Landsat 8 provided the potential of optical
remote sensing data source for estimating a
large spatial distribution of the COD concentration, which was almost impossible via a
traditional field-based approach. However,
there was a limitation in monitoring the temporal distribution of the COD concentration
due to local weather conditions of the coastal
area, significantly reducing the quality of satellite data.
The ANN approach provided better COD
estimation than traditional regression model.
Experimental results also showed that the
combination of reflectance values of bands 1
to 4 of Landsat 8 were the most appropriate
inputs to the applied model.
It should be noted that it is difficult and
time-consuming to determine the optimal architecture of the neural network that could
generalize well without over-fitting the data.
In addition, quantifying the uncertainty in the
network outputs should be considered, especially in cases of relatively small training
data set.
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Vietnam Journal of Earth Sciences, 39(3), 256-269, DOI: 10.15625/0866-7187/39/3/10270
256
(VAST)
Vietnam Academy of Science and Technology
Vietnam Journal of Earth Sciences
Remote Sensing for Monitoring Surface Water Quality
in the Vietnamese Mekong Delta: The Application for
Estimating Chemical Oxygen Demand in River Reaches
in Binh Dai, Ben Tre
Nguyen Thi Binh Phuong*1, Van Pham Dang Tri1, Nguyen Ba Duy2, Nguyen Chanh Nghiem1
1Can Tho University, Campus 2, Xuan Khanh Ward, Ninh Kieu Dist., Can Tho City, Vietnam
2Mining and Geology University, Duc Thang ward, North Tu Liem dist., Ha Noi, Vietnam
Received 9 November 2016. Accepted 23 June 2017
ABSTRACT
Surface water resources played a fundamental role in sustainable development of agriculture and aquaculture. In
this study, the approach of Artificial Neuron Network was used to estimate and detect spatial changes of the Chemi-
cal Oxygen Demand (COD) concentration on optical remote sensing imagery (Landsat 8). Monitoring surface water
quality was one of the essential missions especially in the context of increasing freshwater demands and loads of
wastewater fluxes. Recently, remote sensing technology has been widely applied in monitoring and mapping water
quality at a regional scale, replacing traditional field-based approaches. The study used the Landsat 8 (OLI) imagery
as a main data source for estimating the COD concentration in river reaches of the Binh Dai district, Ben Tre prov-
ince, a downstream river network of the Vietnamese Mekong Delta. The results indicated the significant correlation
(R=0.89) between the spectral reflectance values of Landsat 8 and the COD concentration by applying the Artificial
Neuron Network approach. In short, the spatial distribution of the COD concentration was found slightly exceeded
the national standard for irrigation according to the B1 column of QCVN 08:2015.
Keywords: Surface water quality, Chemical Oxygen Demand (COD), Landsat 8 (OLI), remote sensing, Artificial
Neuron Network (ANN), Vietnamese Mekong Delta.
©2017 Vietnam Academy of Science and Technology
1. Introduction1
Surface water quality monitoring was con-
sidered as one of the important techniques to
achieve characteristics of surface water for
supporting sustainable water resources man-
*Corresponding author, Email: ntbphuong19@gmail.com
agement. Agriculture and aquaculture produc-
tion is the major water consumption factors in
the Vietnamese Mekong Delta (Ines et al.,
2001). Expanding production area did not on-
ly contributes to a substantial increase in fresh
water requirements but also to surface water
pollution of the rivers (Renaud and Claudia,
2012).
Nguyen Thi Binh Phuong, et al./Vietnam Journal of Earth Sciences 39 (2017)
257
Water quality monitoring has been studied
by numerous researchers over the last several
years. Many of them considered the optical
parameters such as the total suspended sedi-
ment (TSS), chlorophyll-a (Chl-a) and turbidi-
ty indices (Lavery et al., 1993; Nas et al.,
2010; Waxter, 2014). Some of the studies em-
ployed the statistical approaches to building
the linear correlation while several studies fo-
cused on the Artificial Neuron Network
(ANN) approach, a kind of nonlinear analyti-
cal technique. According to Chebud et al.
(2012), the Artificial Neuron Network (ANN)
could be used to monitor water quality via the
application of the Landsat TM data; a signifi-
cant relationship (R2) between the observed
data and simulated water quality parameters
was found greater than 0.95 (Imen et al.,
2015). An empirical model was also devel-
oped to estimate the suspended sediment con-
centration due to intensive erosion processes
by using the Landsat TM imagery in the Am-
azonian whitewater rivers (Montanher et al.,
2014). By using the MOD09 and the Landsat
TM 4-5 (TM) or Landsat 7 (ETM+) imagery,
an early warning system for monitoring TSS
concentrations was developed. It showed the
high reliability of R2 value and root mean
square between the observed and simulated
TSS (0.98 and 0.5 respectively) (Imen et al.,
2015). The research of Lim and Choi, (2015)
demonstrated that the Landsat 8 OLI could be
appropriate to monitor water quality parame-
ters including suspended solids, total phos-
phorus, Chl-a and total nitrogen.
It was considered that the Chemical Oxy-
gen Demand (COD) performed a weak optical
characteristic leading to the low accurate es-
timation of COD by remote sensing technolo-
gy (Gholizadeh et al., 2016). However, by us-
ing linear regression approach, the relatively
good correlation between reflectance value
retrieved from the Landsat TM images and
ground data of COD reported by Wang et al.,
2004 in reservoirs of Shenzen, Guangdong
Province, China. It was shown that ANN ap-
proach could provide a better interpretation in
comparison with what could be found via the
linear approach (Sudheer et al., 2006; Wang et
al., 1977). Chebud et al., 2012 applied the
ANN model to monitor phosphorus, Chl-a and
turbidity in Kissimmee River by using Land-
sat TM, their result of the square of significant
correlation coefficient exceeds 0.95 was re-
ported. The results also indicated that the root
mean square error values for phosphorus, tur-
bidity, and Chl-a were around 0.03 mg L-1,
0.5 NTU, and 0.17 mg m-3, respectively. Ac-
cording to Wu et al. (2014), ANN could pre-
dict TSS concentration better than the multi-
ple regression (MR) approach (R2 = 0.66 and
0.58, respectively).
According to the traditional field-based
approaches, COD was monitored locally by
sampling water at monitoring sites where his-
torical records of COD are available. Alt-
hough this method showed its relatively ac-
ceptable accuracy at point level, it was still a
huge challenge to analyze the COD concentra-
tion in a region in terms of substantial time,
human resources consuming and financial
supports for collecting a large sufficient in-
formation (Lim and Minha, 2015). However,
regional monitoring could provide a general
view of the distribution of pollutant concen-
tration through mapping surface water quality
as well as to support the policy-makers in giv-
ing recommendations for local residents. Re-
mote sensing technology indicated its effi-
ciency and helps in monitoring spatial distri-
bution of water quality parameters (Bonansea
et al., 2015; Yusop et al., 2011).
The aim of this study was to investigate the
relationship between spectral reflectance value
of the Landsat 8 and ground data of the COD
concentration and to access spatial changes of
such the parameter in river reaches of the Binh
Dai district, Ben Tre province. The study also
proposed an optical remote sensing approach
based for mapping and monitoring the COD
concentration in downstream river reaches of
the Vietnamese Mekong Delta.
2. Study river reaches
The study river reaches locates in down-
stream of the Mekong River at the Binh Dai
district, Ben Tre province (Figure 1). When
the system flows through Binh Dai, it is
Vietnam Journal of Earth Sciences, 39(3), 256-269
258
divided into two main branches, namely Cua
Dai and Ba Lai before draining into the East
Sea. In the dry season, average flows of Cua
Dai and Ba Lai River are about 1,598 m3/s
and 60 m3/s, respectively while they are ap-
proximately 6,480 m3/s and 350 m3/s respec-
tively in the rainy season. These two rivers are
the main water source for the agriculture
and freshwater-based aquaculture purposes.
Mekong River brings sediments that mainly
contribute to form coastal area in Ben Tre. It
is characterized by flat topography, attaining
an average elevation of 1-2 meters above sea
level (Nguyen et al., 2010; Le et al., 2014).
The irregular semi-diurnal tide (two times of
high and low tides per day) affects significant-
ly on hydrological regime of the coastal area
of Binh Dai. The tidal amplitude is about
2.5 m to 3.0 m in spring tide periods and ap-
proximately 1 m in neap tide periods (Le et
al., 2014; PPC, 2016). It gives the huge im-
pacts of the tidal regime and the COD concen-
tration in the river change substantially in
time and space.
Figure 1. (a) Landsat swath of study area
(a)
Nguyen Thi Binh Phuong, et al./Vietnam Journal of Earth Sciences 39 (2017)
259
Figure 1. (b) water quality monitoring station and sample sites
3. Methodology
There are five main steps (Figure 2) for es-
timating the COD concentration which are: (i)
collecting optical remote sensing data and
ground-truth data, (ii) pre-processing availa-
ble the Landsat-8 images (calibration and at-
mospheric correction and cloud detection);
(iii) detecting riverbank and masking water
related pixel; (iv) extracting reflectance val-
ues; and (v) developing the model for estimat-
ing spatial distribution of COD concentration.
3.1. Optical remote sensing data and ground-
truth data collection
Optical remote sensing data were provided
from the website Earth Resources Observation
and Science Center (EROS), U.S Geological
Survey
Table 1 indicates the information about the
Landsat images collected at the at different
time points. To extract the riverbank, two
cloud-free scenes of the Landsat 7 and Landsat
(b)
Vietnam Journal of Earth Sciences, 39(3), 256-269
260
8 were collected on December 14, 2002, and
September 18, 2014. Two scenes of the Land-
sat 8 (the least cloud cover) were collected on
February 22, 2014, and January 24, 2015, and
then were used to analyze COD concentration.
To establish the correlation algorithms between
spectral reflectance values and ground data, op-
tical remote sensing data was collected on 27
January 2016 in the same day when water
samples were collected at 10:11 am in 23 sites
placed along the main axis of the Cua Dai and
Ba Lai River (Figure 1). However, three sam-
ples were not able to be used because of the
high percentage of cloud cover. Besides, 15
water samples from 15 local monitoring sta-
tions which are administered by Department of
Environment were collected on April 14, 2015,
as the reference data (Figure 1). The input data
was also acquired in the dry season to reduce
adverse effects from the weather conditions,
such as heavy rain or cloud. Water samples
were collected close to the riverbank and a
depth of 0.5 m stored at a reasonable tempera-
ture to avoid changes of samples characteristics
before laboratory work was conducted to ana-
lyze Chemical Oxygen Demand.
Figure 2. The framework for developing of the COD-estimation model
Nguyen Thi Binh Phuong, et al./Vietnam Journal of Earth Sciences 39 (2017)
261
Table 1. The information on the collected Landsat images
Sl.No Date Landsat Revolution (meters) Band 1
1 December 14, 2002 ETM 30 × 30
2 September 18, 2014 OLI 30 × 30
3 January 24, 2015 OLI 30 × 30
4 April 14, 2015 OLI 30 × 30
5 January 27, 2016 OLI 30 × 30
6 February 22, 2014 OLI 30 × 30
3.2. Pre-processing Landsat 8 images
3.2.1. Atmospheric correction
The COST model developed by Chávez
(1996) was applied to correct for effects of the
atmosphere. It converts digital number (DN)
values to into the Top-of-Atmosphere (TOA)
radiance. Moreover, by using information
from the metadata file, TOA reflectance was
converted into ground reflectance values.
Vietnam Journal of Earth Sciences, 39(3), 256-269
262
3.2.2. Cloud detection
In this research, The Fmask package (ver-
sion 3.2) was used to detect clouds and cloud
shadows in the Landsat 8 images. In version
3.2, the new Short Wave Infrared (band 9,
Landsat 8) that is useful for detecting high al-
titude clouds was applied instead of the band
7 (Landsat 7) in the original version (Acker-
man et al., 2010, Zhu and Woodcock, 2012).
The TOA reflectance value of the band 9 was
used to compute a cirrus cloud probability.
The different kind of clouds is able to be de-
tected by applying the old cloud probability
and new cirrus cloud probability. The cirrus
cloud probability is directly proportional to
the TOA reflectance of the cirrus band. If the
cirrus band TOA reflectance equals 0.04, the
cirrus cloud probability equals 1 (Zhu et al.,
2015).
3.3. Riverbank extraction and masking water
related pixel
Riverbank area was defined as a barrier be-
tween land and water was affected by human
activities as well as natural process (Alesheikh
et al., 2007). It was necessary for extracting
water pixel to identify the shape of riverbank
as well as river system (Pham and Nguyen
Duc Anh, 2011). Two scenes of the Landsat 7
and Landsat 8 in study River Reaches were
collected in 2003 and 2014 with the very low
percentage of cloud cover. The atmospheric
correction process was conducted using the
COST model that indicated the accuracy of
correction algorithms. The contrast between
the land and water was highlighted from
Alesheikh's research to meet to South
Vietnam condition (Casse et al., 2012). Then,
the shape of a river was digitized by using
convert vector tool in QGIS. Two layers of
riverbank extracted from the Landsat 7 (2003)
and Landsat 8 (2014) were used to overlap
identifying changes of the riverbank. Based
on these results, fieldwork was conducted in
several areas indicated the changes of the
riverbank. This aims to reevaluate the results
from Alesheikh's research applying to the
coastal area. The results of fieldwork fairly
meet the results of riverbank extraction from
analyzing the satellite scenes. The layer of
river bank extracted from the Landsat 8
(2014) was used to mask water related pixel
by a masking tool in ENVI.
3.4. Reflectance values extraction
In the fieldwork, the coordination of water
sample sites and stations was achieved. After
images of the Landsat 8 were preprocessed,
they were employed for retrieving surface re-
flectance values corresponding with geo-
graphical monitoring sites.
3.5. Developing the model for estimating spa-
tial distribution of COD concentration
3.5.1. The multiple linear regression ap-
proach
The Pearson’s correlation displays the lin-
ear relationship between 2 variables as follow:
R= ∑ሺଡ଼ాౚషాౚതതതതതതതതതതതሻ ∑ሺଢ଼ిోీషౕిోీതതതതതതതതതሻ
ට∑ሺଡ଼ాౚషాౚതതതതതതതതതതതሻଶ ∑ሺଢ଼ిోీషౕాౚതതതതതതതതതതതሻଶ
(1)
Where Xୟ୬ୢ is the reflectance value, Yେୈ is COD value in monitoring site, Xୟ୬ୢതതതതതതതത is mean of the reflectance value, Yେୈതതതതതത is mean of COD value in monitoring site
The multiple linear regression approaches
performs the relationship between two or
more explanatory variables and a response
variable by establishing a linear equation as
follow:
Y= β0 + β1XBand1 + β2XBand2 ++βρ (2)
Where Y is estimated COD, β0 is inter-
cept, β1, β2, βρ are regression coefficients
According to Wang et al. (2004), the high-
er correlation coefficient of 0.626 was found
between COD concentration and reflectance
values of band 1-3 of the Landsat 7 by multi-
ple linear regression approaches in compari-
Nguyen Thi Binh Phuong, et al./Vietnam Journal of Earth Sciences 39 (2017)
263
son with linear, exponential and log transfor-
mations. In order to replace the Landsat 7
with the corresponding wavelengths, reflec-
tance values band 2-4 of the Landsat 8 were
employed as an alternative to reflectance val-
ues of the Landsat TM of band 1-3.
3.5.2. The Artificial Neural Network approach
Previous studies have shown that ANN
could improve the accuracy of estimating wa-
ter quality parameters as compared to tradi-
tional approaches (Sudheer et al., 2006; Che-
bud et al., 2012; Gholizadeh et al., 2016). Ar-
tificial neural networks can capture complex
non-linear relationships between an input and
output (Pham et al., 2015; Tien Bui et al.,
2016). In this research, the structure of ANNs
obtained three layers of interconnected neu-
rons, called input layer, hidden layer and the
output layer (Figure 3). According to Kaur
and Salaria (2013), Bayesian Regularization
showed the best performance of function es-
timation with the capability of overcom-
ing/avoiding the over-fitting problem when
training the network in effort estimation with
obtaining the ability to process over-fitting
during ANN training. Therefore, Bayesian
Regularization was applied to update the
weight and bias values according to Leven-
berg-Marquardt optimization. It minimizes a
combination of squared errors and weights
and then determines the correct combination
so as to produce a network that generalizes
well. According to Tien Bui et al. (2012), in
order to calculate the distance between real
data and detected data, Bayesian Regulariza-
tion employed a common function as follows:
Figure 3. Structure of ANN with three layers
C= αܧ βܧ௪ (3) Where Eୈis the sum of squared errors, E୵ is the sum of squared weights, α and β are
called hyperparameters
The steps of the iterative process are as fol-
lows:
(1) Choose initial values for α, β and the
weights.
(2) Take one step of Levenberg-Marquardt
algorithm to find the weights that minimize C
(3) Calculate the effective number of pa-
rameters γ and new values for α and β. More-
Vietnam Journal of Earth Sciences, 39(3), 256-269
264
over, Gauss-Newton approximation can be
applied to Hessian matrix.
α = ϓଶ౭ (4)
β= ୬ିϓଶ౭ (5) ϓ=N-αtrace(H)-1 (6)
Where ϓ is number of effective parame-
ters; H is Hessian matrix of objective function
S(w); N is the total number of parameters in
the network.
(4) Iterate steps 2 to 3 until convergence.
To solve the over-fitting problem, the data
was divided into two datasets with 70% of the
dataset for training and 30% of the dataset for
testing in the network (Imen et al., 2015). In
this research, a standard feed-forward network
with one hidden layer was employed. There
were five neurons in the hidden layer. The in-
puts to the networks were a combination of
the reflectance values from the bands of the
Landsat 8 corresponding with geographical
monitoring sites. The measured COD concen-
tration values with the corresponding geo-
graphical sites were used as targets. There was
a single neuron that indicated the detected
COD in output player. A number of 14 net-
work models with different inputs were
trained to determine the best combinations of
the reflectance values of the Landsat-8 bands.
The neural network was trained 50 times for
each model. The performance of each network
was evaluated by the root mean square error
(RMSE) and the correlation coefficient (R)
(Were et al., 2015).
4. Results and Discussion
4.1. COD concentration from water samples
Figure 4 indicated COD concentration of
35 sites located along the main axis of Cua
Dai and Ba Lai River. For 20 water samples
collected on 27 January 2016, COD concen-
tration exceeds the standard B1 column of
QCVN 08: 2015 in several points. COD con-
centration exceeding the standard B2 column
of QCVN 08: 2015 was found in 2 water
samples of Cua Dai River.
Figure 4. COD concentration from collected water samples and the national standard according to the A1, A2, B1,
B2 column of QCVN 08: 2015
4.2. The COD-estimation model
In order to investigate the relationship be-
tween COD and reflectance values of Landsat
8, the research employed the multiple linear
regression and ANN approach.
4.3. The multiple linear regression approach
Table 2 indicates the Pearson’s correlation
analysis the individual bands of the Landsat 8
and COD concentration. It is evidenced from
the Table 2 that there are weak negative linear
relationships between reflectance values of
individual bands of the Landsat 8 and COD
concentration, ranging from -0.50 to -0.11.
Reflectance values of band 3 performed the
highest correlation with COD (R = -0.49)
while reflectance values of band 5 performed
the lowest correlation with COD (R = -0.11).
Nguyen Thi Binh Phuong, et al./Vietnam Journal of Earth Sciences 39 (2017)
265
The defective sensor resulted in missing data
in the Landsat 7 images that can lead to errors
in the extracted maps. Therefore, in this re-
search, the Landsat 8 was used to replace the
Landsat 7. However, there is a difference in
the spectral bandwidth between the Landsat 8
and the Landsat 7 (Table 2). To keep corre-
sponding wavelengths, reflectance values of
band 2-4 of the Landsat 8 were used to re-
place reflectance values of Landsat TM of
band 1-3. The multiple linear regression be-
tween the reflectance values of band 2-4 of
the Landsat 8 and COD values showed that
there was a weak correlation of R = -0.53 and
RMSE = 4.50 through this approach although
its correlation coefficient was higher than cor-
relation coefficient of reflectance values of
individual bands and COD concentration.
Table 2. Correlation of the Landsat 8 bands and COD
Index B1 B2 B3 B4 B5 B6 B7
COD -0.3 -0.42 -0.49 -0.38 -0.11 -0.27 -0.12
4.4. Artificial Neural Network
The performance of the networks is pre-
sented by the correlation coefficient and the
root mean square in Table 3 after they were
trained using Bayesian regulation. Comparing
the correlation coefficients of the networks
using only the reflectance value of a single
band as input, it is obvious that network M2,
M3, and M4 have the higher correlation coef-
ficients for both training and testing. The M3
displayed highest R for training, test and all,
having 0.87, 0.76 and 0.86 respectively while
there was an insignificant relationship be-
tween M5 and observed COD concentration.
Although B2, B3 and B4 combination (M9)
correlated significantly with COD concentra-
tion (R=0.87), the combination of B1, B2, B3
and B4 (M10) showed the highest correlation
coefficient (R=0.89). These results demon-
strated that COD estimation using ANN was
more accurate than the linear regression
approach.
4.5. Assessing the COD concentration in
2014 and 2015
The research focused on two scenes of the
Landsat 8 with the low percentage of cloud
cover (Figure 5, Figure 6).
Table 3. Performance of the COD concentration in ANN
Model
Input band Training Test Training and Testing
R RMSE R RMSE R RMSE
M1 B1 0.26 15.15 0.50 10.66 0.30 13.90
M2 B2 0.81 13.01 0.55 7.00 0.79 11.46
M3 B3 0.87 23.78 0.76 9.49 0.86 20.40
M4 B4 0.39 24.26 0.50 15.54 0.42 21.90
M5 B5 0.13 24.02 0.13 18.28 0.11 22.38
M6 B6 0.34 10.82 0.49 11.96 0.30 11.19
M7 B7 0.45 9.16 0.59 37.15 0.34 22.16
M8 B3, B4 0.91 10.52 0.78 13.20 0.87 11.43
M9 B2, B3, B4 0.92 10.15 0.80 11.57 0.87 10.62
M10 B1, B2, B3, B4 0.92 9.35 0.82 21.43 0.89 14.29
M11 B1, B2, B3, B4, B5, B6 0.93 25.03 0.79 10.72 0.82 21.58
M12 B2, B3, B4, B5, B7 0.66 19.65 0.75 15.39 0.60 18.41
M13 B1, B2, B3, B4, B5 0.99 4.21 0.54 14.94 0.92 9.07
M14 B1, B2, B3, B4, B5, B6, B7 0.71 17.60 0.77 13.52 0.72 16.42
Vietnam Journal of Earth Sciences, 39(3), 256-269
266
Figure 5. Estimated COD concentration map on February 22, 2014 in Binh Dai
Figure 6. Estimated COD concentration map on January 24, 2015 in Binh Dai
Hydrological regime of Ba Lai River is af-
fected by sluice gate systems while Cua Dai
river has no control by construction irrigation
systems. The operation schedule of Ba Lai
sluice is one of the reasons caused a consider-
able distribution of COD concentration in sur-
face water in Ba Lai River. On February 22,
2014, it was evidenced that COD concentra-
Nguyen Thi Binh Phuong, et al./Vietnam Journal of Earth Sciences 39 (2017)
267
tion inside Ba Lai sluice was low, ranging
from 1 to 10 mg/l in comparison with COD
concentration outside Ba Lai sluice, ranging
from 5 to 21 mg/l (Figure 5). The map also
dedicated COD concentration reduced gradu-
ally from Ba Lai sluice to the estuary. On Jan-
uary 24, 2015, there was a fluctuation from 22
mg/l to approximately 30 mg/l in the river
section between Ba Lai sluice and the estuary
although several sites were found that the
COD concentration exceeded slightly the na-
tional standard for irrigation according to the
B1 column of QCVN 08:2015 (Figure 6). Aq-
uaculture activities are the major likelihood of
resident in the coastal area with increasing
annual production area, one of the main
sources of pollutant in this area. The distribu-
tion of high COD concentration was also
found on a section of Cua Dai river, from Tam
Hiep to Thoi Trung Island, ranging from 25 to
31 mg/l. In several sites of this section, COD
concentration exceeded slightly the national
standard of 30 mg/l shown in B1 column of
QCVN 08: 2015.
5. Conclusions
Landsat 8 provided the potential of optical
remote sensing data source for estimating a
large spatial distribution of the COD concen-
tration, which was almost impossible via a
traditional field-based approach. However,
there was a limitation in monitoring the tem-
poral distribution of the COD concentration
due to local weather conditions of the coastal
area, significantly reducing the quality of sat-
ellite data.
The ANN approach provided better COD
estimation than traditional regression model.
Experimental results also showed that the
combination of reflectance values of bands 1
to 4 of Landsat 8 were the most appropriate
inputs to the applied model.
It should be noted that it is difficult and
time-consuming to determine the optimal ar-
chitecture of the neural network that could
generalize well without over-fitting the data.
In addition, quantifying the uncertainty in the
network outputs should be considered, espe-
cially in cases of relatively small training
data set.
Acknowledgments
We would like to express greatly our ap-
preciation to The Kurita Water and Environ-
ment Foundation Grant funded for this study.
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