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Remote Sensing of Environment 76 (2000) 239 ± 249
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How precise are SeaWiFS ocean color estimates? Implications of
digitization-noise errors
Chuanmin Hu*, Kendall L. Carder, Frank E. Muller-Karger
College of Marine Science, University of South Florida, 140 Seventh Avenue S., St. Petersburg, FL 33701, USA
Received 26 June 2000; accepted 21 November 2000
Abstract
Various subtle but important digitization round-off and noise errors are found in SeaWiFS imagery. These errors often cause large
relative errors at a pixel and cause pixelization or ``speckling'' across the image, which is particularly obvious in the SeaWiFS
chlorophyll standard product. Using simulations and current SeaWiFS algorithms, we show the effect of digitization-noise errors on
the SeaWiFS ocean-color data products. It is found that the SeaWiFS mission goals, namely to estimate water-leaving radiances to
within ‹ 5% and chlorophyll-a concentrations to within ‹ 35% for Case I waters, cannot always be met. For maritime aerosol
conditions the errors in the estimated chlorophyll concentrations over oligotrophic waters can easily reach ‹ 60% and the absolute
values over adjacent pixels can vary 2 ± 3 fold. Several schemes can be used to reduce this type of error, among which the spatial
smoothing of the atmospheric-correction bands is recommended. This is because the errors in those bands are propagated and
exaggerated to the visible bands and to the chlorophyll product through the atmospheric-correction process. The smoothing scheme,
however, will cause more pixels to be discarded over cloud edges. Ultimately, a significant increase in both digitization bits and
sensitivity is essential to achieve the stated mission goals. Such improved specifications are available on MODIS. D 2001 Elsevier
Science Inc. All rights reserved.
Keywords: SeaWiFS; MODIS; CZCS; Digitization ± noise; Ocean color; Water ± leaving radiance; Chlorophyll concentration; Atmospheric correction
1. Introduction
Since the launch of the Sea-viewing Wide Field-of-view
Sensor (SeaWiFS, Hooker, Esaias, Feldman, Gregg &
McClain, 1992) in August 1997, global ocean color data
are available in near-real time to the science community
(McClain, Cleave, Feldman, Gregg, & Hooker, 1998).
SeaWiFS is on a sun-synchronous satellite with a 2801km swath width, providing 2-day coverage of the global
ocean with a nadir resolution of 1 km2 per pixel. It has
10-bit digitization for its eight spectral bands (Table 1).
The two near-IR (NIR) bands, bands 7 (765 nm) and 8
(865 nm), are used for atmospheric correction. The visible
bands are used for biooptical applications. Intensive vicarious and lunar calibration efforts have been conducted to
help meet mission specifications (Barnes, Eplee, Patt, &
McClain, 1999; McClain et al., 1998). A sophisticated
* Corresponding author. Tel.: +1-727-553-1186; fax: +1-727-553-1103.
E-mail address: [email protected] (C. Hu).
atmospheric-correction scheme (Ding & Gordon, 1995;
Gordon & Wang, 1994a) is applied in the data processing
software package (SeaDAS) to remove atmospheric path
radiance, which contributes 80 ±90% of the total signal in the
visible bands. Consequently, the SeaWiFS mission goals, to
estimate water-leaving radiances to within ‹ 5% and chlorophyll concentrations to within ‹ 35% for case I waters, are
often met (McClain et al., 1998).
However, since the SeaWiFS data are processed pixel by
pixel, significant pixelization (or speckling) effects are often
found in the data products (e.g., Hu, Carder, & MullerKarger, 2000). Although it has been shown that highaltitude aerosols, cirrus clouds, and digitization errors may
cause speckling (Hu et al., 2000), the effect of digitization
on the data products had not been quantified. In this paper,
using simulations and the current atmospheric-correction
and biooptical algorithms, the effects of digitization-noise
errors on the data products are estimated.
We begin by briefly reviewing the atmospheric-correction scheme (Gordon & Wang, 1994a). Then, we show
how the digitization-noise errors, assumed randomly dis-
0034-4257/00/$ ± see front matter D 2001 Elsevier Science Inc. All rights reserved.
PII: S 0 0 3 4 - 4 2 5 7 ( 0 0 ) 0 0 2 0 6 - 6
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C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
Table 1
Radiance (L, mW cm ÿ 2 mm ÿ 1 sr ÿ 1) and reflectance (r, dimensionless)
corresponding to 1 DN, and noise equivalent reflectance (NEDr) for the
SeaWiFS bands (Gordon & Wang, 1994a; Hooker et al., 1992)
Band
l (nm)
1 DN in L
1 DN in r
NEDr
1
2
3
4
5
6
7
8
402 ± 422
433 ± 453
480 ± 500
500 ± 520
545 ± 565
660 ± 680
745 ± 785
845 ± 885
0.0139
0.0136
0.0108
0.0093
0.0076
0.0042
0.0030
0.0022
0.00049
0.00045
0.00035
0.00031
0.00026
0.00017
0.00015
0.00014
0.00068
0.00043
0.00034
0.00031
0.00027
0.00023
0.00018
0.00015
tributed, affect the estimates of water-leaving radiance and
chlorophyll concentration. Finally we discuss ways to
reduce the errors.
2. Atmospheric correction of SeaWiFS
The Gordon and Wang algorithm uses two NIR bands
(bands 7 and 8, Table 1) to estimate the spectral aerosol
reflectance. The ultimate goal of the atmospheric correction
is to obtain the water-leaving reflectance, rw(l), from rt(l)
measured by the sensor:
rt …l† ˆ rr …l† ‡ ra …l† ‡ t…l†rw …l†;
…1†
where r = pL/( F0 cosq0), L is the upward radiance, F0 is
the extraterrestrial solar irradiance, q0 is the solar zenith
angle, and l is the wavelength of the band. rt is the total
reflectance, rr is that due to Rayleigh scattering, and ra is
that due to aerosol scattering and aerosol ± Rayleigh
interactions. t is the diffuse transmittance from the target
(pixel of the imagery) to the sensor (satellite). Ozone
absorption effects are not considered in either of the terms
on the right-hand side of Eq. (1), since rt has already
been corrected for those effects by using near-real-time
ozone data. For simplicity the sun glitter and whitecap
effects are omitted since they can be either avoided by
tilting the sensor or estimated from wind data (Gordon &
Wang, 1994b).
rr in the equation can be computed using an exact
formulation to account for multiple scattering and polarization (polarization sensitivity of the SeaWiFS sensor is less
than 2%, Hooker et al., 1992). Assuming rw = 0 at 765 and
865 nm, ra(765) and ra(865) can be derived. From precomputed aerosol lookup tables, ra(765) and ra(865) are used to
determine the aerosol optical thickness at 865 nm (ta865)
and the aerosol type (represented by 2 of the 12 candidate
aerosol models with different contribution weights, see
below). ra in other bands is then obtained by extrapolation
according to the lookup tables.
Following Gordon and Wang (1994a), ela,lb is defined
as the ratio of the aerosol single-scattering reflectance,
ras , between bands a and b (without subscripts,
e = e765,865). ela,lb can be computed for a given aerosol
type, which determines the single-scattering albedo and
scattering phase function. Fig. 1a shows that using the
spectral ela,lb, ras in one band can be extrapolated from
ras in band 8. The conversion coefficients between ras
and ra for all candidate aerosol models are precomputed
using simulations and stored in aerosol lookup tables
(computer files) for data processing. At a pixel of
p r o c e s s i n g , ra ( 7 6 5 ) a n d ra ( 8 6 5 ) , d e r i v e d a s
rt(765) ÿ rr(765) and rt(865) ÿ rr(865) (rw(765)  0 and
rw(865)  0), are converted to ras(765) and ras(865) for
each of the aerosol models. e = ras(765)/ras(865) for each
model is then computed. The mean e will generally fall
between those for two of the models with different
contribution weights, a and
(1 ÿ a) where 0 a 1
N
i
e
)/N = ae1+(1 ÿ a)e2. N is
and a is determined by (
iˆ1
the total number of aerosols models. e1 and e2 are for the
two selected models. This is because each aerosol model has
its distinguishable e, as shown in Fig. 1b. The two aerosol
models and a derived above are used to represent the
aerosol type. ra in other bands is extrapolated using Fig. 1a
and the conversion coefficients from the lookup tables (to
convert ras to ra) for each of the two models, and then mixed
using a and (1 ÿ a) in the same manner as for e. All other
quantities associated with aerosols, such as ta865, are also
derived using each of the two models and mixed in the
same way (Gordon & Wang, 1994a).
Fig. 1. ela,lb for the solar zenith angle q0 = 60° at scene center (the sensor
zenith angle q = 22.7° and azimuth difference Df = 16.4°) for all the 12
candidate aerosol models currently used in the SeaWiFS atmospheric
correction, namely, oceanic aerosol with relative humidity (RH) 90%, 99%,
maritime aerosol with RH 50%, 70%, 90%, 99%, coastal aerosol with RH
50%, 90%, 99%, and tropospheric aerosol with RH 50%, 90%, 99% (see
Gordon & Wang, 1994a). (a) Spectral ela,lb; (b) e (i.e., e765,865) for the 12
aerosol models.
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
241
Knowing the aerosol type and ta865, ta(l) and t(l)
can be derived (Gordon et al., 1983; Gordon & Wang,
1994a). Finally, rw (reflectance equivalent of water-leaving radiance) is computed as (rt ÿ rr ÿ ra)/t. Simulations
(Ding & Gordon, 1995; Gordon & Wang, 1994a) show
that under most circumstances, rw(443) can be estimated
to within ‹ 0.001, corresponding to ‹ 5% error for clear,
Case I waters.
3. Digitization round-off and noise
The above scheme assumes an error-free rt(l). Although
conceptually this can be achieved by providing for an errorfree calibration, digitization round-off and noise errors are
inevitable in any satellite data stream, which will produce
errors in rt(l), and eventually in rw(l).
The data downlinked from the satellite are quantized
with the smallest incremental value presented as 1 digital
number (DN). For SeaWiFS, data are digitized at the 10-bit
level. For oceanographic applications with small radiometric signals, high gain settings are used. Table 1 lists
the radiance (L, mW cm ÿ 2 mm ÿ 1 sr ÿ 1) corresponding to
1 DN for each SeaWiFS band (Gordon & Wang, 1994a;
Hooker et al., 1992). Also listed in the table are the
corresponding reflectance, r, for a solar zenith angle
q0 = 60° and the noise equivalent reflectance (NEDr, Gordon & Wang, 1994a).
If the digitized signal from the sensor reads Ltd, the
analog signal, Lta, can be written as Lta = Ltd ÿ DL where DL
is the digitization round-off or truncation error. In the final
Fig. 3. Effects of digitization-noise on the SeaWiFS data collected on 9
February 1999 over the Sargasso Sea. (a) rt(412) jumps between odd and
even scan lines for an area of 28 14 pixels; (d) data products are clustered
for the same area.
radiometric calibration, the gain and offset coefficients are
adjusted statistically using multiple-pixel averages. Therefore DL can be regarded to be randomly distributed from
ÿ 0.5 to 0.5 DN. Lta contains noise, DN, which can be
assumed ``white,'' also ranging roughly from ÿ 0.5 to 0.5
DN (see NEDr in Table 1) for the same calibration reason.
Therefore we will have the ``true'' signal, Lt, as
Lt ˆ Ldt ÿ DL ÿ DN :
Fig. 2. Effects of digitization-noise on the SeaWiFS data collected on 24
December 1999 over the Gulf of Mexico. (a) Digitized total radiance (in
DN) in bands 7 and 8 along a scan line segment; (b) two aerosol models and
the corresponding weight distribution between them determined by the
SeaWiFS atmospheric-correction algorithm.
…2†
Since DL and DN are randomly distributed from ÿ 0.5 to
0.5 DN, Ltd can differ from Lt by up to ‹ 1 DN. Fig. 2a
displays the total digitized radiance (in DN) in bands 7 and
8 along a scan-line segment. The difference in the geometry
of the pixels (solar and viewing angles) is too small to effect
a difference in the total radiance, and band 7 does not
covary with band 8. Therefore, the variations in the DN
values are not likely due to geophysical phenomena but
rather an expression of digitization round-off and readout
noise errors. As a result, the two aerosol models and the
weight distribution between them determined by the two
bands with the SeaWiFS atmospheric correction also change
along the scan-line segment, as shown in Fig. 2b.
Similar errors can be found across alternating scan lines
as well. Fig. 3a shows that rt(412) jumps between odd and
even scan lines over the Sargasso Sea. The values in Fig. 3a
are the averages over 28 pixels along each scan line to
increase the signal-to-noise to observe the underlying pattern. The cause of the error is unclear at this time, but is
possibly due in part to reflectance differences between the
sides of the double-sided scanning mirror of the SeaWiFS
sensor. Fig. 3b illustrates more evidence of digitization
effects resulting in data products that are ``clustered.''
242
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
These digitization-noise errors will have at least two
related impacts on the standard SeaWiFS data products:
(1) speckling across a scene that affects the visual quality;
and (2) errors that affect quantitative retrievals at any
individual pixel. We will use simulations to estimate the
effect of propagation of these errors into the standard
SeaWiFS level-2 products.
elb,l8 = eb where e = elb,l8 and b = (l8 ÿ lb)/(l8 ÿ l7). Thus,
we have ra(lb) = ra(l8)elb,l8 = ra(l8)[ra(l7)/ra(l8)]b. Similarly, rad(lb) can be derived as rad(lb) = rad(l8)[rad(l7)/
rad(l8)]b. Combining Eqs. (4) and (5a and b) and using a
Taylor expansion to first-order approximation (i.e., products
of any two small quantities, such as Drt(l7)Drt(l8), are
omitted), we will have
D…trw †…lb † ˆ Drt …lb † ‡ …ra …lb † ÿ rda …lb ††
 Drt …lb † ‡ ‰…b ÿ 1†elb ;l8 Drt …l8 † ÿ bDrt …l7 †elb ;l8 =eŠ
4. Method
Assuming a random distribution from ÿ 0.5 to 0.5 DN
each for DL and DN in Eq. (2), from Eq. (1) we have (Eqs.
3a ±c)
rdt ˆ rr ‡ rda ‡ t d rdw ;
…3a†
rt ˆ rr ‡ ra ‡ trw ;
…3b†
rt ˆ rdt ÿ DrL ÿ DrN ˆ rdt ÿ Drt ;
…3c†
where the superscript ``d'' stands for the data derived from
the digitized satellite signal, and the quantities without the
superscript are for the ``true'' signal, i.e., signal with no
digitization round-off or noise errors. DrL and DrN are the
reflectance counterparts for DL and DN, respectively. For
simplicity they can be expressed in one term, Drt. The
wavelength dependency of each term is suppressed in this
notation. Since rr is purely a computed quantity, it remains
the same in Eq. (3a) and (b). Therefore we have
D…trw † ˆ t d rdw ÿ trw ˆ Drt ‡ …ra ÿ rda †:
…6†
…4†
 Drt …lb † ‡ ‰…b ÿ 1†eb Drt …l8 † ÿ bebÿ1 Drt …l7 †Š;
where the first term on the right-hand side represents the
digitization-noise error at lb, and the terms in the bracket
represent the errors caused by the digitization-noise errors in
bands 7 and 8 propagated to lb through the atmospheric
correction. For a given aerosol type, e is fixed at a certain
solar and viewing geometry as indicated by Fig. 1b, but will
change as digitization-noise errors occur, as implied by the
definition edlb,l8 = rad(lb)/rad(l8). From Eq. (6), D(trw)(lb)
can be estimated assuming DrL and DrN in Drt each varies
randomly from ÿ r0.5 DN to r0.5 DN.
Using e values provided by the aerosol lookup tables of
SeaDAS (Gordon & Wang, 1994a), frequency distribution
curves (FDCs) of D(trw)(lb) in several bands for maritime
aerosols (model #5 of the lookup tables) at scene center
(solar zenith angle q0 = 60°, sensor zenith angle q = 22.7°,
azimuth difference Df = 16.4°) and for tropospheric aerosols (model #10 of the lookup tables) at scene edge
(q0 = 60°, q = 53.4°, Df = 66°) are provided in Fig. 4a and
Eq. (4) holds true for all bands. It shows that the error
in the estimated water reflectance term in a certain band,
D(trw), comes from two sources: one is from the digitization round-off and readout noise error in this band, Drt,
and the other is from the errors in the aerosol reflectance
estimates, (ra ÿ rad), which can be estimated using bands
7 and 8.
Since rw for bands 7 and 8 is assumed zero, for bands 7
and 8 Eq. (4) becomes (Eqs. 5a and b)
ra …l7 † ˆ rda …l7 † ÿ Drt …l7 †;
…5a†
ra …l8 † ˆ rda …l8 † ÿ Drt …l8 †;
…5b†
where l7 (765 nm) and l8 (865 nm) are the wavelengths for
bands 7 and 8, respectively. For a certain band at lb, rad(lb)
can be estimated from rad(l7) and rad(l8), and ra(lb) can be
estimated from ra(l7) and ra(l8) in the following ways.
4.1. Single-scattering approximation
Assuming single scattering, i.e., ras  ra , we have
elb , l8  ra (lb )/ra (l8 ). Following Gordon and Wang
(1994a), for a certain aerosol type, to a good approximation
elb,l8 can also be written as elb,l8 = exp[c(l8 ÿ lb)] where c
is a constant independent of wavelength. Therefore we have
Fig. 4. FDCs of the errors in the trw estimates caused by digitization-noise
errors in the SeaWiFS bands. The single-scattering approximation was used
and the aerosol type defined in the SeaWiFS lookup tables was used to
yield e values free of digitization-noise errors. The actual e values vary with
digitization-noise errors. (a) Maritime aerosol at scene center; (b) tropospheric aerosol at scene edge.
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
b, respectively. There are a total of 10 000 data points used
in the simulations and the increments of the FDCs (horizontal axis of Fig. 4) are 0.00005. The figures show that
even with an error-free calibration, the sensor and algorithm
specifications (to estimate trw with uncertainties less than
‹ 5%, corresponding to ‹ 0.001 at 443 and 490 nm, and
‹ 0.0002 at 555 nm for oligotrophic waters) cannot always
be met, especially at 555 nm. Indeed, Fig. 4b indicates that
trw at 555 nm can vary as much as ‹ 0.0011 from its ``true''
value. For oligotrophic waters where the ``true'' value is
0.004 (Gordon & Wang, 1994a), the relative errors can be
as much as ‹ 27%. However, since SeaWiFS uses a more
sophisticated atmospheric-correction scheme than singlescattering approximations, the actual results are more complicated than shown here.
4.2. Multiple scattering (SeaWiFS)
As mentioned earlier, ra(lb) can be derived by calling a
routine of SeaDAS that uses ra(l7) and ra(l8) to determine
the aerosol type and optical thickness. rad(lb) can be
derived similarly with the routine, assuming random digitization-noise errors in rad(l7) and rad(l8). Here the ra terms
represent the reflectance caused by aerosol multiple-scattering and aerosol± Rayleigh interactions. Unlike the singlescattering method which assumes a fixed aerosol type (e
was allowed to vary with digitization-noise errors, though),
the aerosol type (represented by two aerosol models with
different weights) is determined from ra(l7) and ra(l8) and
can vary with digitization-noise perturbations in bands 7
and 8. The results typically vary with aerosol type, aerosol
optical thickness, and solar and viewing geometry, as
shown below.
243
related to changes in the aerosol type selection, which can
be explained by Fig. 1b. If the scheme chooses model #5 for
error-free ra(l7) and ra(l8), a slight perturbation in bands 7
and 8 will make the scheme choose model #9 or #6 to result
in a slightly smaller e, or choose model #4 to result in a
slightly larger e (recall that the aerosol type is a mixture of
two aerosol models with different weights). For example,
for the 1-DN change in bands 7 and 8 shown in Fig. 2a, the
two aerosol models and the weight between them also
change (Fig. 2b). Thus, the errors can be much larger than
using a fixed aerosol type. In contrast to model #5, model
#10 has a distinguishable e from others (Fig. 1b), and small
perturbations in bands 7 and 8 will less frequently cause the
scheme to choose another model (model #11. Note the
unsymmetrical FDCs caused by selection of model #11
for some of the negative errors). Therefore the errors in
Fig. 5b are less than those in Fig. 5a. Unlike the singlescattering approximation where e varies with perturbations
in bands 7 and 8, here e depends on the aerosol model only.
Therefore, if the digitization-noise in bands 7 and 8 does not
5. Results and discussion
For the same situations as in Fig. 4a and b (i.e., maritime
aerosol at scene center and tropospheric aerosol at scene
edge), assuming ta865 = 0.04 (compare: ta865 0.08 for
typical North Atlantic atmosphere), FDCs of the errors in
bands 2 (443 nm), 3 (490 nm), and 5 (555 nm) are presented
in Fig. 5a and b. Statistics of the results for the former case
(maritime aerosol at scene center) for the first five SeaWiFS
bands (412, 443, 490, 510, and 555 nm) are listed in Table
2. Similar to Gordon and Wang (1994a), 5% of trw was
assumed to be 0.001, 0.001, 0.001, 0.001, and 0.0002 for
the five bands, respectively.
Similar to the single-scattering results, the < ‹ 5%
requirement cannot always be met, particularly for the
555-nm band. Compared with Fig. 4, the results are
reversed, i.e., pixels with maritime aerosols tend to have
larger errors than those with tropospheric aerosols. Since
most of the time maritime aerosols prevail over the open
ocean, large relative errors are inevitable at some pixels due
to digitization-noise. The bimodal features in Fig. 5a are
Fig. 5. Same as for Fig. 4, but the SeaWiFS atmospheric-correction
scheme (Ding & Gordon, 1995; Gordon & Wang, 1994a) was used. The
aerosol labels shown in (a) and (b) are those if derived with signals free
of digitization-noise errors. The actual aerosol types may be different
because the scheme derives the aerosol type according to the signals in
bands 7 and 8, which contain digitization-noise errors. This is evidenced
by the bimodal features in (a). In (c), the aerosol type was fixed
regardless of the digitization-noise errors in bands 7 and 8. ta865 was
assumed 0.04 in the simulations.
244
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
Table 2
Statistics of D(trw) in the first five SeaWiFS bands caused by digitizationnoise errors
Band
Min
Max
Mean
s
< ‹ 5% (%)
1
2
3
4
5
ÿ 0.00173
ÿ 0.00156
ÿ 0.00130
ÿ 0.00112
ÿ 0.00097
0.00272
0.00237
0.00190
0.00169
0.00136
0.000108
0.000091
0.000061
0.000054
0.000030
0.00083
0.00075
0.00061
0.00056
0.00043
75.3
81.7
92.1
94.8
26.5
Maritime aerosol at scene center (ta865 = 0.04) was assumed and the
standard atmospheric-correction scheme of SeaWiFS (Ding & Gordon,
1995; Gordon & Wang, 1994a) was used in the simulations. FDCs of bands
2, 3, and 5 are shown in Fig. 5a.
change the aerosol type selection as for the positive errors in
Fig. 5b, e will remain the same and the errors propagated to
the visible bands will be smaller than those from the singlescattering approximations (compare: Fig. 5b vs. Fig. 4b).
Indeed, if we use the same simulation as in Fig. 5a, but force
the scheme to always choose model #5, the errors are much
smaller, as shown in Fig. 5c. This perhaps explains why the
speckling effects in the Coastal Zone Color Scanner (CZCS,
Hovis et al., 1980) ocean-color products are not as severe as
SeaWiFS Ð CZCS used a fixed maritime aerosol type to
effect a vicarious calibration for automated global processing (Evans & Gordon, 1994). This also suggests one way to
reduce the speckling errors in the data products, namely to
use a fixed aerosol type.
The errors in the water-reflectance estimates will propagate to other data products, such as chlorophyll concentrations (chl, mg/m3). These are estimated using the remote
sensing reflectance, Rrs (1/sr), which to a good approximation can be related to rw as Rrs  rw/(t0p), where t0 is the
diffuse transmittance from the sun to the location (pixel) of
interest (compare: t is from the pixel to the satellite sensor).
Knowing the solar zenith angle, t0 can be derived similarly
as done with t. Since the variations in both t0 and t are
negligible with regard to perturbations in bands 7 and 8, the
errors in Rrs can be estimated as DRrs  D(trw)/(tt0p) where
D(trw) is estimated using methods described above. Note
that these errors are ``absolute,'' i.e., independent of the
magnitude of Rrs. Therefore the relative errors will change
with Rrs.
Fig. 6. FDCs of chlorophyll estimates (mg/m3) obtained with the D(trw)
distributions (Fig. 5a and Table 2) and the mean Rrs data associated with
each chlorophyll concentration listed in Table 3. Statistics of these curves
are listed in Table 4.
To see how DRrs will affect the chl estimates, we pooled
some pixels with various chl concentrations estimated with
the OC2 algorithm (O'Reilly et al., 1998) from some
SeaWiFS imagery (Sargasso Sea for low concentrations
and Gulf of Mexico continental shelves for high concentrations), and averaged the spectral Rrs values associated with
each chl concentration. Table 3 lists the mean spectral Rrs
values together with the chl concentrations estimated with
the OC2 algorithm. These values will be used as baseline or
error-free values to compare with the chl concentrations
estimated with Rrs + DRrs to determine the errors in chl
estimates caused by the digitization-noise errors.
FDCs of chl estimates resulting from the digitizationnoise errors for each chl concentration listed in Table 3 are
presented in Fig. 6 for the case of maritime aerosols at the
scene center. ta865 was assumed to be 0.04 in the simulations. To show the distributions effectively in one figure, the
increments of the FDCs (horizontal axis) are adjusted for
each concentration. For example, the curve with the lowest
concentrations has increments of 0.002 mg/m3, and the
curve with the highest concentrations has 0.1 mg/m3. The
statistics of the results are listed in Table 4. The relative
errors (variances) are generally larger at very low and very
high concentrations than those at moderate concentrations.
This can be well explained by the Rrs values used in the
analysis (Table 3). Since the magnitude of DRrs is absolute,
the smaller the Rrs value, the larger the relative error. For
Number of pixels pooled
58
3313
903
496
16
Table 4
Statistics of distribution of chlorophyll concentrations (mg/m3, Fig. 6)
corresponding to the D(trw) errors in Fig. 5a and Table 2 at various
chlorophyll concentrations (Table 3)
Rrs(412) 103 (1/sr)
Rrs(443) 103 (1/sr)
Rrs(490) 103 (1/sr)
Rrs(510) 103 (1/sr)
Rrs(555) 103 (1/sr)
chl (OC2, mg/m3)
11.418
10.104
6.818
4.212
1.427
0.051
8.207
7.850
5.569
3.444
1.492
0.100
3.895
4.045
4.473
3.822
2.510
0.520
2.870
2.976
3.433
3.253
2.602
1.002
1.100
1.233
2.056
2.289
2.640
3.460
chl
Min
Max
Mean
s
< ‹ 35% (%)
0.051
0.100
0.520
1.002
3.460
0.018
0.055
0.434
0.852
2.262
0.091
0.153
0.594
1.240
5.978
0.051
0.101
0.519
0.999
3.491
0.013
0.017
0.025
0.057
0.586
84.2
97.1
100
100
97.3
Table 3
Mean remote sensing reflectance (Rrs) values pooled over the pixels with
various chlorophyll concentrations from some SeaWiFS imagery
Chlorophyll concentrations estimated with the mean Rrs values using
the OC2 algorithm (O'Reilly et al., 1998) are also listed.
The first column is regarded as the ``true'' values from the mean Rrs data
listed in Table 3. FDCs of the data are shown in Fig. 6.
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
245
Table 5
Similar to Table 2 but ta865 was set to 0.25 instead of 0.04 in the
simulations
Band
Min
Max
Mean
s
< ‹ 5% (%)
1
2
3
4
5
ÿ 0.00194
ÿ 0.00186
ÿ 0.00161
ÿ 0.00151
ÿ 0.00138
0.00335
0.00308
0.00256
0.00237
0.00184
0.000060
0.000041
ÿ 0.000015
ÿ 0.000030
ÿ 0.000062
0.00113
0.00105
0.00090
0.00085
0.00070
69.3
69.6
71.7
72.9
27.3
FDCs of bands 2, 3, and 5 are shown in Fig. 8a.
Fig. 7. Pixelization observed for adjacent data points from the simulations.
Twenty data points from Figs. 5a and 6 are displayed along a line.
example, mean Rrs555 = 0.001427 sr ÿ 1 at chl = 0.051 mg/
m3, and mean Rrs490 = 0.002056 sr ÿ 1 at chl = 3.46 mg/m3.
Therefore, small DRrs will cause larger relative errors in the
chl estimates since chl is a function of the Rrs ratio between
these two bands in the OC2 algorithm.
Results in Fig. 6 for high pigment concentrations can
generally not be applied globally. Typically, at chl>3 mg/m3
the water is likely to be Case II, particularly in coastal
environments. The baseline Rrs values used in our simulations are the mean values averaged over many pixels (Table
3). The actual Rrs spectra can be different than listed in Table
3. In Gelbstoff-dominated Case II waters, with high absorption in the blue, relative Rrs errors can be larger in the blue,
causing higher variations in the data products than shown in
Fig. 6 and Table 4. For the same reason, in suspended-
sediment dominated Case II waters, due to the high backscattering, relative Rrs errors are smaller. Therefore, the
variations in the data products can be smaller. However,
for low-chlorophyll waters (e.g., the Sargasso Sea), since Rrs
in band 5 (555 nm) is constantly low ( 0.0015), high
variations from pixel to pixel are inevitable. Indeed, if we
choose 20 data points from the simulation results and
display D(trw) in band 5 and chlorophyll estimates for the
low concentrations along a line, Fig. 7 can be obtained.
Chlorophyll varies two- to threefold from 0.023 to 0.08 mg/
m3 around the true value of 0.05 mg/m3, and severe
speckling features are apparent. For this type of water
rw 0.004 in band 5 (Gordon & Wang, 1994a), resulting
in relative errors in rw that vary from ÿ 20% to 20%.
The errors shown in Figs. 5 and 6 will generally vary
with solar and viewing geometry, aerosol type, and aerosol
optical thickness. We have performed similar simulations
for various situations and found that the errors in trw
generally (1) increase with increasing solar zenith angle
and increasing aerosol optical thickness; (2) are larger for
spectrally flat aerosol types (i.e., e 1 as for aerosol models
#5 and #6) than for other aerosol types (e.g., aerosol model
#10); and (3) depend weakly on the location within the
scene. Aerosol types with e close to 1 are more sensitive to
digitization-noise errors in bands 7 and 8, resulting in an
erroneous aerosol type being chosen, extrapolating to larger
errors in the visible bands (compare: Fig. 5a and b). Since ra
in the visible is extrapolated from ra(865) (equivalent to
ta865 for a given aerosol type) according to the spectral
shape defined by e (Fig. 1a), digitization-noise for larger
ta865 will likely yield larger errors in the ra estimates in the
visible, thus larger errors in the data products. For example,
if we set ta865 = 0.25 and perform the same simulations as
for Figs. 5a and 6 where ta865 was assumed 0.04, larger
Table 6
Similar to Table 4, but ta865 was set to 0.25 instead of 0.04 in the
simulations
Fig. 8. Similar to Figs. 5a and 6, but ta865 was set to 0.25 instead of 0.04 in
the simulations. The bimodal features are due to the selection of two aerosol
models by the atmospheric-correction scheme. Statistics of the data are
listed in Tables 5 and 6 for (a) and (b), respectively.
chl
Min
Max
Mean
s
< ‹ 35% (%)
0.051
0.100
0.520
1.002
3.460
0.004
0.034
0.388
0.809
2.034
0.114
0.184
0.614
1.224
7.170
0.048
0.096
0.510
0.988
3.598
0.023
0.030
0.037
0.060
0.761
54.7
68.2
100
100
88.5
FDCs of the data are shown in Fig. 8b.
246
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
Fig. 9. Similar to Figs. 5a and 6, but band 6 (670 nm) instead of band 7 was
used in the simulations. ta865 was assumed to be 0.04.
errors are obtained, as shown in Fig. 8 and Tables 5 and 6
for D(trw) and chl estimates.
The above results show that the estimated ocean color
data, either rw, Rrs, or chl, are correct only as statistical
aggregates (e.g., the average values) given an error-free
calibration. For any particular pixel, the errors can be
larger than the specified mission goals (D(trw) < ‹ 5%,
Dchl < ‹ 35%). This is particularly true at 555 nm for
oligotrophic waters (chl < 0.25 mg/m3) and at 412 and
443 nm for highly productive waters and Gelbstoff-dominated Case II waters. Over adjacent pixels, the variations
can reach 40% for rw and Rrs, and two- to threefold for chl
(Fig. 7).
The errors are mainly due to anomalies propagated
into the atmospheric-correction scheme, which determines
the aerosol type and optical thickness from pixel to pixel.
However, even with an error-free atmospheric correction
that chooses the same aerosol type regardless of the
errors in bands 7 and 8, the relative errors in rw555
can still be larger than ‹ 5% for oligotrophic waters where
rw555 0.004 (Gordon & Wang, 1994a). For turbid waters
where rw412 is small, the relative errors in this band can
also be larger than ‹ 5%. The errors in the visible bands
tend to have the same sign because of the same aerosol
extrapolation used in the atmospheric correction, therefore
band-ratio algorithms may reduce the errors in the chl
estimates. Thus, using a fixed aerosol type, the ‹ 35%
requirement can typically be met assuming the correct
aerosol type is used. The difficulty in this approach is that
the aerosol type must be known a priori. Although in
principle the aerosol type for an area can be pooled to
select the one with the highest frequency of occurrence,
and the data can then be reprocessed using this fixed
aerosol type, in practice this is often difficult to achieve
because of the reprocessing time involved.
Hu et al. (2000) have shown that use of band 6 instead of
band 7 in the atmospheric-correction procedure can reduce
errors caused by perturbations of the total signal by either
high-altitude aerosol, cirrus clouds, or even digitization
errors. Indeed, if we use bands 6 and 8 in our simulations,
the errors in trw and chl estimates are reduced significantly.
For the case of maritime aerosols at scene center with
ta865 = 0.04, results are shown in Fig. 9a and b for D(trw)
and chl, respectively. The errors for all data products are
much smaller than those using bands 7 and 8 in the atmospheric correction, and the FDCs are much tighter, indicating less pixelization or speckling. However, this scheme
requires that rw in band 6 must be known a priori, which is
often difficult even for moderate colored waters (chl>0.25
mg/m3) unless an iterative approach (e.g., Siegel, Wang,
Maritorena, & Robinson, 2000) is implemented.
Another way to reduce the pixelization effects is to
smooth the data in bands 7 and 8 before use of the atmospheric correction. This will reduce the chance to select an
incorrect aerosol type. For the case of maritime aerosols at
scene center with ta865 = 0.04, results from a 3 3 smoothing of bands 7 and 8 data in the simulations are shown in
Fig. 10a and b for D(trw) and chl, respectively. Compared
Fig. 10. Similar to Figs. 5a and 6, but bands 7 and 8 data were smoothed
by 3 3 before use in the atmospheric correction. ta865 was assumed to
be 0.04.
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
with the curves in Figs. 5a and 6, the errors are significantly
reduced. Indeed, chl distributions are all within the ‹ 35%
limit. Except for band 5 where trw is small, more than 99%
of the data points have relative trw errors within ‹ 5%. This
procedure should be used with caution, though, since the
aerosol type and thickness may change quickly around
atmospheric frontal zones, and a 3 3 smoothing will cause
more data points to be discarded around cloud edges.
The mean errors of the simulation results are not significantly different from zero for trw and chl, implying that
if the data products are averaged or ``binned,'' either
spatially or temporally (e.g., weekly mean), the results are
not significantly biased at least for high-resolution data
(e.g., 1 km2 per pixel). However, the implications from
our simulation results are very important for data validation
purposes Ð use of in situ data to validate the satellite
estimates. For any pixel, the errors in the data products (rw
or chl) can be much larger than the sensor specifications,
making it necessary to average several surrounding pixels to
reduce the error in comparison with the in situ data. For
example, if we smooth the D(trw) data by 3 3, except for
band 5 more than 99% of the data points have D(trw) within
‹ 5%. Chl estimated using the smoothed D(trw) data generally have errors < ‹ 35% (probability >99.9%). Similarly,
the 3 3 smoothing can be used on the chl data products.
However, this smoothing technique can generally not be
used when inhomogeneous water surfaces are encountered,
otherwise the features will be smeared. This is likely to
occur in bloom or shelf waters.
The SeaWiFS data processing has been updated several
times since launch, as for both calibration and algorithm
improvements (whitecaps estimates, biooptical algorithms,
atmospheric-correction options, etc.). The updated software
package (SeaDAS version 4, released in May 2000) has
several options for atmospheric correction and biooptical
algorithm, including an iterative approach to account for
the nonzero water-leaving radiance (Lw) in the atmospheric
correction bands in the NIR (Siegel et al., 2000), an
atmospheric correction using bands 6 and 8 instead of
bands 7 and 8, an atmospheric correction using fixed
aerosol type, and an updated biooptical algorithm (OC4
version 4, O'Reilly et al., 2000). Although our simulations
were based on an earlier version of SeaDAS (version 3.3)
that assumed Lw(NIR) = 0 in the atmospheric correction
and used OC2 algorithm for chlorophyll products, the new
iterative approach and OC4 algorithm will unlikely alter
the results shown here. For example, for a SeaWiFS scene
collected on 15 September 2000 over the Sargasso Sea
(20°N±36°N, 62°W ± 57°W) where the mean chlorophyll
concentration was estimated as 0.07 mg/m3 and mean
ta865 was estimated as 0.1, FDCs of the normalized
water-leaving radiance (nLw,  (rwF0)/(pt0), Gordon &
Wang, 1994a) in band 5 (555 nm) estimated with the
Lw(NIR) = 0 assumption and with the Lw(NIR) iteration are
presented in Fig. 11. Note that for this type of water, nLw
for the CZCS band at 550 nm is measured as 0.28 mW
247
Fig. 11. FDCs of normalized water-leaving radiance (nLw, mW cm ÿ 2
mm ÿ 1 sr ÿ 1) in band 5 (555 nm) of a Sargasso scene collected on 15
September 2000. The increments of the FDCs (horizontal axis) are 0.001.
cm ÿ 2 mm ÿ 1 sr ÿ 1 (Gordon & Clark, 1981), and for the
SeaWiFS band at 555 nm is measured as 0.26 mW cm ÿ 2
mm ÿ 1 sr ÿ 1 (McClain et al., 1998). The median and mode
values from the two methods (Fig. 11) are close to these
values. Except for a small horizontal shift, the results from
the two methods are nearly identical. Of the 440,000
valid pixels (all suspicious pixels are discarded according
to the quality control flags), only 20% of the pixels
meet the ‹ 5% error requirement, which agrees with our
simulations ( 27%, Table 2). Similarly, OC2 and OC4
algorithms yield nearly identical results for this scene. For
turbid waters, although the iterative approach will improve
the Lw estimates by taking account of the nonzero
Lw(NIR), Fig. 11 implies that the approach is not sensitive
enough to reduce the digitization-noise caused errors. For
the same reason, OC4 will unlikely perform better than
OC2 in terms of reducing this type of errors.
The Moderate Resolution Imaging Spectroradiometer
(MODIS, Salomonson et al., 1989) was launched in
December 1999 and has been put in operational mode in
spring 2000. It has more digitization bits (12 vs. 10 of
SeaWiFS) and much higher radiometric sensitivity, which
implies smaller D terms in Eq. (6). MODIS will use the
same atmospheric-correction scheme as for SeaWiFS;
therefore the speckling effects will hopefully be reduced.
If the sensitivity is twice as high as that of SeaWiFS, the
FDCs in the above figures will be at least twice as
narrower, resulting in less pixelization or speckling. We
plan to evaluate the pixelization effects of MODIS data in
the near future.
6. Concluding remarks
Through simulations we have shown that even with an
error-free calibration, the SeaWiFS mission goal of estimating water reflectance to within ‹ 5% and chlorophyll con-
248
C. Hu et al. / Remote Sensing of Environment 76 (2000) 239±249
centrations to within ‹ 35% cannot always be met for any
individual pixel. A major portion of the error comes from
the digitization-noise errors in the atmospheric-correction
bands (bands 7 and 8), which will propagate to the data
products through the atmospheric-correction process. This
can be clearly explained by Eq. (6). Indeed, as a simplification of the sophisticated atmospheric-correction algorithm
of SeaWiFS, the single-scattering approximations in Eq. (6)
can be used conceptually to understand the errors in the data
products caused by any perturbations in the total signal, by
either digitization round-off, readout noise, or even calibration errors. Unlike calibration errors that provide incorrect,
but constant calibration gains or offsets within the image,
digitization-noise errors are randomly distributed and can
result in errors in the final products with both signs.
The traditional CZCS processing scheme applies one
Angstrom exponent (related to aerosol type) derived from
a clear-water area to the whole scene (Gordon et al., 1983).
This scheme, as noted by many researchers, suffers from the
variations of the Angstrom-exponent across the scene. For
example, Andre and Morel (1991) concluded that ``Natural
(or artificial) variations in the Angstrom exponent cannot be
ignored and the use of a mean value for this exponent must
be avoided as far as possible (over Case I waters). Therefore
the pixel-by-pixel procedure, which does not require such
averaging, is recommended.'' However, with the pixel-bypixel scheme, image pixelization caused by digitizationnoise errors has been shown inevitable, even with the
improved digitization-bits and sensitivity on SeaWiFS.
The simulation results show that for typical atmospheric
conditions (maritime aerorols), at a particular pixel the
errors in the data products can be as large as ‹ 35% and
‹ 65% for reflectances and chlorophyll concentrations for
oligotrophic waters, respectively. Therefore the chlorophyll
values for adjacent pixels can vary by 2 ±3 fold, causing
pixelization or speckling. This suggests that when using in
situ data to validate the satellite data products over homogenous water surfaces, surrounding pixels should be averaged to reduce the errors caused by readout noise and
digitization round-off.
The pixelization errors typically increase with increasing
solar zenith angle and increasing aerosol optical thickness.
They are larger for spectrally flat aerosol types (i.e., maritime aerosols) than for other aerosol types (e.g., tropospheric aerosols). Since most of the time maritime aerosols
prevail over the open ocean, the pixelization errors are
inevitable with the current SeaWiFS algorithms.
The results shown here are for ideal conditions, i.e.,
error-free calibration, homogenous water surface and atmosphere, and no whitecap or sun glitter. An erroneous
calibration will yield erroneous data products, but not
pixelization because the error terms in Eq. (6) remain
virtually unchanged from pixel to pixel. However, when
inhomogeneous water surface or atmosphere is encountered as for bloom water, shelf water, waters with severe
whitecaps, cirrus clouds in the atmosphere, or atmospheric
frontal zones, the pixelization effects may get worse
because of the patchiness nature under those circumstances. This is clearly evidenced in Fig. 11 where the
relative standard deviation (0.1/0.28 36%) is much larger
than that from the simulation ( 15%), and where the nLw
values cover a wider range.
There are several ways to reduce the digitization-noise
caused errors. One approach requires some assumptions
on either aerosol type or water-leaving radiance in band 6.
The approach is available in the updated data processing
software package (SeaDAS version 4). It is difficult,
however, to know the aerosol type or water-leaving
radiance in band 6 a priori, particularly for turbid waters.
Therefore a 3 3 smoothing of bands 7 and 8 before
atmospheric correction seems promising in reducing the
errors to within the SeaWiFS mission goals. The scheme
should be used with caution, though, over cloud edges.
Since the errors are caused by digitization round-off and
noise, the ultimate way to reduce the errors is the
reduction of both of these, which will be available
for MODIS.
Acknowledgments
This work was supported by NASA's Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) investigation number
NAS5-97128 to Frank Muller-Karger and NAS5-31716
to Kendall Carder. We thank the two anonymous reviewers
for their comments and suggestions. We thank the SeaDAS
development group (GSFC, NASA) for providing the
codes. Doug Myhre assisted the management and processing of the SeaWiFS data at the USF HRPT station.
SeaWiFS data are property of Orbimage Corporation, and
their use here is in accordance with the SeaWiFS Research
Data Use Terms and Conditions Agreement of the NASA
SeaWiFS Project.
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