# Effect of Open Boundary Conditions and Bottom Roughness on Tidal Modeling around the West Coast of Korea

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Modeling

#### 2.1. Basic Equations

_{f}are the free surface and bottom elevations, respectively;

_{x}and F

_{y}are body forces in x and y directions including Coriolis (${F}_{x}^{c},{F}_{y}^{c})$, bottom friction ${F}_{x}^{f},{F}_{y}^{f})$, and surface wind ${F}_{x}^{w},{F}_{y}^{w})$ forces determined as ${F}_{x}={F}_{x}^{c}+{F}_{x}^{f}+{F}_{x}^{w}$ and ${F}_{y}={F}_{y}^{c}+{F}_{y}^{f}+{F}_{y}^{w}$

_{f}is the bottom friction coefficient, ${C}_{f}=\frac{g{n}^{2}}{{h}^{1/3}}$, n is Manning’s coefficient;

_{t}${\nu}_{e}=\nu +{\nu}_{t}$; where

_{i}(=U or V) is an average over time of velocity components; and P is the production term:

_{kv}and P

_{εv}are vertical shear terms: ${P}_{kv}={c}_{k}\frac{{u}_{*}^{3}}{h};{P}_{\epsilon v}={c}_{\epsilon}\frac{{u}_{*}^{4}}{{h}^{2}}$ where ${c}_{k}=\frac{1}{\sqrt{{c}_{f}}}$ and ${c}_{\epsilon}=3.6\frac{{c}_{2\epsilon}\sqrt{{c}_{\mu}}}{{c}_{f}{}^{3/4}}$

#### 2.2. Boundary Conditions

#### 2.2.1. At the Solid Boundary

_{f}is obtained from the calibration procedure, which is shown in Section 3.1 below.

#### 2.2.2. At the Free Surface

#### 2.2.3. At the Open Boundary

_{i}is the water elevation, ${A}_{{F}_{i}}$ is amplitude; T is period and ${\phi}_{{F}_{i}}$ is phase of each tidal constituent.

#### 2.3. Study Region

## 3. Numerical Results and Discussion

#### 3.1. Response of the Tide around WCK to the Bottom Roughness

#### 3.1.1. Applying Uniform Roughness Coefficient

_{f}= 0.0023 provides the best result obtained from FES2014 and TPXO9.1, while the numerical results obtained from NAO99Jb were not significantly different between C

_{f}= 0.0023 and 0.0025. For the tidal constituent K1, the bottom roughness coefficient C

_{f}= 0.002 provides the best result obtained from NAO99Jb, while the numerical results obtained from FES2014 were not significantly different between C

_{f}= 0.0015 and 0.002; the numerical results obtained from TPXO9.1 were not significantly different between C

_{f}= 0.002, 0.0023 and 0.0025. For the tidal constituent S2, the bottom roughness coefficient C

_{f}= 0.0015 provides the best result obtained from all three assimilated tidal models. For the tidal constituent O1, the bottom roughness coefficient C

_{f}= 0.0015 provides the best result obtained from FES2014 and TPXO9.1, while the numerical results obtained from NAO99Jb were not significantly different between C

_{f}= 0.0015 and 0.002. In addition, based on the RMSE values in Table A2, Table A3 and Table A4, the results show that for M2 the most appropriate roughness values for Mokpo, Gunsan and Incheon regions were 0.0025, 0.003 and 0.0023, respectively. Whereas, for S2, the most appropriate roughness values for Mokpo, Gunsan and Incheon regions were 0.002, 0.0023 and 0.0015, respectively. For O1, the most appropriate roughness value for Mokpo, Gunsan and Incheon regions was 0.0015 and for K1 the most appropriate roughness values with FES2014 and NAO99Jb for Mokpo, Gunsan and Incheon regions were 0.0015, 0.002 and 0.002, respectively. However, with TPXO9.1 the values for Mokpo, Gunsan and Incheon regions were 0.002, 0.0023 and 0.002, respectively.

#### 3.1.2. Applying Non-Uniform Roughness Coefficient

_{f}took a value of 0.0025 for the Mokpo region, 0.0035 for the Gunsan region, and 0.002 for Incheon and other regions. These values are in the range suggested by [31,32] applying also for four tidal constituents (M2, K1, S2 and O1).

#### 3.2. Response of the Tide around the WCK to the Open Boundary

#### 3.2.1. Sensitivity Analysis

#### Response of the Tide around the WCK to Individual Boundary Forcing

#### Response of the Tide around the WCK to the Tidal Amplitude at Open Boundary

_{1}and a

_{2}are different boundary tidal amplitudes in comparison, and ${r}_{i}{\left({a}_{j}\right)}_{j=1,2}$ is a response of coastal amplitude at the i-th gauge location.

_{a}did not significantly increase. Meanwhile, an increase of K1 amplitude at the boundary B with an increment of 20 cm caused less significant change on mean D

_{a}within all three regions of WCK.

#### 3.3. Comparison between the Numerical Results and Observations

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Validation of amplitude and phase obtained from three tidal models against observation data.

Tidal Constituent | RMSE | Range of Amplitudes and Phases | |||
---|---|---|---|---|---|

FES2014 (1/16°) | NAO99Jb (1/12°) | TPXO9.1 (1/6°) | |||

M2 | Amp (cm) | 20.2 | 16.1 | 25 | 107.3 $\xf7$ 295.8 |

Phase (°) | 8.2 | 5.4 | 6.6 | 36.8 $\xf7$ 275.6 | |

K1 | Amp (cm) | 4.2 | 4.9 | 6.2 | 21.7 $\xf7$ 35.4 |

Phase (°) | 5.4 | 7.6 | 7.5 | 75.6 $\xf7$ 193.1 | |

S2 | Amp (cm) | 14.6 | 8.4 | 11.4 | 37.8 $\xf7$ 114.1 |

Phase (°) | 10.9 | 8.8 | 7.1 | 59.6 $\xf7$ 328.9 | |

O1 | Amp (cm) | 3.8 | 4.8 | 3.9 | 16.3 $\xf7$ 25 |

Phase (°) | 11 | 31.8 | 6.1 | 39 $\xf7$ 142.9 |

Tidal Model | Constituent | Cd | RMSE (cm) | |||
---|---|---|---|---|---|---|

Mokpo (M) | Gunsan (G) | Incheon (I) | Mean | |||

FES2014 | M2 | 0.0015 | 10.17 | 34.83 | 40.18 | 36.30 |

0.002 | 5.67 | 22.87 | 16.62 | 18.63 | ||

0.0023 | 3.22 | 16.49 | 14.39 | 14.59 | ||

0.0025 | 2.79 | 12.99 | 19.28 | 16.12 | ||

0.003 | 6.24 | 10.58 | 35.57 | 26.63 | ||

K1 | 0.0015 | 0.79 | 1.46 | 2.07 | 1.77 | |

0.002 | 0.98 | 1.30 | 2.03 | 1.70 | ||

0.0023 | 1.16 | 1.48 | 2.34 | 1.96 | ||

0.0025 | 1.29 | 1.70 | 2.64 | 2.21 | ||

0.003 | 1.67 | 2.35 | 3.51 | 2.97 | ||

S2 | 0.0015 | 2.63 | 10.94 | 12.21 | 11.15 | |

0.002 | 1.29 | 6.92 | 19.21 | 14.55 | ||

0.0023 | 1.58 | 6.24 | 23.41 | 17.38 | ||

0.0025 | 2.16 | 6.59 | 26.12 | 19.35 | ||

0.003 | 3.76 | 8.99 | 31.90 | 23.77 | ||

O1 | 0.0015 | 1.42 | 1.71 | 1.33 | 1.49 | |

0.002 | 1.82 | 2.38 | 1.86 | 2.07 | ||

0.0023 | 1.99 | 2.67 | 2.26 | 2.40 | ||

0.0025 | 2.10 | 2.86 | 2.53 | 2.63 | ||

0.003 | 2.43 | 3.38 | 3.27 | 3.24 |

Tidal Model | Constituent | Cd | RMSE (cm) | |||
---|---|---|---|---|---|---|

Mokpo (M) | Gunsan (G) | Incheon (I) | Mean | |||

NAO99Jb | M2 | 0.0015 | 12.90 | 40.56 | 45.18 | 41.37 |

0.002 | 7.38 | 26.96 | 19.39 | 21.89 | ||

0.0023 | 4.14 | 19.93 | 14.16 | 16.06 | ||

0.0025 | 2.29 | 15.75 | 17.64 | 16.07 | ||

0.003 | 4.40 | 10.46 | 33.32 | 25.00 | ||

K1 | 0.0015 | 0.95 | 1.65 | 2.17 | 1.90 | |

0.002 | 1.04 | 1.35 | 2.13 | 1.78 | ||

0.0023 | 1.17 | 1.47 | 2.42 | 2.01 | ||

0.0025 | 1.28 | 1.64 | 2.70 | 2.24 | ||

0.003 | 1.64 | 2.30 | 3.60 | 3.01 | ||

S2 | 0.0015 | 2.62 | 11.03 | 12.85 | 11.56 | |

0.002 | 1.53 | 7.07 | 19.89 | 15.05 | ||

0.0023 | 1.82 | 6.39 | 24.02 | 17.84 | ||

0.0025 | 2.37 | 6.77 | 26.70 | 19.78 | ||

0.003 | 4.03 | 9.32 | 32.58 | 24.31 | ||

O1 | 0.0015 | 0.49 | 0.84 | 1.49 | 1.21 | |

0.002 | 0.83 | 1.21 | 1.22 | 1.19 | ||

0.0023 | 1.05 | 1.53 | 1.46 | 1.46 | ||

0.0025 | 1.19 | 1.75 | 1.69 | 1.67 | ||

0.003 | 1.54 | 2.28 | 2.37 | 2.27 |

Tidal Model | Constituent | Cd | RMSE (cm) | |||
---|---|---|---|---|---|---|

Mokpo (M) | Gunsan (G) | Incheon (I) | Mean | |||

TPXO9.1 | M2 | 0.0015 | 10.49 | 34.68 | 40.07 | 36.19 |

0.002 | 5.33 | 21.39 | 15.72 | 17.51 | ||

0.0023 | 3.29 | 15.14 | 14.63 | 14.16 | ||

0.0025 | 3.25 | 12.13 | 19.90 | 16.26 | ||

0.003 | 7.42 | 11.13 | 36.85 | 27.64 | ||

K1 | 0.0015 | 1.12 | 2.02 | 2.46 | 2.20 | |

0.002 | 0.99 | 1.36 | 1.91 | 1.65 | ||

0.0023 | 1.01 | 1.21 | 1.93 | 1.62 | ||

0.0025 | 1.06 | 1.25 | 2.10 | 1.74 | ||

0.003 | 1.31 | 1.75 | 2.87 | 2.37 | ||

S2 | 0.0015 | 2.17 | 10.22 | 12.63 | 11.13 | |

0.002 | 1.05 | 6.53 | 19.79 | 14.88 | ||

0.0023 | 1.70 | 6.26 | 24.07 | 17.85 | ||

0.0025 | 2.26 | 6.76 | 26.51 | 19.65 | ||

0.003 | 4.07 | 9.54 | 32.34 | 24.17 | ||

O1 | 0.0015 | 1.07 | 1.31 | 1.24 | 1.25 | |

0.002 | 1.46 | 1.95 | 1.55 | 1.71 | ||

0.0023 | 1.70 | 2.33 | 1.98 | 2.10 | ||

0.0025 | 1.80 | 2.50 | 2.25 | 2.31 | ||

0.003 | 2.18 | 3.09 | 3.00 | 2.97 |

**Table A5.**List of simulation cases applying non-uniform bottom roughness coefficients to different sub-regions of WCK.

Case | Tide Model | Bottom Friction Coefficient | |||
---|---|---|---|---|---|

Mokpo | Gunsan | Incheon | Other Sub-Region | ||

FES 2-1 | FES2014 | 0.0025 | 0.0027 | 0.002 | 0.002 |

FES 2-2 | FES2014 | 0.0025 | 0.003 | 0.002 | 0.002 |

FES 2-3 | FES2014 | 0.0025 | 0.0035 | 0.0018 | 0.002 |

FES 2-4 | FES2014 | 0.0025 | 0.0035 | 0.002 | 0.002 |

NAO 2-1 | NAO99Jb | 0.0025 | 0.0027 | 0.002 | 0.002 |

NAO 2-2 | NAO99Jb | 0.0025 | 0.003 | 0.002 | 0.002 |

NAO 2-3 | NAO99Jb | 0.0025 | 0.0035 | 0.0018 | 0.002 |

NAO 2-4 | NAO99Jb | 0.0025 | 0.0035 | 0.002 | 0.002 |

TPX 2-1 | TPXO9.1 | 0.0025 | 0.0027 | 0.002 | 0.002 |

TPX 2-2 | TPXO9.1 | 0.0025 | 0.003 | 0.002 | 0.002 |

TPX 2-3 | TPXO9.1 | 0.0025 | 0.0035 | 0.0018 | 0.002 |

TPX 2-4 | TPXO9.1 | 0.0025 | 0.0035 | 0.002 | 0.002 |

Tidal Constituent | Simulation Case | RMSE (cm) | |||
---|---|---|---|---|---|

Mokpo | Gunsan | Incheon | Mean | ||

M2 | FES 2-1 | 3.33 | 12.04 | 11.94 | 11.44 |

FES 2-2 | 3.26 | 11.77 | 11.90 | 11.31 | |

FES 2-3 | 3.29 | 11.61 | 12.12 | 11.37 | |

FES 2-4 | 3.65 | 11.40 | 12.06 | 11.27 | |

NAO 2-1 | 2.25 | 15.00 | 12.75 | 13.09 | |

NAO 2-2 | 2.25 | 14.15 | 12.38 | 12.53 | |

NAO 2-3 | 2.27 | 13.39 | 13.83 | 13.00 | |

NAO 2-4 | 2.26 | 13.53 | 12.03 | 12.09 | |

TPX 2-1 | 4.10 | 11.09 | 11.91 | 11.08 | |

TPX 2-2 | 3.74 | 11.17 | 11.91 | 11.10 | |

TPX 2-3 | 3.88 | 11.18 | 11.68 | 10.97 | |

TPX 2-4 | 3.79 | 11.24 | 12.09 | 11.23 |

Tidal Constituent | Simulation Case | RMSE (cm) | |||
---|---|---|---|---|---|

Mokpo | Gunsan | Incheon | Mean | ||

K1 | FES 2-1 | 1.28 | 1.75 | 2.32 | 2.04 |

FES 2-2 | 1.30 | 1.87 | 2.37 | 2.11 | |

FES 2-3 | 1.28 | 2.01 | 2.28 | 2.10 | |

FES 2-4 | 1.23 | 1.92 | 2.30 | 2.08 | |

NAO 2-1 | 1.28 | 1.72 | 2.42 | 2.09 | |

NAO 2-2 | 1.28 | 1.81 | 2.43 | 2.12 | |

NAO 2-3 | 1.28 | 1.96 | 2.36 | 2.13 | |

NAO 2-4 | 1.28 | 1.95 | 2.46 | 2.18 | |

TPX 2-1 | 1.04 | 1.32 | 1.90 | 1.63 | |

TPX 2-2 | 1.05 | 1.38 | 1.90 | 1.65 | |

TPX 2-3 | 1.05 | 1.50 | 1.84 | 1.66 | |

TPX 2-4 | 1.05 | 1.49 | 1.91 | 1.69 |

Tidal Constituent | Simulation Case | RMSE (cm) | |||
---|---|---|---|---|---|

Mokpo | Gunsan | Incheon | Mean | ||

S2 | FES 2-1 | 2.25 | 6.92 | 22.09 | 16.56 |

FES 2-2 | 2.13 | 7.25 | 22.04 | 16.58 | |

FES 2-3 | 2.14 | 8.08 | 20.63 | 15.75 | |

FES 2-4 | 1.94 | 7.81 | 21.98 | 16.63 | |

NAO 2-1 | 2.38 | 7.03 | 22.60 | 16.94 | |

NAO 2-2 | 2.39 | 7.52 | 22.91 | 17.23 | |

NAO 2-3 | 2.37 | 8.29 | 21.31 | 16.27 | |

NAO 2-4 | 2.37 | 8.31 | 23.28 | 17.62 | |

TPX 2-1 | 2.38 | 7.10 | 22.36 | 16.78 | |

TPX 2-2 | 2.34 | 7.61 | 22.72 | 17.12 | |

TPX 2-3 | 2.30 | 8.40 | 21.09 | 16.14 | |

TPX 2-4 | 2.31 | 8.43 | 23.03 | 17.48 |

Tidal Constituent | Simulation Case | RMSE (cm) | |||
---|---|---|---|---|---|

Mokpo | Gunsan | Incheon | Mean | ||

O1 | FES 2-1 | 2.13 | 2.95 | 2.44 | 2.62 |

FES 2-2 | 2.18 | 3.06 | 2.51 | 2.71 | |

FES 2-3 | 2.14 | 3.09 | 2.48 | 2.70 | |

FES 2-4 | 2.12 | 3.07 | 2.43 | 2.67 | |

NAO 2-1 | 1.21 | 1.82 | 1.62 | 1.67 | |

NAO 2-2 | 1.20 | 1.86 | 1.62 | 1.68 | |

NAO 2-3 | 1.22 | 1.97 | 1.62 | 1.73 | |

NAO 2-4 | 1.21 | 1.95 | 1.65 | 1.74 | |

TPX 2-1 | 1.91 | 2.70 | 2.22 | 2.39 | |

TPX 2-2 | 1.83 | 2.64 | 2.17 | 2.33 | |

TPX 2-3 | 1.82 | 2.71 | 2.16 | 2.36 | |

TPX 2-4 | 1.87 | 2.77 | 2.24 | 2.42 |

Tidal Constituent | Ocean Tide Model | Mean Amplitude (cm) | ||
---|---|---|---|---|

A | B | C | ||

M2 | FES2014 | 188.7 | 55.5 | 21.3 |

NAO99Jb | 186.3 | 56.9 | 20.9 | |

TPXO9.1 | 191.1 | 55.8 | 20.5 | |

K1 | FES2014 | 27.4 | 21.5 | 3.8 |

NAO99Jb | 30.1 | 21.6 | 4.2 | |

TPXO9.1 | 26.5 | 21.4 | 3.4 | |

S2 | FES2014 | 55.4 | 23.8 | 10.6 |

NAO99Jb | 57.4 | 24.0 | 10.4 | |

TPXO9.1 | 52.0 | 23.9 | 10.5 | |

O1 | FES2014 | 22.0 | 16.8 | 4.2 |

NAO99Jb | 21.6 | 17.2 | 4.2 | |

TPXO9.1 | 22.9 | 17.0 | 3.3 |

Tidal Constituent | Ocean Tide Model | RMSE (cm) | |||
---|---|---|---|---|---|

A | B | C | Mean | ||

M2 | FES2014 | 2.65 | 1.85 | 0.83 | 1.84 |

TPXO9.1 | 5.20 | 2.78 | 1.09 | 2.91 | |

K1 | FES2014 | 2.72 | 0.41 | 0.78 | 0.91 |

TPXO9.1 | 3.66 | 0.42 | 1.70 | 1.27 | |

S2 | FES2014 | 2.07 | 0.57 | 0.20 | 0.80 |

TPXO9.1 | 5.43 | 0.91 | 0.41 | 1.77 | |

O1 | FES2014 | 0.50 | 0.53 | 0.55 | 0.53 |

TPXO9.1 | 1.38 | 0.58 | 1.17 | 0.78 |

Tidal Constituent | ${\mathit{a}}_{1}-{\mathit{a}}_{2}$ | D_{a} | |||
---|---|---|---|---|---|

Incheon | Gunsan | Mokpo | Mean | ||

M2 | 20–40 | 3.40 | 3.76 | 2.39 | 3.25 |

40–60 | 2.51 | 3.04 | 1.80 | 2.62 | |

60–80 | 1.75 | 2.30 | 1.36 | 2.01 | |

80–100 | 1.60 | 2.15 | 1.26 | 1.91 | |

K1 | 20–40 | 1.27 | 0.99 | 0.81 | 0.91 |

40–60 | 1.51 | 1.20 | 0.97 | 1.09 | |

60–80 | 1.48 | 1.20 | 0.99 | 1.10 | |

80–100 | 1.30 | 1.07 | 0.91 | 1.00 |

Tidal Constituent | D_{a} | ||||
---|---|---|---|---|---|

Incheon | Gunsan | Mokpo | Mean | ||

M2 | 10–20 | 2.02 | 2.54 | 1.48 | 2.16 |

20–30 | 1.80 | 2.33 | 1.36 | 1.96 | |

K1 | 10–20 | 1.37 | 1.29 | 1.03 | 1.31 |

20–30 | 1.37 | 1.29 | 1.04 | 1.31 |

Sta. No. | Station Name | Water Surface Amplitude (m) | |||||
---|---|---|---|---|---|---|---|

Neap Tide | Percentage Difference | Spring Tide | Percentage Difference | ||||

Obs. | Sim. | Obs. | Sim. | ||||

M1 | Heuksando | 1.18 | 0.9 | 24% | 3.48 | 3.09 | 11% |

M2 | Mokpo | 1.6 | 1.75 | 9% | 4.99 | 4.04 | 19% |

G1 | Yeonggwang | 2.06 | 2.43 | 15% | 6.34 | 6.16 | 3% |

G2 | Wido | 1.95 | 2.29 | 15% | 6.2 | 5.95 | 4% |

G3 | Gunsan | 2.08 | 2.64 | 21% | 6.81 | 6.66 | 2% |

G4 | Janghang | 2.19 | 2.8 | 22% | 7.01 | 6.89 | 2% |

G5 | Eocheongdo | 1.78 | 1.95 | 9% | 5.85 | 5.28 | 10% |

G6 | Seocheonmaryang | 2.13 | 2.54 | 16% | 6.8 | 6.48 | 5% |

G7 | Boryeong | 2.23 | 2.76 | 19% | 7.15 | 6.14 | 14% |

G8 | Anheung | X^{(*)} | 2.29 | 6.46 | 5.86 | 9% | |

I1 | Taean | 2.2 | 2.9 | 24% | 7.2 | 6.52 | 9% |

I2 | Pyeongtaek | 2.8 | 2.62 | 7% | 9 | 7.39 | 18% |

I3 | Daesan | 2.35 | 3.18 | 26% | 7.68 | 6.92 | 10% |

I4 | Ansan | X^{(*)} | 3.1 | 8.43 | 7.1 | 16% | |

I5 | Gureopdo | 2.16 | 2.57 | 16% | 7.15 | 6.04 | 16% |

I6 | Yeongheungdo | 2.54 | 3.41 | 26% | 8.58 | 7.19 | 16% |

I7 | IncheonSongdo | 2.15 | 3.08 | 30% | 9.35 | 7.15 | 24% |

I8 | Incheon | 2.23 | 3.26 | 32% | 9.59 | 7.33 | 24% |

I9 | Yeongjongbridge | 2.35 | 2.89 | 19% | 9.87 | 7.03 | 29% |

I10 | Gyeongin | 2.27 | 2.98 | 24% | 8.68 | 7.08 | 18% |

I11 | Ganghwa | 2.47 | 3.63 | 32% | 7 | 5.73 | 18% |

^{(*)}: observation data were missing at this station.

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**Figure 2.**Validation of amplitudes and phases obtained from assimilated tidal models (FES2014, NAO99Jb, NAO99 and TPXO9) against observed data at tidal gauges; (

**a**): M2’s amplitude, (

**b**): M2’s phase, (

**c**): K1’s amplitude, (

**d**): K1’s phase, (

**e**): S2’s amplitude S2, (

**f**): S2’s phase, (

**g**): O1’s amplitude, (

**h**): O1’s phase.

**Figure 3.**The value of the form number (F) in the WCK. Grey color in the background shows the WCK, from left to right corresponding to north to south.

**Figure 6.**Tidal gauge locations in the WCK selected for the evaluation of the modeling; three sub-regions: Mokpo (M), Gunsan (G) and Incheon (I) Regions.

**Figure 8.**The numerical results of tidal amplitudes M2 and K1 obtained from different uniform bottom roughness; (

**a**), (

**c**) and (

**e**): M2’s amplitude; (

**b**), (

**d**) and (

**f**): K1’s amplitude.

**Figure 9.**The numerical results of tidal amplitudes M2 and K1 obtained from non-uniform bottom roughness; (

**a**), (

**c**) and (

**e**): M2’s amplitude; (

**b**), (

**d**) and (

**f**): K1’s amplitude.

**Figure 10.**Computed amplitudes at gauge locations with respect to the assumed forcing with an amplitude of 100 cm at each open boundaries A, B and C; (

**a**): M2’s amplitude; (

**b**): M2’s amplitude.

**Figure 11.**M2 and K1 amplitudes at gauge locations with respect to the forcing with the amplitudes of 20, 40, 60, 80 and 100 cm at the open boundary B; (

**a**): M2’s amplitude; (

**b**): M2’s amplitude.

**Figure 12.**Value R

_{a}at tide station locations with respect to the increase of the amplitude of M2 (

**a**) and K1 (

**b**) at the open boundary B; (

**a**): R

_{a}of M2’s amplitude; (

**b**): R

_{a}of K1’s amplitude.

**Figure 13.**Comparison of the amplitudes between the observation and numerical simulation at tidal gauge stations (refer to Figure 6); (

**a**,

**c**,

**e**): M2’s amplitude; (

**b**,

**d**,

**f**): K1’s amplitude.

**Figure 14.**A comparison of water level between numerical results and observations at typical gauge stations; (

**a**,

**b**): water level at gauge station I3 and I5 (located in Incheon Region); (

**c**,

**d**): water level at gauge station G3 and G5 (located in Gunsan Region); (

**e**,

**f**): water level at gauge station M1 and M2 (located in Mokpo Region).

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**MDPI and ACS Style**

Nguyen, V.T.; Lee, M.
Effect of Open Boundary Conditions and Bottom Roughness on Tidal Modeling around the West Coast of Korea. *Water* **2020**, *12*, 1706.
https://doi.org/10.3390/w12061706

**AMA Style**

Nguyen VT, Lee M.
Effect of Open Boundary Conditions and Bottom Roughness on Tidal Modeling around the West Coast of Korea. *Water*. 2020; 12(6):1706.
https://doi.org/10.3390/w12061706

**Chicago/Turabian Style**

Nguyen, Van Thinh, and Minjae Lee.
2020. "Effect of Open Boundary Conditions and Bottom Roughness on Tidal Modeling around the West Coast of Korea" *Water* 12, no. 6: 1706.
https://doi.org/10.3390/w12061706