# Sensitivity Analysis of Runoff and Wind with Respect to Yellow River Estuary Salinity Plume Based on FVCOM

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

^{8}m

^{3}. In 2002, the YR runoff reached only 4.19 × 10

^{6}m

^{3}. After 2002, runoff was regulated and increased [19].

## 2. Materials and Method

#### 2.1. FVCOM Model

- (a)
- momentum equation

- (b)
- continuity equation

- (c)
- salinity equation

_{m}is the vertical rotational viscosity coefficient; K

_{ℎ}is the vertical rotational diffusion coefficient of heat; F

_{u}is the horizontal momentum diffusion term; F

_{v}is the vertical momentum diffusion term; and F

_{s}is the diffusion term of salinity, which is calculated by the Smagorinsky parametric method.

#### 2.2. Boundary Conditions

_{H}is the horizontal heat diffusion coefficient; α is the angle formed from the sea floor; $\widehat{P}$ is the precipitation rate; $\widehat{E}$ is the evaporation rate; D is the total depth; H is the water depth below the average sea level; σ increases from the seabed (σ = −1) to the sea surface (σ = 0); and $\zeta $ is the height of the free sea above the average sea level.

#### 2.3. Model Setting

- A.
- River discharge

^{3}/s in the wet season, and 209.783 m

^{3}/s in the dry season. Figure 3 shows the statistical results of multiyear average daily river discharge data during the dry and wet periods from 2007 to 2017. Additionally, the statistical results of multiyear daily average river discharge data in the dry season and wet season from 2007 to 2017 are presented. From 2007 to 2017, the average river discharge in the YR Estuary was 1059.595 m

^{3}/s. The average river discharge in the dry season was 264.662 m

^{3}/s. Compared to the previous year, the river discharge into the BHS during the dry season changed little in 2020, but the average river discharge during the wet season was 2.6 times higher than the average of the previous years.

- B.
- Wind

- C.
- Tide

_{2}, S

_{2}, N

_{2}, K

_{2}, K

_{1}, O

_{1}, P

_{1}, and Q

_{1}) were selected for the model, and the open boundary conditions were defined according to harmonic constants.

- D.
- Salinity

#### 2.4. Model Verification

## 3. Results

#### 3.1. Distribution of Surface Current in the Wet and Dry Seasons

#### 3.2. Horizontal Distribution Characteristics of Salinity Fields around the Yellow River Estuary and Laizhou Bay

#### 3.3. Vertical Distribution Characteristics of Salinity in Laizhou Bay

## 4. Discussions

#### 4.1. Influence of River Discharge on Salinity Diffusion

^{3}/s (case 2), and the average river discharge during the wet season from 2007 to 2017 was 1059.6 m

^{3}/s (case 1). The volume of river discharge mainly affected the area, distance, and depth of salinity diffusion. Figure 12 (top) shows the surface salinity distribution of the two cases. Figure 12 (bottom) shows the vertical salinity distribution of the two cases. With increasing runoff, the horizontal diffusion area of the plume became larger and the diffusion distance of the salinity front became longer, and the diffusion depth of low salinity water became deeper at the same location. In addition, fresh water from the YR can directly affected the offshore seabed.

#### 4.2. Influence of Different Wind Speeds on Salinity Diffusion in the Wet Season

#### 4.3. Influence of Different Wind Speeds on Salinity Diffusion in the Dry Season

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The locations of the Yellow River and Lijin station (

**a**) and annual runoff of the Yellow River from 1952 to 2017 (

**b**).

**Figure 3.**River discharge statistics in the wet season (

**a**) and the dry season (

**b**) in 2020 and 2007–2017 (wet season: 1 July–31 August; dry season: 1 January–28 February; data link: http://61.163.88.227:8006/hwsq.aspx?sr=0nkRxv6s9CTRMlwRgmfFF6jTpJPtAv87, accessed on 29 March 2023).

**Figure 4.**Wind rose in the wet season (

**right**) and the dry season (

**left**) in 2020 (

**a**,

**b**) and 2007–2017 (

**c**,

**d**) (wet season: 1 July–31 August; dry season: 1 January–28 February; data link: https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5, accessed on 29 March 2023).

**Figure 9.**Distribution of the surface residual current field in the wet season (

**a**) and the dry season (

**b**).

**Figure 10.**Distribution of surface (

**right**) and bottom (

**left**) salinity in the wet (

**top**) and dry (

**bottom**) seasons.

**Figure 11.**Salinity vertical distribution in Laizhou Bay during the wet season (

**left**) and the dry season (

**right**).

**Figure 12.**Surface (

**top**) and vertical (

**bottom**) salinity distribution of case 1 (

**left**) and case 2 (

**right**).

**Figure 13.**Surface salinity distribution at different wind speeds in the wet season. ((

**a**): case 3, (

**b**): case 4, (

**c**): case 5, (

**d**): case 6).

**Figure 14.**Vertical salinity distribution at different wind speeds in the wet season ((

**a**): case 3, (

**b**): case 4, (

**c**): case 5, (

**d**): case 6).

**Figure 16.**Surface salinity distribution at different wind speeds in the dry season ((

**a**): case 3, (

**b**): case 4, (

**c**): case 5, (

**d**): case 6).

**Figure 17.**Vertical salinity distribution at different wind speeds in the dry season ((

**a**): case 3, (

**b**): case 4, (

**c**): case 5, (

**d**): case 6).

Station Type | Station Name | Longitude | Latitude | Time |
---|---|---|---|---|

Tidal current and tide | H1 | 119.077247 | 38.207694 | 10 October 2018–11 October 2018 |

H2 | 119.322183 | 37.885078 | 10 October 2018–11 October 2018 | |

H3 | 119.535017 | 37.603250 | 10 October 2018–11 October 2018 | |

H4 | 119.751378 | 38.539094 | 10 October 2018–11 October 2018 | |

H5 | 119.987794 | 38.236428 | 10 October 2018–11 October 2018 | |

H6 | 120.212142 | 37.935142 | 10 October 2018–11 October 2018 | |

Salinity | S1 | 118.99837 | 38.08946 | 20 February–28 February 2020, 20 August–27 February |

S2 | 120.25612 | 37.64275 | 20 February–28 February 2020, 20 August–27 February |

Station | Tide | Surface (V) | Surface (D) | Middle (V) | Middle (D) | Bottom (V) | Bottom (D) | Dry | Wet |
---|---|---|---|---|---|---|---|---|---|

H1 | 0.47 | 0.94 | 0.87 | 0.96 | 0.98 | 0.96 | 0.98 | - | - |

H2 | 0.97 | 0.93 | 0.76 | 0.94 | 0.99 | 0.90 | 0.99 | - | - |

H3 | 0.98 | 0.67 | 0.98 | 0.74 | 0.98 | 0.77 | 0.98 | - | - |

H4 | 0.99 | 0.93 | 1.00 | 0.93 | 1.00 | 0.89 | 1.00 | - | - |

H5 | 0.99 | 0.82 | 0.99 | 0.81 | 0.99 | 0.77 | 0.99 | - | - |

H6 | 0.98 | 0.91 | 1.00 | 0.93 | 1.00 | 0.88 | 0.99 | - | - |

S1 | - | - | - | - | - | - | - | 0.60 | 0.47 |

S2 | - | - | - | - | - | - | - | 0.73 | 0.65 |

Case | Period | River Discharge | Wind |
---|---|---|---|

1 | wet season | Average daily river discharge from 2007 to 2017 | Hourly variation |

2 | wet season | Average daily river discharge in 2020 | Hourly variation |

3 | wet season | None | |

4 | wet season | Constant wind, south with speed of 4 m/s | |

5 | wet season | Constant wind, south with speed of 8 m/s | |

6 | wet season | Constant wind, south with speed of 12 m/s | |

7 | dry season | None | |

8 | dry season | Constant wind, northeast with speed of 5 m/s | |

9 | dry season | Constant wind, northeast with speed of 10 m/s | |

10 | dry season | Constant wind, northeast with speed of 15 m/s |

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**MDPI and ACS Style**

Qin, H.; Shi, H.; Gai, Y.; Qiao, S.; Li, Q.
Sensitivity Analysis of Runoff and Wind with Respect to Yellow River Estuary Salinity Plume Based on FVCOM. *Water* **2023**, *15*, 1378.
https://doi.org/10.3390/w15071378

**AMA Style**

Qin H, Shi H, Gai Y, Qiao S, Li Q.
Sensitivity Analysis of Runoff and Wind with Respect to Yellow River Estuary Salinity Plume Based on FVCOM. *Water*. 2023; 15(7):1378.
https://doi.org/10.3390/w15071378

**Chicago/Turabian Style**

Qin, Huawei, Hongyuan Shi, Yunyun Gai, Shouwen Qiao, and Qingjie Li.
2023. "Sensitivity Analysis of Runoff and Wind with Respect to Yellow River Estuary Salinity Plume Based on FVCOM" *Water* 15, no. 7: 1378.
https://doi.org/10.3390/w15071378