band. The retrieved scene 
spectral radiance  tL ap ,  is calculated by 
   
 
 
 EV
2
210
RVSt,RSR
t,RSR,


EVEVap dncdnccF
d
dtL 



 .   (2)                       
In Eq. (2), RVS is the reflectivity of the half-angle-mirror 
(HAM) relative to the value when the rotating telescope 
assembly (RTA) observes the onboard solar diffuser (SD), 
EV  is the angle between the HAM surface normal and the 
incident light, F is a correction factor so that the right hand 
side of Eq. (2) gives the correct scene spectral radiance, 
 210 ,, ccc  are determined prelaunch, and EVdn  is the 
background subtracted detector digital count for the scene.  
The F in Eq. (2) is calibrated through observations of the 
fully solar illuminated SD [2, 3] 
 
     
   
   
      





















ddnccdnccctR
dtt
tt
tt
tF
SDSD
sun
sunsun
sunsunSD
RSR//'4
',RSR',
',,H0,,BRDF
''cos
'
2
12101
2
RTARTA


.   (3) 
In Eq. (3), sunSD   is the angle between the SD surface 
normal and the solar vector,  is SD screen transmittance, 
sun

 is the solar angle, RTABRDF  is the SD bidirectional 
reflectance distribution function at the RTA-SD view 
direction at launch, RTAH  is the relative change in the 
RTABRDF  since launch, and SDdn  is the background 
subtracted digital counts when the sensor observes the fully 
sunlit SD. The t’ in Eq. (3) and the t in Eq. (2) should be 
close enough so that the F is assumed to remain constant 
over the time interval.  
Considering the small separation between t and t’, 
 tsun ,  and  ', tsun   are essentially the same and for 
the purpose of calculating the variance of the retrieved 
reflectance, we need to consider only the wavelength 
integral over the RSR central peak. We combine Eqs. (1-3) 
to obtain the spectral reflectance as  
https://ntrs.nasa.gov/search.jsp?R=20180001745 2019-08-30T13:03:08+00:00Z
 
    
  
 
 
 
 
   tHt
tR
tR
tc
tc
dn
c
c
dn
c
c
dn
c
c
dn
c
c
t
tt
sunBsunB
SDSD
EVEV
sunearth
sunsunSD
,,0,,BRDF
''
cos
''cos
RVS
RTARTA
2
2
1
1
2
1
2
1
0
2
1
2
1
0
EV















 .             (4) 
We use the prelaunch error estimate for the RVS, which has 
a standard deviation of less than 0.1% for the RSBs [4].  The 
c1 ratio, affected mainly by the detector focal plane 
temperature variation, differs from one by less than 0.1% 
because the focal plane temperature varies  by less than 0.5 
degrees over the daylight time of an orbit and the 
temperature’s impact on c1  is less than 1% for every 10 
degrees of the temperature change [5]. Additionally, the 
VIIRS-Sun distance is accurately known, with a relative 
error less than 10-8.  The noise in dnSD is small since on a per 
scan basis it is the average over 48 RTA angular positions 
and further effectively averaged over many scans on a single 
satellite orbit. Furthermore, the co-variances are either zero 
or negligibly small. Hence, we write the relative variance of 
the TOA reflectance as 
     
  
  
    
    
2
RTA
RTA
2
RTA
RTA
2
2
1
2
1
0
2
1
2
1
0
222
0,,BRDF
0,,BRDFvar
,,H
,,Hvar
var
cos
cosvar
cos
cosvarvar
sunsunB
sunsunB
sunB
sunB
EVEV
EVEV
sunearth
sunearth
sunSD
sunSD
t
t
t
t
dn
c
c
dn
c
c
dn
c
c
dn
c
c








































 . (5)           
We calculate each term on the right hand side of Eq. (5).  
The first term is    sunSDsunSD   vartan
2 . During the 
calibration data collection process, sunSD   varies from 50 
to 59 degrees.  sunSD var  has contributions from the 
errors in the solar vector direction and the SD surface 
normal vector. The solar vector direction has a standard 
deviation of about 0.001 prior to February 23, 2012 and 
about 0.00008 afterward [6]. We estimate that the standard 
deviation of the SD surface normal vector error is much less 
than 0.001 and thus we ignore this error. As a result, 
 sunSD var  is only marginally significant prior to 
February 23, 2012 and negligibly small afterward. 
The second term is    sunearthsunearth   vartan
2 . Similar 
to sunSD  , the error in sunearth   is primarily caused by 
the solar vector directional error and thus  sunearth var  is 
about 0.0012 prior to February 23, 2012 and about 0.000082 
afterward. Hence, the second term does not contribute much 
to the variance of the retrieved reflectance until sunearth   is 
close to  90 . For example, for the second term to be larger 
than 0.012, sunearth   needs to be larger than 3.84 . 
The third term is dominated by the linear term in EVdn  and 
thus is simplified to   2/var EVEV dndn . EVdn  is 
avgSVEV DNDN ,375.0   with  EVDN  a 12-bit integer 
and avgSVDN ,  is typically the average of 48 SV digital 
numbers in the same scan. The 0.375 is added to the 12-bit 
EVDN  to remove the bias due to the truncation. SVDN  at 
each sample is a 14-bit number with 2 bits for the fraction. 
The truncation of EVDN  to 12-bit adds roughly 1/12 to the 
original analog signal variance. Mathematically, we write  
     
    avgSVEV
avgSVEVEV
DNDN
DNDNdn
,
,
var12/1analogvar
varvarvar


 .            (6) 
We calculate the original signal variance 
  analogvar EVDN  from the variance of a single sample 
SDdn   as 
     
    avgSVSD
avgSVSDSD
DNDN
DNDNdn
,
,
var192/1analogvar
varvarvar


 .          (7) 
In Eq. (7), 1/192 is the additional variance due to the 
digitization of SDDN , a 14-bit number with 2 bits for the 
fraction. Combining Eqs. (6) and (7) by taking 
     analogvaranalogvar SDEV DNDN   when 
SDEV DNDN  375.0  (roughly when SDdn  matches 
EVdn  in strength), we retrieve  EVdnvar  by 
    192/112/1varvar  SDEV dndn . 
We would like to use a simple function of EVdn  to calculate 
 EVdnvar . Considering the white noise which includes the 
thermal and digitization noises and the Poisson noise as the 
main contributions to the noise in EVdn , we use the 
functional form of [7]   EVEV dnkkdn  10var , where 
0k and 1k  are associated with the white and the Poisson 
noises, respectively, and are approximately EVdn  
independent. This linear functional dependence is 
demonstrated by Fig. 1 that shows the variance vs. dnSD for 
detector 8 of band M6 at orbit 25986.   2/var EVEV dndn  at 
Ltyp at this writing are larger than 201-2 for the VISNIR 
bands at the high-gain stage for dual-gain bands, and 137-2 
for the SWIR bands, except the M11 band for which 
  2/var
EVEV
dndn  is about 21-2. 
 
Fig. 1. Variance vs. dnSD for detector 8 of band M6 on satellite 
orbit 25986. 
 
Fig. 2. 0k  versus satellite orbit numbers for the M1 band detector 
1 at the high-gain stage. The blue dots are for the 0k  obtained 
from a least-squares fit with the retrieved  EVdnvar . The black 
dots are for 
0k  obtained from a least-squares fit to the SD data 
without the digitization correction. Near the mission start, the 
black dots have higher values since prior to orbit around 5010 
SDdn  was a 12-bit integer and afterward has become a 14-bit 
number with 2 bits for the fraction. 
We determine 0k  and 1k  by performing a least-squares fit to 
the SD data over a wide range of signal levels. In Fig. 2, we 
show an example of 0k  versus satellite orbit number. The 
curve shows that 0k may be described by a linear function of 
time, orbitaak  100 . Similarly, we may describe 1k  by 
a linear function of time, orbitbbk  101 ,                                                    
as suggested by Fig. 3. We tabulate a0, a1, b0, and b1 for 
each detector, gain, and band; 0k  and 1k  are not HAM 
dependent because they are independent of EVdn . 
 
Fig. 3. 1k  versus satellite orbit numbers for the M1 band detector 1 
at the high-gain stage. The blue dots are for the 1k  obtained from a 
least-squares fit with the retrieved  EVdnvar  and the black dots 
are 
1k  without the digitization correction. Since the digitization 
correction is independent of signal level, it has no impact on 
1k . 
The fourth term on the right hand side of Eq. (5) is related to 
the uncertainty of RTAH . This uncertainty is influenced by 
the uncertainty of SDSMH  and the F calculated with lunar 
observation data, as well as the SD positional dependence of 
RTAH . The F from the lunar data tells us how much RTAH  
differs from SDSMH . The multi-year lunar F relative to its 
value at a particular time has an accuracy of about 0.1%.  
We approximate that the accuracy of SDSMH  is less than 
0.1%, except at the M1 band central wavelength where the 
accuracy is about 0.0012 + 0.00052 /HRTA2 [9]. Note that the 
positional dependence of RTAH  has not been estimated. As 
a result, we write the relative variance of RTAH  as 
22
RTA
2
0005.0/001.02  H  for the M1 band and 
2
RTA
2
/001.0 H  for the rest of the RSBs.  
The fifth term on the right hand side of Eq. (5) is dominated 
by the errors in the prelaunch BRDFRTA [8]. For each 
angular data point, the prelaunch   has a relative 
uncertainty of 0.24%. The relative value of 
  0,,BRDF
RTA
t
sunB

 is determined by on-orbit yaw 
maneuver data (further improvements with regular on-orbit 
data have been made but are not used in this study) and the 
relative    0,,BRDF RTA tsunB

 is scaled to match the 
prelaunch RTABRDF . Consequently, we effectively 
average the prelaunch   over many angular data points and 
the uncertainty of this average should be much smaller than 
0.24% and is ignored. Bias in the prelaunch    is not 
estimated here. The prelaunch BRDFRTA has a relative 
variance of 0.0112+0.0052 for the VISNIR bands and 
0.0132+0.0052 for the SWIR bands [8]. We added 0.0052 to 
the originally given prelaunch BRDFRTA variance to account 
for the additional uncertainty associated with the possible 
change in the BRDF between prelaunch BRDFRTA 
measurement time and the satellite launch time. 
Hence, when the angle between the sunlight and the Earth 
surface normal is not close to ±90°, for non-aggregated 
Earth views, the reflectance uncertainties for the RSBs at 
Ltyp, as measured by    /std , are dominated by dnEV 
noise and the prelaunch BRDF uncertainties. At Ltyp, at the 
current time, the uncertainty is less than 1.3% for the 
VISNIR bands, and 1.6% for the SWIR bands, except for 
the M11 band which has an uncertainty of about 4.9%.     
3.  AGGREGATION IMPACT 
Since VIIRS aggregates samples together for some scan 
angles, we need to consider the impact of the aggregation on 
the relative variance of the retrieved TOA reflectance. The 
aggregation for the dual-gain bands happens after the 
radiometric calibration for each sample is performed and 
thus the average is performed on the retrieved scene 
reflectance. As a result, the variance contribution from 
EVdn  is given by 
         2
1
10 /DG;var agg
N
i
EViiEV NidnGkGkdn
agg
 

 ,  (8) 
where DG indicates a dual-gain band, aggN  indicates the 
number of per sample EVdn  to be averaged, and iG  
indicates the detector gain stage. 
For the single-gain bands, the aggregation happens before 
the digital number is truncated to a 12-bit integer and we 
have 
   
    aggavgSV
agg
N
i
iEVEV
NDN
NdnkkSGdn
agg
/11var12/1
/;var
,
2
1
,10










 
  .   (9) 
 
4. SUMMARY 
We showed the mathematical expressions to calculate the 
relative variance of the retrieved TOA solar radiation 
spectral reflectance for the SNPP VIIRS RSBs. The variance 
is dominated by the variance of the prelaunch SD BRDF at 
the RTA direction when the scene signal level is high. The 
white and Poisson noises contribute significantly to the 
relative variance when the signal level is low.  Possible 
biases in the SD positional dependence of the BRDF 
degradation factor and the prelaunch SD screen 
transmittance and BRDF are ignored. The uncertainty can be 
easily calculated with a few time-independent parameters 
and the measured background subtracted detector digital 
count. We determined the values of the time-independent 
parameters from observations of the sunlit SD. Additionally, 
we derived mathematical expressions to calculate the 
reflectance variance when detector samples are aggregated. 
The formulas allow us to implement the uncertainty as part 
of the Level one product on a per (pixel, detector) basis. 
When the angle between the sunlight and the Earth surface 
normal is not close to ±90°, for non-aggregated Earth views, 
the reflectance uncertainties for the RSBs at the respective 
typical scene spectral radiances are less than 1.3% for the 
VISNIR bands and 1.6% for the SWIR bands, except for the 
M11 band which has an uncertainty of about 4.9%. 
5. REFERENCES 
[1] R. M. Durham, “Sensor specification for the visible infrared 
imager radiometer suite,” Raytheon Systems Company, Goleta, 
CA, USA, Tech. Rep. PRT PS 154640-101A, 2002. 
[2] Joint Polar Satellite System (JPSS) VIIRS Radiometric 
Calibration Algorithm Theoretical Basis Document (ATBD); 
NASA Goddard Space Flight Center: Greenbelt, MD, USA, 2013. 
[3] N. Lei, Z. Wang, and X. Xiong, “On-orbit Radiometric 
Calibration of Suomi NPP VIIRS Reflective Solar Bands through 
Observations of a Sunlit Solar Diffuser Panel”, IEEE Trans. 
Geosci. Remote Sens., vol. 53, pp. 5983-5990, 2015, DOI: 
10.1109/TGRS.2015.2430814 
[4] A. Wu, X. Xiong, and C. Cao, “Tracking on-orbit stability of 
the response versus scan angle for the S-NPP VIIRS reflective 
solar bands”, Proc. SPIE, vol. 9972, Art ID:9972-1C, 2016, doi: 
10.1117/12.2238106. 
 
[5] N. Lei and X. Xiong, “Functional form of the radiometric 
equation for the SNPP VIIRS reflective solar bands”, Proc. SPIE, 
vol. 9972, Art ID. 9972-19, 2016; doi:10.1117/12.2236950. 
[6] R. Wolfe, G. Lin, M. Nishihama, K. Tewari, J. Tilton, and A, 
Issacman, “Suomi NPP VIIRS prelaunch and on-orbit geometric 
calibration and characterization”, JGR: Atmos., vol 118, 2013. 
[7] N. Lei, X. Xiong, and B. Guenther, “Modeling the Detector 
Radiometric Gains of the Suomi NPP VIIRS Reflective Solar 
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[8] L. Lessel and S. McClain, “Low Uncertainty Measurements of 
Bidirectional Reflectance Factor on the NPOESS/VIIRS Solar 
Diffuser”, Proc. SPIE, vol. 6677, Art ID 6677-1O, 2007. 
[9] N. Lei and X. Xiong, “Estimation of the Accuracy of the SNPP 
VIIRS SD BRDF Degradation Factor Determined by the Solar 
Diffuser Stability Monitor”, Proc. SPIE, vol. 9607, Art ID. 9607-
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SNPP VIIRS RSB Earth View Reflectance Uncertainty

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