# Optimal Design of Water Quality Monitoring Networks in Semi-Enclosed Estuaries

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Characteristics of the Study Area

#### 2.2. Numerical Model (Input Data)

#### 2.3. Design Variables

#### 2.4. Finding the Optimal Solutions

#### 2.5. Methods of Performance Evaluation

## 3. Results and Discussion

#### 3.1. Decomposition of the Spatiotemporally Dependent Variable

#### 3.2. Solutions for the Monitoring Array

#### 3.3. Optimal Design of the Water Quality Monitoring Network

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

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

Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Annual | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Season | Winter | Spring | Summer | Autumn | Winter | |||||||||

Discharge (10^{6} ton) | 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 |

**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 |

**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.

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**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.

**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.

**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).

**Figure 4.**The spatial distribution of the true field of cosine angle composed of 38 points arranged at first.

**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).

**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.

**Figure 7.**(

**a**) Root mean square differences (RMSDs) and (

**b**) correlation coefficient (CORs) of spatial distribution reconstructed by array of quantitative and graphical optimization.

**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.

**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 |

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 |

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 |

**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 |

**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 |

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## Share and Cite

**MDPI and ACS Style**

Kim, N.-H.; Hwang, J.H.
Optimal Design of Water Quality Monitoring Networks in Semi-Enclosed Estuaries. *Sensors* **2020**, *20*, 1498.
https://doi.org/10.3390/s20051498

**AMA Style**

Kim N-H, Hwang JH.
Optimal Design of Water Quality Monitoring Networks in Semi-Enclosed Estuaries. *Sensors*. 2020; 20(5):1498.
https://doi.org/10.3390/s20051498

**Chicago/Turabian Style**

Kim, Nam-Hoon, and Jin Hwan Hwang.
2020. "Optimal Design of Water Quality Monitoring Networks in Semi-Enclosed Estuaries" *Sensors* 20, no. 5: 1498.
https://doi.org/10.3390/s20051498