Optical closure in highly absorptive coastal waters: significance of inelastic scattering processes

Abstract

In hydrological optics, “optical closure” means consistency between the apparent optical properties (AOPs) determined from radiometric measurements and those derived from radiative transfer modelling based on concurrently measured inherent optical properties (IOPs) and boundary conditions (sea and sky states). Good optical closure not only provides confidence in the data quality but also informs on the adequacy of the radiative transfer parameterization. Achieving optical closure in highly absorptive coastal waters is challenging due to the low signal-to-noise ratio of radiometric measurements and uncertainties in the measurements of IOPs, namely the spectral absorption and backscattering coefficients. Here, we present an optical closure assessment using a comprehensive set of in situ IOPs acquired in highly absorptive coastal waters optically dominated by chromophoric dissolved organic matter (CDOM). The spectral remote sensing reflectance, Rrs(λ), was modeled using the software HydroLight (HL) with measured IOPs and observed boundary conditions. Corresponding in-water in situ Rrs(λ) was derived from radiometric measurements made with a Compact Optical Profiling System (C-OPS; Biospherical). The assessment revealed that the inclusion of inelastic scattering processes in the model, specifically sun-induced CDOM fluorescence (fDOM) and sun-induced chlorophyll fluorescence (SICF) from Chlorophyll-a ([chl]), significantly improved the optical closure and led to good agreement between measured and modeled Rrs (i.e., for 440 ≤ λ ≤ 710 nm with no inelastic processes: R²=0.90, slope=0.64; with inelastic processes: R²=0.96, slope=0.90). The analysis also indicated that fDOM and SICF contributed a substantial fraction of the green-red wavelength Rrs in these waters. Specifically, fDOM contributed ∼18% of the modeled Rrs in the green region and SICF accounted for ∼20% of the modeled Rrs in the red region. Overall, this study points out the importance of accounting for fDOM in remote sensing applications in CDOM-dominated waters.

Full text

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35178
Optical closure in highly absorptive coastal
waters: significance of inelastic scattering
processes
SOHAM MUKHERJEE,1,2,* JOHN D. HEDLEY,3CÉDRIC G. FICHOT,4
JULIEN LALIBERTÉ,5AND SIMON BÉLANGER1,2
1Département de Biologie, Chimie et Géographie, Université du Québec à Rimouski, Rimouski 300 Allée
des Ursulines, Rimouski, QC G5L 3A1, Canada
2
Québec-Océan: Groupe interinstitutionnel de recherches océanographiques du Québec, Québec, QC G1V
0A6, Canada
3Numerical Optics Ltd., Belmont House, 19 West Street, Witheridge, Tiverton, Devon, EX16 8AA, UK
4Boston University, 675 Commonwealth Avenue, Boston, MA 02215, USA
5
Fisheries and Oceans Canada, Maurice-Lamontagne Institute, 850 route de la Mer, Mont-Joli, QC, G5H
3Z4, Canada
*saion523@gmail.com
Abstract:
In hydrological optics, “optical closure” means consistency between the apparent
optical properties (AOPs) determined from radiometric measurements and those derived from
radiative transfer modelling based on concurrently measured inherent optical properties (IOPs)
and boundary conditions (sea and sky states). Good optical closure not only provides confidence
in the data quality but also informs on the adequacy of the radiative transfer parameterization.
Achieving optical closure in highly absorptive coastal waters is challenging due to the low
signal-to-noise ratio of radiometric measurements and uncertainties in the measurements of
IOPs, namely the spectral absorption and backscattering coefficients. Here, we present an optical
closure assessment using a comprehensive set of in situ IOPs acquired in highly absorptive coastal
waters optically dominated by chromophoric dissolved organic matter (CDOM). The spectral
remote sensing reflectance, R
rs
(
λ
), was modeled using the software HydroLight (HL) with
measured IOPs and observed boundary conditions. Corresponding in-water in situ R
rs
(
λ
) was
derived from radiometric measurements made with a Compact Optical Profiling System (C-OPS;
Biospherical). The assessment revealed that the inclusion of inelastic scattering processes in
the model, specifically sun-induced CDOM fluorescence (f
DOM
) and sun-induced chlorophyll
fluorescence (SICF) from Chlorophyll-a ([chl]), significantly improved the optical closure and
led to good agreement between measured and modeled R
rs
(i.e., for 440
≤λ≤
710 nm with no
inelastic processes: R2=0.90, slope=0.64; with inelastic processes: R2=0.96, slope=0.90). The
analysis also indicated that f
DOM
and SICF contributed a substantial fraction of the green-red
wavelength R
rs
in these waters. Specifically, f
DOM
contributed
∼
18% of the modeled R
rs
in
the green region and SICF accounted for
∼
20% of the modeled R
rs
in the red region. Overall,
this study points out the importance of accounting for f
DOM
in remote sensing applications in
CDOM-dominated waters.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Sunlight propagating into the oceanic water column is absorbed and scattered by pure water
and optically significant constituents (OSCs), resulting in changes in the underwater light field
as a function of depth. OSCs are characterized in terms of Inherent Optical Properties (IOPs),
namely the coefficients of spectral absorption a
(λ)
[m
−1
], backscattering b
b(λ)
[m
−1
] and beam
attenuation c
(λ)=
a
(λ)+
b
(λ)
[m
−1
] (where
λ
is wavelength and bis total scattering). These
IOPs depend on the biogeochemical composition of the OSCs [1]. Along with IOPs, viewing
#501732 https://doi.org/10.1364/OE.501732
Journal © 2023 Received 28 Jul 2023; revised 31 Aug 2023; accepted 11 Sep 2023; published 4 Oct 2023

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35179
geometry and boundary conditions also determine the radiance distribution of the underwater
light field (Apparent Optical Property; AOP) [2,3]. In Ocean Colour Remote Sensing (OCRS),
the main AOP of interest is the Remote Sensing reflectance (R
rs
, sr
−1
), defined as the ratio
of upwelling water-leaving radiance (L
u
) and downwelling irradiance (E
d
) just above the sea
surface [3]. A radiative transfer model (RTM) can be used to estimate the AOPs in the water
column based on the measured total (bulk) IOPs or by using IOPs constructed as the sum of the
individual mass-normalized IOPs for each OSC, multiplied by their corresponding concentrations
[3]. Conversely, in applied remote sensing, an ‘inversion’ of a radiative transfer model is often
performed with the aim of retrieving IOPs or OSCs from measured R
rs(λ)
spectra [4]. Prior
to attempting this inversion, it is a good practice to check the consistency of in situ IOP and
AOP measurements to assess the degree of uncertainty in the measurements and the model, and
also to build confidence in the analysis. One approach to do this is to use vertical profile data;
where in situ water-column profiles of IOPs are input to the model, with appropriate boundary
conditions, to estimate AOPs. These are then compared to AOPs determined from radiometric
measurements from the independent deployment of radiometer(s) in close space-time proximity
to the acquisition of in situ IOP profiles. This consistency check between in situ IOPs and AOPs
is referred to as testing for “optical closure” [3,5,6]. The degree of optical closure under different
conditions can give insight regarding underlying assumptions in the model, e.g., the shape of the
volume scattering function or the significance of inelastic processes, [7]. However, great care
must be taken in the interpretation since closure is also dependent on the accuracy of the IOP and
AOP measurements.
One application of optical closure is to assess the data corrections that must be applied to
IOPs obtained from in situ instruments. For example, Lefering et al. [8] showed that inadequate
scattering corrections of flow-tube AC (absorption - attenuation meter) data can lead up to
∼
30% error in the simulated R
rs
. Commercially available in situ instruments for IOPs mainly
include, among others, the WETLabs AC-S or AC-9, which use a flow-tube design for a
(λ)
and
c
(λ)
, and the HOBILabs Hydroscat-6 or WETLabs BB-9 for the volume scattering function
(VSF) - these measure at a fixed angle in the backward direction allowing an estimation of
the b
b(λ)
following various assumptions. For estimation of non-water absorption, there are
also Integrating Cavity Absorption Meters (ICAM), such as Point-Source ICAM (PSICAM) for
discrete samples [9] or HOBILabs A-Sphere for in situ vertical profiles [10]. Unlike flow-tube
designs, spherical-cavity ICAM instruments allow absorption measurements with potentially
minimal errors from scattering losses [11], but to date, they have not been commonly used in
optical closure experiments.
Recent research using optical closure showed a significant discrepancy of modelled R
rs
at green
maxima wavelengths (
∼
555 nm) in coastal waters when AC-S is used for a
(λ)
and c
(λ)
[8,12].
Uncertainty in a
(λ)
from AC-S measurements mainly comes from the uncollected scattered
photons inside the reflective a-tube. Several scattering correction schemes have been proposed
in the literature [13–17], which have been the subject of numerous studies in coastal waters
[5,8,18]. Similarly, b
b(λ)
obtained from a single fixed VSF angle is also subject to corrections,
such as to compensate for attenuation along the optical path length (“sigma” (
σ
) correction,
required especially in coastal waters with high concentrations of OSCs) [19,20], or to quantify
the uncertainty in b
b(λ)
from variability in VSF angular distribution [21]. The first issue is worse
for backscatter acquired from instruments with longer path lengths such as the HydroScat (
∼
0.15
m vs.
∼
0.04 m for the BB9 [19]). For example, Tuchow et al. [20] showed that the
σ
correction
of Doxaran et al. [19], in which the backscatter is corrected for both absorption and scattering
along the path length, improved the optical closure in a plankton bloom in Monterey Bay.
Optical closure studies have also addressed the consequences of the assumed shape of the VSF
(equivalently, the phase function: the angular probability distribution of the scattering when it
occurs). While Petzold’s phase function has been frequently used in the past for open oceanic

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35180
waters [22], newer studies on optical closure in coastal waters imply that the Fournier-Forand (FF)
phase function [23] is a better choice [5,8,18,20]. The FF phase function can be parameterized
as a function of the backscatter fraction;
˜
B(λ)
, the ratio of backscatter b
b(λ)
to total scattering
coefficient b
(λ)
[24]. Tzortziou et al. [5] compared FF phase function, parameterized by
˜
B
obtained from the combination of an ECO-VSF-derived b
b
and AC-9-derived b, with both the
Petzold’s and FF phase functions in a closure exercise in Chesapeake Bay. They found that the
error was reduced by
∼
20% when the FF phase function was used over Petzold’s one. Tuchow
et al. [20] assessed optical closure for measurements in a plankton bloom in Monterey Bay
where the FF phase function was also found to perform better than Petzold’s. The optical
closure demonstrated by Gallegos et al. (2008) [6] over a range of highly contrasting optical
conditions, from lakes dominated by scattering or absorption, highlighted both the importance of
the scattering correction of AC-9 data for turbid lakes and the use of the FF phase function with
lower
˜
B
values in humic lakes. Furthermore, Gallegos et al. (2008) [6] recognized the potentially
important contribution of CDOM fluorescence in their humic lakes, but the lack of vertical
resolution of their AOP measurements prevented the assessment of these inelastic processes.
Here, we examined optical closure in coastal waters dominated by high concentrations of
CDOM. Specifically, we assessed how the inclusion of inelastic scattering due to CDOM
(f
DOM
) affects the optical closure in blue and green wavelengths in a coastal absorptive aquatic
environment. We also considered sun-induced chlorophyll fluorescence (SICF) to assess its effect
on R
rs
in the red wavelengths. The implications of using in situ absorption coefficient acquired
using an ICAM integrating sphere in characterizing the optical closure is also explored.
2. Materials and methods
The study area is located in the lower part of the Estuary of St. Lawrence (ESL) in Québec,
Canada (Fig. 1(a)). In this region a
CDOM
is the dominant component of total a
t−w
, especially in
blue and green wavelengths [25]. Two sets of IOP instruments were deployed: 1. WETLabs
AC-S & BB9; and 2. HOBILabs A-Sphere & HydroScat6. Each IOP package was accompanied
by in-water radiometric profilers (C-OPS) for AOP determinations.
2.1. Study area
The Manicouagan Peninsula (
∼
49
◦
N, 68.3
◦
W; Fig. 1(b)) is a deltaic formation located on the
north shore of the ESL and comprises a cold temperate environment with a rich marine ecosystem
[26,27]. The mixed freshwater flow from three surrounding rivers (Betsiamites, Aux-Outardes,
and Manicouagan) with an averaged mean annual discharge of
∼
1600 m
3
s
−1
[28], provides
large inputs of terrigenous CDOM and makes the coastal waters of the ESL highly absorptive
[10,25,29]. The main area of interest has a bathymetry reaching
∼
150 m after a relatively
extensive tidal flat (
∼
2 km). The bottom type of the tidal flat consists of sand with both small and
coarse particles, partly covered by eelgrass meadows (Zostera marina L.) [26].
2.2. In situ data sets
2.2.1. Sampling strategy
An intensive interdisciplinary fieldwork campaign was carried out in August 2019 as part of
the WaterSat Imaging Spectrometer Experiment (the WISE-Man project). The main objective
of the fieldwork was to collect high-quality optical and biogeochemical measurements for the
calibration and validation of WISE, a hyperspectral prototype camera developed by ITRES Inc
(Calgary, Canada) for coastal and inland water assessment (see also [25,30,31]).
The in situ sampling was performed using two small boats, FJ Saucier and Kildir (Fig. 1(b)).
The boats were used to deploy instruments measuring conductivity-temperature-depth (CTD),
radiometric quantities and IOPs, and to collect discrete water samples for the determination of

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35181
Fig. 1.
Illustration of the study area: (a) Map of Québec province in Canada where the red
dot represents the location of the study area, (b) study area at a finer scale; Manicouagan
Peninsula situated in the Lower Estuary of Saint Lawrence. The blue points show the
sampling locations for boat Kildir (A-Sphere and HydroScat) and the red ones show the same
for FJ Saucier (AC-S and BB9). The points are overlaid on CHS NONNA-10 bathymetry data
and the land area is a true color composite of R
rs
obtained from Sentinel-2 multi-spectral data
acquired on July 2019. (c1)-(c4) C-OPS mounted Go-Pro acquired RGB images showing
the variability of water color among all sampling sites in the study area (both optically deep
and shallow).
biogeochemical constituents and properties. A total of 65 stations were visited over a 9-day
period from August 17th to 25th in 2019. Among these, 36 stations had depths greater than 10 m.
The remaining 29 stations were shallower.
Each boat was equipped with a Compact Optical Profiling System (C-OPS) for measuring
in-water radiometric profiles to facilitate the estimation of R
rs(λ)
. For the IOPs, the Kildir
deployed an optical package consisting of an A-Sphere (ASPH) and a HydroScat-6p (HS6) from
HOBILabs, as well as a Seabird SBE19
+
CTD for synchronous data acquisition. A total of 30
profiles were performed with this setup. The FJ Saucier was equipped with an AC-S and BB9
from WETLabs along with a Seabird SBE19
+
CTD. This package was used to acquire data at 32
stations (Fig. 1(b)). Discrete water samples were also collected at each station for laboratory
analysis of OSCs. Specifically, the water was sampled using a 5-L Niskin or a 4.2-L Wildco
Beta horizontal sampler at
∼
0.5 m depth (“surface”) at all stations (N
=
64). Samples were also

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35182
collected at
∼
5 m depth (“sub-surface”) at some selected stations (N
=
15). The discrete water
samples were stored in clean, 20-L insulated carboys rinsed three times with sample water.
2.2.2. Remote sensing reflectance
The C-OPS measured downwelling irradiance E
d(
z,
λ)
, upwelling irradiance E
u(
z,
λ)
and up-
welling radiance L
u(
z,
λ)
in the water column (where zis depth) at 19 wavelengths across 305-780
nm spectral domain (
λ
), at a frequency of 15 Hz [32,33]. Simultaneous above-surface downward
irradiance, E
d(
0
+
,
λ)
, was measured with a radiometer attached to the top of the boat, making
sure there were no obstructions in the field of view. The C-OPS was deployed for 3-to-5 vertical
profiles at each station, and care was taken to avoid the boat shadow and limit boat pitching and
rolling [25].
The C-OPS data were processed using the software R and the
Cops
package (https://github.com/
belasi01/Cops); [10,25,30]). The data was processed following the NASA radiometric protocols
[34], with some modifications. Radiometric measurements with high tilt, i.e.,
>
5
◦
were discarded,
although the tilt threshold was increased to 7
◦
or 8
◦
near the surface and in highly stratified
waters, to account for the extra turbulent nature of the air-water interface. Data collected near the
air-water interface was typically noisy and was therefore discarded and replaced by extrapolating
the radiometric data from the sub-surface to just below the air-water interface (see description
below). A wavelength-specific detection limit threshold was used to remove noisy radiometric
measurements (i.e., when the C-OPS is just measuring noise). Normalization to account for
changing incident surface irradiance during the vertical profiles was done by multiplying E
d(
z,
λ)
,
E
u(
z,
λ)
, and L
u(
z,
λ)
) by the ratio
ˆ
Ed(
0
+
,
λ
,t
)/
E
d(
0
+
,
λ
,t
0)
, where
ˆ
Ed(
0
+
,
λ
,t
)
refers to the mean
in-air surface irradiance over time tin the profile, and t
0
is the time reference of a particular
observation in the same profile [34].
After normalization, the data was fitted using a linear regression applied to the log-transformed
radiometric quantity versus depth. This allowed extrapolation of the quantities of interest to
just below the sea surface (z
=
0
−
). An instrument self-shading correction was also applied
to the normalized L
u(
0
−
,
λ)
, using the total absorption coefficient at each C-OPS wavelength
[35,36] measured coincidently with the ASPH or the AC-S. Finally, the surface remote sensing
reflectance, i.e., Rrs(0−,λ)was calculated as:
Rrs(0−,λ)=Lu(0−,λ)
Ed(0−,λ)(1)
2.2.3. IOP data
Vertical profiles of IOPs were collected using two separate instrument setups (referred to here as
“IOP packages”) consisting of an ASPH and a HydroScat on the Kildir and an AC-S and BB9 on
the FJ Saucier, each integrated with a Seabird SBE19
+
CTD in the IOP package. Each package
was vertically deployed using a mechanical pulley attached to the deployment cable, which was
only ∼5 m in length for the FJ Saucier, limiting the IOP acquisition to sub-surface waters only.
All instruments were calibrated by the manufacturer, but additional calibration checks were
performed prior to the fieldwork. Blank measurements with the ASPH, a submersible Teflon
ICAM, were checked before the field campaign using nano-pure water. The instrument measures
the absorption at 1,500 wavelengths between 360 and 764 nm, which are binned at 1-nm
spectral resolution. Raw data were converted into non-water absorption coefficients (a
t−w
) using
the manufacturer software and the calibration file that was included for the pure water offset.
Absorption coefficients were corrected for temperature (T) and salinity (S) differences relative to
the calibration using data from the CTD at the same depth, using the coefficients published by
Röttgers et al. (2014) [37].
The AC-S instrument measured in situ non-water absorption (a
t−w
) and attenuation coefficients
(c
t−w
) at a frequency of 5 Hz. The instrument uses a pump to pull water through two flow tubes,

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35183
each having a path length of
∼
25 cm and an integrated light source, detector and filter wheel.
a
t−w
and c
t−w
were measured at 81 wavebands between 400 and 756 nm. The field-acquired
binary data was converted to raw text data using the manufacturer’s software (WETLabs, WAP).
The raw data were converted into engineering units by applying a calibration file obtained from
the manufacturer after the fieldwork (post-cruise calibration) [38]. Corrections for the effects of
temperature and salinity, as measured by the CTD, were applied following the manufacturer’s
standard recommendations [37]. Pure water calibration files required for the data processing were
obtained in the laboratory before and after the fieldwork, and the average of the two calibrations
was used.
The AC-S data were also corrected for scattered photons failing to be detected in the a-tube and
c-tube. Several scattering correction methods were tested, including Zaneveld et al. (1994, 1999)
[13,39], Röttgers et al. (2013) [17], McKee et al. (2008) [15], and McKee et al. (2013) [16]. A
detailed comparison of the implemented scattering correction methods and their respective effect
on the radiative transfer modeling is presented in Section S1 in Supplement 1. Based on this
analysis, the McKee et al. (2008) method, which uses measured b
bp
as ancillary input for the
correction, was judged to perform best, however, the use of potentially overestimated VSF from
BB9 (see 3.2.1 afterwards and Section 1-3 in Supplement 1) might have introduced uncertainty
in this choice of scatter correction.
The total backscattering coefficient, b
b
, at selected wavelengths was measured using the
HydroScat and BB9 instruments. The HydroScat was calibrated by HOBI Service Inc. prior to the
fieldwork following the method of [40]. The BB9 was sent to the manufacturer (SeaBird/WetLabs)
for calibration after the cruise (post-calibration), and the data were processed using the post-
calibration coefficients. The HydroScat measured the VSF at 140
◦
at 6 wavebands centered at
394, 420, 470, 532, 620 and 700 nm. The HydroScat has an effective optical path length of
∼
15
cm. A first-order correction factor,
σ
, for attenuation along this long path was derived using
the a
t−w
measured coincidently by the ASPH, as recommended by [19]. Finally, the particulate
backscattering coefficient, bbp, was derived as following:
bbp =2π χp(β(θ◦) − βw(θ◦)) (2)
where
χp=
1.08 is a value provided by the manufacturer assuming a VSF shape estimated from
a specific backscatter fraction value at
θ=
140
◦
[40].
βw(θ◦)
is the pure seawater VSF at 140
◦
computed following [41] using the Tand Smeasured at the same depth with the CTD. The BB9
measures the VSF at an effective scattering angle of 117
◦
,
β(
117
◦)
, for wavebands centered at
412, 440, 488, 510, 532, 595, 650, 676 and 715 nm. The effective pathlength is
∼
3.9 cm and
β(
117
◦)
was
σ
-corrected using a
t−w
values obtained from adjacent AC-S following [19]. Finally,
bbp was calculated using the same equation (Eq. (2)) above but with χp=1.1 [42].
The ASPH and HydroScat package did not include any measurement of beam attenuation (c).
As a result, non water beam attenuation (c
t−w
) could not be measured directly at the stations
visited by the Kildir. Instead, c
t−w
was estimated by calculating c
t−w(λ)=
a
t−w(λ)+
b
bp(λ)/ ˜
B
,
where
˜
B
is an assumed and spectrally constant value of the backscatter fraction derived from
three possible options:
1. The Petzold phase function value of 0.018 [22];
2. The mean ˜
B(532)derived from BB9 and AC-S data (this was 0.013, see results);
3.
A value was estimated from HydroScat and AC-S data from two physically close stations.
The latter value was based on HydroScat-derived b
bp
and AC-S-derived b
p
at two nearby offshore
stations sampled simultaneously on August 23rd 2019. Assuming spatial homogeneity between
stations, a
˜
B(
532
)
value of 0.0105
±
0.006 was obtained. Similar values have been reported in
the literature for CDOM-rich waters. For example, Gallegos et al. (2008) [6] reported a constant

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35184
˜
B=
0.0115 for humic-rich lakes. In addition, it has been shown that nearshore ESL particles
were organic-rich and had low b
bp
to Suspended particulate matter ratio but high for the ratio
with both organic dominated non-algal particulate absorption and particulate organic matter in
ESL waters [25,30]. Similarly, some studies have also shown that the organic-rich particles
generally present low
˜
B
[43] as well as b
bp
[44]. These three values of
˜
B
were retained as potential
candidates and applied in a sensitivity analysis as part of the optical closure experiment.
Finally, all the corrected IOP values were binned at 0.5m depth intervals for stations deeper
than 10 m, and at 0.1m depth intervals for shallower stations. Binning was performed using a
non-linear LOESS smoothing function implemented in R using the open source package
Riops
developed by Dr. Simon Bélanger (for details, see https://github.com/belasi01/Riops).
2.2.4. Laboratory analysis
Several measurements of spectrophotometric IOPs and biogeochemical variables were determined
from the discrete water samples:
•CDOM spectral absorption, aCDOM(λ).
•Total particulate and non-algal particulate spectral absorption, ap(λ)and aNAP(λ).
•Chlorophyll-a concentration [chl].
•Suspended particulate matter (SPM) concentration.
The CDOM spectral absorption coefficient, a
CDOM(λ)
, was measured for water samples filtered
under low vacuum using 47-mm Nucleopore filters (Whatman, 0.2
µ
m nominal pore size)
[30]. CDOM absorbance (A) was measured between 220 and 800 nm using a Perkin Elmer
double-beam Lambda-850 spectrophotometer, 10 cm quartz cells, and nano-pure water as the
reference. A baseline correction was applied on the measured Avalues by subtracting the average
values over a spectral window of 5 nm centred at 685 nm [45]. Finally, a
CDOM
was calculated by
normalizing the corrected absorbance values by the path length of the quartz cells (L
=
0.1 m)
and converting to a Napierian logarithm scale: aCDOM (λ)=2.303A(λ)/L.
Particulate spectral absorption coefficient, a
p(λ)
, was measured following the filter-pad
technique as described in [46]. First, a known volume of sampled water (replicates between two
and five) was filtered through Whatman GF/F glass fiber filters shortly after sampling (
<
3h). The
filters were placed inside a 150-mm integrating sphere fitted to the Perkin Elmer Lambda-850
spectrophotometer. Absorbance was scanned from 300 to 800 nm at every 1 nm. The absorbance
of a blank filter was subtracted from total absorbance [46]. Blank-corrected absorbance values
were corrected for path length amplification and converted to a
p
using eq. 1 in Stramski et al.
(2015) [47]. Similarly, a
NAP
was measured by placing the filters inside the sphere after extraction
of the phytoplankton pigments using methanol 90% for ∼18 to 24 hours [48].
Chlorophyll-a concentration [chl] was determined fluorometrically from triplicate sub-samples
filtered onto 25-mm Whatman GF/F filters (varied known volumes between 200-550 ml). [chl]
values were measured using a Turner Designs 10-AU fluorometer, following a 24-hour extraction
in 90% acetone at 4
◦
C in the dark following the acidification method of Parsons et al. (1984)
[49].
SPM concentration was measured following the recommendations of [50]. Known volumes
(V) of seawater (varies between 500-1250 ml) were filtered in water sample triplicates through
pre-ashed (1 hour at 450
◦
C), pre-rinsed and pre-weighed (mass M
0
mg) 47-mm GF/F filters.
Each filter was then rinsed with Milli-Q water and dried for 24 hours at 60
◦
C prior to weighing
under a dry atmosphere (mass M
1
, mg) to obtain the SPM concentration as SPM
=(
M
1−
M
0)/
V.
The final value from triplicates [chl] and SPM was determined considering their average,
within a confidence interval of 95%.

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35185
2.3. Radiative transfer simulations
The radiative transfer model HydroLight version 6.0 [3] was used to simulate surface remote
sensing reflectance, R
rs(
0
−
,
λ)
. HydroLight models directional radiance in the water column and
irradiance above the surface using an invariant embedding approach to solve the radiative transfer
equation. The details of this model can be found in [3].
Vertical profiles of a
t−w(λ)
,c
t−w(λ)
and b
bp(λ)
for each station were input into HydroLight
with 0.25 m depth interval obtained by fitting a spline interpolation to bin the actual IOP
profiles. The phase function was modelled using the Fournier–Forand (FF) phase function with
shape specified by
˜
B(λ)
[24]. The pure water absorption coefficients from [51] and pure water
scattering coefficients from [52] were used in the model configuration to yield the total IOPs. The
RADTRAN-X routine was used to model the sky radiance distribution with viewing geometry
and atmospheric transmittance calculated from field-acquired time, location and approximate
cloud cover. The water surface roughness model of Cox & Munk (1954) [53] was used with
wind speeds measured by a hand-held anemometer (always
<
5 ms
−1
). The water column was
considered infinitely deep, as only stations with a physical depth greater than 10 m were used
in the modeling. Since these waters are optically deep (c
(λ)>
1.3 m
−1
) the effect of bottom
reflectance could be considered negligible.
HydroLight simulations were performed with and without inelastic scattering, with both f
DOM
and SICF included in the inelastic scattering treatment. To include inelastic scattering in the
modelling, two additional depth-dependent input variables must be provided, i.e., [chl] and
a
CDOM(
443
)
. These were obtained from the surface (0.5 m) discrete water samples as described
in the previous sections. For consistency between in-water a
t−w(
443
)
profile measurements and
benchtop spectrophotometric measurements, we estimated the profile aCDOM(443)as:

aCDOM(z, 443)=at−w(z, 443) × aCDOM(443)
aCDOM(443)+ap(443)(3)
where

aCDOM(
z, 443
)
is the estimated a
CDOM(
443
)
at depth z,a
t−w(
z, 443
)
is the in situ non-water
absorption (ASPH or AC-S derived), and a
CDOM(
443
)
and a
p(
443
)
are the spectrophometrically-
determined absorption coefficients. The relative CDOM contribution to non-water absorption
is therefore assumed constant in the water column. Vertical profiles of [chl] were assumed
constant and equivalent to the surface [chl] values obtained from the laboratory analysis. In
HydroLight, inelastic scattering equivalent radiance is calculated via integrating the volume
inelastic scattering function given as
βg(ψ
,
λ∗
,
λ)=
b
g(λ∗)
f
g(λ∗
,
λ)βg(ψ)
. Here b
g(λ∗)
is loss of
photon at excitation wavelength (
λ∗
),
βg(ψ)
is scattering phase function set to 1
/
4
π
,f
g(λ∗
,
λ)
is the wavelength redistribution function (WRF) calculated as, f
g(λ∗
,
λ)=ηg(λ∗
,
λ)λ∗
λ
, where,
ηg(λ∗
,
λ)
is the shape of quantum efficiency, for which the parameterization of [3,54] were used
for SICF and f
DOM
along with HydroLight set default quantum yield. HydroLight runs were
performed for the wavelength range 360 - 800 nm (interval 5 nm, the IOPs were spectrally
extrapolated where necessary using LOESS function in R) with the lower bound set to ensure the
excitation range of fluorescence was included.
2.4. Statistical metrics used
The following statistical metrics were used in the various comparisons between IOPs and
measured and modeled R
rs
: Median Absolute Percentage Error
MDAPE(
%
)
, median %-
Bias
and
Root Mean Square Percentage Error, RMS%E. These are defined as:
MDAPE(%)=median (|δyi|) ×100 (4a)
%−Bias =median (δyi)×100 (4b)

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35186
RMS%E =⌜
⎷1
n
n

i=1
(δyi)2×100 (4c)
In general, y
i
is the observed or actual value, and
ˆ
yi
is the predicted value, iis a specific
observation where nis the number of observations, so
δyi=(ˆ
yi)−yi
yi
is the relative difference for
one observation. In different contexts the values in question could be at−w(λ),bbp(λ)or Rrs (λ).
3. Results
3.1. Optical and biogeochemical conditions of the study area
The sampled surface waters (0.5 m depth) were typically brackish with a salinity of 22.74
±
4.65
(st.dev.) PSU (Practical Salinity Units) and with a temperature of 10.66
±
1.85
◦
C (Table 1).
Chlorophyll-a concentration ranged from 1.05 to 5.3 mg m
−3
indicating moderate phytoplankton
biomass. High absorption coefficients (
∼
1.00
±
0.31 m
−1
at 443 nm) and low backscattering
coefficients (0.007
±
0.002 m
−1
at 532 nm) resulted in visually dark waters (Fig. 1(c), Fig. 4(a)).
Table 1. Descriptive statistics of IOPs and
relevant BGC data used for HL simulation.a
Min Max Med sd(±)
at−w(443)[m−1]0.51 1.50 0.94 0.31
ct−w(443)[m−1]1.33 2.52 1.68 0.42
bbp(532)[m−1]0.004 0.010 0.007 0.002
[chl][mg m−3]1.05 5.30 2.68 1.15
SPM[mg1L−1]2.51 18.40 7.90 5.14
Salinity [PSU] 11.34 27.80 22.74 4.65
Temperature [◦C] 7.60 12.80 10.66 1.85
a
The data here is from Kildir collected samples for deep
stations (depth
≥
10m). statistical parameters are min;
minimum, max; maximum, med; median and sd; standard
deviation.
3.2. IOP consistency evaluation
First, we examined the consistency between the laboratory determined coefficients and biogeo-
chemical quantities from the water samples and the in situ IOP data collected from the two IOP
packages, the ASPH and HydroScat (n
=
12 stations), and the AC-S and BB9 (n
=
15 stations).
The following two sections discuss the backscatter and absorption respectively.
3.2.1. Particulate backscattering coefficient
On average, b
bp(
532
)
values for the HydroScat and BB9 showed different ranges of variability
with medians of 0.007 m
−1
(0.004 to 0.010 m
−1
) and 0.015 m
−1
(0.012 to 0.026 m
−1
), respectively
(Fig. 2). A discrepancy in spectral shape was also observed between the sensors, with noisier
spectra for BB9 relative to the HydroScat (Fig. 2(a)). To get more insight on the reliability
of in situ b
bp(λ)
, we examined the relationship between b
bp(
555
)
and both the SPM and the
non-algal absorption coefficients. These can be treated as independent proxies for particulate
matter as they have frequently been demonstrated to co-vary with backscattering [25,44,55].
The BB9 data showed greater spread and a systematically higher magnitude than the HydroScat
data for a similar range of a
NAP(
443
)
(Fig. 2(b)). Similarly, there was only a weak relationship
between SPM and BB9-derived b
bp(
555
)
(Fig. 2(c)), whereas the HydroScat data was much better

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35187
correlated to SPM (correlation coefficient, r, of -0.26 and
+
0.58 for the BB9 and HydroScat,
respectively).
Fig. 2.
Consistency check of measured particulate backscattering coefficient (b
bp
): (a) Spec-
tral particulate backscattering from the HydroScat and BB9 for deep water stations (water
depth
≥
10 m). General relationships between b
bp(
0
−
, 555
)
(as Y-axis) from both b
b
sensors and (b) non-algal particulate absorption coefficient at 443 nm, a
NAP(
443
)
, and (c)
corresponding suspended particulate matter (SPM) concentration (both as X-axis). The
elliptical clusters are drawn to provide a visual estimate of the trend and its variability. The
solid lines represent the power regression (y=a·xb) fitted line for each bbp sensor.
Additional comparisons were performed to determine which backscatter instrument yielded
more reliable results. First, we used a quasi-analytical algorithm (QAA) [56] to get an independent
estimate of b
bp
from the in situ R
rs
(Fig. S3 in Supplement 1). Good agreement was obtained
for the HydroScat values with mean relative error δbbp(532) ≈ 9%. In contrast, the BB9 values
were consistently overestimated and exhibited more spread relative to the QAA-derived b
bp(
532
)
values, with a mean
δbbp(
532
)
of
∼
30%, and three stations showing discrepancy larger than
70% (Fig. S3). Finally, when the data from the nine stations with concurrently acquired AC-S
and BB9 profiles was propagated through the optical closure experiment, there was a constant
overestimation of R
rs
regardless of the modeling treatment applied (Fig. S4; see section S3 in
Supplement 1). The overall conclusion of these results was that BB9 data were mostly erroneous,
with b
bp
being systematically overestimated. Therefore, only the data from the ASPH and
HydroScat optical package was further considered in this paper. The AC-S and BB9 obtained
optical closure results are available in Supplement 1 (Fig. S4).

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35188
3.2.2. Non-water absorption coefficient
The ASPH-derived a
t−w
was systematically lower than spectrophotometric absorption measured
on the discrete samples, a
spec
t−w=
a
CDOM +
a
p
, except for one station (OUT-R03) (Fig. 3(a)).
The %-Bias peaks at
∼
30% around 570 nm and drops sharply to
∼
10% around 670 nm before
increasing again toward 700 nm (Fig. 3(b)). Interestingly, the inverted spectral shape of the
%-Bias suggests that part of the relative ASPH underestimation may be due to CDOM and
chlorophyll-a fluorescence taking place inside the ICAM. Fluorescence in the ICAM would
be stimulated by the continuous spectral LED source ranging from 360 nm to 764 nm (see
Discussion). Assuming the spectrophotometric measurements can be used as the reference, we
applied a bias correction to all ASPH spectral a
t−w
. The implications of the a
t−w
underestimation
and the bias correction on the optical closure results are presented in the next section.
Fig. 3.
Consistency check for the ASPH absorption data: (a) The comparison of ASPH
a
t−w(
0
−
,
λ)
with a
spec
t−w
from the surface waters. (b) %-Bias (sign inverted) between ASPH
and a
spec
t−w
values plotted against
λ
. The sign is inverted for ease of comparison with the shape
of fluorescence. The shaded region shows a 95% Confidence Interval calculated between
360-710 nm for each
λ
. The vertical dotted lines show the %-Bias for three distinct
λ
(blue,
green, red).
3.3. Optical closure
The assessment of optical closure was performed for the 12 stations where simultaneously
acquired data from the ASPH, HydroScat and C-OPS were available. Modeled R
rs(
0
−
,
λ)
from
HydroLight were compared to the R
rs(
0
−
,
λ)
derived from C-OPS measurements (Fig. 4(a)).
HydroLight simulations were performed using in situ IOPs (Fig. 4(b)–(d) to obtain R
rs(
0
−
,
λ)
with both only elastic scattering (denoted
HLel
), as well as for elastic and inelastic scattering
combined (denoted HLel+inel).
3.3.1. Sensitivity to backscatter fraction
From the sensitivity analysis for
˜
B
, we found that the simulated R
rs
with
˜
B=
0.018 and
˜
B=
0.013
were similar in shape and magnitude with each other (spectral % difference for all
λ
of 2.8%). In
both cases, simulated R
rs
were higher than the in situ values (spectral %-Bias over all
λ
,
+
8.33%
and
+
11%).
˜
B=
0.010 generated comparatively lower values of R
rs
by 4 to 10% relative to
Petzold’s
˜
B
(0.018) and the resulting R
rs
were in better agreement with the in situ R
rs
. These

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35189
Fig. 4.
In situ R
rs
and IOP data for 12 Kildir stations used in optical closure. In (a) the R
rs
here is shown for subsurface depth (
∼
0.5 m inside water, z
=
0
−
). The corresponding IOP
data, i.e., at−w,bbp and ct−w(b)–(d) are also shown for subsurface depth (z=0−).
results are consistent with the previous interpretation of the BB9-derived b
bp
being overestimated
(giving the value of
˜
B=
0.013) and since that instrument’s data was discarded in the remainder
of the study, it was applied in this context also. The value of
˜
B=
0.018 was just based on
the assumption of Petzold’s phase function, whereas the value
˜
B=
0.010 was obtained from
measurements in the study area using the HydroScat. Thus,
˜
B=
0.010 was preferred for the
APSH and HydroScat stations and the other values were not propagated further in the analysis.
3.3.2. Impact of the ASPH bias correction
The impact of the a
t−w
underestimation by the ASPH on the optical closure was investigated.
HydroLight was run using four configurations: 1) bias-corrected and
HLel
, 2) bias-corrected and
HLel+inel
, 3) bias-uncorrected and
HLel
, and 4) bias-uncorrected and
HLel+inel
. The corresponding
σ
-corrected b
bp
from the HydroScat was used in all cases. The modeled R
rs(
0
−
,
λ)
were compared
to the corresponding in situ R
rs(
0
−
,
λ)
and the spectral %-Bias was used as the evaluation metric.
For R
rs(
0
−
,
λ)
governed by elastic scattering components, i.e., a
t−w
and b
bp
mainly, an
underestimation in magnitude was observed for both bias-corrected and bias-uncorrected
absorption. The underestimation was dependent on
λ
and reached maximum values in the
“green maxima” (555
≤λ(nm) ≤
560) (Fig. 5(a)). However, the underestimation of R
rs(
0
−
,
λ)
was almost twice higher when using bias corrected ASPH absorption than when using their
uncorrected version. A similar pattern was observed when inelastic scattering was included in

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35190
Fig. 5.
(a1) Spectral plots of variation in HydroLight modeled R
rs(
0
−
,
λ)
from
HLel
for
bias-corrected and bias-uncorrected ASPH a
t−w
data along in situ R
rs(
0
−
,
λ)
derived from
the C-OPS (solid black line). The encapsulated plot (a2) shows the spectral %-Bias between
C-OPS acquired R
rs(
0
−
,
λ)
and modeled R
rs(
0
−
,
λ)
for bias-corrected and bias-uncorrected
ASPH a
t−w
respectively. (b1),(b2) Same as (a1),(a2) but obtained with
HLel+inel
. (c)
Boxplot of %-Bias at “green-maxima” for modeled R
rs(
0
−
,
λ)
for both elastic and inelastic
scattering including bias-corrected and bias-uncorrected ASPH a
t−w
respectively for all 12
stations.
the simulations. However, the underestimation of R
rs(
0
−
,
λ)
at “green maxima” was much lower
when the
HLel+inel
used bias-uncorrected ASPH absorption as an input (Fig. 5(b)). Aggregating
the results for the 12 stations revealed that the R
rs(
0
−
,
λ)
at “green maxima” simulated using the
bias-corrected absorption led to a worse %-Bias (
HLel
: -45.5%,
HLel+inel
: -30%) compared to
those generated with the bias-uncorrected absorption (
HLel
: -16%,
HLel+inel
: -1.5%) (Fig. 5(c)).
Compiling the results at all
λ
, the precision and linearity of the fit were also better when the
bias-uncorrected absorption was used, especially for
HLel+inel
(bias uncorrected: R
2=
0.96; bias
corrected: R2=0.84)(Fig. 6).
As a result of these comparisons, the bias-uncorrected ASPH a
t−w
was used in the rest of
this study. However, these comparisons also suggest some possible discrepancies (see 4.1) in
the a
spec
t−w
apart from the internal fluorescence inside ASPH previously discussed. Regardless
of the a
t−w
used, the inclusion of inelastic scattering considerably reduced the severity of the

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35191
Fig. 6.
Scatterplot of in situ versus modeled R
rs(
0
−
,
λ)
using a
t−w
and corresponding
σ
-
corrected b
bp
from the HydroScat using (a) bias-uncorrected ASPH a
t−w
, (b) bias-corrected
a
t−w
. In both panels, diamonds and circles are for HydroLight simulations with and without
inelastic scattering, (HLel and HLel+inel) respectively.
underestimation in simulated R
rs
relative to the reference in situ R
rs(
0
−
,
λ)
. The next section
further analyzes the importance of inelastic scattering in a more detailed manner.
3.3.3. Significance of inelastic scattering
At blue wavelengths (440-490 nm), modeled R
rs(
0
−
,
λ)
with and without inelastic scattering
had approximately the same precision; R
2=
0.84 and 0.85 respectively (Fig. 7(a) and Table 2).
However, the regression slope improved slightly (0.62 to 0.75) when inelastic scattering was
included. In terms of accuracy, the MDAPE, RMS%E and %-Bias metrics showed slightly
better results without inelastic scattering (Table 2). In particular, there was a decreasing trend
in %-Bias (overestimation of R
rs(
0
−
,
λ)
) with increasing
λ
. At 443, 465, and 490 nm %-Bias
without inelastic scattering was 20%, 13% and -3%; vs. with inelastic scattering, 28%, 24% and
11%, respectively) (Fig. 8(b)). Note however that R
rs(
0
−
, 443
)
values were very low (
≤
0.002
sr
−1
), making it prone to high relative errors. In addition, there is relatively less contribution
from inelastic scattering by CDOM and chlorophyll-a at blue wavelengths in this study, which
explains the small differences observed between the two sets of simulations (Fig. 7(a), 8(b)).
Table 2. Statistics on the goodness of fit between C-OPS acquired in
situRrs(0−,λ)data and HydroLight modeled Rrs(0−,λ)with (inel) and
without (el) inelastic scattering.a
λR2Slope (m) MDAPE (%) RMS%E %-Bias
el inel el inel el inel el inel el inel
Blue 0.84 0.85 0.62 0.75 22 28 29 35 +11 +21
Green 0.90 0.97 0.57 0.91 21 0.05 23 14 -14 +1
Red 0.81 0.92 0.69 0.95 22 9 21 13 -13 +7
RGB 0.90 0.96 0.64 0.90 21 12 26 22 -8 +6
a
Statistical metrics are the coefficient of determination (R
2
), the slope of the linear fit (m)
along with MDAPE (%), RMS%E and %-Bias defined in equations (4a)-(4c). The R
2
and
mare obtained with the Major Axis regression of the Type-II family.
At green wavelengths (510-590 nm), where inelastic scattering is primarily from CDOM
fluorescence, the inclusion of inelastic scattering improved the agreement with in situ R
rs(
0
−
,
λ)
in all stations significantly (Fig. 7(b)), the precision improved by 7% (R
2=
0.97 from 0.90) and

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35192
Fig. 7.
Scatterplots for optical closure obtained for three spectral groups, i.e., (a) Blue
(440-490nm), (b) Green (510-590nm), (c) Red (620-710nm) and (d) RGB (440-710nm). The
solid-colored diagonal line (slope; m
=
1) in each plot is the 1:1 line. The black solid lines
(Fit
el
) show the linear fit between in situ R
rs(
0
−
,
λ)
and HL simulated R
rs(
0
−
,
λ)
with elastic
scattering (HL
el
) whereas, the black dashed lines (Fit
el+inel
) represent linear fit between in
situ R
rs(
0
−
,
λ)
and HydroLight modeled R
rs(
0
−
,
λ)
with both elastic and inelastic scattering
(HLel+inel).
the regression slope increased considerably from 0.57 to 0.91. Accuracy was also significantly
improved; MDAPE and RMS%E were reduced to
<
1%and 14%, respectively, and the %-Bias
was almost null (i.e., 1%). The best improvements were observed at 555 and 589 nm, with the
%-Bias decreasing from -16% to -1.1% at 555 nm, and from -17% to -3.9% at 589 nm (Fig. 8(b)).
These results revealed the importance of f
DOM
for attaining good optical closure in CDOM-rich,
highly absorptive waters.
At red wavelengths (620-710 nm), the sun-induced chlorophyll-a fluorescence (SICF) made a
large contribution to inelastic scattering, and the optical closure was considerably improved when
this process was included in the simulations (Fig. 7(c), Table 2). Both precision and linearity
increased (i.e., R
2
and m), the MDAPE decreased from 22%to 9%, the RMS%E improved by 8%,
and the %-Bias changed from a large underestimation (-13%) to a moderate overestimation (7%).
The highest reductions in %-Bias were observed at 667 nm and 685 nm. At 667 nm, the%-Bias
dropped from -13% to -1%. At 685 nm, which corresponds to the SICF emission peak [3], the
large underestimation of -27% changed to a small overestimation of 6% (Fig. 8(b)). These results
strongly imply that the omission of SICF in the radiative transfer simulations was responsible for
the underestimation of Rrs in the red region.

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35193
Fig. 8.
Contribution of inelastic scattering (in %) to R
rs(
0
−
,
λ)
from HydroLight simulations:
(a) Spectral box-plots from modeled outputs across C-OPS
λ
. The solid black line shows
the mean contributions of inelastic scattering. (b) Mean
δRrs
(in %) compared to
in situ
measurements from all stations for both
HLel
(Blue dotted line) and
HLel+inel
(Black solid
line) (
+
is overestimation in simulation and - is underestimation). The vertical whiskers
around each point show a 95% confidence interval of the mean
δRrs
from all stations and for
each λ.
Finally, the contributions of f
DOM
and SICF to the modeled R
rs(
0
−)
were estimated (Fig. 8(a)) by
using HydroLight configurations that enabled the calculation of inelastic scattering contributions.
When including all stations, the mean contribution from f
DOM
was
∼
18% in the green region and
was highest at 555 nm (
∼
21%). Similarly, the mean contribution of SICF in red wavelengths was
∼20%, with the highest contribution being ∼30% at 685 nm (Fig. 8(a)).
4. Discussion
4.1. IOP determination in absorbing waters
The color of the water varied between yellowish green to yellowish-brown where R
rs
peaked
between 570 nm and 600 nm for most of the stations (Fig. 4(a)), suggesting OSCs absorb the
majority of light in blue and green
λ
. As shown by Araujo & Bélanger (2022) [25], CDOM
largely dominates the absorption budget across the whole visible spectrum in these nearshore
waters, with a
CDOM
accounting for
∼
80%of a
t−w
in the blue. Similar CDOM-rich characteristics
in ESL have also been reported by multiple studies [10,25,28,57].
A noticeable result in the current study was the systematic underestimation of in situ a
t−w
relative to the spectrophotometric reference, in data from both the ASPH and AC-S. One
possible explanation is the depth discrepancy between the water sampling and optical package(s).
Freshwater lensing of the river outflow could lead to waters very close to the surface being higher
in CDOM than subsurface waters. For example, at station OUT-R09, a
t−w(
443
)
dropped by
70% (
∼
1.4 m
−1
to
∼
0.4 m
−1
) between 1 m to 2.5 m depth, while the salinity changed from
∼
23
PSU to
∼
28 PSU. However, in general, water was sampled carefully using a Niskin bottle at
∼
0.5 m at most stations without any issues and it should be comparable to the shallowest valid
measurements of the IOP package.
The ASPH underestimation relative to spectrophotometric determination was almost systematic
and present at 11 out of 12 stations. The underestimation was not spectrally flat and has features
that resemble the combined shape of [chl] and CDOM fluorescence contribution to remote
sensing reflectance (Fig. 3(b), Fig. 8(a)). The ASPH uses a flow-through ICAM to acquire the

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35194
a
t−w
values, is theoretically free of scattering errors, unlike the AC-S a-tube. However, the finite
volume of pumped water inside the sphere is exposed to a continuous polychromatic light field
that may be sufficient to excite DOM fluorophores and pigments, which would re-emit some
photons in blue-green and red wavelengths, respectively. The remitted light would yield lower
a
t−w
than expected in these spectral ranges. A similar result of ASPH underestimation in the
St. Lawrence River waters was reported by [58], where both f
DOM
and SICF were hypothesized
to be the cause of ASPH underestimation of a
t−w
values by
∼
20% and
∼
30% in green and red,
respectively, while underestimation was negligible in the Ultra-Violet (UV) range. However, in
the current study, the underestimation was non-negligible in the UV (360-400 nm). In these
spectral ranges, inelastic scattering within the instrument can not explain this result.
Another source of discrepancy between in situ and spectrophotometric a
t−w
could be linked
to scattering by very small particles (VSP) (
≤
0.2
µ
m) in CDOM-rich coastal waters [59,60].
Balch et al. [59] stated a 100% increase in b
b
values in the Gulf of Maine (GoM), which were
associated with flocculation of CDOM under very high river discharge. Moreover, the study
by Zhang et al. [60] in lakes found a significant correlation (r
=
0.59) between estimated
b
bVSP(
532
)
and spectrophotometric a
CDOM(
412
)
, which suggest a common DOM origin for both
the variables. As a result, if we assume that VSP arising from CDOM in high concentration
does scatter light in coastal environments, and these particles are not fully removed by filtering,
spectrophotometric in lab a
CDOM
might be overestimated due to the loss of photons by scattering
along the 10 cm pathlength. Part of this loss of photons is corrected by subtracting a flat offset
by assuming null absorption at 685 nm, but this may be ineffective if the VSP scattering has
a steep spectral dependency toward decreasing
λ
, which is likely since the particles are small.
Moreover, the filter pad-based spectrophotometric values of particulate absorption (a
p
) also have
been reported to be affected by the uncertainty from path length amplification factor (
β
F) and
scattering offset (o) even after null correction at the NIR wavelengths [61]. Lefering et al. (2016)
[61] showed an improved regression-based correction to determine optimal
β
Fand ousing the
regression slopes and intercepts, respectively obtained from the linear relationship between the
spectrophotometric values of a
p
and the same obtained from a PSICAM. In our study, we did not
have concurrent measurements with PSICAM which limits our correction for filter-pad to often
used flat offset correction, which might have introduced potential error in our spectrophotometric
a
p
. This interpretation is consistent with the HydroLight simulations performed using ASPH
data corrected to be aligned with the spectrophotometric measurements, which resulted in much
lower R
rs
relative to the ASPH bias uncorrected results, and were further from the C-OPS derived
Rrs (Fig. 5,6).
Overall, we hypothesize that ASPH-derived a
t−w
was underestimated relative to the spectropho-
tometer measurements due to the combination of both potential fluorescence within the ASPH
and uncertainty in spectrophotometric a
t−w
from the possible uncertainties in a
p
and a
CDOM
discussed above, yet the net contribution of each of these processes remains to be quantified. But,
consequentially, neither the uncorrected ASPH nor the spectrophotometer measurements can be
definitively treated as a reliable baseline in this study.
4.2.
Optical closure in absorbing waters: significance of inelastic scattering processes
The best closure results were obtained when IOPs from the ASPH (uncorrected) and HydroScat
measurements were used in the modeling, and inelastic scattering of both CDOM and SICF was
also included. However, simulated R
rs
in the blue wavelengths were still overestimated. This
might be related to the discrepancy of a
t−w
by the ASPH discussed above, especially in the blue
spectral range. As the absorption budget in our study area is CDOM driven, the uncertainty in
the ASPH absorption magnitude can be considered as critical for the closure disparity in the blue
range. The corresponding b
bp
values at blue (420 nm) had higher variability than green
λ
(sd at
420nm
=∼
0.0028m
−1
; at 532nm
=
0.002m
−1
) which incorporates uncertainty to some extent in

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35195
the obtained R
rs
at blue wavelengths. In addition, the in situ R
rs(
0
−)
at blue wavelengths was very
low (
≤
0.002 sr
−1
). For some stations, in-water upwelling radiance near the sea surface was lower
than the sensor detection limit, which resulted in larger uncertainty in R
rs
values for
λ≤
490nm.
In summary, the main source of the error for the closure in the blue range is likely caused by
uncertainty in both in situ IOPs (especially, at−w) and Rrs in these the CDOM-rich dark waters.
The improvement in optical closure arising from the inclusion of inelastic scattering in the
modeling was greatest in green wavelengths, resulting in an underestimation of only 1% vs.
14% (Table 2). Fluorescence in green wavelengths was dominated by f
DOM
and these results
are consistent with the findings of other studies [5,8,12]. Tzortziou et al. (2006) [5] showed
that inclusion of f
DOM
improved the closure in green by 2-5% in the Chesapeake Bay. In this
environment, mineral particles are an important OSC, and the surface b
bp
values in green reported
by [5] were almost twice the magnitude of our b
bp
(0.007 m
−1
versus 0.015 m
−1
). In another
study, Lefering et al. (2016) [8] reported underestimation in L
w
from HydroLight modeling in
green wavelengths and suggested exclusion of f
DOM
might be one of the reasons. While some of
these studies suggested that the underestimation in green could be in part due to an erroneous
scattering correction method for flow-tube meters such as AC-S, that is not applicable to the
ICAM-based sensor used here.
The contribution of f
DOM
to green R
rs
reached
∼
18%in our study, which is higher than other
closure studies, e.g., [5]. This makes sense for this environment, as the Manicouagan nearshore
waters are characterized by high CDOM and are relatively low in terms of particle load, resulting
in dark waters [25]. These conditions increase the relative importance of CDOM fluorescence at
the emission wavelengths (500 to 600 nm). We also considered if the large CDOM fluorescence
contribution to modeled R
rs
could be an artefact of the assumption of vertically-homogeneous
a
CDOM/
a
t−w
ratio in the water column (0 to 4 m); this might be erroneous in the presence of
strong stratification in the water column [25]. However, we assessed the impact of considering
vertically homogeneous IOP data (see Supplement 1 Section S4) and found that stratification
at greater depths had a negligible impact on optical closure at most stations. This is consistent
with the shallow penetration depth in the study area that does not typically exceed
∼
3.5 m in the
green-yellow bands (555-589 nm) (see Fig. S6).
It is well known that SICF makes a critical contribution to R
rs(
0
−)
in red wavelengths (see
[62] and references therein). Our results are consistent with the closure results observed in
[5], which reported an underestimation of 30%-40% in 670-690 nm in simulated water-leaving
radiance when ignoring SICF. In our results, the most substantial improvement from including
SICF in the modeling was at 685 nm (Fig. 8(b)), although overestimation was observed at a few
stations (Fig. S8 (b, d, i)). A possible explanation could be mismatched [chl] values in a stratified
environment however, the same for CDOM had a negligible impact on the closure (see Section
S4 in Supplement 1). Uncertainty in fluorescence quantum yield may also be a factor, for both
f
DOM
and SICF. The default HydroLight quantum yield values were used in this study [3,54], but
the values for f
DOM
in particular compared to that of SICF are subject to high uncertainty due
to a lack of published data. Moreover, The estimation of fluorescence quantum yields or more
detailed measurement of [chl] profiles was out of the scope of this work. Still, nevertheless, the
results obtained give a good overall picture of the importance of considering inelastic processes
in nearshore CDOM rich waters for remote sensing applications.
5. Conclusion
This study has assessed the criteria required to obtain good optical closure in CDOM-rich coastal
waters. The study consisted of two in situ IOP packages (ASPH and HydroScat, AC-S and BB9),
spectrophotometric determination of absorption coefficients and HydroLight simulations, where
a number of challenges were identified to reach good optical closure in this water type.

Research Article Vol. 31, No. 21 / 9 Oct 2023 / Optics Express 35196
In terms of IOPs, ASPH-derived a
t−w
values were systematically lower than laboratory-
measured spectrophotometric absorption but yielded good closure results. Potential explanations
for this observation are fluorescence inside the ASPH integrating sphere or from very small
particle (VSP) scattering leading to inaccuracies in the spectrophotometer CDOM absorption
measurements followed by experimental uncertainty from
β
Fand oin filter pad measured
particulate absorption due to absence of concurrent absorption measurements with PSICAM.
In particular, HydroLight simulations performed using bias-corrected a
t−w
(aligned with the
spectrophotometer) did not improve the optical closure, which implies the dual-beam spec-
trophotometer measurements may not be free of errors in our study. With respect to particulate
backscatter, b
bp
, the HydroScat acquired values were almost half the magnitude of the BB9
values, the HydroScat data was spectrally smoother and almost flat, whereas the BB9 data
were comparatively noisy. Various consistency checks, including correlation with SPM and
the non-algal absorption coefficients, along with the overall pattern of the HydroScat and BB9
datasets, led to the conclusion the BB9 data were not sufficiently reliable for the current optical
closure analysis. The BB9 data, together with the AC-S data, were therefore not further considered
for the optical closure presented here (see Supplement 1 for AC-S and BB9 closure).
Overall, the best closure results were obtained from the ASPH and HydroScat data with
incorporating inelastic scattering processes in the RT model simulations. Based on the Hydrolight
runs, we estimated the contribution of f
DOM
to R
rs
in the green was
∼
18 %, and SICF in the red
of
∼
20 %. While most optical closure studies consider SICF, f
DOM
is generally considered of
secondary importance or negligible. Our results indicate that in CDOM-dominated coastal waters,
the significance of CDOM fluorescence may need to be reviewed as an important component of
remote sensing reflectance. However, especially for f
DOM
, there is a general lack of knowledge
of the possible range of the quantum yield, and the wavelength redistribution function, which
determines the fluorescence spectral shape. These parameters, which are likely to vary dependent
on specific materials present in the environment, undoubtedly propagate their own uncertainties
to the modeled reflectance. Sensitivity analyses could be useful for quantifying this uncertainty.
Ideally, methods for measuring quantum yields or full spectral functions for f
DOM
could be further
developed. We conclude that including CDOM inelastic scattering is important to obtain good
optical closure in absorbing waters.
Funding.
Canadian Space Agency (18FARIMA20); Fisheries and Oceans Canada (2018-032-QC-UQAR-Bélanger);
Natural Sciences and Engineering Research Council of Canada (RGPIN-2019-06070); Québec-Ocean.
Acknowledgments. We acknowledge all persons involved in the fieldwork campaigns and laboratory analyses of
the WISE-Man project for the support they provided. The first author also expresses his sincere gratitude to Dr. Rakesh
Kumar Singh for his technical guidance and suggestions.
Disclosures. The authors declare no conflicts of interest.
Data availability. The used dataset along with a detailed description of the acquisition and processing steps for all
the data from WISE-Man 2019 fieldwork is publicly available at [63].
Supplemental document. See Supplement 1 for supporting content.
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