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Sensors and Materials, Vol. 35, No. 11 (2023) 3807–3828
MYU Tokyo
S & M 3452

Uncertainty Analysis of Particle Backscattering Coefficient
Measurement for Multiple Highly Turbid Water Areas
in Ocean Color Remote Sensing
Hiroto Higa,1* Ryota Ideno,1 Salem Ibrahim Salem,2,3 and Hiroshi Kobayashi4
1Institute of Urban Innovation, Yokohama National University,

Hodogaya, Yokohama, Kanagawa 240-8501, Japan

2Faculty of Engineering, Kyoto University of Advanced Science,

18 Yamanouchi Gotanda-cho, Ukyo-ku, Kyoto 615-8577, Japan
3Faculty of Engineering, Alexandria University,
Lotfy El-Sied St. off Gamal Abd El-Naser-Alexandria, Alexandria Governorate 11432, Egypt
4Division of Life and Environmental Sciences, University of Yamanashi,
Takeda, Kofu, Yamanashi 400-8510, Japan(Received July 11, 2023; accepted October 19, 2023)

Keywords: backscattering coefficient, Hydroscat-6P, σ correction, Hydrolight

In this study, we aimed to understand the uncertainty of measured values of the particle
backscattering coefficient (bbp) obtained using the in situ backscattering meter Hydroscat-6P in
three highly turbid water bodies with distinct optical properties and assess their impact on theestimation results through inversion. The field observations were conducted in Tokyo Bay,
where organic matter dominates, Lake Kasumigaura, where cyanobacteria are abundant andmixed with inorganic suspended matter, and the estuary of Bangpankong River in the Upper
Gulf of Thailand, where inorganic suspended matter is highly concentrated. To understand theuncertainty of bbp measurements, radiative transfer simulations were performed using
Hydrolight, and the influence of bbp measurements on the reproduction calculation of remotesensing reflectance (Rrs) was assessed. The results revealed that the reproducibility of Rrs variedamong the water bodies, with a particularly pronounced overestimation compared with themeasured values in the highly scattering environments of Lake Kasumigaura and the Upper
Gulf of Thailand. This overestimation originated from the optical path length without lightattenuation correction (σ correction) in Hydroscat-6P, and the σ correction amplified theoverestimation of Rrs. Although the cause of this overestimation is unclear, it suggests that thecalculation conditions of the radiative transfer model and the effect of multiple scattering
between the sensors of Hydroscat-6P may be contributing factors. The magnitude of thisoverestimation ranged from 64 to 75% in Lake Kasumigaura and from 29 to 39% in the Upper
Gulf of Thailand, significantly affecting the accuracy verification of bbp estimation using
inversion models. These results highlight the uncertainty of bbp measurements in highly turbid
water bodies with high light scattering, emphasizing the need for careful attention to the qualityof previously acquired in situ data when evaluating the performance of inversion algorithms.
*Corresponding author: e-mail: higa@ynu.ac.jp

https://doi.org/10.18494/SAM4576

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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1.

Sensors and Materials, Vol. 35, No. 11 (2023)

Introduction

In ocean color remote sensing, the inherent optical properties (IOPs) represent the absorption
and scattering of light dependent on water and its constituents. IOPs are important parameters
for understanding the physical, biological, and chemical properties of marine substances, andnumerous estimation algorithms have been proposed in previous studies.(1) One of the IOPs, thebackscattering coefficient (bbp), is a parameter obtained by integrating the volume scatteringfunction (VSF) over the backward hemisphere and varies with the size, shape, and compositionof the substances in the water. Particularly in coastal areas, it has been reported that scatteringcharacteristics vary owing to the occurrence of highly scattering phytoplankton and theconcentrations, particle sizes, and compositions of inorganic suspended solids such as sand. In
highly turbid water areas with various substances mixed together, these variations are considered
to become more complex.(2)In such highly turbid water areas, the decrease in estimation accuracy by inversion models of
IOPs has been a concern.(3,4) At the same time, uncertainties in the measurement of bbp itself
have been pointed out.(5) Various methods have been proposed for measuring bbp, and among
them, commercially available field-type backscattering meters have been widely used in manystudies and employed for radiative transfer calculations and validation of IOP estimation
models.(6,7) One of these field-type backscattering meters is the Hydroscat series by HOBI Labs,
Inc., which enables simple measurement of bbp in the field and has been utilized in manystudies. (8,9) In the measurement of bbp using the Hydroscat series, the sensor of the instrument
measures the VSF at a fixed angle of 140° [β (140)] in multiple spectral bands. The conversion
coefficient χ is then used to convert the VSF at a fixed angle to bbp.(10,11)
In general, field-type backscattering measurement devices such as Hydroscat require
correction methods to account for the attenuation of light along the optical path between theemission of light from the light emitting diode and its reception at the photodiode. In the case of
Hydroscat, a correction method called σ correction has been proposed, which evaluates and adds
the attenuation component of scattered light along the optical path.(11) However, it has been
pointed out that errors in bbp measurement occur during the σ correction stage in highly turbid
water areas,(12) and new correction methods suitable for such areas have also been proposed.(5)For these correction methods, including the σ correction, it is important to determine the opticalcharacteristics of the water area in advance and apply the appropriate method. However, theapplicability of these methods to water areas with different optical characteristics has not beenclearly established. Furthermore, in previous studies, to verify the measurement accuracy of bbp,
radiative transfer models have been used to calculate apparent optical properties such as remotesensing reflectance (Rrs) using IOPs as input values, and these calculated values are comparedwith the measured values.(5,13,14) The calculation conditions for the absorption coefficients andthe angular distribution of scattering in radiative transfer calculations ideally should use
measured values. However, there are often limited examples where all parameters are measured,and it is important to evaluate the effect of differences in calculation conditions on the calculation
accuracy using the limited measured values. Furthermore, the uncertainty of the measured
values of bbp may also lead to incorrect interpretations of the validation results of inversion
models, highlighting the importance of understanding its impact.

Sensors and Materials, Vol. 35, No. 11 (2023)

3809

Therefore, in this study, we aim to assess the uncertainties in bbp measurements using thefield-type backscattering instrument Hydroscat-6P in three highly turbid water areas withsignificantly different optical characteristics: Tokyo Bay, Lake Kasumigaura, and the mouth of
Bangpankong River in the Upper Gulf of Thailand. The characteristics of bbp measurements andthe tendencies for uncertainty in each water area were investigated by comparing the calculated
values of Rrs using the radiative transfer model Hydrolight with the measured values.
Furthermore, the impact of uncertainties in bbp measurements on the validation results of theinversion models in each water area was assessed. In this study, the definition of high-turbidity
water areas refers to regions where organic and inorganic suspended matter coexist, leading to ahigh concentration of particulate matter in the water.

2.

Materials and Methods

2.1

Field observations

In this study, optical and water quality observations were conducted at the observation sites
shown in Fig. 1, focusing on Tokyo Bay and Lake Kasumigaura in Japan, and the estuary of the
Bangpankong River in the Upper Gulf of Thailand (referred to as the Upper Gulf of Thailand).
In Tokyo Bay, a total of 10 observation campaigns (N = 49) were conducted between September

Fig. 1. Observation sites in Tokyo Bay, Lake Kasumigaura and at the estuary of Bangpankong River, Upper Gulfof Thailand

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Sensors and Materials, Vol. 35, No. 11 (2023)

2011 and September 2022. In Lake Kasumigaura, three observation campaigns (N = 12) took
place between August 2017 and August 2018. In the Upper Gulf of Thailand, one observation
campaign (N = 8) was conducted in July 2011.
Tokyo Bay is located between approximately 35.45 to 35.62°N latitude and 139.77 to 140.02°E
longitude, with a north–south extent of 50 km and an east–west extent of 10–30 km, covering an
area of 960 km². The bay is highly eutrophic with significant organic pollution, and red tides
occur approximately 70 times per year. Lake Kasumigaura is the second largest lake in Japan,
located between approximately 35.97 to 36.12°N latitude and 139.77 to 140.02°E longitude. It has
a surface area of 168 km², a water volume of 800 × 106 m³, and a catchment area of 220 km². The
lake is shallow with an average depth of 4.0 m. The water level of the lake is controlled by gatesat its outlet, and it takes about 200 days to replace the lake water. The lake is also eutrophic, andoccurrences of Microcystis-dominated cyanobacterial blooms have been reported. The estuaryof Bangpankong River in the Upper Gulf of Thailand is located between approximately 13.30 to
13.15°N latitude and 100.45 to 101.00°E longitude. In the river mouth area, inorganic suspended
matter dominates, resulting in significant light scattering.(15)In the measurement of bbp, the Hydroscat-6P instrument from HOBI Labs, Inc. was deployedvertically from a ship to measure the vertical profiles of β (140) at six wavelengths: 420, 442,
488, 510, 550, and 676 nm. The measured β (140) values were converted to bbp by the method
described in Sect. 2.2. In this study, the vertical profiles of bbp were examined, and any sudden
abnormal values were removed. The average values from depths of 0.5 to 1.5 m were used as thesurface bbp values.
For the measurement of absorption coefficients, water samples were collected at eachlocation. Subsequently, 25 mm Whatman Grade GF/F filters with a pore size of 0.7 μm wereused to measure the phytoplankton absorption (aph) and the non-algal particle absorption (aNAP)
using a spectrophotometer (JASCO V-550) based on the filter pad method. The colored dissolved
organic matter absorption (aCDOM) was measured by filtering through 47 mm Whatman Grade
GF/F filters with a pore size of 0.7 μm, followed by sequential filtration through 47 mm
Nuclepore membrane filters with a pore size of 0.4 μm and 47 mm Nuclepore membrane filterswith a pore size of 0.2 μm. The filtrate was then transferred to a 14 cm quartz cell with adiameter of 25 mm for measurement using the spectrophotometer (JASCO V-550).
For the measurement of apparent optical properties, such as upwelling radiance anddownwelling irradiance, the TriOS RAMSES ARC/ACC instrument was used, and the ratio Rrs
was calculated. The chlorophyll-a (Chl-a) concentration was measured using a fluorometer(Turner Designs 10-AU-005-CE). Total suspended solids (TSS) and inorganic suspended solids(ISS) were measured by the dry weight method.
2.2

Calculation method of backscattering coefficient

The field-deployable backscattering instrument used in this study, Hydroscat-6P, measures
bbp at six wavelengths using a 140° scattering light measurement method. The instrument
consists of an emitter and a receiver located at the bottom. The emitter emits light from an LED,
forming a sampling volume in the water, while the receiver’s photodiode measures the volume

Sensors and Materials, Vol. 35, No. 11 (2023)

3811

scattering function β (140) by detecting the scattered light at 140°. Along the optical path
between the emitter and receiver, the emitted light is attenuated by water and substances present
in the water, resulting in light attenuation. The σ correction method is used to account for theattenuation caused by light scattering. In the σ correction, the following equation considers theeffect of light attenuation:β (140=) k1exp ( kexp × kbb ) × βu (140 ) .

(1)

k1 is set to 1 for practical purposes at all wavelengths. kexp represents the wavelength-dependent
optical path length between the emitter and receiver, βu is the measured volume scatteringfunction, and β is the volume scattering function after σ correction is applied. Here, σ (kbb) isexpressed as σ (kbb) = k1exp (kexp × kbb), where σ (kbb) represents the σ coefficient. kbb is theattenuation coefficient of light along the optical path, and it is described by the following
equation as reported by HOBI Labs, Inc. (2008).(16)kbb = anw + 0.4 × bp

(2)

Here, anw represents the nonwater-contributed absorption coefficient, and bp represents thenonwater-contributed scattering coefficient. bp can be calculated using the following equation:=bp (bbu − bbw ) / B.

(3)

Here, bbu is the backscattering coefficient before correction, bbw is the backscattering coefficientof water, and B is the backscattering probability. In previous studies, the actual measured valuesof bp were used, and methods for calculating kbb were employed.(17) However, instruments suchas the absorption and attenuation meter (AC-9) and AC-spectral absorption and attenuation
sensor (AC-S), which are used to measure bp, have uncertainties in the correction for lightattenuation in highly turbid waters.(12) Additionally, in commonly available optical datasets, datafor bp are often not measured. Therefore, in this study, reference was made to HOBI Labs, Inc.
(2008),(16) and B was set to a constant value of 0.015. The anw in Eq. (2) was determined using
measured values. The conversion from β to bbp was performed using a scaling factor χ, as shownin the following equation. When no σ correction is applied, it is denoted as bbp,u and expressed asshown in Eq. (5).
bbp =2π × χ × ( β (140 ) − β w (140 ) )(4)

bbp , u =2π × χ × ( β u (140 ) − β w (140 ) )(5)

bb is obtained by integrating the volume scattering function over the backward hemisphere.
Using the mean value theorem of integration, it can be expressed as bb = 2πβ (θ) using thevolume scattering function β (θ) at a certain angle θ. A scaling factor χ has been proposed to
calculate bb from the volume scattering function at a specific angle.(10) In this study, χ = 1.08 wasused for β (140).(16)

3812

2.3

Sensors and Materials, Vol. 35, No. 11 (2023)

Radiative transfer model and IOP inversion model

In this study, we conducted an accuracy assessment of the measured values of bp using theradiative transfer model Hydrolight 6.0.(18) The radiative transfer model solves the onedimensional and time-independent radiative transfer equation in the vertical direction of thewater column to calculate the distribution of radiance in a parallel plane in the marine area. The
input value for the beam attenuation coefficient (c) was calculated as the sum of the measured
total absorption coefficient (a) and the total scattering coefficient (b). The total scattering
coefficient was converted by adding the contribution of backscattering by water to Eq. (4) andthen dividing it by a value equivalent to the parameter B used in Eq. (3). It was then calculated as
the sum of a measured value. The phase function was represented using the Fournier–Forandphase function(19) to express the scattering characteristics with respect to B. The solar zenith
angle and wind speed were set to constant values of 30° and 5.0 m/s, respectively. Furthermore,
for the boundary conditions at the seafloor, considering the high turbidity and large water depths
in the three study areas, it was assumed that light does not reach the seafloor and the calculations
were performed with an infinite water depth. The calculation wavelengths were set to the six
wavelengths measured by Hydroscat-6P, and chlorophyll fluorescence was taken into accountusing the model proposed by Gilerson et al.(20)The IOP inversion model, based on the Bio-Optical model, used the Quasi-Analytical
Algorithm v6(21) to estimate the IOPs step by step. This allowed us to assess the influence of theuncertainty in the measured values on the accuracy of bbp estimation.
2.4

Error metrics

The comparison between the estimated bbp obtained through QAA, the calculated Rrs using
the radiative transfer model, and their respective measured values was evaluated using two error
metrics: root mean square logarithmic error (RMSLE) and Bias.
1

2 2
1 N
=
RMSLE  ∑ log10 ( X iE ) − log10 ( X iM )  N i =1


(

=
Bias

N
1
( X iE − X iM )
∑
i =1
N

)

(6)

(7)

Here, N represents the number of samples, X iE denotes the estimated values obtained from themodel, and X iM represents the corresponding measured values.

Sensors and Materials, Vol. 35, No. 11 (2023)

3.

Results

3.1

Field observation results

3813

Table 1 presents the statistical indicators of water quality and IOPs for each study area, Fig. 2
shows the spectral distribution of Rrs for each study area, and Fig. 3 depicts the spectral
distribution of bbp. When comparing the spectral distributions of Rrs for each study area, theintensity of Rrs at 550 nm is approximately three times greater in Lake Kasumigaura and theUpper Gulf of Thailand than in Tokyo Bay. On the other hand, the average value of bbp at 550 nm
in Lake Kasumigaura and the Upper Gulf of Thailand is more than ten times higher than that inTokyo Bay, suggesting an increase in Rrs owing to the effect of light scattering. Although thedifference in the average values of Chl-a between Tokyo Bay and Lake Kasumigaura is small, it
is evident that the maximum Chl-a in Tokyo Bay reaches a high level of 93.6 mg/l. In a
Table 1Minimum, maximum, mean, and standard deviation (SD) values of water quality parameters (Chl-a, TSS, OSS,
ISS) and IOPs [aph (443), aCDOM (443), aNAP (443), bbp (443), bbp (550)] for Tokyo Bay, Lake Kasumigaura, and theUpper Gulf of Thailand.
Minimum
Maximum
Mean
SD
Tokyo Bay (N = 43)
2.90
93.64
28.80
27.90
Chl-a (mg/m3)
2.99
23.43
10.79
5.51
TSS (g/m3)
0.32
13.35
5.66
3.26
OSS (g/m3)
0.81
12.54
5.14
2.80
ISS (g/m3)
0.23
4.00
1.15
0.83
aph (443) (/m)
0.06
0.67
0.31
0.14
aCDOM (443) (/m)
0.10
4.43
0.62
0.88
aNAP (443) (/m)
0.009
0.100
0.034
0.019
bbp (443) (/m)
0.006
0.064
0.027
0.013
bbp (550) (/m)
Lake Kasumigaura (N = 12)
16.32
43.27
26.06
8.33
Chl-a (mg/m3)
17.61
33.75
25.54
5.95
TSS (g/m3)
5.08
8.16
6.86
1.25
OSS (g/m3)
11.82
26.00
18.68
5.34
ISS (g/m3)
0.28
1.48
0.68
0.38
aph (443) (m−1)
0.09
1.48
0.81
0.54
aCDOM (443) (m−1)
0.48
1.03
0.76
0.19
aNAP (443) (m−1)
0.168
0.590
0.342
0.149
bbp (443) (m−1)
0.177
0.530
0.328
0.133
bbp (550) (m−1)
Upper Gulf of Thailand (N = 8)
3.05
32.00
13.46
11.91
Chl-a (mg/m3)
2.70
32.60
14.61
10.53
TSS (g/m3)
0.80
4.40
2.51
1.33
OSS (g/m3)
1.70
28.10
12.09
9.25
ISS (g/m3)
0.21
1.41
0.64
0.43
aph (443) (m−1)
0.06
0.43
0.20
0.13
aCDOM (443) (m−1)
0.33
2.07
1.01
0.61
aNAP (443) (m−1)
0.045
0.881
0.356
0.265
bbp (443) (m−1)
0.036
0.711
0.288
0.218
bbp (550) (m−1)

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Sensors and Materials, Vol. 35, No. 11 (2023)

(a)

(b)

(c)
Fig. 2. Spectral distribution of Rrs in each water body. (a) Tokyo Bay, (b) Lake Kasumigaura, and (c) Upper Gulf ofThailand.

(a)

(b)

Fig. 3. Spectral distribution of bbp in each water body. (a) Tokyo Bay, (b) Lake Kasumigaura, and (c) Upper Gulf ofThailand.

Sensors and Materials, Vol. 35, No. 11 (2023)

3815

(c)
Fig. 3. (Continued) Spectral distribution of bbp in each water body. (a) Tokyo Bay, (b) Lake Kasumigaura, and (c)Upper Gulf of Thailand.

comparison of Chl-a among the three water bodies, the average value in the Upper Gulf ofThailand is approximately half of the levels observed in Tokyo Bay and Lake Kasumigaura. The
maximum values of ISS are 26.0 mg/l in Lake Kasumigaura and 28.1 mg/l in the Upper Gulf ofThailand, which are higher than the maximum value of 12.5 mg/l in Tokyo Bay. The percentagesof ISS relative to TSS are 48% in Tokyo Bay, 73% in Lake Kasumigaura, and 83% in the Upper
Gulf of Thailand. It is noteworthy that even in Lake Kasumigaura, the proportion of ISS isrelatively high, similar to the Upper Gulf of Thailand. This can be attributed to rainfall observedon the days preceding the observation, specifically, on July 10 and August 7 to 9, 2018, which
resulted in the influx of ISS from rivers and the resuspension of sediments owing to wind action.
In the Upper Gulf of Thailand, the high concentration of ISS near the river mouth is considered
to be the main cause of increased light scattering and the subsequent increase in Rrs intensity.
3.2

Calculation results of Rrs using radiative transfer simulation

Figure 4 shows the comparison between the calculated values and measured values of Rrs
obtained through radiative transfer simulations using the measured values of bbp after applying
the σ correction method. Table 2 presents the error metrics (Bias, RMSLE) for each water bodyand wavelength based on the results in Fig. 4. Analyzing the Bias for each wavelength in eachwater body, we observed that Lake Kasumigaura and the Upper Gulf of Thailand had positive
Bias values across the six wavelengths, indicating an overall overestimation compared with
Tokyo Bay. Tokyo Bay, as indicated in Table 2, is a water body where the effect of lightabsorption is significant, resulting in lower Rrs values at each wavelength. The average RMSLE
for each wavelength in Tokyo Bay was 0.197, the lowest among the three water bodies. On theother hand, Lake Kasumigaura and the Upper Gulf of Thailand had higher RMSLE values of
0.533 and 0.288, respectively. In Tokyo Bay, the calculated Rrs values were overestimatedcompared with the measured values at shorter wavelengths (420, 442, and 480 nm), while they
were underestimated at longer wavelengths (510, 550, and 676 nm). In Lake Kasumigaura and3816

Sensors and Materials, Vol. 35, No. 11 (2023)

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 4. Calculated and measured values of Rrs at six wavelengths obtained using the radiative transfer model. The
results in the figure represent the following wavelengths: (a) 420, (b) 442, (c) 488, (d) 510, (e) 550, and (f) 676 nm.
The circles represent Tokyo Bay, squares represent Lake Kasumigaura, and triangles represent the Upper Gulf ofThailand.

Sensors and Materials, Vol. 35, No. 11 (2023)

3817

Table 2
Results of Bias and RMSLE for the calculated values of Rrs and the measured values obtained using the radiativetransfer model. The results are presented for Tokyo Bay, Lake Kasumigaura, and the Upper Gulf of Thailand at six
different wavelengths.
Upper Gulf
Wavelength (nm)Tokyo Bay
Lake Kasumigauraof Thailand
420
0.156
3.536
2.942
442
0.163
5.724
4.698
480
0.018
7.494
5.479
–3
Bias (×10 )510−0.09712.0496.743
550−0.25015.1409.038
676−0.408
3.401
1.278
420
0.170
0.629
0.332
442
0.181
0.664
0.369
480
0.184
0.524
0.327
RMSLE
510
0.185
0.567
0.333
550
0.179
0.488
0.329
676
0.203
0.301
0.242

the Upper Gulf of Thailand, the Bias values were positive for all wavelengths, indicating an
overall overestimation of Rrs compared with the measured values, and the relative errors werealso found to be larger. These results confirm that the reproducibility of the radiative transfer
calculations is lower in water bodies with a significant effect of light scattering.
3.3

Estimation results of bbp using the inversion model

Using the inversion model, specifically, the QAA, we estimated bbp at six different
wavelengths based on the Rrs values for each water area. The estimated values and the measured
values are shown in Fig. 5. Table 3 presents the Bias and RMSLE for each water area at the six
wavelengths. In this case, the measured values of bbp on the horizontal axis are the results ofapplying the previous σ correction. For Tokyo Bay, the average RMSLE at the six wavelengths is0.20, indicating a relatively high accuracy in the estimation. On the other hand, for Lake
Kasumigaura and the Upper Gulf of Thailand, the average RMSLE at the six wavelengths is 0.72
and 0.35, respectively, which is 1.5 to 3.5 times larger than that for Tokyo Bay. Moreover, in allcases, the Bias values are negative, indicating an underestimation of the estimated values
compared with the measured values. These results suggest the possibility of errors in theestimation using inversion, particularly for Lake Kasumigaura and the Upper Gulf of Thailand,
which have distinct characteristics with higher values of bbp. However, as pointed out by deCarvalho et al.(12) and Doxaran et al.,(5) the uncertainty of the measurement results at themeasurement stage, including corrections for the optical path length of bbp measured values,
may also affect the validation results.

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 5. Estimated and measured values of bbp at six different wavelengths using the inversion model. Results at (a)420, (b) 442, (c) 488, (d) 510, (e) 550, and (f) 676 nm. The circles represent Tokyo Bay, the squares represent Lake
Kasumigaura, and the triangles represent the Upper Gulf of Thailand.

Sensors and Materials, Vol. 35, No. 11 (2023)

3819

Table 3Results of Bias and RMSLE for the estimated values of bbp calculated using the inversion model shown in
Fig. 5, compared with the measured values. The results are presented for Tokyo Bay, Lake Kasumigaura, andthe Upper Gulf of Thailand at six different wavelengths.
Upper Gulf
Wavelength (nm)Tokyo Bay
Lake Kasumigauraof Thailand
420−1.167−22.440−12.613442−1.316−28.030−16.071480−0.816−22.307−11.482−2
Bias (×10 )510−0.792−28.371−11.612550−0.690−26.716−11.628676−0.198−16.200−5.858
420
0.229
0.708
0.356
442
0.245
0.774
0.417
480
0.197
0.701
0.346
RMSLE
510
0.195
0.782
0.354
550
0.186
0.765
0.358
676
0.142
0.605
0.234

3.4

Calculation results of Rrs using bbp with and without σ correction

To understand the effect of σ correction in Hydroscat-6P backscattering measurements on
bbp, the measured values of bbp were used as input to Hydrolight to calculate Rrs at six different
wavelengths, considering two cases: one with σ correction applied and the other without σcorrection. The relationship between the calculated Rrs values and the measured values is shownin Fig. 6. Additionally, Table 4 presents the error metrics for the calculated Rrs values andmeasured values in these two cases and for each water body. Focusing on the results for Tokyo
Bay at each wavelength in Fig. 6, we observed that the variations in Bias and RMSLE owing to
the application or absence of σ correction are small. However, for Lake Kasumigaura and theUpper Gulf of Thailand, when σ correction is applied, Bias is positive and large, indicating an
overestimation. Furthermore, except for 676 nm in the Upper Gulf of Thailand, in the absence of
σ correction, Bias and RMSLE are significantly smaller than in cases with σ correction, and the
distribution of Rrs approaches the 1:1 line. In the case of the Upper Gulf of Thailand, thecalculated Rrs values exhibit positive Bias in all wavelengths when σ correction is applied,
whereas in the absence of correction, all Bias values are negative. This indicates a transition
from an overestimation tendency to an underestimation tendency due to the absence of σcorrection. On the other hand, in the case of Lake Kasumigaura, the calculated Rrs values are
already overestimated compared with the measured values at all six wavelengths in the absenceof σ correction. The application of σ correction further amplifies the overestimation, resulting in
an approximately 2.5-fold increase in RMSLE. This suggests that in highly turbid water bodies
with significant light scattering, the excessive correction of light attenuation due to σ correction
may lead to an overestimation of the bbp measurement.

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Sensors and Materials, Vol. 35, No. 11 (2023)

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 6. Rrs values calculated using the radiative transfer model with the measured bbp values are compared with theactual measurements. The results at six different wavelengths are shown: (a) 420, (b) 442, (c) 488, (d) 510, (e) 550,
and (f) 676 nm. The circles represent Tokyo Bay, squares represent Lake Kasumigaura, and triangles represent theUpper Gulf of Thailand. The unfilled symbols represent the case with σ correction, whereas the filled symbols
represent the case without σ correction.

Sensors and Materials, Vol. 35, No. 11 (2023)

3821

Table 4
Bias and RMSLE for the relationship between calculated Rrs values and actual measurements at six wavelengths,
using measured bbp values as input for the radiative transfer model in two cases: with and without σ correction.
Tokyo Bay
Lake Kasumigaura
Upper Gulf of Thailand
Wavelength
without
without
without
with σ corr.
with σ corr.
with σ corr.
(nm)
σ corr.
σ corr.
σ corr.
420
0.156−0.060
3.536
0.605
2.942
−1.432442
0.163−0.088
5.724
0.924
4.698
−1.642480
0.018−0.239
7.494
1.239
5.479
−2.450−3
Bias (×10 )510−0.097−0.36112.0492.353
6.743−2.317550−0.250−0.55015.140
3.124
9.038−1.942676−0.408−0.4933.401−0.0201.278−2.935
420
0.170
0.186
0.629
0.306
0.332
0.254
442
0.181
0.201
0.664
0.299
0.369
0.247
480
0.184
0.227
0.524
0.225
0.327
0.250
RMSLE
510
0.185
0.231
0.567
0.239
0.333
0.233
550
0.179
0.216
0.488
0.199
0.329
0.225
676
0.203
0.233
0.301
0.127
0.242
0.284

4.

Discussion

4.1

Correction of light attenuation due to optical path length in backscattering
measurements

As shown in Fig. 6, it is suggested that the measured bbp values may be overestimated due tothe excessive correction of light attenuation caused by the σ correction. As indicated by Eq. (1),the σ coefficient is expressed exponentially and always has a value greater than or equal to 1.
This correction method adds the light attenuation component in the optical path length
cumulatively and is a reasonable formulation. However, in highly turbid waters, the βu value,
which is the volume scattering function before σ correction, may already be overestimatedduring the measurement stage, resulting in a further increase in bbp through the σ correction.
The exact factors contributing to the overestimation of βu at this optical path length are unclear,but it is possible that the effects of multiple scattering, caused by the presence of densely packed
particulate matter in highly turbid waters, lead to a shorter effective optical path length between
the sensors, affecting βu or the measured bbp value before the σ correction. Zhang et al.(22)evaluated how fixed-angle backscattering sensors detect photons with specific scattering angles
in situations where multiple scattering occurs, using Monte Carlo simulations. Under theconditions of a = 2 (/m) and Fournier–Forand phase function (B = 0.022), Hydroscat-6 (not 6P)
showed that the proportion of detected scattered photons that were due to multiple scattering
increased for b values greater than 5 (/m), reaching 92% at b = 20 (/m). It was also mentioned thatmultiple scattering can lead to an extension of the optical path length, causing changes in the
scattering angles of detected light. On the other hand, an increase in absorption results in ashorter optical path length, and variations in the size of absorption and scattering lead to changes
in the scattering angles of detected light. Considering the effect of multiple scattering on sensor
detection based on the magnitude of absorption and scattering in the measurement area, it is3822

Sensors and Materials, Vol. 35, No. 11 (2023)

important to appropriately evaluate βu. In this study, the average values of bbp(550) in thesurveyed areas of Lake Kasumigaura and the Upper Gulf of Thailand were 0.34 and 0.29 (/m),
respectively, which is more than 10 times higher than Tokyo Bay’s 0.03 (/m). In water areas withsuch significant light scattering, it can be inferred that the effect of multiple scattering cannot beignored. Furthermore, in the three study areas, the average values of TSS were 10.8, 25.5, and14.6 (mg/l) for Tokyo Bay, Lake Kasumigaura, and the Upper Gulf of Thailand, respectively.
The maximum values were 23.4, 33.8, and 32.6 (mg/l), respectively, indicating highconcentrations. The proportions of ISS to TSS were 48% in Tokyo Bay, 72% in Lake
Kasumigaura, and 78% in the Upper Gulf of Thailand. Notably, Lake Kasumigaura and theUpper Gulf of Thailand exhibited significantly higher proportions of ISS, which is considered tobe the primary factor contributing to the heightened light scattering observed in these regions.
In addition, Doxaran et al.(5) addressed the uncertainties in bbp measurements in highly
turbid waters and proposed a new correction method for light attenuation. Additionally, their
method, which utilizes the Fournier–Forand function, has demonstrated improved
reproducibility of radiative transfer calculations in Monterey Bay, California, where harmful
algal blooms occur.(6) However, they used Hydroscat-4, which has a shorter optical path lengththan Hydroscat-6P used in this research, and reported that the difference in optical path length
has a significant impact on the degree of multiple scattering effects. Therefore, in future studies,a correction method is needed to reduce the overestimation of light scattering for sensors withlonger optical path lengths, such as Hydroscat-6P, in highly turbid waters where multiple
scattering occurs.
4.2

Uncertainties in radiative transfer calculations

While we examined the uncertainties associated with the measurement of the bbp in thisstudy, there are remaining challenges in understanding the uncertainties related to themeasurement of the absorption coefficient, the setting of the backscattering probability in theradiative transfer model, the setting of the scattering phase function, and the vertical distribution
of IOPs. The measured values of the absorption coefficient used as input in the radiative transfer
model in this study were obtained using a spectrophotometer in transmittance mode. Boss etal.(23) recommends spectrophotometry in internally-mounted cuvettes inside an integrating
sphere (IS-mode) to minimize uncertainties caused by scattering losses for the accurate
measurement of the particle absorption coefficient. It is particularly important to pay attention to
the quality of measured absorption coefficients in highly turbid waters. Additionally, in the filter
pad method for absorption coefficient measurement, a pathlength amplification factor β, namely,
β correction factor, is applied to correct for various scattering effects occurring between particles
and filters or within filters. In this study, the β correction factor from Stramski et al.(24) wasused, and the differentiation of the β correction factor usage across multiple water bodies has notbeen implemented, so evaluating its impact in the future is necessary. Moreover, regarding thevertical distribution of IOPs, since the target water bodies mainly consist of highly turbid waterwith low transparency, a uniform distribution of IOPs was assumed. However, the effects ofchanges in the vertical distribution on radiation have been reported,(25) and this should beSensors and Materials, Vol. 35, No. 11 (2023)

3823

considered as a future research challenge. Furthermore, in this study, the calculation of bbp was
performed by fixing χ based on the average theorem of integrating from a single angle of the
VSF. However, for highly turbid water where the angular distribution of the VSF can becomecomplex, considering variations in χ is necessary. According to Xiong et al.,(26) approximately
71% of the uncertainty in Rrs attributed to the shape of the VSF can be explained by thebackscattering probability of particles (Bp), approximately 90% by the scattering phase function,
and approximately 97% by the conversion coefficient χ p for particles. Additionally, theapplicability of analytical functions such as the Fournier–Forand function in highly turbid water
is known to be uncertain,(27,28) and further research on its applicability is needed in the future.
4.3

Overestimation in backscattering measurements and its proportion

As shown in Sect. 3.4, in highly turbid water bodies such as Lake Kasumigaura and theUpper Gulf of Thailand, the calculated Rrs values obtained from the radiative transfer modelusing IOPs as inputs were found to be overestimated compared with the measured values. Thissuggests the possibility of overestimation in scattering measurements, including the σ correction.
To investigate the proportion of overestimation caused by excessive scattering, the bbp values
obtained from the σ corrected measurements were multiplied by a constant A ranging from 0.01
to 1 with an interval of 0.01. The calculated Rrs values using these modified inputs in Hydrolight
were compared with the measured values to determine the proportion of overestimation using
the RMSLE metric. Table 5 shows the results of the constants A corresponding to the minimum
RMSLE for each wavelength in each water body. Examining the results, we found that for Tokyo
Bay, the RMSLE between the calculated Rrs values and the measured values was minimized
when using the σ-corrected bbp values (A = 1) for wavelengths of 510, 550, and 676 nm. Thissuggests that in Tokyo Bay, where light absorption is dominant, the impact of scattering
measurement uncertainty on the calculation results of Rrs is limited, and the conventional σcorrection method appropriately compensates for the effect of light attenuation. In contrast, in
Lake Kasumigaura and the Upper Gulf of Thailand, characterized by significant light scattering,
there was a potential overestimation of light scattering in 64–75% and 29–39% proportions,
respectively, for the five wavelengths excluding 676 nm. The cause of this overestimation could
be attributed to multiple scattering effects occurring in the optical path length between sensors.
The proportions of overestimation were specific to each water body, indicating their uniquecharacteristics within the limited sample range of this study. Additionally, for Lake Kasumigaura
and the Upper Gulf of Thailand, the proportion of overestimation at 676 nm, in the near-infrared
region, was smaller than at other wavelengths, suggesting a relationship with the suitability of
Table 5The optimal value of constant A, which minimized the RMSLE between the calculated and measured Rrs values,
was determined for each water body and wavelength combination using the σ-corrected bbp measurements.
Wavelength (nm)
420
442
480
510
550
676
Tokyo Bay
0.81
0.81
0.97
1.00
1.00
1.00
Lake Kasumigaura
0.27
0.25
0.35
0.31
0.36
0.59
Upper Gulf of Thailand
0.65
0.61
0.70
0.69
0.71
1.00

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Sensors and Materials, Vol. 35, No. 11 (2023)

chlorophyll fluorescence models. Furthermore, as mentioned in Sect. 4.2, the results of the
proportion of A are also influenced by the computational conditions of the radiative transfer
calculations.
Next, the QAA inversion algorithm was used to estimate bbp using the measured Rrs values.
Figure 7 shows the relationship between the measured bbp values, including the proportion ofoverestimation, and the estimated bbp values. The error metrics are presented in Table 6. From
the results for Lake Kasumigaura and the Upper Gulf of Thailand, the relationship between themeasured and calculated bbp values using the conventional method showed negative biases of−0.24 and −0.115, indicating underestimation. However, when considering the proportion ofoverestimation in the measured bbp values, the biases were still negative (−0.042 and −0.058), butwith lower RMSLE than the conventional method. This suggests that the distribution of bbp
values approached the 1:1 line. These findings indicate that overestimation in bbp measurements
can significantly affect the accuracy validation of the inversion algorithm. These findings
emphasize the importance of improving the accuracy of bbp measurements in the performance
evaluation of inversion algorithms targeting highly turbid water bodies and the need to carefully
assess the quality of previously acquired measured data.

(a)

(b)

(c)

(d)

Fig. 7. Estimated values of bbp obtained from the inversion model and the measured values of bbp multiplied by aconstant A. The wavelengths (a) 420, (b) 442, (c) 488, (d) 510, (e) 550, and (f) 676 nm indicate the measurement
wavelengths of bbp.

Sensors and Materials, Vol. 35, No. 11 (2023)

(e)

3825

(f)

Fig. 7. (Continued) Estimated values of bbp obtained from the inversion model and the measured values of bbp
multiplied by a constant A. The wavelengths (a) 420, (b) 442, (c) 488, (d) 510, (e) 550, and (f) 676 nm indicate themeasurement wavelengths of bbp.

Table 6
Results of Bias and RMSLE for the estimated bbp values obtained from the inversion model, measured values, andmeasured values multiplied by constant A. Results are presented for Tokyo Bay, Lake Kasumigaura, and the Upper
Gulf of Thailand at six wavelengths.
Tokyo Bay
Lake Kasumigaura
Upper Gulf of Thailand
Wavelengthin situ bbp in situ bbp × A in situ bbp in situ bbp × A in situ bbp in situ bbp × A(nm)
420−1.167−0.552−22.440−1.504−12.613−5.141442−1.316−0.677−28.030−2.356−16.071−6.485480−0.816−0.731−22.307−3.810−11.482−5.575
Bias (×10 −2)510−0.792−0.792−28.371−4.578−11.612−5.537550−0.690−0.690−26.716−5.727−11.628−5.995676−0.198−0.198−16.200−7.099−5.858−5.858
420
0.229
0.176
0.708
0.178
0.356
0.199
442
0.245
0.185
0.774
0.201
0.417
0.237
480
0.197
0.189
0.701
0.265
0.346
0.214
RMSLE
510
0.195
0.195
0.782
0.291
0.354
0.220
550
0.186
0.186
0.765
0.338
0.358
0.234
676
0.142
0.142
0.605
0.383
0.234
0.234

5.

Conclusions

In this study, optical and water quality observations were conducted in multiple highturbidity coastal areas with different optical characteristics. Tokyo Bay exhibited eutrophication
with a dominance of phytoplankton and a significant effect of light absorption rather thanscattering. On the other hand, Lake Kasumigaura had a mixture of organic and inorganic
substances, whereas the Upper Gulf of Thailand was characterized by the prevalence of
inorganic suspended matter, both exhibiting significant light scattering. By using the measured

3826

Sensors and Materials, Vol. 35, No. 11 (2023)

values of bbp and absorption coefficients obtained from each area as input values, Rrs wascalculated using a radiative transfer model and compared with the measured values to assess theuncertainty of bbp measurements. The results showed that the reproducibility of Rrs had different
trends for each water area, particularly in the highly scattering waters of Lake Kasumigaura andthe Upper Gulf of Thailand, where the calculated values were found to be overestimatedcompared with the measured values. This overestimation was observed even at the stage of
calculating Rrs with the input of precorrection βu values and further magnified by the applicationof σ correction.
Furthermore, the impact of σ correction on bbp measurements was assessed by comparing the
calculated Rrs values with and without σ correction using the respective bbp measurements as
input in Hydrolight. The results indicated that in the highly scattering waters of Lake
Kasumigaura and the Upper Gulf of Thailand, the calculated Rrs values without σ correction
were consistently higher than the measured Rrs values at all wavelengths. This suggests a
potential overestimation of the detected scattering light owing to multiple scattering in the
optical path between Hydroscat-6P sensors when suspended particles are present at high density.
Moreover, the percentage of overestimation was found to be 64–75% for Lake Kasumigaura and
29–39% for the Upper Gulf of Thailand, highlighting its significant impact on the accuracy
assessment of bbp estimation using inversion models. These findings underline the uncertainty
of bbp measurements in high-turbidity waters and emphasize the need for developing correction
methods that appropriately account for the optical path length of light attenuation processes.
Additionally, they suggest the importance of carefully evaluating the quality of past measured
data when assessing the performance of inversion algorithms.

Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP20K14836 and JP22H05716.
In addition, this work was also supported by the Japan Aerospace Exploration Agency (JAXA)
Global Change Observation Mission-Climate (GCOM-C) to PI No. ER3GCF301.

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About the Authors
Hiroto Higa received his B.S. degree from Tokyo University of Science,
Japan, in 2010 and his M.S. and Ph.D. degrees from The University of Tokyo,
Japan, in 2012 and 2015, respectively. From 2016 to 2022, he was an assistantprofessor at Yokohama National University, Japan. Since 2023, he has been an
associate professor at Yokohama National University. His research interests
are in water environmental engineering and ocean color remote sensing.
(higa@ynu.ac.jp)

		Ryota Ideno received his B.S. degree from Yokohama National University,
Japan, in 2022. Since 2022, he has been pursuing his master's degree at
Yokohama National University. His research interests are in the measurementof backscattering coefficients of marine particles and radiative transfer
simulation for the purpose of ocean color remote sensing.
(ideno-ryota-dr@ynu.jp)

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Sensors and Materials, Vol. 35, No. 11 (2023)

Salem Ibrahim Salem received his B.Sc. and M.Sc. degrees from Alexandria
University, Egypt, in 2005 and 2010, respectively. He obtained his Ph.D.
degree from The University of Tokyo, Japan in 2017. Following that, he served
as a postdoctoral researcher at The University of Tokyo from 2017 to 2019.
Since 2019, he has been a junior associate professor at Kyoto University of
Advanced Science, Japan. His research interests lie in the field ofenvironmental monitoring, remote sensing, and data science.
(salem.ibrahim@kuas.ac.jp; eng.salemsalem@gmail.com)
Hiroshi Kobayashi received his B.S., M.S., and Ph.D. degrees from Hokkaido
University, Japan, in 1994, 1996, and 1999, respectively. From 1999 to 2010,
he was an assistant professor at the University of Yamanashi, Japan. Since
2010, he has been an associate professor at the University of Yamanashi. His
research interests are in ocean color remote sensing and measurement of
atmospheric aerosol optical properties. (kobachu@yamanashi.ac.jp)