# Storm Surges in the Bohai Sea: The Role of Waves and Tides

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## Abstract

**:**

## 1. Introduction

_{s}) is ~0.6 m [20]. As a populated zone in the north and the northeast of China, the region around the Bohai Sea is experiencing a fast social and economic development, with several important ports and metropolises located there. Because of the social and economic importance of this area, the disasters caused by the frequent storm surges that result from the Bohai Sea climatic and physical characteristics have attracted the attention of researchers, the public and the government.

## 2. Materials and Methods

#### 2.1. Numerical Model

_{s}is the atmospheric pressure on the water surface; τ

_{sx}and τ

_{sy}are the wave forces; τ

_{wx}and τ

_{wy}are the wind stresses; τ

_{bx}and τ

_{b}

_{y}are the bottom stresses; and ε is the comprehensive eddy diffusion coefficient including the horizontal molecular and eddy viscous diffusions. The equations are solved using the Finite Difference Method (FDM) on staggered rectangle cells. The local water levels and water depths are specified at the centers of the cells and the velocities and fluxes are defined at the middle points of the cell edges.

_{x}and c

_{y}are the group velocity components of waves in x and y directions, respectively; σ and θ are the frequency and direction of waves, respectively; c

_{σ}and c

_{θ}are the variation rates of σ and θ, respectively; N is the action density spectrum, defined as

_{in}is the wind-induced production of wave energy; s

_{ds}is the wave dissipation due to white capping, breaking and bottom friction; and s

_{nl}is the nonlinear wave–wave interactions including the quadruplet interaction in the deep water region and the triad interaction in the shallow water region.

#### 2.2. Model Setup

_{2}, S

_{2}, N

_{2}, K

_{2}, K

_{1}, O

_{1}, P

_{1}, Q

_{1}, and M

_{4}) obtained from the OTIS Regional Tidal Solution [40] are used to calculate the time series of water levels along the open boundary (Figure 1). Due to the lack of wave data along the open boundary, all boundaries in the wave model are set as closed boundaries. According to the user manual of SWAN [7], this setting would not affect the accuracy of the wave simulation because the open boundary is far from the Bohai Sea.

#### 2.3. Model Validation

_{s}) and wave period (T) (output from run 5). The field-measured and model-simulated wave periods and heights are in acceptable agreement in magnitude and variation, with the correlation coefficients (CC) between the model-simulated results and field-data being around or superior to 0.7.

^{−3}(Figure 4). This means that the radiation stress does not affect the wave calculation, which agrees with the conclusion by Kim et al. [9] and Yoon and Jun [12].

## 3. Results

#### 3.1. Surge Distribution

#### 3.2. Wave-Induced Current and High Surges

#### 3.3. Relationships between Tide and Surge

_{2}. For most of the coast around the Bohai Sea, the tidal height ranges from 0 to 2.5 m. Due to flood and ebb tides, the water depth changes significantly when the amplitude of the tide is large enough, which may significantly affect the wave deformation and propagation in shallow water.

_{2}, which is the dominant tidal component in the Bohai Sea, has a wavelength (~600 km) of approximately twice the spatial scale (~300 km) of the Bohai Sea [41]. When the western coast of the Bohai Bay experiences high tide, the water level in the central part of the Bohai Sea and the Bohai Strait is relatively low. Under these conditions, the gravity force hinders the inflow of water from the central basin of the Bohai Sea to the western part of the Bohai Sea. This explains that the peak surges calculated by considering the tide in run 4 are lower than those without tides in runs 2 and 3. Secondly, an increase and decrease of water depth caused by flood and ebb tides is related to wave deformation in shallow water regions. As mentioned above, wave deformation in shallow water regions causes a significant set-up, which raises the water level in the coastal region. However, during high tide, water depth is higher, weakening the wave deformation near the coast and thereby also the longshore currents. If the surge is calculated without considering tidal effects, the water depth at the coast is lower than the real hydrodynamic conditions in which waves propagate. Due to the underestimation of water depth, the modelled wave deformation is overestimated and thereby the calculated set-up becomes more obvious in the coastal region. By comparing the water depth at the three locations, it can be found that the water depths at Huanghua and Tanggu are smaller than that at Caofeidian (Figure 1). The model results show that the tidal amplitudes at Huanghua and Tanggu are larger than that at Caofeidian. As a result, for the surge of 2009, the differences between the peak surge values calculated by runs 3 and 4 vary with the location (Figure 12a–c), with significant differences at Huanghua and Tanggu and a lower difference at Caofeidian.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Validation of the wave model (run 5). (

**a**) Significant wave height (H

_{s}) at W1. (

**b**) Significant wave period (T) at W1. (

**c**) Significant wave height at W2. (

**d**) Significant wave period at W2.

**Figure 4.**Comparison between the wave parameters output from the 1st iteration (run 5, blue dots) and the 2nd iteration (run 7, black line). (

**a**) Significant wave height (H

_{s}) at W1. (

**b**) Significant wave period (T) at W1. (

**c**) Significant wave height at W2. (

**d**) Significant wave period at W2.

**Figure 6.**Wave effects on the surge (at the time step for which the surge in the south Bohai Sea peaks). (

**a**) Surge distribution without waves (run 6). (

**b**) Surge distribution with waves (run 4). (

**c**) Difference between surge distributions with and without waves (surge with waves subtracted by that without waves).

**Figure 7.**Wave effect on currents (at the time step for which the surge in the south Bohai Sea peaks). (

**a**) Currents without waves (run 6). (

**b**) Currents with waves (run 4). (

**c**) Difference between currents with and without waves. The red circles in (

**c**) indicate regions with strong longshore currents.

**Figure 8.**Longshore currents near the Yellow River estuary (at the time step for which the surge in the south Bohai Sea peaks).

**Figure 9.**Wave force distributions in the Bohai Bay during the 2009 (

**a**) and 2010 (

**b**) storms (at the time step for which the surge in the south Bohai Sea peaks). The red rectangles represent the regions with a unidirectional wave force and the orange circles represent the regions with a non-uniform wave force.

**Figure 11.**Evolution of surge, tide and total water level during the surge events beginning on 13 April 2009 (panels (

**a**–

**c**)) and on 21 September 2010 (panels (

**d**–

**f**)). The total water levels are calculated using run 4, the tidal levels are calculated using run 1 and the surges are calculated as the difference of water levels between run 4 and run 1.

**Figure 12.**Simulated surges at Caofeidian (panels (

**a**,

**d**)), Huanghua (panels (

**b**,

**e**)), and Tanggu (panels (

**c**,

**f**)) during the 2009 event (panels (

**a**–

**c**)) and 2010 events (panel (

**d**–

**f**)) with consideration of wind (run 2, dashed blue line), wind and waves (run 3, dashed red line), wind, waves and tide (run 4, black line) and wind and tide (run 6, dashed green line).

**Table 1.**Runs of simulations and the setup for sub-models. √ indicates the sub-model and driving force that are considered. The final output of the run comes from the last used sub-model.

Run No. | Model Initialization | 1st Iteration | 2nd Iteration | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Tidal Current Model | Wave Model | Tidal Current Model | Wave Model | Tidal Current Model | ||||||

Tide | Wind | Wind | Tide | Wind | Wave | Wind | Tide | Wind | Wave | |

1 | √ | |||||||||

2 | √ | |||||||||

3 | √ | √ | √ | |||||||

4 | √ | √ | √ | √ | √ | √ | ||||

5 | √ | √ | √ | |||||||

6 | √ | √ | ||||||||

7 | √ | √ | √ | √ | √ | √ | √ | |||

8 | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ |

Case | Location | Time (UTC) | Reference |
---|---|---|---|

1 | Caofeidian | 13 April 2009 19:00–16 April 2009 07:00 | Fu et al. [28] |

2 | Huanghua | 13 April 2009 19:00–16 April 2009 07:00 | |

3 | Tanggu | 13 April 2009 19:00–16 April 2009 07:00 | |

4 | Caofeidian | 20 September 2010 16:00–21 September 2010 17:00 | Fu et al. [29] |

5 | Huanghua | 20 September 2010 16:00–21 September 2010 17:00 | |

6 | Tanggu | 20 September 2010 16:00–21 September 2010 17:00 |

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**MDPI and ACS Style**

Li, Y.; Feng, H.; Vigouroux, G.; Yuan, D.; Zhang, G.; Ma, X.; Lei, K.
Storm Surges in the Bohai Sea: The Role of Waves and Tides. *Water* **2020**, *12*, 1509.
https://doi.org/10.3390/w12051509

**AMA Style**

Li Y, Feng H, Vigouroux G, Yuan D, Zhang G, Ma X, Lei K.
Storm Surges in the Bohai Sea: The Role of Waves and Tides. *Water*. 2020; 12(5):1509.
https://doi.org/10.3390/w12051509

**Chicago/Turabian Style**

Li, Yuanyi, Huan Feng, Guillaume Vigouroux, Dekui Yuan, Guangyu Zhang, Xiaodi Ma, and Kun Lei.
2020. "Storm Surges in the Bohai Sea: The Role of Waves and Tides" *Water* 12, no. 5: 1509.
https://doi.org/10.3390/w12051509