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sensors
Article
Optimal Design of Water Quality Monitoring
Networks in Semi-Enclosed Estuaries
Nam-Hoon Kim 1and Jin Hwan Hwang 2, *
1Marine Disaster Research Center, Korea Institute of Ocean Science & Technology, Busan 49111, Korea;
nhkim426@gmail.com
2Institute of Construction and Environmental Engineering, Seoul National University, Seoul 08826, Korea
*Correspondence: jinhwang@snu.ac.kr
Received: 30 December 2019; Accepted: 7 March 2020; Published: 9 March 2020
Abstract:
The semi-enclosed estuary is very susceptible to changes in the physical and environmental
characteristics of the inflow from the land. Therefore, continuous and comprehensive monitoring
of such changes is necessary for managing the estuary. Nevertheless, the procedure or framework
has not been proposed appropriately to determine how many instruments are necessary and where
they need to be monitored and standardized to detect critical changes. The present work proposes
a systematical strategy for the deployments of the monitoring array by using the combination of
graphical optimization with the objective mapping technique. In order to reflect the spatiotemporal
characteristics of the bay, the representative variables and eigenvectors were determined by the
Empirical Orthogonal Function (EOF), and the cosine angle among them calculated and used as a
design index of optimization. At the recommended locations, the sampled representative variables
were interpolated to reconstruct their spatiotemporal distribution and compared with the true
distribution. The analysis confirmed that the selected locations, even with a minimal number of
points, can be used for on-site monitoring. In addition, the present framework suggests how to
determine installable regions for real-time monitoring stations, which reflect the global and local
characteristics of the semi-enclosed estuary.
Keywords:
optimal design procedure; monitoring network; water quality; graphical optimization;
objective mapping
1. Introduction
An estuary is a coastal area where seawater from offshore meets freshwater from rivers and is
dominated by various control sources such as wind, solar radiations, tidal strength, river discharge,
bathymetry, etc. In particular, river discharge is a source of nutrients for estuaries, but can sometimes
have a negative impact due to releasing contaminants from upstream together. Moreover, due to the
fast urban-sprawl or urbanization near coastal areas, the amounts of released pollutants are increasing
vigorously and flowing into coastal seas through the river from urbanized watershed. The coastal
areas influenced by freshwater are often semi-enclosed, hence, once contaminants originating from the
watershed flow into the bay, they can accumulate and continuously deteriorate water quality [
1
–
3
].
Along with the deterioration of the water environment, the demands for water supply have soared,
ultimately leading to the request for the construction of many sea-dikes for the coastal reservoir to
secure the water resources. However, such sea-dikes efficiently inhibit the tidal momentum of the
offshore sea from advecting to the river and near coastal waters, and, therefore, significantly affects
the physical characteristics of the water column, such as the stratification, mixing, and circulation of
flow [
4
–
6
]. In addition, the gates of the sea-dikes are discharging freshwater irregularly to maintain
Sensors 2020,20, 1498; doi:10.3390/s20051498 www.mdpi.com/journal/sensors
Sensors 2020,20, 1498 2 of 23
the water level of the upstream to be constant, hence the physical characteristics and water quality of
the coastal sea change complicatedly and unexpectedly [7–9].
The estuaries of the West Sea of Korea are shallow, with wide tidal-flats, considerable tidal
variations of the macro level, and complex geomorphology. Moreover, they are exposed to the physical
and environmental alterations caused by the irregular discharges of freshwater from the gates of
the coastal reservoir [
7
,
10
,
11
]. Inflows from the watershed lead to unexpected imbalances in the
nutrients and red tides, caused by eutrophication, often occur in the summer (i.e., flood season) [
12
,
13
].
Sometimes, water quality worsens due to the leakage of the green algae from the upstream of the
reservoir [
14
]. Furthermore, a decrease in numbers of freshwater discharge in the winter due to low
rainfall (i.e., dry season) can severely affect salt-sensitive aquacultures [
15
,
16
]. Therefore, an earlier
detection of changes in the nutrients, water temperature, and salinity are essential to mitigate the
impact in advance, understand the natural process, and manage the environment soundly.
Generally, two approaches have been mainly used to monitor the coastal sea: on-site monitoring
and continuous real-time monitoring [
17
]. The on-site monitoring is a way of visiting the site of
interest, carrying instruments regularly to monitor the characteristics of the bay. The continuous
real-time monitoring is a way of collecting data remotely by installing the unmanned observatory.
In any case, an important question can be raised as to how many and where the sensors or stations
should be installed to sufficiently represent the spatial and temporal characteristics of the region
of interest. Therefore, strategies need to be established and standardized to deploy and operate
the monitoring array for managing sound environments. Even though several strategies have been
proposed previously, such as the guidelines of the United States Environmental Protection Agency
(US EPA) [
18
], the monitoring locations have been judged arbitrarily by the discussions of stakeholders,
engineers, and decision-makers rather than based on robust and reliable systematic protocol or design
guidelines [
17
,
19
,
20
]. Therefore, the strategies for deploying and operating a monitoring network need
to be provided for the sound management of the coastal and ocean environment since the scientifically
solid and robust data are essential in preparing countermeasures for decision making [17].
In the design of the monitoring locations, some requirements should be specified. Since the
variables of interest are best measured simultaneously over the whole domain within a predetermined
time, limited numbers of measuring points should be optimally selected, which still must be sufficient
to represent the spatiotemporal characteristics of the target region. Several prior studies have been
carried out to meet these requirements. In [
21
], the authors conducted a trial-and-error method to
find the points to best reconstruct the so-called objective mapping for visualizing the data. After the
introduction of the objective mapping technique, some studies have followed, focusing mainly on
mapping-based optimization, which can compensate for the limitations of the trial-and-error method
(e.g., [22–24]). Such prior studies designed arrays that can best reconstruct the spatial distribution by
applying the optimization technique, such as the simulated annealing [
22
] and genetic algorithm [
23
]
to minimize the covariance function or spatial averaged quadratic error [
24
]. Furthermore, many types
of research have been performed to find the best objective mapping for the applications in diverse
fields, such as mooring locations to measure the sea level altitudes [
25
], sensor arrays to monitor the
oceanic meridional overturning circulation [
26
], and the collection data for the modeling with the data
assimilation [27,28].
Such developments recently led to the redesign of the existing monitoring network, that had
been intuitively and arbitrarily designed in the past. For example, [
29
] constructed the objective
function based on the principal component analysis and solved it with spatial sampling optimization
to eliminate redundant points in the Yangtze River Estuary, China. In addition, [
30
] and [
31
] performed
a similar study using the Kriging and spatially simulated annealing method in the Changjiang Estuary
and Hangzhou Bay, China, respectively. Most recently, [
19
], which is a work that set the precedent
for the present study, also proposed a primitive version of the framework designing the monitoring
system using a similar method to the previously researched.
Sensors 2020,20, 1498 3 of 23
Most of the prior studies performed analyses mainly on the ideal case (e.g., [
21
–
23
]) or for the
large-scale ocean (>5000 km) (e.g., [
24
,
26
]) rather than small-scale waters (<50 km) such as the coastal bays
or estuaries, except [
19
]. In general, the spatial and temporal variabilities of hydrodynamic and water
quality variables on the global- or large-scale seem to follow a more natural variation. However, the coastal
water must depend not only on the global- or large-scale variability, but also significantly on the process of
the land through the river. Therefore, the spatial variability of the characteristics in the coastal domain
cannot be adequately represented by the same technique for the large-scale area. In addition, most of
the prior studies did not design an integrated monitoring network which can detect the diverse variables
simultaneously, but focused on a single variable, such as current [
22
,
23
,
26
], salinity [
32
], or water quality
variables [29–31] to find the design variable for optimization.
As a recent study, [
33
] used the objective function as the quantitative function (i.e., scalar function),
such as Root-Mean-Square-Error (RMSE) or covariance, etc. They found that such a quantitative
objective function not only requires a long computation time to find the solutions, but that it is also hard
to prevent the results from falling into the local solutions. Furthermore, the optimization techniques
based on the quantitative objective function are only suitable for the solutions of “how many” points
are to be arranged, and it is hard to find the solutions to “where” they are to be located. Moreover, there
is little research to determine the locations of the real-time monitoring station [34–36].
Therefore, the present study is to propose a well-organized framework for designing a water
quality monitoring network in the small-scale estuarine area. In order to reconstruct the spatiotemporal
distribution to represent the variabilities of the target variables in the small-scale area, a graphical
optimization technique is applied to find the best locations for the representative monitoring array by
constructing the objective function of the optimal mapping approach. Since the graphical optimization
technique can directly select the arrays of monitoring points in the continuous field, the computation
time is short, and there is no possibility of falling into the local problems. Moreover, this technique
is excellent in its application to the problems of the steep gradient of signals with significant spatial
variations due to the freshwater discharges. We present the methodologies for setting up the experiment
in Section 2, the results and discussion of the design for a water quality monitoring network based on
the scenarios in Section 3, and the conclusions in Section 4.
2. Materials and Methods
2.1. Characteristics of the Study Area
The Geumgang Estuary (hereafter GE) is located at the west coast of Korea (Figure 1) and
categorized as a well-mixed estuary, where a semidiurnal tide dominates [
5
]. The sea-dike is located in
the mouth of the Geumgang river, which is one of the main rivers in Korea, and GE refers to the sea
area about 55 km in the x-direction and 35 km in the y-direction from the sea-dike (Figure 1b). GE has
substantial variabilities of salinity since the freshwater is released irregularly and artificially from the
coastal reservoir [37]. The amount of artificially discharged freshwater depends on the water level of
the reservoir, which is closely related to the rainfall on the upstream watershed (Table A1). The amount
of the discharged freshwater also determines the physical and environmental characteristics of the
coastal seawater, such as water temperature and salinity, along with the concentrations of dissolved
materials (e.g., nitrogen, phosphorus, chlorophyll, dissolved oxygen, etc.) and so significant changes
in freshwater discharge cause large variations in the water quality. In [
19
], the authors conducted
an on-site observation for three years using the Conductivity, Temperature, Depth (CTD) sensor,
the multi-parameter water quality sensor, and water sampling at GE to acquire water temperature,
salinity, and water quality variables (i.e., dissolved oxygen, chlorophyll-a, total nitrogen, and total
phosphorus). They found that measured variables are controlled by the amount of rainfall (i.e.,
the main factor of freshwater discharge) and seasonal variability. Specifically, water temperature moves
together with dissolved oxygen, total phosphorus, and chlorophyll-a and salinity with total nitrogen.
Moreover, [
4
,
5
] performed line measurements, suggesting that the physical characteristics (e.g., mixing
Sensors 2020,20, 1498 4 of 23
and stratification) have seasonal variability depending on the frequency of rainfall, and that the
intrinsic characteristics could change. There needs to be an advanced awareness of such changes in the
water quality, which occur mainly due to freshwater discharge, to sustain the sound environmental
conditions, but the monitoring points of the GE are currently sporadically arranged without any specific
guidelines (Figure 1b). In particular, the on-site monitoring points are randomly arranged, and there is
only one real-time water quality monitoring station (yellow triangle). Since the monitoring network
of GE was arbitrarily designed, GE may be monitored irrationally at the moment. Therefore, it is
somewhat difficult to analyze and find intrinsic characteristics of the GE, where it is strongly affected by
the freshwater discharged from the upstream. Therefore, well-organized guidelines for the monitoring
network design are necessary.
Sensors 2020, 20, x FOR PEER REVIEW 4 of 23
sustain the sound environmental conditions, but the monitoring points of the GE are currently
sporadically arranged without any specific guidelines (Figure 1b). In particular, the on-site
monitoring points are randomly arranged, and there is only one real-time water quality monitoring
station (yellow triangle). Since the monitoring network of GE was arbitrarily designed, GE may be
monitored irrationally at the moment. Therefore, it is somewhat difficult to analyze and find intrinsic
characteristics of the GE, where it is strongly affected by the freshwater discharged from the
upstream. Therefore, well-organized guidelines for the monitoring network design are necessary.
(b)
(a)
(c)
Figure 1. Monitoring status and computation grid of the (a) large scale model (117.88˚E–131.36˚E;
23.92˚N–41.15˚N) and downscaled model (125.85˚E–127.01˚E; 35.19˚N–36.33˚N), (b) Geumgang
Estuary (126.3˚E–126.8˚E; 35.9˚N–36.2˚N) and position of the sea-dike (126.75˚E; 36.02˚N), and
(c) concept of the integrated modeling. The abbreviations of KHOA, KOEM, and MOF imply Korea
Hydrographic and Oceanographic Agency, Korea Marine Environment Management Corporation,
Ministry of Oceans and Fisheries, respectively.
2.2. Numerical Model (Input Data)
Seamless spatiotemporal information should be used as input data to design a monitoring
network appropriately, but it is hard and expensive to perform field measurements for a long enough
duration and in large enough areas. Because of this, the scattered data of field measurements have
limitations in their direct use for the design, since they are available only at several specific points
and during certain periods. An alternative approach could be to use the data from the satellite images
instead, but they depend too much on the daily weather. Therefore, it is tough to obtain continuous
spatiotemporal information, hence using the satellite data can potentially miss some critical points
and certain periods. For these reasons, the present work hired sets of the spatiotemporally highly
resolved and well-validated numerical simulation data. The advantage of using the results from the
numerical simulations is that diverse physical and environmental variables can be extracted from the
numerical model simultaneously, which can be considered together as input data for designing the
monitoring network.
This study assumed that the numerical model results simulated by [15] are real data to design
the monitoring network. Figure 1 shows a conceptual diagram, domain, and grid of the numerical
model. A three-dimensional hydrodynamic model of Delft-3D [38] simulated the hydrodynamics and
water quality near the coast. The initial and boundary conditions were carefully downscaled from
KOREA
JAPAN
CHINA
Large scale model
Downscaled model
: KHOA
: KOEM
: Tidal station (KHOA)
: MOF
: Tidal station (KHOA)
: Monitoring station (KOEM)
Real-time monitoring
On-site monitoring
Study area (Geumg angEstua ry)
Sea-dike
Study area (Geumgang Estuary)
Sea-dike
•Wave
•Tide
•Current
•Sediment
•Water Quality
•Ecology
Geumgang
Sea-dike
Estuary boun dary
Internal boun dary
Geumgang
Catchment
Intake for agriculture
and industry etc.
Baekje Wier
: Upstream b oundary
Q5
Q4
Q6
Q1
Q2
Q3
Ocean bou ndary
Q7
Large scale model
Downscaled model
Figure 1.
Monitoring status and computation grid of the (
a
) large scale model (117.88
◦
E–131.36
◦
E;
23.92
◦
N–41.15
◦
N) and downscaled model (125.85
◦
E–127.01
◦
E; 35.19
◦
N–36.33
◦
N), (
b
) Geumgang
Estuary (126.3
◦
E–126.8
◦
E; 35.9
◦
N–36.2
◦
N) and position of the sea-dike (126.75
◦
E; 36.02
◦
N),
and (
c
) concept of the integrated modeling. The abbreviations of KHOA, KOEM, and MOF imply Korea
Hydrographic and Oceanographic Agency, Korea Marine Environment Management Corporation,
Ministry of Oceans and Fisheries, respectively.
2.2. Numerical Model (Input Data)
Seamless spatiotemporal information should be used as input data to design a monitoring
network appropriately, but it is hard and expensive to perform field measurements for a long enough
duration and in large enough areas. Because of this, the scattered data of field measurements have
limitations in their direct use for the design, since they are available only at several specific points and
during certain periods. An alternative approach could be to use the data from the satellite images
instead, but they depend too much on the daily weather. Therefore, it is tough to obtain continuous
spatiotemporal information, hence using the satellite data can potentially miss some critical points
and certain periods. For these reasons, the present work hired sets of the spatiotemporally highly
resolved and well-validated numerical simulation data. The advantage of using the results from the
numerical simulations is that diverse physical and environmental variables can be extracted from the
Sensors 2020,20, 1498 5 of 23
numerical model simultaneously, which can be considered together as input data for designing the
monitoring network.
This study assumed that the numerical model results simulated by [
15
] are real data to design
the monitoring network. Figure 1shows a conceptual diagram, domain, and grid of the numerical
model. A three-dimensional hydrodynamic model of Delft-3D [
38
] simulated the hydrodynamics and
water quality near the coast. The initial and boundary conditions were carefully downscaled from
the large-scale model of the Yellow Sea regional model (Figure 1a) [
15
]. The numerical model was
simulated for two years from January 2014 to December 2015 and the model results, corresponding to
about 55 km in the x-direction and about 35 km in the y-direction (i.e., GE), were extracted to apply and
analyze (Figure 1b). In the numerical simulation, the initial and boundary conditions of freshwater
discharge from the upstream were generated by a watershed model, STREAM [
15
]. This model is
a squared uniform grid and quasi-distributed watershed model that can simulate flow, sediment,
and water quality of the watershed (Figure 1c).
The simulation results were calibrated and validated for each variable using data measured
directly by the author during the same period as the simulation period, and data obtained from
monitoring points shown in Figure 1a operated by various organizations (see more detail in [
15
,
19
]).
Moreover, the accuracy of the model results has been improved with the calibration and validation step
for each variable using the Index of Agreement (IOA) [
39
] and Relative Error (RE) [
40
], respectively.
Overall, even though the water quality variables have slightly lower skill scores than the hydrodynamic,
both variables still have strong correlations with the observation data (Table A2).
2.3. Design Variables
Six variables were selected for analysis and applied as depth-averaged values; water temperature
(T), salinity (S), dissolved oxygen (DO), chlorophyll-a (Chl-a), total nitrogen (TN), and total phosphorus
(TP), which can commonly be obtained from the real field monitoring. The reason for considering
multiple variables is to select representative variables among them to design the monitoring network.
If the optimal location is determined by the representative variables, and other variables with high
reliability are detected at that location, then we do not need to design the monitoring network
complicatedly considering all the other variables. Therefore, it is imperative to select variables that can
reflect the characteristics of other variables as a design variable. To reduce the number of variables and
find a variable representing others, we used the Empirical Orthogonal Function (hereafter EOF) to
compress an extensive data set into a smaller number of independent pieces of information [
41
,
42
],
since it is hard and expensive to determine the convergence threshold of the objective function for
each variable.
As the first step of the EOF, the eigenvalues corresponding to the series of a linear system need to
be found, which can be expressed as follows:
Cφ−λIφ=0, (1)
where the covariance matrix,
C
, consists of Melements of the data with the length of N(M
×
N).
I
is the
unity matrix, and
φ
is the EOF. The EOF, corresponding to the eigenvalue
λM
, is the uncorrelated (i.e.,
orthogonal) mode of variability. If equation (1) is to have a nontrivial solution, the determinant of the
coefficients must vanish and yield an Mth order polynomial,
λM+αλM−1+· · ·
, whose Meigenvalues
satisfy
λ1> λ2>· · · > λM
[
42
]. Thus, the variances associated with each statistical mode are ordered
according to their corresponding eigenvectors. The first mode,
λ1
contains the highest percentage of
the total variance, and among the remaining variances, the greatest percentage is in the second mode,
λ2
, and so on [
42
]. This method can reduce the information of each variable to represent the variance
concerning the eigenvectors.
The present work also chose a cosine angle between two eigenvectors of the representative
variables in the three-dimensional Euclidean principal component (hereafter PC) space as a design
Sensors 2020,20, 1498 6 of 23
variable for constructing the monitoring network. PC is constructed by the normalized six variables in
this work, and two eigenvectors refer to the two most independent variables among six variables of T,
S, DO, Chl-a, TN, and TP. The reason we selected a slightly complicated index as a design index is
that if one variable is chosen for a design variable, other variables are hard to monitor appropriately
since each variable could have different spatiotemporal variabilities due to their different sources.
For example, water temperature is mainly determined by the local solar radiation and also, water
temperature from the open sea. However, salinity is mainly determined locally by the amount of
the freshwater discharge from the river, so if the monitoring array is designed solely by salinity, this
designed array is not likely adequate to detect the variations of water temperature (Figure A1a,A1c).
Conversely, when the monitoring array is designed only by water temperature, the reconstructed
distribution of salinity is totally different from the true distribution (Figure A1b,A1d).
Therefore, since the cosine angle can represent the characteristics of variables with different origins,
the use of it allows for considering several variables simultaneously by the monitoring networks.
The cosine angle between two vectors can be expressed as follows:
cos(a,b)=a·b
kak · kbk=
n
P
i=1
aibi
( n
P
i=1
aiai!× n
P
i=1
bibi!)1/2, (2)
where
a=(a1,a2,. . . ,an)
and
b=(b1,b2,. . . ,bn)
are two eigenvectors of the representative variables.
In the three-dimensional Euclidean PC space, nmust be three.
2.4. Finding the Optimal Solutions
Once the design variable is determined, the optimization is performed to find solutions of the
most appropriate numbers and locations for the monitoring in the domain of target. The general
optimization problem is posed as follows:
Minimize f(X)
subject to gi(X)≤0(i=1, 2, . . . ,m);
hj(X)=0(j=1, 2, . . . ,p);
Xlower ≤X≤Xupper;
(3)
where
f(X)
is the objective function;
gi(X)
is the ith inequality constraint; mis the total number of
inequality constraint functions;
hj(X)
is the jth equality constraint; pis the total number of equality
constraints;
X
is the vector of design variables; and
Xlower
and
Xupper
are the lower and upper bounds of
the design variables, respectively. To find the optimal solutions in a constrained optimization problem,
it is necessary to construct feasible regions reflecting various constraint violations. Thus, the constrained
optimization problem needs to be transformed into the unconstrained optimization problem by adding
penalty terms for each constraint violation [
19
,
43
–
46
]. Finally, after transforming, the objective
function (i.e., augmented function) is solved by heuristic optimization, such as a genetic algorithm.
This procedure is called an Augmented Lagrangian Genetic Algorithm (ALGA), which finds a set of
stable solutions satisfying the Kuhn–Tucker conditions by mathematically handling a large number of
constraint functions with less computational cost [46,47].
To find the optimal solutions, we employed two optimization problems for comparison; one was
a quantitative approach, and the other a graphical approach. The quantitative optimization finds
an optimal arrangement, which can reconstruct the spatiotemporal distribution by constructing a
quantitative objective function of the root-mean-square error (RMSE), which is expressed as follows:
Sensors 2020,20, 1498 7 of 23
f(X)=v
u
t1
N
N
X
i=1
Ei−Ti, (4)
where
Ei=(E1,E2,. . . ,EN)
and
T=(T1,X2,. . . ,TN)
are the estimated and true values, respectively.
The quantitative objective function, such as RMSE, requires a long computation time to find a solution,
and its result could easily fall into the location solution, hence there is no means to prove whether a
given solution is the best. Therefore, even though this method has been applied to the selections of
numbers of the observation points [
32
], the different arrays are possible to determine for each iteration
due to arbitrary array selection of the locations.
The graphical optimization constructs the primary function of the optimal interpolation as an
objective function and can find the optimal arrangement that represents the continuous spatiotemporal
distribution [
19
]. Currently, the most widely used optimal interpolation schemes in meteorological and
oceanographic applications may be the statistical interpolation, also known as the Optimal Interpolation
(OI) scheme [
48
], or the Barnes Objective Analysis (BOA) [
49
]. Even though the OI is most prevalent to
estimate the ocean data field (e.g., [
21
,
50
–
53
]), it is not ideal to use in this study since the assumptions
of spatial homogeneity and isotropy are not relevant to a small (
≤
50 km) and highly dynamic area
such as the small coastal seas.
The objective analysis is often referred to as a process of transforming data from observations
at irregularly spaced points into data at the points on a regular space grid [
54
] for meteorological
purposes. In [
49
], the authors modified this scheme to interpolate the whole complex region of interest
by repeatedly applying a distance-dependent weighting [
55
–
57
]. The objective function of the graphical
optimization for designing the array of the monitoring points can be constructed by the loop function
of BOA and can be expressed as follows:
f(X)=±
N
P
m=1
wmR(Xm)
N
P
m=1
wm
+
N
P
m=1
w0
m2R(Xm)−E1(Xm)−E2(Xm)
N
P
m=1
w0
m
, (5)
where
R(Xm)
is the reference value (i.e., design variable) at the location m, and
E1,2(Xm)
are the
estimates at each loop extracted at the same location to the reference value. The mth weights are as
expressed in equations (6) and (7):
wm=exp
−
d2
mx
c2
x
+d2
my
c2
y
, (6)
w0
m=exp
−
d2
mx
γc2
x
+d2
my
γc2
y
, (7)
where
dm
is the distance between the grid point and the mth reference point, and the length scales
cx
and
cy
control the fall-offrate of the weighting function in the different rates to xand ydirections [
55
,
56
,
58
].
The length scale could be solved by a nonlinear curve-fitting method of the Levenberg–Marquardt
least square method [
59
].
γ
is a numerical convergence parameter that controls the difference between
the weights on each step for the range of 0 to 1 [60].
In the graphical optimization, the objective function of Equation (5) constructs the spatial
distribution (i.e., domain) of the design variables to describe the target bay. The elliptic radius
weighting function of Equation (6) is the distance from the center to the border of an area described by
the constrained function, which keeps the solution to be out of the radius of influence while finding
the optimal solution. In addition, land and structures can be composed of several exterior nonlinear
and graphical functions [
19
]. Therefore, the solutions of maximum and minimum are located inside
Sensors 2020,20, 1498 8 of 23
of the ellipse constraints (i.e., feasible region), refraining geomorphology from constraining them.
To construct the objective function, BOA is selected due to its simplicity and applicability to the wide
ranges of scales. It is also suitable for use in conjunction with the graphical optimization technique.
2.5. Methods of Performance Evaluation
Once the optimal solutions (i.e., monitoring array) are found, the spatiotemporal distribution of
the variables is reconstructed with the solutions, and validated by comparing them to the original
data. The skills of the reconstruction can be evaluated by the statistical metrics [
61
], which tell the
difference between true and estimated values. The present work used two types of skill metrics; the
Taylor diagram [
62
] and the target diagram [
63
]. These diagrams compile the statistical measures of
the reconstruction skill into a single graph to allow for the comparison and analysis of the various
cases. The Taylor diagram graphically summarizes and compares two sets of results regarding three
statistics: correlation coefficient (COR), standard deviation (SD) of the true (subscript T) and estimated
(subscription E) fields, and centered (i.e., unbiased) root mean square difference (CRMSD), which have
the following relationship:
CRMSD2=SD2
T+SD2
E−2×SDT×SDE×COR. (8)
Another tool to evaluate the skills is a target diagram, which is derived from the relationship
between the metrics of Bias, which means the difference of the mean values, CRMSD, and RMSD.
This diagram used a Cartesian coordinate system where the x-axis represents the CRMSD, the y-axis
represents the Bias, and the diagonal distance (radius) indicates the RMSD.CRMSD is an unbiased
RMSD and removes any potentially biased information [
63
]. The following relationship relates these
three statistics:
RMSD2=Bias2+CRMSD2(9)
3. Results and Discussion
3.1. Decomposition of the Spatiotemporally Dependent Variable
As the first step to find the design variable, the initial monitoring points were distributed over the
entire domain (Figure A2), and the time-series of each variable were extracted at those points from the
numerical model. In order to avoid dimensional heterogeneity, each variable was subtracted from the
mean values of each variable, and we divided those differences by the standard deviations to obtain
normalized values to represent each variable (Figure A2).
The most representative ones among the given variables were selected by the EOF analysis of
the spatial distributions of the normalized six variables. Figure 2shows the eigenvectors of the six
variables, and Table 1summarizes the results of the EOF analysis in detail. When the eigenvalues from
the EOF are smaller than 1, those values are not significant, and so we used the first three among the
six PCs for which the eigenvalues were larger than 1 [
64
]. The vectors in Figure 2are constructed
with the PCs representing the distribution of each variable. For example, the eigenvector representing
salinity is composed of
−
0.5 of the first component,
−
0.36 of the second one, and 0.15 of the third
one (Figure 2and Table 1). In Figure 2, the x-axis represents the contribution of the variable to the
first PC, the y-axis represents that for the second PC, and z-axis does for the third PC. When the
magnitudes of the eigenvector are smaller than 0.5, the variables represented by that eigenvector are
not significant [64], and so we do not consider them in the analysis.
Sensors 2020,20, 1498 9 of 23
Sensors 2020, 20, x FOR PEER REVIEW 8 of 23
correlation coefficient (COR), standard deviation (SD) of the true (subscript T) and estimated
(subscription E) fields, and centered (i.e., unbiased) root mean square difference (CRMSD), which have
the following relationship:
2 22
2.
T E TE
CRMSD SD SD SD SD COR= + −×××
(8)
Another tool to evaluate the skills is a target diagram, which is derived from the relationship
between the metrics of Bias, which means the difference of the mean values, CRMSD, and RMSD. This
diagram used a Cartesian coordinate system where the x-axis represents the CRMSD, the y-axis
represents the Bias, and the diagonal distance (radius) indicates the RMSD. CRMSD is an unbiased
RMSD and removes any potentially biased information [63]. The following relationship relates these
three statistics:
= +
22 2
RMSD Bias CRMSD
(9)
3. Results and Discussion
3.1. Decomposition of the Spatiotemporally Dependent Variable
As the first step to find the design variable, the initial monitoring points were distributed over
the entire domain (Figure A2), and the time-series of each variable were extracted at those points
from the numerical model. In order to avoid dimensional heterogeneity, each variable was subtracted
from the mean values of each variable, and we divided those differences by the standard deviations
to obtain normalized values to represent each variable (Figure A2).
The most representative ones among the given variables were selected by the EOF analysis of
the spatial distributions of the normalized six variables. Figure 2 shows the eigenvectors of the six
variables, and Table 1 summarizes the results of the EOF analysis in detail. When the eigenvalues
from the EOF are smaller than 1, those values are not significant, and so we used the first three among
the six PCs for which the eigenvalues were larger than 1 [64]. The vectors in Figure 2 are constructed
with the PCs representing the distribution of each variable. For example, the eigenvector representing
salinity is composed of −0.5 of the first component, −0.36 of the second one, and 0.15 of the third one
(Figure 2 and Table 1). In Figure 2, the x-axis represents the contribution of the variable to the first
PC, the y-axis represents that for the second PC, and z-axis does for the third PC. When the
magnitudes of the eigenvector are smaller than 0.5, the variables represented by that eigenvector are
not significant [64], and so we do not consider them in the analysis.
(a)
(b)
Figure 2. The results of the empirical orthogonal function (EOF) corresponding to the (a) 2D and
(b) 3D principal components (PCs) for the spatial distribution. The sky blue, orange, and light green
mean a group of variables that contribute to the first PC, second PC, and third PC, respectively.
T
S
DO
Chla
TN
TP
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
1st Principal Component (43%)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
2nd Principal Component (32%)
-1
1
-0.5
TN
0.5 1
0
TP
3rd PC (18%)
DO
0.5
0.5
2nd PC (32%)
0
1st PC (43%)
0
1
T
-0.5
Chla
-0.5
S
-1 -1
Figure 2.
The results of the empirical orthogonal function (EOF) corresponding to the (
a
) 2D and (
b
) 3D
principal components (PCs) for the spatial distribution. The sky blue, orange, and light green mean a
group of variables that contribute to the first PC, second PC, and third PC, respectively.
Table 1.
The results of the EOF corresponding to the PCs for the spatial distribution. The sky blue,
orange, and light green mean a group of variables that contribute to the first PC, second PC, and third
PC, respectively.
Category Principal
Component Eigenvalue Eigenvector
T S DO Chl-a TN TP
Spatial
(Entire
domain)
1st PC (43%) 2.56 0.26 −0.50 −0.21 0.11 0.57 0.55
2nd PC (32%) 1.91 −0.64 −0.36 0.64 −0.10 0.23 0.01
3rd PC (18%) 1.06 0.02 0.15 0.27 0.94 −0.07 0.12
Once the eigenvectors for each variable are calculated, six variables are categorized in the three
groups depending on which PCs they contribute to. Among six variables, TN, TP, and S contribute to
the first PC, which is 43% of the total variances, and T and DO contribute to the second PC of 32%
(Figure 2a and Table 1). Chl-a mainly contributes to the third PC, but only by 18% of the total variances,
hence was excluded from consideration (Figure 2b and Table 1). Therefore, the two groups contributing
to the first and second PC are independent of each other since all PCs are orthogonal to each other.
Of all the variables in the two groups, S and T each contribute to the first and second PCs with a
relatively larger magnitude than the other variables. Furthermore, they are also usually measured
by one instrument simultaneously. Therefore, T and S were selected as representative variables to
construct an index.
Once selecting the two most representative variables from the spatial PC analysis, the variables
were analyzed again by the temporal EOF. Figure 3shows an example of the time-series of the first,
second, and third PCs at pt.1 and pt. 38. The first PC at pt.1, which is close to the gate of the sea-dike,
shows a sinusoidal tendency with irregular fluctuations, while the second and third PCs have very large
irregular fluctuations as compared to the first PC (Figure 3a). The irregular fluctuations appearing on
the PCs have strong correlations of above 0.9 with those appearing on the real signals of salinity, which
may be directly related to the releases of freshwater. Therefore, irregular fluctuations are probably due
to the high frequency of artificial freshwater discharge. On the ocean side (pt.38), irregular fluctuations
were not significantly observed on all PCs since this area is far from the gate, and the clearer sinusoidal
time-series appears on the first PC (Figure 3b). The second and third PCs may have some tendencies,
but we do not explain them here since the present work is aiming only to find an index rather than
explain whole processes appearing in the area. Overall, sinusoidal characteristics are commonly
decomposed in the first PC regardless of location, which is presumably due to seasonal variability.
Sensors 2020,20, 1498 10 of 23
Sensors 2020, 20, x FOR PEER REVIEW 9 of 23
Table 1. The results of the EOF corresponding to the PCs for the spatial distribution. The sky blue,
orange, and light green mean a group of variables that contribute to the first PC, second PC, and third
PC, respectively.
Category Principal
Component Eigenvalue Eigenvector
T S DO Chl-a TN TP
Spatial
(Entire
domain)
1st PC (43%) 2.56 0.26 −0.50 −0.21 0.11 0.57 0.55
2nd PC (32%) 1.91 −0.64 −0.36 0.64 −0.10 0.23 0.01
3rd PC (18%) 1.06 0.02 0.15 0.27 0.94 −0.07 0.12
Once the eigenvectors for each variable are calculated, six variables are categorized in the three
groups depending on which PCs they contribute to. Among six variables, TN, TP, and S contribute
to the first PC, which is 43% of the total variances, and T and DO contribute to the second PC of 32%
(Figure 2a and Table 1). Chl-a mainly contributes to the third PC, but only by 18% of the total
variances, hence was excluded from consideration (Figure 2b and Table 1). Therefore, the two groups
contributing to the first and second PC are independent of each other since all PCs are orthogonal to
each other. Of all the variables in the two groups, S and T each contribute to the first and second PCs
with a relatively larger magnitude than the other variables. Furthermore, they are also usually
measured by one instrument simultaneously. Therefore, T and S were selected as representative
variables to construct an index.
Once selecting the two most representative variables from the spatial PC analysis, the variables
were analyzed again by the temporal EOF. Figure 3 shows an example of the time-series of the first,
second, and third PCs at pt.1 and pt. 38. The first PC at pt.1, which is close to the gate of the sea-dike,
shows a sinusoidal tendency with irregular fluctuations, while the second and third PCs have very
large irregular fluctuations as compared to the first PC (Figure 3a). The irregular fluctuations
appearing on the PCs have strong correlations of above 0.9 with those appearing on the real signals
of salinity, which may be directly related to the releases of freshwater. Therefore, irregular
fluctuations are probably due to the high frequency of artificial freshwater discharge. On the ocean
side (pt.38), irregular fluctuations were not significantly observed on all PCs since this area is far from
the gate, and the clearer sinusoidal time-series appears on the first PC (Figure 3b). The second and
third PCs may have some tendencies, but we do not explain them here since the present work is
aiming only to find an index rather than explain whole processes appearing in the area. Overall,
sinusoidal characteristics are commonly decomposed in the first PC regardless of location, which is
presumably due to seasonal variability.
(a) (b)
Figure 3. First, second, and third PC time-series of six decomposed variables extracted from (a) pt. 1
(near the sea-dike) and (b) pt. 38 (ocean side).
In order to see how T and S contribute to each PC, and how they relate to the other four variables,
the eigenvectors of six variables were calculated with the values measured at all 38 points of Figure
A2a. Among the 38 sets of time-series of PCs from the EOF, the results of pt.1 and pt.38 are presented
in Table 2. On the closest location to the gate, pt.1, the first PC contributes 43% to the total variances,
the second 32%, and the third 18%. The eigenvectors of T, DO, and TP appear to be greater than 0.5
on the first PC and S, Chl-a, and TN on the second PC. Chl-a and TN are mainly projected on the
Wint er Spri ng Autu mnSummer Spring Aut umnSummer
Wint er Wi nter
Spring Au tum nSummer
Wint er Spri ng Autum nSummer
Wint er Wi nte r
Figure 3.
First, second, and third PC time-series of six decomposed variables extracted from (
a
) pt. 1
(near the sea-dike) and (b) pt. 38 (ocean side).
In order to see how T and S contribute to each PC, and how they relate to the other four variables,
the eigenvectors of six variables were calculated with the values measured at all 38 points of Figure A2a.
Among the 38 sets of time-series of PCs from the EOF, the results of pt.1 and pt.38 are presented in
Table 2. On the closest location to the gate, pt.1, the first PC contributes 43% to the total variances,
the second 32%, and the third 18%. The eigenvectors of T, DO, and TP appear to be greater than 0.5 on
the first PC and S, Chl-a, and TN on the second PC. Chl-a and TN are mainly projected on the third PC,
but the third PC does not contribute much to the total variances. On the ocean side, pt.38, the first
PC contributes 47% to the total variances, the second 35%, and the third 11%. Here, T, S, and DO are
projected onto the first PC with eigenvectors greater than 0.5, while TN and TP are on the second PC,
and only Chl-a on the third PC.
Table 2. The results of the EOF corresponding to the PCs for the temporal distribution.
Category Principal
Component Eigenvalue Eigenvector
T S DO Chl-a TN TP
Temporal
(Pt.1 –
near the sea-dike)
1st PC (43%) 2.59 0.58 0.10 −0.53 0.18 0.22 0.54
2nd PC (32%) 2.20 −0.03 0.62 −0.20 0.51 −0.50 −0.25
3rd PC (18%) 0.67 −0.14 0.10 0.39 0.66 0.62 0.05
Temporal
(Pt.38 –
ocean side)
1st PC (47%) 2.85 0.58 0.50 −0.52 0.31 0.04 0.23
2nd PC (35%) 2.11 −0.10 −0.20 0.23 0.41 0.65 0.55
3rd PC (11%) 0.67 −0.18 0.38 0.37 0.69 −0.09 −0.46
The first PC is mainly affected by T and DO, regardless of location, and their sinusoidal trends
are associated with seasonal variability. In addition, the first PC near the gate shows irregular and
highly frequent fluctuations, which is due to the gate operation. Those fluctuations seem to reflect the
contribution of TP, which is originated from the upstream of the gate. While, S contributes a lot to the
second PC along with Chl-a and TN. On the ocean side, T, S, and DO show a large contribution to the
first PC, reflecting the seasonality. After all, T and S show seasonal variability together in the ocean
side, while near the gate, T still shows seasonal variability, but S appears close to the strong irregular
variabilities. In other words, T mainly exhibits the seasonal variability along with DO, but S varies
along with different variables depending on the locations (i.e., Chl-a and TN near the gate and T and
DO on the ocean side). Therefore, T and S are selected as representative variables to be considered in
the design of the monitoring network since they can reflect the effects of the seasonality and freshwater
discharge, respectively, and also help to deduce the changes of other variables.
As a next step, we calculated the cosine angle between T and S in a three-dimensional PC space,
which can be a single design index representing the whole domain of the system. A low cosine angle
(i.e., near zero) means that two variables representing the eigenvectors to construct that angle originate
from different sources. On the other hand, a high cosine angle (i.e., near 1) means that two variables
are somewhat related and originated from similar sources.
Figure 4shows the contour map of the cosine angles between the eigenvectors of T and S.
The values of the cosine angle are increasing towards the open sea since T and S are simultaneously
Sensors 2020,20, 1498 11 of 23
controlled by global open sea conditions such as current, solar radiation, and wind. Meanwhile, near
the sea-dike, the values of cosine angles are low since, while T still responds to global open sea
conditions, S reflects not only to global conditions but also to a local condition such as artificially
released freshwater. The cosine angle values near pt.6 are almost 0, which means that T and S have
an orthogonal (independent) tendency. This is because this area has a shallow tidal flat, so the
bottom surfaces are frequently exposed to the atmosphere during low tides (tidal amplitude is around
7.5 m, [
4
]). Such shallow tidal flats seem to be heated up and cooled down much faster than the deep
southern navigation channel (near pt.4 and 7). In addition, this area is far from the gate and, therefore,
may be less affected by the freshwater discharge.
Sensors 2020, 20, x FOR PEER REVIEW 11 of 23
Figure 4. The spatial distribution of the true field of cosine angle composed of 38 points arranged at first.
Moreover, the cosine angle has the advantage of being more reasonable because it can imply
how much the representative variables have a relationship within the spatiotemporal characteristics
of the other variables. Therefore, if the spatial distribution shown in Figure 4 is created and used as
a design variable for optimization, a comprehensive monitoring network design that can reflect the
inherent characteristics of the bay is possible.
3.2. Solutions for the Monitoring Array
As described earlier, the objective function of quantitative optimization was composed of RMSE,
and we solved it using a genetic algorithm until converging to an optimal solution. On the other hand,
the graphical optimization configured the objective function by the BOA method, and the optimal
array was graphically selected by using a genetic algorithm. These quantitative and graphical
methods were used for searching 4 to 10 monitoring points to compare those two methods and
recommend a better one. Figure 5 compares the reconstructed spatial distribution using the design
index of 4, 7, and 10 monitoring points selected by quantitative and graphical optimization with the
true spatial distribution. The dotted lines are the contours of the true values, and the solid lines are
those of the reconstructed estimates. The spatial distribution of the graphical optimization (the panels
on the right columns of the figure) reconstructs the contours more similarly to the true distribution
than the quantitative optimization (the panels on the left columns of the figure). Furthermore, no
matter how many searching points we want to include, the graphical optimization can find a
consistent location of points (Figure 5b,d,f). However, the quantitative optimization finds different
locations for each desired number of points (Figure 5a,c,e). For example, the location of 7 points
searched by the graphical optimization is the same as the location of 7 points out of 10 points
(Figure 5d,f). Nevertheless, 7 points found by quantitative optimization are arranged in different
locations from the 10 points (Figure 5c,e).
Figure 4.
The spatial distribution of the true field of cosine angle composed of 38 points arranged
at first.
Selecting the representative variables using EOF can extract multiple variables that represent the
inherent characteristics of the coastal area. Thus, it is possible to have a complex interpretation, unlike
the previous studies that used a single variable to select the monitoring points [22,23,26,29–32].
Moreover, the cosine angle has the advantage of being more reasonable because it can imply how
much the representative variables have a relationship within the spatiotemporal characteristics of the
other variables. Therefore, if the spatial distribution shown in Figure 4is created and used as a design
variable for optimization, a comprehensive monitoring network design that can reflect the inherent
characteristics of the bay is possible.
3.2. Solutions for the Monitoring Array
As described earlier, the objective function of quantitative optimization was composed of RMSE,
and we solved it using a genetic algorithm until converging to an optimal solution. On the other hand,
the graphical optimization configured the objective function by the BOA method, and the optimal
array was graphically selected by using a genetic algorithm. These quantitative and graphical methods
were used for searching 4 to 10 monitoring points to compare those two methods and recommend
a better one. Figure 5compares the reconstructed spatial distribution using the design index of 4, 7,
and 10 monitoring points selected by quantitative and graphical optimization with the true spatial
distribution. The dotted lines are the contours of the true values, and the solid lines are those of the
reconstructed estimates. The spatial distribution of the graphical optimization (the panels on the
right columns of the figure) reconstructs the contours more similarly to the true distribution than the
Sensors 2020,20, 1498 12 of 23
quantitative optimization (the panels on the left columns of the figure). Furthermore, no matter how
many searching points we want to include, the graphical optimization can find a consistent location of
points (Figure 5b,d,f). However, the quantitative optimization finds different locations for each desired
number of points (Figure 5a,c,e). For example, the location of 7 points searched by the graphical
optimization is the same as the location of 7 points out of 10 points (Figure 5d,f). Nevertheless, 7 points
found by quantitative optimization are arranged in different locations from the 10 points (Figure 5c,e).
Sensors 2020, 20, x FOR PEER REVIEW 12 of 23
(a) (b)
(c) (d)
(e) (f)
Figure 5. Comparison of the spatial distribution between true and estimated field reconstructed by
using 4 (a and b), 7 (c and d), and 10 (e and f) points of the monitoring array, based on the quantitative
optimization (left) and graphical optimization (right).
The optimal array was evaluated by the skill metrics, which plot the statistical parameters
between true and estimated spatial distribution (Figure 6). First, the statistical parameters are plotted
on a Taylor diagram to figure out how similar the estimated spatial distribution is to the true
distribution (Figure 6a). The spatial distribution reconstructed using seven to 10 points selected by
graphical optimization agrees with the true spatial distribution, with a high correlation of about 0.95
or more, and a very low CRMSD. On the other hand, if the points are selected to be six or less, the
statistical points are located farther from the origin, which means poor reconstruction performance.
In order to confirm how well the reconstructed distribution reproduces the variabilities of the true
ones, we have identified the bias and RMSD on the target diagram (Figure 6b). The variabilities of
the spatial distribution of the graphically selected points are within 0.1 of CRMSD, RMSD, and bias,
for the cases with seven to 10 points. In the case of less than six points, the results do not reconstruct
the true values well. On the other hand, even though nine or 10 points are selected by quantitative
optimization, the results are slightly worse than seven points of graphical optimization. Therefore,
quantitative optimization has a relatively poor reconstruction performance compared to the
graphical optimization, except for the cases of less than four points.
Figure 5.
Comparison of the spatial distribution between true and estimated field reconstructed by
using 4 (
a
,
b
), 7 (
c
,
d
), and 10 (
e
,
f
) points of the monitoring array, based on the quantitative optimization
(left) and graphical optimization (right).
The optimal array was evaluated by the skill metrics, which plot the statistical parameters between
true and estimated spatial distribution (Figure 6). First, the statistical parameters are plotted on a
Taylor diagram to figure out how similar the estimated spatial distribution is to the true distribution
(Figure 6a). The spatial distribution reconstructed using seven to 10 points selected by graphical
optimization agrees with the true spatial distribution, with a high correlation of about 0.95 or more,
and a very low CRMSD. On the other hand, if the points are selected to be six or less, the statistical
points are located farther from the origin, which means poor reconstruction performance. In order to
confirm how well the reconstructed distribution reproduces the variabilities of the true ones, we have
identified the bias and RMSD on the target diagram (Figure 6b). The variabilities of the spatial
distribution of the graphically selected points are within 0.1 of CRMSD, RMSD, and bias, for the cases
Sensors 2020,20, 1498 13 of 23
with seven to 10 points. In the case of less than six points, the results do not reconstruct the true values
well. On the other hand, even though nine or 10 points are selected by quantitative optimization,
the results are slightly worse than seven points of graphical optimization. Therefore, quantitative
optimization has a relatively poor reconstruction performance compared to the graphical optimization,
except for the cases of less than four points.
Sensors 2020, 20, x FOR PEER REVIEW 13 of 23
(a) (b)
Figure 6. (a) Taylor diagram and (b) target diagram representing the statistics between the true and
estimated spatial distribution. The abbreviation “Q” and “G” imply the quantitative and graphical
optimization, respectively. The numbers after “Q” and “G” indicate the number of points selected by
quantitative optimization (Q) and graphical optimization (G), respectively.
In order to determine how many points should be selected to construct a monitoring network,
RMSDs and CORs obtained by the quantitative and graphical solutions are presented in Figure 7.
The box plots are the quantiles of the populations obtained by many iterations in the quantitative
optimization, and the red circles are the single values found by the graphical optimization. Overall,
the solutions found by the graphical optimization show better reconstruction performance, even with
fewer numbers than the quantitative optimization. In addition, the graphical solution reaches a
certain threshold with seven or eight points and, after reaching the threshold, converges regardless
of the number of points. The solutions of quantitative optimization are different from each other
depending on the number of iterations without converging on a certain value. Therefore, quantitative
optimization has some statistical distributions, but graphical optimization provides a single solution
without statistical distribution, since this method does not require iteration to find a solution. As a
result, the graphical optimization finds the solution (i.e., representative monitoring array) with a
more stable convergence to an optimal solution and less computation time [33].
(a) (b)
Figure 7. (a) Root mean square differences (RMSDs) and (b) correlation coefficient (CORs) of spatial
distribution reconstructed by array of quantitative and graphical optimization.
The use of graphical optimization suggests several important issues in the design of the
monitoring network. The first is that the inherent characteristics of the coastal area can be reflected
200
150
100
50
0
100 60 30 10
Tru e
Relative CRMSD (%)
Ratio of SD (%)
G4
G5
G6
G7
G8 G9
G10
Q4
Q5
Q6
Q7
Q8
Q9
Q10
CRMSD
Bias
G4
Q4
Q5
Q7
Q6
Q8
Q9
Q10
G5
G7
G6
G8
G9
G10
Tru e
Figure 6.
(
a
) Taylor diagram and (
b
) target diagram representing the statistics between the true and
estimated spatial distribution. The abbreviation “Q” and “G” imply the quantitative and graphical
optimization, respectively. The numbers after “Q” and “G” indicate the number of points selected by
quantitative optimization (Q) and graphical optimization (G), respectively.
In order to determine how many points should be selected to construct a monitoring network,
RMSDs and CORs obtained by the quantitative and graphical solutions are presented in Figure 7.
The box plots are the quantiles of the populations obtained by many iterations in the quantitative
optimization, and the red circles are the single values found by the graphical optimization.
Overall, the solutions found by the graphical optimization show better reconstruction performance,
even with fewer numbers than the quantitative optimization. In addition, the graphical solution reaches
a certain threshold with seven or eight points and, after reaching the threshold, converges regardless
of the number of points. The solutions of quantitative optimization are different from each other
depending on the number of iterations without converging on a certain value. Therefore, quantitative
optimization has some statistical distributions, but graphical optimization provides a single solution
without statistical distribution, since this method does not require iteration to find a solution. As a
result, the graphical optimization finds the solution (i.e., representative monitoring array) with a more
stable convergence to an optimal solution and less computation time [33].
The use of graphical optimization suggests several important issues in the design of the monitoring
network. The first is that the inherent characteristics of the coastal area can be reflected in the objective
and constrained function. For example, high spatial variability can be reflected in BOA and complex
terrains and structures with a number of exterior and interior nonlinear constrained functions [
19
].
The second is that a complex nonlinear optimization problem can be solved with ALGA, which is
known for high computational performance and global convergence [
46
,
47
]. The third is that the
developed module can solve the problem of “how many” as well as “where” the monitoring points
should be placed. The graphical optimization can produce arrays with consistent locations, no matter
how many target monitoring points we require [
33
]. Therefore, implementing such an optimization
module could extend the applicability of the nonlinear constraint optimization problem that can be
considered for the ocean as well as for coastal areas [23].
Sensors 2020,20, 1498 14 of 23
Sensors 2020, 20, x FOR PEER REVIEW 13 of 23
(a)
(b)
Figure 6. (a) Taylor diagram and (b) target diagram representing the statistics between the true and
estimated spatial distribution. The abbreviation “Q” and “G” imply the quantitative and graphical
optimization, respectively. The numbers after “Q” and “G” indicate the number of points selected by
quantitative optimization (Q) and graphical optimization (G), respectively.
In order to determine how many points should be selected to construct a monitoring network,
RMSDs and CORs obtained by the quantitative and graphical solutions are presented in Figure 7.
The box plots are the quantiles of the populations obtained by many iterations in the quantitative
optimization, and the red circles are the single values found by the graphical optimization. Overall,
the solutions found by the graphical optimization show better reconstruction performance, even with
fewer numbers than the quantitative optimization. In addition, the graphical solution reaches a
certain threshold with seven or eight points and, after reaching the threshold, converges regardless
of the number of points. The solutions of quantitative optimization are different from each other
depending on the number of iterations without converging on a certain value. Therefore, quantitative
optimization has some statistical distributions, but graphical optimization provides a single solution
without statistical distribution, since this method does not require iteration to find a solution. As a
result, the graphical optimization finds the solution (i.e., representative monitoring array) with a
more stable convergence to an optimal solution and less computation time [33].
(a)
(b)
Figure 7. (a) Root mean square differences (RMSDs) and (b) correlation coefficient (CORs) of spatial
distribution reconstructed by array of quantitative and graphical optimization.
The use of graphical optimization suggests several important issues in the design of the
monitoring network. The first is that the inherent characteristics of the coastal area can be reflected
in the objective and constrained function. For example, high spatial variability can be reflected in
200
150
100
Ratio of SD (%)
CRMSD
45678910
Number of points
0
0.1
0.2
0.3
0.4
0.5
0.6
RMSD
45678910
Number of points
-1
-0.5
0
0.5
1
Correlation
Figure 7.
(
a
) Root mean square differences (RMSDs) and (
b
) correlation coefficient (CORs) of spatial
distribution reconstructed by array of quantitative and graphical optimization.
The GE has considerable spatial and temporal variabilities of water quality due to the change of
freshwater discharge, which can cause extreme situations [
37
]. Therefore, in addition to the normal
case discussed earlier, and named as the scenario N here, three more scenarios were built and tested.
The scenario 2N releases twice the amount of freshwater discharge than the scenario N, and the scenario
3N releases three times the amount. The scenario I reduces the amount of freshwater discharge to 50%
and increases to twice the frequency of release relative to the scenario N. The numerical simulations were
performed based on the scenarios, and the same method was applied to design the monitoring network for
extreme events. Even though the scenarios are the functions of the amount of freshwater discharge and
frequency, the representative variables are T and S, as in the scenario N. Furthermore, the trend of the first
and second PCs from the EOF represents seasonality and irregular freshwater discharge and contributes to
about 90% to the total time-series variance. As a result, the number of points required to reconstruct the
spatial distribution by graphical optimization for three extreme scenarios is the same as for the scenario N,
but their locations are slightly different from the scenario N (Figure 8).
Sensors 2020, 20, x FOR PEER REVIEW 14 of 23
in the objective and constrained function. For example, high spatial variability can be reflected in
BOA and complex terrains and structures with a number of exterior and interior nonlinear
constrained functions [19]. The second is that a complex nonlinear optimization problem can be
solved with ALGA, which is known for high computational performance and global
convergence [46,47]. The third is that the developed module can solve the problem of “how many”
as well as “where” the monitoring points should be placed. The graphical optimization can produce
arrays with consistent locations, no matter how many target monitoring points we require [33].
Therefore, implementing such an optimization module could extend the applicability of the nonlinear
constraint optimization problem that can be considered for the ocean as well as for coastal areas [23].
The GE has considerable spatial and temporal variabilities of water quality due to the change of
freshwater discharge, which can cause extreme situations [37]. Therefore, in addition to the normal
case discussed earlier, and named as the scenario N here, three more scenarios were built and tested.
The scenario 2N releases twice the amount of freshwater discharge than the scenario N, and the
scenario 3N releases three times the amount. The scenario I reduces the amount of freshwater
discharge to 50% and increases to twice the frequency of release relative to the scenario N. The
numerical simulations were performed based on the scenarios, and the same method was applied to
design the monitoring network for extreme events. Even though the scenarios are the functions of
the amount of freshwater discharge and frequency, the representative variables are T and S, as in the
scenario N. Furthermore, the trend of the first and second PCs from the EOF represents seasonality
and irregular freshwater discharge and contributes to about 90% to the total time-series variance. As
a result, the number of points required to reconstruct the spatial distribution by graphical
optimization for three extreme scenarios is the same as for the scenario N, but their locations are
slightly different from the scenario N (Figure 8).
Figure 8. The selected points of the on-site monitoring (red ‘+’) and the installable area of real-time
monitoring station (blue rectangles) in accordance with each scenario. The series of black dotted
ellipses indicate maximum distances from the reference points (red ‘+’) corresponding to weight 1,
and the blue rectangular regions are the installation area of the real-time monitoring station, which
represent the temporal distribution of the local characteristics well. The blue triangle located in the
outside of the target domain is the reference point of the offshore real-time monitoring station. The
abbreviation “RA” imply the representative area.
3.3. Optimal Design of the Water Quality Monitoring Network
Since the on-site monitoring points selected in the four scenarios are distributed at slightly
different locations, it is necessary to find a way to determine a location representing them. The time-
Figure 8.
The selected points of the on-site monitoring (
red ‘+’
) and the installable area of real-time
monitoring station (
blue rectangles
) in accordance with each scenario. The series of black dotted
ellipses indicate maximum distances from the reference points (
red ‘+’
) corresponding to weight 1,
and the blue rectangular regions are the installation area of the real-time monitoring station, which
represent the temporal distribution of the local characteristics well. The blue triangle located in
the outside of the target domain is the reference point of the offshore real-time monitoring station.
The abbreviation “RA” imply the representative area.
Sensors 2020,20, 1498 15 of 23
3.3. Optimal Design of the Water Quality Monitoring Network
Since the on-site monitoring points selected in the four scenarios are distributed at slightly different
locations, it is necessary to find a way to determine a location representing them. The time-series of data
at the monitoring points of each scenario were analyzed, and the representative locations were expressed
in the form of influence radius by grouping the points located near each other (Figure 8). The influence
radius (black dotted ellipse) was determined by a distance-dependent weighting function of the
time-series of the variable characteristics, and the center (red+) was determined by using the nonlinear
least square method using Equation (7) with
γ=
1 and e-folding value. Since the marked points in each
ellipse are solutions of each scenario, the center of the ellipsis could be regarded as a representative
point that characterizes the elliptic region with the influence radius. Therefore, time-series of data
acquired within the radius of influence are almost similar to the values corresponding to weight 1 from
the center. Such a series of steps led to select seven representative points in GE.
In order to evaluate how well those representative points reconstruct the true distribution of all
variables, the spatial distribution of each water quality variable was reconstructed and compared
with the true values (Table 3). Overall, the CORs are much higher than 0.8, and the RMSD is very
low in terms of their scale of mean and standard deviation. These statistical quantities mean that
the representative points can reconstruct the spatial distribution to be similar to the true distribution,
while expressing the spatial variability of each variable effectively. Aside from this, if the locations are
selected reasonably, then with deploying even the minimum number of representative monitoring
points, the spatial distribution of the six water quality variables can be relatively well reconstructed
individually. Therefore, if the on-site monitoring network is designed by the framework of this study,
an array, a set of representative points that have the influence radius, can be considered as an example
of a good representation of GE’s spatial characteristics.
Table 3. Statistical quantities of the reconstructed spatial distribution for six variables.
Statistics Water
Temperature Salinity Dissolved
Oxygen Chlorophyll-a Total
Nitrogen
Total
Phosphorus
COR 0.99 0.99 0.80 0.93 0.98 0.96
RMSD 0.07 0.46 0.06 0.24 0.06 0.00
MEAN 15.48 31.64 8.43 4.39 0.52 0.05
STD 0.45 2.68 0.10 0.60 0.25 0.01
In order to determine where to install the real-time monitoring station in the representative area
(i.e., area within influence radius), the signals at each area were compared and analyzed based on the
reference signals of an area with the high external force or variations. The signals of the representative
area (hereafter RA) 1 are assigned as a reference; RA1 is closest to the sea-dike and compared with the
signals of the remaining areas. Table 4shows the comparison of the time-series for six variables in each
area with that of RA1 statistically. The CORs of the time-series show that all variables except T and
DO decrease as the monitoring point gets farther away from the reference point of RA1. In addition,
RMSDs increase as the points get farther away from RA1, but T and DO do not increase much relative
to the magnitudes of mean and standard deviation. This is because T and DO are strongly subject
to seasonal variability rather than freshwater discharge, while other variables are more significantly
affected by the amount of freshwater discharge. Furthermore, in the area close to the sea-dike (i.e.,
RA2 and 3), the time-series of irregular freshwater discharge is reflected more than the others (i.e.,
RA4-7). From these results, global signals, such as seasonal variability, can be obtained in any area,
while local signals, such as freshwater discharge, can only be obtained in certain areas (e.g., RA1-3).
Therefore, one station must be unconditionally installed close to RA1, and other stations should be
deployed near RA2 and RA3 in order to obtain the local water quality characteristics of GE.
Sensors 2020,20, 1498 16 of 23
Table 4.
Statistical quantities of the time-series distribution for six variables at each optimal point, with
representative area 1 (RA1) as a reference point.
Statistics Water temperature
RA1 RA2 RA3 RA4 RA5 RA6 RA7
COR 1.00 0.99 1.00 0.96 0.95 0.88 0.90
RMSD 0.00 1.65 0.85 2.80 3.20 4.79 4.26
BIAS 0.00 0.50 −0.02 0.94 1.00 1.53 1.32
MEAN 16.38 15.88 16.40 15.44 15.38 14.85 15.06
STD 9.35 9.17 9.52 8.83 8.47 7.72 8.15
Salinity
COR 1.00 0.38 0.45 0.35 0.37 0.22 0.26
RMSD 0.00 14.36 16.87 17.53 18.15 18.71 18.75
BIAS 0.00 −13.02 −15.73 −16.37 −17.01 −17.56 −17.61
MEAN 15.47 28.48 31.20 31.84 32.48 33.03 33.08
STD 6.55 2.50 1.28 1.01 0.67 0.51 0.53
Dissolved Oxygen
COR 1.00 0.75 0.72 0.72 0.72 0.72 0.72
RMSD 0.00 1.94 2.01 2.05 2.10 2.12 2.11
BIAS 0.00 0.52 0.17 0.45 0.40 0.44 0.49
MEAN 8.82 8.31 8.65 8.38 8.43 8.38 8.33
STD 2.73 1.53 1.28 1.29 1.16 1.11 1.17
Chlorophyll-a
COR 1.00 0.82 0.80 0.77 0.73 0.66 0.69
RMSD 0.00 1.57 2.81 1.79 1.90 2.32 2.03
BIAS 0.00 −0.20 −2.02 0.37 −0.13 −0.35 0.20
MEAN 4.07 4.27 6.08 3.70 4.20 4.41 3.87
STD 2.71 2.22 3.30 1.91 2.31 2.86 2.32
Total Nitrogen
COR 1.00 0.54 0.30 0.27 0.16 0.20 0.15
RMSD 0.00 1.26 1.68 1.67 1.72 1.72 1.72
BIAS 0.00 1.10 1.51 1.50 1.56 1.56 1.56
MEAN 1.99 0.89 0.47 0.48 0.43 0.43 0.43
STD 0.74 0.27 0.05 0.05 0.04 0.04 0.04
Total Phosphorus
COR 1.00 0.84 0.59 0.62 0.62 0.66 0.64
RMSD 0.00 0.03 0.04 0.04 0.04 0.04 0.04
BIAS 0.00 0.02 0.03 0.03 0.03 0.03 0.03
MEAN 0.07 0.06 0.04 0.05 0.04 0.05 0.05
STD 0.03 0.02 0.01 0.01 0.01 0.01 0.01
Once a station is chosen and installed on RA1, 2, and 3 to acquire local signals, it is necessary
to determine whether to install the monitoring stations in RA4, 5, 6, and 7. This is because irregular
signals due to freshwater discharge can be obtained from S, Chl-a, TN, TP, in RA 1-3, while it is difficult
to obtain their global signals originating from offshore characteristics. In order to determine whether
to install the monitoring stations in RA4, 5, 6, and 7, the signals from the seven RAs were compared
with the reference signals of an offshore observatory, which is the same location currently operated by
the Korean government (Figure 8). Table 5shows the statistical comparison of the time-series for six
variables at each location with the offshore signals as the reference.
Sensors 2020,20, 1498 17 of 23
Table 5.
Statistical quantities of the time-series distribution for six variables at each optimal point with
the offshore as a reference point.
Statistics Water temperature
RA1 RA2 RA3 RA4 RA5 RA6 RA7 Offshore
COR 0.76 0.84 0.79 0.90 0.92 0.97 0.96 1.00
RMSD 6.58 5.51 6.49 4.52 3.98 2.49 3.09 0.00
BIAS −2.28 −1.78 −2.30 −1.34 −1.27 −0.75 −0.96 0.00
MEAN 16.38 15.88 16.40 15.44 15.38 14.85 15.06 14.10
STD 9.35 9.17 9.52 8.83 8.47 7.72 8.15 5.99
Salinity
COR 0.16 0.29 0.10 0.65 0.56 0.89 0.85 1.00
RMSD 18.79 5.21 2.30 1.50 0.83 0.26 0.29 0.00
BIAS 17.63 4.61 1.89 1.26 0.62 0.06 0.02 0.00
MEAN 15.47 28.48 31.20 31.84 32.48 33.03 33.08 33.10
STD 6.55 2.50 1.28 1.01 0.67 0.51 0.53 0.38
Dissolved Oxygen
COR 0.72 0.97 0.97 0.99 0.99 1.00 1.00 1.00
RMSD 2.13 0.59 0.41 0.31 0.17 0.13 0.21 0.00
BIAS −0.35 0.17 −0.17 0.10 0.05 0.10 0.15 0.00
MEAN 8.82 8.31 8.65 8.38 8.43 8.38 8.33 8.48
STD 2.73 1.53 1.28 1.29 1.16 1.11 1.17 1.04
Chlorophyll-a
COR 0.62 0.76 0.80 0.82 0.94 0.99 0.96 1.00
RMSD 3.37 2.90 2.45 3.11 2.27 1.53 2.39 0.00
BIAS 1.32 1.13 −0.69 1.69 1.19 0.98 1.53 0.00
MEAN 4.07 4.27 6.08 3.70 4.20 4.41 3.87 5.39
STD 2.71 2.22 3.30 1.91 2.31 2.86 2.32 3.93
Total Nitrogen
COR 0.28 0.40 0.75 0.80 0.94 0.98 0.95 1.00
RMSD 1.71 0.52 0.05 0.06 0.02 0.01 0.02 0.00
BIAS −1.55 −0.46 −0.04 −0.05 0.00 0.01 0.01 0.00
MEAN 1.99 0.89 0.47 0.48 0.43 0.43 0.43 0.43
STD 0.74 0.27 0.05 0.05 0.04 0.04 0.04 0.05
Total Phosphorus
COR 0.69 0.90 0.94 0.96 0.98 0.99 0.99 1.00
RMSD 0.03 0.01 0.00 0.00 0.00 0.00 0.00 0.00
BIAS −0.03 −0.01 0.00 0.00 0.00 0.00 0.00 0.00
MEAN 0.07 0.06 0.04 0.05 0.04 0.05 0.05 0.05
STD 0.03 0.02 0.01 0.01 0.01 0.01 0.01 0.01
The signals in RA4, 5, 6, and 7 are highly correlated with the offshore signals for all variables.
In addition, their RMSDs show relatively low values considering the magnitudes of their means and
standard deviations. However, the signals in RA1, 2, and 3 have a relatively low correlation with the
signals in the offshore. In particular, S and TN cannot infer the global signals originating from the
offshore with the signal in RA1, 2, and 3. Consequently, the global signals of six variables in RA4, 5, 6,
and 7 are not necessarily monitored in this domain because they can be obtained from the outside of
the domain and sufficiently infer all of them.
The monitoring network in Korea has been arbitrarily determined by consultation between
stakeholders, engineers, and decision-makers. Moreover, no engineering studies have been conducted
to design the monitoring network in the coastal area except by the authors of this study [
19
,
33
].
The marine environmental monitoring network configuration and operation plan, issued by Ministry of
Sensors 2020,20, 1498 18 of 23
Maritime Affairs and Fisheries, states that “the periodic on-site observations perform in a place where
it can be assumed to be representative of the area” and “real-time monitoring stations are installed and
operated close to the land considering the accessibility”. After all, this is probably due to the lack of
systematic procedures for designing the monitoring network [
19
]. As a result, a random monitoring
network is composed of various national organizations (Figure 1a,b). Therefore, the monitoring
network shown in Figure 8can be a useful resource for redesigning GE’s existing monitoring network
(Figure 1b) that was arbitrarily selected. In addition, the use of the present framework in other
coastal regions or open oceans enables the design of more reliable monitoring networks based on an
engineering basis rather than the arbitrarily designed monitoring network.
4. Summary and Conclusions
The coastal monitoring system, which is composed of several different series of sensors, aims
to provide reliable information to forecast sea weather, sustain sound water quality, and plan for
decision-making. Therefore, monitoring has been carried out to understand the inherent characteristics
of the bay [
19
] carefully, but how the monitoring network is constructed has still not been schematically
determined, but rather, it has been arbitrarily chosen. Therefore, the present study proposed a way
to design an optimal monitoring network to fully reflect the spatiotemporal variability of water
quality in semi-enclosed estuaries such as GE, which is a complex coastal system connected to the
upstream watershed.
For designing an optimal monitoring network, instead of using ground-truth data that is
not available realistically, the results from a well-validated numerical model were used to secure
high-resolution assuming as ground-truth data. Such highly resolved numerical models allowed us to
design a comprehensive monitoring network. With the results from the simulation, design variables
were chosen to reflect the spatiotemporal characteristics of the bay adequately. As a representative
design variable, the present work selected the cosine angle between the two eigenvectors of the
representative variables in the three-dimensional PC space, which was determined by EOF analysis.
This approach analyzed the inherent characteristics of the representative variables with other variables
so that, even if the monitoring network is designed with only a variable, it can sufficiently represent
the characteristics of the other variables.
The most challenging part of the present study was that we considered “where” as well as “how
many” monitoring points were to be placed. Conventional quantitative optimization could determine
“how many” monitoring points are needed, but the solutions converged locally so that at every trial,
a consistent arrangement of solutions could not be achieved. Therefore, the graphical optimization
was applied and resulted in a consistent array for each simulation once the target number of points
was set without high computational cost. With the distance-dependent weighting, the interpolation
functions were constrained for bounding a region to be feasible for converging the objective function to
the optimal solution. After that, the array of the monitoring points could be found on the interpolated
space by applying the ALGA.
Finally, the spatiotemporal distribution, reconstructed by using the selected optimal array,
was compared to the true distribution. The estimated spatial distribution was statistically
evaluated by the skill metrics, on which an array of the on-site monitoring network was designed.
Moreover, the installable region of the real-time monitoring station could be determined by a time-series
comparison based on the reference point from which the bay’s global and local signals could be
acquired. As a result, GE required a total of seven on-site monitoring points to fully represent the
spatial distribution of water quality variables, and three real-time monitoring stations within the
installable regions to simultaneously acquire global and local time-series characteristics.
Such a design method for finding the optimal estuarine monitoring network could be useful as a
tool for strategically supporting decision-making. Besides, it is more meaningful in that the method
can help not only designing the on-site monitoring array but also finding the installable regions of the
real-time monitoring station that has been rarely studied so far. Such a monitoring network can reduce
Sensors 2020,20, 1498 19 of 23
the cost, time, and effort for operating and managing the coastal monitoring and increase the reliability
of the monitoring data [
17
]. Also, the design procedure of this study can strategically organize the
standard framework to determine the monitoring network in a semi-enclosed estuary, as well as
the lake, bay, and open ocean. Moreover, an appropriate monitoring network can secure additional
advantages in improving the accuracy of hydrodynamic models for data assimilation [36,65].
Author Contributions:
N.-H.K. proposed the original idea, designed the research and wrote the article and J.H.H.
supervise the present research and edited the manuscript. All authors have read and agreed to the published
version of the manuscript.
Funding:
This research was funded by National Research Foundation of Korea (NRF) grant funded by
Korean Government Ministry of Science, ICT & Future Planning (No. 2020R1A2B5B01002249), Korea
Ministry of Environment (MOE) as “Chemical Accident Response R&D Program (No. ARG201901179001)”,
and administratively supported by the Institute of Engineering Research at the Seoul National University.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
BOA Barnes Objective Analysis
Chl-a Chlorophyll-a
COR Correlation
CRMSD Centered Root Mean Square Difference
DO Dissolved Oxygen
EOF Empirical Orthogonal Function
G Graphical optimization
GE Geumgang Estuary
IOA Index Of Agreement
OI Optimal Interpolation
PC Principal Component
Q Quantitative optimization
RA Representative Area
RE Relative Error
RMSE Root-Mean-Square Error
S Salinity
SD Standard Deviation
T Water Temperature
TN Total Nitrogen
TP Total Phosphorus
Appendix A
Table A1. Monthly freshwater discharge in Geumgang Estuary (Sep. 1994 – Aug. 2017).
Month 1 2 3 4 5 6 7 8 9 10 11 12 Annual
Season Winter Spring Summer Autumn Winter
Discharge (106ton) 159 160 179 228 263 468
1202 1111
795 284 200 201 5250
Frequency 9 9 11 13 16 19 33 33 25 15 12 11 206
Total Time 22 23 28 35 42 59 131 127 93 38 28 28 654
Time/count 2.4 2.6 2.5 2.7 2.6 3.1 4.0 3.8 3.7 2.5 2.3 2.5 3.2
Sensors 2020,20, 1498 20 of 23
Table A2.
Calibration and validation of the numerical model [
19
]. The abbreviation of
“SSC”, “Hs”, and “Amp” imply the suspended sediment concentration, significant wave height,
and amplitude, respectively.
Variable Parameter Skill Score Skill Index
Calibration Validation
Wave Hs 0.95 0.96 IOA
Tide Semi-range 0.98 0.98 RE
Phase-lag 1.00 0.99
Tidal current Amp. 0.82 0.87 RE
Phase-lag 0.89 0.97
SSC - 0.65 0.64 RE
Water quality
Water temperature 0.99 0.99
IOA
Salinity 0.57 0.85
Chl-a 0.67 0.67
TN 0.95 0.95
TP 0.71 0.71
DO 0.85 0.65
Sensors 2020, 20, x FOR PEER REVIEW 20 of 23
Total Time 22 23 28 35 42 59 131 127 93 38 28 28 654
Time/count 2.4 2.6 2.5 2.7 2.6 3.1 4.0 3.8 3.7 2.5 2.3 2.5 3.2
Table A2. Calibration and validation of the numerical model [19]. The abbreviation of “SSC”, “Hs”,
and “Amp” imply the suspended sediment concentration, significant wave height, and amplitude,
respectively.
Variable Parameter Skill score Skill index
Calibration Validation
Wave Hs 0.95 0.96 IOA
Tide Semi-range 0.98 0.98
RE
Phase-lag 1.00 0.99
Tidal current Amp. 0.82 0.87
RE
Phase-lag 0.89 0.97
SSC - 0.65 0.64 RE
Water quality
Water temperature 0.99 0.99
IOA
Salinity 0.57 0.85
Chl-a 0.67 0.67
TN 0.95 0.95
TP 0.71 0.71
DO 0.85 0.65
(a) (b)
(c) (d)
Figure A1. The true field of (a) water temperature and (b) salinity, and the example of the monitoring
array (c) designed by considering only salinity and reconstructing the spatial distribution of the water
temperature, and (d) designed by considering only water temperature and reconstructing the spatial
distribution of the salinity.
Figure A1.
The true field of (
a
) water temperature and (
b
) salinity, and the example of the monitoring
array (
c
) designed by considering only salinity and reconstructing the spatial distribution of the water
temperature, and (
d
) designed by considering only water temperature and reconstructing the spatial
distribution of the salinity.
Sensors 2020,20, 1498 21 of 23
Sensors 2020, 20, x FOR PEER REVIEW 21 of 23
(a) (b)
Figure A2. (a) The initial placement of the monitoring points and (b) boxplot of each variable.
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