and K. G. Ruddick
CNRS, UMR 8187, Universit´e Lille Nord de France, ULCO, LOG, F-62930 Wimereux,
Management Unit of the North Sea Mathematical Models (MUMM), Royal Belgian Institute
Spectral relationships, reﬂecting the spectral dependence of
), can be easily implemented in current AC
) retrievals where the algorithms
prove the MUMM (Ruddick et al., 2006, Limnol. Oceanogr. 51, 1167-1179)
and standard NASA (Bailey et al., 2010, Opt. Express 18, 7521-7527) near
infra-red (NIR) modeling schemes included in the AC algorithm to account
) and simulated
are investigated: (1) the standard NASA NIR-modeling scheme is forced
with bounding relationships in the red spectral domain and with a NIR
polynomial relationship and, (2) the constant NIR
MUMM NIR-modeling scheme is replaced by a NIR polynomial spectral
relationship. Results suggest that the standard NASA NIR-modeling scheme
performs better for all turbidity ranges and in particular in the blue spectral
domain (percentage bias decreased by approximately 50%) when it is
forced with the red and NIR spectral relationships. However, with these
new constrains, more reﬂectance spectra are ﬂagged due to non-physical
Chlorophyll-a concentration estimations. The new polynomial-based
MUMM NIR-modeling scheme yielded lower
) retrieval errors and
NIR relationship signiﬁcantly increased the sensitivity of the algorithm to
errors on the selected aerosol model from nearby clear water pixels.
© 2013 Optical Society of America
(010.4450) Oceanic optics; (010.1690) Color.
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#193504 - $15.00 USD
Received 8 Jul 2013; revised 12 Aug 2013; accepted 13 Aug 2013; published 3 Sep 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021176 | OPTICS EXPRESS 21176
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The marine reﬂectance
the inherent optical properties of the water (e.g., sea water absorption a
) and backscattering
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021176 | OPTICS EXPRESS 21177
radiance at the top of the atmosphere (TOA) used to obtain
among others, the removal of the atmospheric contribution, the so-called atmospheric correc-
tion (AC) .
Initially, it was assumed that sea water absorbs all the incident light in the NIR spectral region
(referred to as the black pixel assumption) allowing to estimate the atmospheric contributions
and to select the appropriate aerosol model from the total signal. Next, the aerosol properties are
extrapolated from the NIR to the visible spectral domain to obtain
)  (referred to as the
the aerosol contributions and subsequently to an underestimation of
or turbid waters . Numerous algorithms have been developed with alternative hypotheses or
including NIR-modeling schemes to account for the NIR ocean contribution to the measured
signal [2–6]. However, global evaluations of these algorithms concluded that improvement is
still required, especially in optically complex waters [7, 8].
In a previous study, Goyens et al.  concluded, based on a validation of MODIS-Aqua im-
ages processed with four commonly used AC algorithms [4, 5, 9, 10], that the standard NASA
GW94-based AC algorithm, which includes a NIR-modeling scheme to retrieve
in water masses optically dominated by detrital and mineral material, the GW94-based AC al-
gorithm assuming a NIR similarity spectrum to account for non-zero
referred to as the MUMM algorithm) performed slightly better. The NIR-modeling scheme
used in the STD algorithm is based on an iterative procedure including a bio-optical model
with a Chlorophyll-a (Chl
) based relationship to estimate a
(667) and assumptions on b
the GW94 AC algorithm is extended to turbid waters by considering spatial homogeneity in
the aerosol properties over the area of interest and approximating the NIR
) ratio by a
fections in the AC. For instance, in waters optically dominated by non-algal particles, the Chl
based relationship used in the bio-optical model of the STD algorithm may not be appropri-
ate resulting in imperfections in the retrieved backscattering coefﬁcients and subsequently in
the assumption that the NIR reﬂectance spectral shape is merely determined by the pure water
absorption [4, 6]. However, this assumption is not veriﬁed for all turbidity ranges and is valid
for a limited spectral range [4, 11, 12].
An alternative to improve the STD algorithm is to constrain the iterative NIR-modeling
scheme with spectral relationships. Similarly, a NIR spectral relationship may be used to cor-
rect the MUMM algorithm when the constant NIR reﬂectance ratio is not valid. Similar ap-
proaches have already been applied in several studies [12–18]. However, as observed by Goyens
et al. , most spectral relationships appeared to be only valid for a certain range of turbidity.
Nonetheless, the authors concluded that the bounding red spectral relationships, suggested by
Lee et al.  to correct
(667) according to
(555) in the Quasi-Analytical Algorithm,
and that the NIR polynomial relationship, suggested by Wang et al.  to extent the GW94
AC algorithm to the turbid western Paciﬁc region for the processing of the GOCI ocean color
images, were globally valid and potentially useful to improve satellite
The objective of this study is to evaluate if the STD and MUMM algorithms can be improved
by forcing the NIR-modeling schemes in both algorithms with these spectral relationships. Two
modiﬁed NIR-modeling schemes are evaluated: (1) a modiﬁed MUMM NIR modeling scheme
where the NIR constant
) ratio is replaced by the polynomial NIR spectral relationship,
Received 8 Jul 2013; revised 12 Aug 2013; accepted 13 Aug 2013; published 3 Sep 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021176 | OPTICS EXPRESS 21178
relationships suggested by Lee et al.  and the NIR polynomial relationship  to evaluate
(748). Hence two original algorithms are taken into account (i.e., MUMM and
STD algorithms) and different modiﬁcations are applied to each algorithm.
The evaluation is based on a sensitivity test including in situ
and Southern Atlantic coastal waters. Data and methods are outlined in section 2. To evaluate
the degree of improvement, initial algorithms are compared with modiﬁed algorithms, brieﬂy
discussed in sections 2.2 and 2.3, respectively. The performances of the initial algorithms are
evaluated for moderately and very turbid waters (section 3.1) and compared to the modiﬁed
algorithms evaluated and discussed in section 3.2.
The top of atmosphere (TOA) reﬂectance,
ance and corrected for gas absorption, Rayleigh scattering, white-caps reﬂection and sun glint,
to obtain the Rayleigh corrected reﬂectance,
pling between both air and aerosol molecules, respectively. t
of the atmosphere along the viewing direction and t
) is the diffuse transmittance of the
atmosphere along the incident direction. According to Eq. (1), if the optical properties and the
concentrations of the aerosols are known, the quantities
) and t
can be estimated and subsequently the above water
notation is dropped hereafter.
For the present research a simulated dataset of
) is build by combining the 105 in situ
in the companion paper of this study ) with a simpliﬁed power law model for the multiple-
scattering aerosol reﬂectance,
being the ˚
atmospheric diffuse transmittances, t
), to 1 and simulate
). As shown by the ﬂowchart in Fig. 1,
inverted using either the STD or the MUMM algorithm to estimate
model would be equal to the in situ
For the sensitivity study two coastal models are selected, considered as the dominating
aerosol types in coastal regions and derived from the work of Shettle and Fenn  and in-
troduced by Gordon and Wang  with 50 and 90% relative humidity (hereafter referred to
as C50 and C90). The corresponding ˚
are set equal to 0.75 and 0.43,
The initial and modiﬁed algorithms are evaluated and compared based on the median per-
centage bias between the estimated and in situ
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021176 | OPTICS EXPRESS 21179
(869) values between 10
and superior to 3
, which is approximately the upper limit
53% present moderate turbidity with
(869) ranging from 10
and 47% of the
(869) exceeding 3.10
. This latter value corresponds
NIR-SWIR GW94-based AC process. Among the very turbid waters, extremely turbid waters
are also investigated. These are water masses presenting
(869) values superior to 10
The NIR-modeling scheme within the STD algorithm, initially developed by Stumpf et al. 
and later revised by Bailey et al. , uses an iterative method including a bio-optical model to
account for the water contribution in the NIR region of the spectrum. The STD algorithm can
be resumed as follows: First the algorithm uses the GW94 AC algorithm, assuming the black
pixel assumption, to obtain a ﬁrst guess in
) estimations are then
concentrations (MODIS Chl-a OC3 algorithm , assumption 1 in Fig.
1), which in turn serves to retrieve particulate and CDOM absorption in the red  (assump-
tion 2 in Fig. 1), a
(667). Knowing a
) and below water
) (by converting the
estimated above water
(667) to below water radiance reﬂectance ) it is possible to deter-
mine the red particulate backscattering coefﬁcient, b
). Next, b
) is approximated
by a power-law function of wavelength  (assumption 3 in Fig. 1). As, in the NIR region
of the spectrum, absorption by CDOM, phytoplankton-related pigments, and other suspended
particulate matter is assumed to be negligible, a
) can be approximated by the pure water
). Accordingly, knowing a(
) and b
), below water
be estimated  and converted in above water
) is removed from
and the newly estimated
is exceeded. In this study, when the estimated Chl
is non-physical (e.g., because the retrieved
) is set to 0 and Chl
to 10 mg l
for the next iteration. If the AC failure
The MUMM algorithm includes two alternative assumptions, one on the atmosphere (assump-
tion 1 in Fig. 1) and one on the water optical properties, the NIR similarity spectrum assumption
(assumption 2 in Fig. 1) [4,6]. The ﬁrst assumption is based on the fact that the atmosphere com-
position does not vary signiﬁcantly in space and time and therefore the ˚
Angstr¨om coefﬁcient for
the aerosol reﬂectance,
, can be considered as spatially homogeneous over the area of interest.
) in the NIR region of the spectrum is close to zero,
) and, subsequently,
can be retrieved. The clear water retrieved
is then used for the AC of the entire image.
spectral domain is largely determined by pure water absorption, and hence invariant. The mag-
nitude of the signal is approximately proportional to the backscatter coefﬁcient. Consequently,
the ratio of any two NIR water leaving reﬂectances,
), is constant. For MODIS-Aqua
#193504 - $15.00 USD
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021176 | OPTICS EXPRESS 21180
), respectively, and
designate the two wavelengths in the NIR spectral region. Dashed lines indicate the
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021176 | OPTICS EXPRESS 21181
(748,869) is deﬁned as:
the appropriate aerosol model.
As shown in Fig. 1, the MUMM algorithm requires thus an a priori deﬁned
. For the sen-
is initially assumed. Next, to assess the sensitivity of the
value corresponding to the
) (error on
∼ −40%) and vice versa (error on
The MUMM algorithm is modiﬁed here to take into account also extremely turbid waters.
Indeed, the validation exercise conducted by Goyens et al.  showed that the validity range
of the constant NIR reﬂectance ratio [4, 6] was limited to moderately and very turbid waters
) < 10
, while the polynomial function of Wang et al.  was also valid for
) retrievals in extremely turbid
replaced by the polynomial function of Wang et al.  (therefore referred to as the polynomial-
based MUMM algorithm). This includes some modiﬁcations in the initial algorithm. Using Eq.
(1) and the polynomial function from Wang et al. , the following relationships and unknown
quantities are obtained:
(748) + b
incident atmospheric transmittance corrected for the two-way ozone and oxygen absorption
using the terminology of Ruddick et al. .
Provided that the aerosol model is correctly retrieved, the atmospheric correction parameter
(748,869) (written hereafter as
for notational simplicity) is equal to the aerosol reﬂectance
ratio at 748 and 869 nm and thus, according to Eq. (2), related to
Eq. (8) can then be rewritten as:
(748) + at
(748) + bt
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.021176 | OPTICS EXPRESS 21182
(748) + [
and incident geometry and selected aerosol model. Hence, the remaining unknown quantity
physical. Accordingly, the unique solution for
(869) can be retrieved by evaluating the polynomial function
of Wang et al.  and, by means of Eqs. (1) and (2),
) can be retrieved for the entire
modeling scheme within the STD algorithm (therefore referred to as the constrained-STD al-
gorithm). The red spectral relationships are already used as bounding relationships in the last
updated version of the Quasi Analytical Algorithm (QAA v5) to correct imperfections in the
(667) . Similarly to the polynomial relationship suggested by Wang et al. ,
these red spectral relationships have been validated previously by Goyens et al.  with the
are implemented within the iterative process as follows: If within the iterative process, the pre-
(555) is non-negative and
(667) is out of limit according the bounding
red spectral relationships,
(667) is corrected and set equal to the closest limit. Next, the NIR
spectral polynomial relationship  is used to retrieve
(869) from the estimated
avoiding imperfections due to the extrapolation of b