# 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

## References

- Xing, Y.; Ai, C.F.; Jin, S. A three-dimensional hydrodynamic and salinity transport model of estuarine circulation with an application to a macrotidal estuary. Appl. Ocean Res.
**2013**, 39, 53–71. [Google Scholar] [CrossRef] - Dong, L.X.; Su, J.L.; Wong, L.A.; Cao, Z.; Chen, J.C. Seasonal variation and dynamics of the Pearl River plume. Cont. Shelf Res.
**2004**, 24, 1761–1777. [Google Scholar] [CrossRef] - Xia, M.; Xie, L.; Leonard, J.; Pietrafesa, L.J. Modeling of the Cape Fear River Estuary plume. Geophys. Res. Lett.
**2007**, 30, 698–709. [Google Scholar] [CrossRef] - Granskog, M.A.; Ehn, J.; Niemel, M. Characteristics and potential impacts of under-ice river plumes in the seasonally ice-covered Bothnian Bay (Baltic Sea). J. Mar. Syst.
**2005**, 53, 187–196. [Google Scholar] [CrossRef] - Restrepo, J.C.; Schrottke, K.; Bartholomae, A.; Ospino, S.; Ortíz, J.C.; Orejarena, A. Estuarine and sediment dynamics in a microtidal tropical estuary of high fluvial discharge: Magdalena River (Colombia, South America). Mar. Geol.
**2018**, 398, 86–98. [Google Scholar] [CrossRef] - Pritchard, M.; Huntley, D.A. A simplified energy and mixing budget for a small river plume discharge. J. Geophys. Res. Ocean
**2006**, 111, C3. [Google Scholar] [CrossRef] - Walker, N.D.; Wiseman, W.J.; Rouse, L.J.; Babin, A. Effects of River Discharge, Wind Stress, and Slope Eddies on Circulation and the Satellite-Observed Structure of the Mississippi River Plume. J. Coast. Res.
**2005**, 216, 1228–1244. [Google Scholar] [CrossRef] - Molleri, G.S.F.; Novo, E.M.L.d.M.; Kampel, M. Space-time variability of the Amazon River plume based on satellite ocean color. Cont. Shelf Res.
**2010**, 30, 342–352. [Google Scholar] [CrossRef] - Kourafalou, V.H. river plume development in semi-enclosed mediterranean regions: North adriatic sea and northwestern aegean sea. J. Marrine Syst.
**2001**, 30, 181–205. [Google Scholar] [CrossRef] - Fong, D.A.; Geyre, W.R. The alongshore transport of freshwater in a surface-trapped river plume. J. Phys. Oceanogr.
**2002**, 32, 957–972. [Google Scholar] [CrossRef] - Cheng, R.T.; Casulli, V. Modeling a three-dimensional river plume over continental shelf using a 3D unstructured grid model. In Estuarine and Coastal Modeling; ASCE: Reston, VA, USA, 2004. [Google Scholar]
- Wang, F.; Meng, Q.; Tang, X.; Hu, D. The long-term variability of sea surface temperature in the seas east of China in the past 40 a. Acta Oceanol. Sin.
**2013**, 32, 48–53. [Google Scholar] [CrossRef] - Zhou, J.H.; Matthew, J.; Deitcha, S.G.; Screaton, E.J.; Olabarrieta, M. Effect of Mississippi River discharge and local hydrological variables on salinity of nearby estuaries using a machine learning algorithm—ScienceDirect. Estuar. Coast. Shelf Sci.
**2021**, 263, 107628. [Google Scholar] [CrossRef] - Salmela, J.; Kasvi, E.; Alho, P. River plume and sediment transport seasonality in a non-tidal semi-enclosed brackish water estuary of the Baltic Sea. Estuar. Coast. Shelf Sci.
**2020**, 245, 106986. [Google Scholar] [CrossRef] - Coogan, J.; Dzwonkowski, B. Observations of Wind Forcing Effects on Estuary Length and Salinity Flux in a River-Dominated, Microtidal Estuary, Mobile Bay, Alabama. J. Phys. Oceanogr.
**2018**, 48, 1787–1802. [Google Scholar] [CrossRef] - Abolfathi, S.; Pearson, J.M. Solute dispersion in the nearshore due to oblique waves. In Proceedings of the 34th Conference on Coastal Engineering, Seoul, Republic of Korea, 15–20 June 2014; ISBN 9780989661126. [Google Scholar] [CrossRef][Green Version]
- Zeinabi, A.; Kohansal, A. Numerical modeling of sediment transport patterns under the effects of waves and tidal currents at Pars port complex inlet. Int. J. Marit. Technol.
**2020**, 14, 33–40. [Google Scholar] - Xu, J.X. The Water Fluxes of the Yellow River to the Sea in the Past 50 Years, in Response to Climate Change and Human Activities. Environ. Manag.
**2005**, 35, 620. [Google Scholar] - Wang, Q.; Guo, X.; Takeoka, H. Seasonal variations of the Yellow River plume in the Bohai Sea: A model study. J. Geophys. Res.
**2008**, 113, C08046. [Google Scholar] [CrossRef] - Mao, X.Y.; Jiang, W.; Zhao, P.; Gao, H. A 3-D numerical study of salinity variations in the Bohai Sea during the recent years. Cont. Shelf Res.
**2008**, 28, 2689–2699. [Google Scholar] [CrossRef] - Lin, C.; Su, J.L.; Xu, B.R.; Tang, Q. Long-term variations of temperature and salinity of the Bohai Sea and their influence on its ecosystem. Prog. Oceanogr.
**2001**, 49, 7–19. [Google Scholar] [CrossRef] - Wang, Y.; Liu, Z.H.; Gao, H.W.; Guo, X. Response of salinity distribution around the Yellow River mouth to abrupt changes in river discharge. J. Cont. Shelf Res.
**2011**, 31, 685–694. [Google Scholar] [CrossRef] - Sui, Y.; Shi, H.Y.; You, Z.J.; Qiao, S.; Sun, J. Long-term Trend and Change Point Analysis on Runoff and Sediment Flux into the Sea from the Yellow River during the Period of 1950–2018. J. Coast. Res.
**2020**, 99, 203. [Google Scholar] [CrossRef] - Liu, H. Fate of three major rivers in the Bohai Sea: A model study. Cont. Shelf Res.
**2011**, 31, 1490–1499. [Google Scholar] [CrossRef] - Shi, H.Y.; Li, Q.J.; Sun, J.C.; Gao, G.; Sui, Y.; Qiao, S.; You, Z. Variation of Yellow River Runoff and Its Influence on Salinity in Laizhou Bay. J. Ocean. Univ. China
**2020**, 19, 1235–1244. [Google Scholar] [CrossRef] - Cheng, X.Y.; Zhu, J.R.; Chen, S.L. Extensions of the river plume under various Yellow River courses into the Bohai Sea at different times. Estuar. Coast. Shelf Sci.
**2020**, 249, 107092. [Google Scholar] [CrossRef] - Chen, C.S.; Beardsley, R.C. An Unstructured Grid, Finite-Volume Coastal Ocean Model. In FVCOM User Manual, 2nd ed.; SMAST/UMASSD: New Bedford, MA, USA, 2006; pp. 1–135. [Google Scholar]
- Chen, C.S.; Liu, H.D.; Robert, C. An Unstructured Grid, Finite-Volume, Three-dimensional, primitive equations ocean model: Application to Coastal and Estuaries. J. Atmos. Ocean.
**2003**, 20, 159–186. [Google Scholar] [CrossRef] - Li, S.; Chen, C. Air-sea interaction processes during hurricane Sandy: Coupled WRF-FVCOM model simulations. Prog. Oceanogr.
**2022**, 206, 102855. [Google Scholar] [CrossRef] - Chen, C.; Huang, H.; Lin, H.; Blanton, J.; Li, C.; Andrade, F. A Wet/Dry Point Treatment Method of FVCOM, Part II: Application to the Okatee/Colleton River in South Carolina. J. Mar. Sci. Eng.
**2022**, 10, 982. [Google Scholar] [CrossRef] - Yang, Z.; Shao, W.; Ding, Y.; Shi, J.; Ji, Q. Wave Simulation by the SWAN Model and FVCOM Considering the Sea-Water Level around the Zhoushan Islands. J. Mar. Sci. Eng.
**2020**, 8, 783. [Google Scholar] [CrossRef] - Goodarzi, D.; Mohammadian, A.; Pearson, J.; Abolfathi, S. Numerical modelling of hydraulic efficiency and pollution transport in waste stabilization ponds. Ecol. Eng.
**2022**, 182, 106702. [Google Scholar] [CrossRef] - Goodarzi, D.; Abolfathi, S.; Borzooei, S. Modelling solute transport in water disinfection systems: Effects of temperature gradient on the hydraulic and disinfection efficiency of serpentine chlorine contact tanks. J. Water Process. Eng.
**2020**, 37, 101411. [Google Scholar] [CrossRef] - SL 160-2012; Regulation for Hydraulic and Thermal Model in Cooling Water Projects. Ministry of Water Resources of the People’s Republic of China: Beijing, China, 2017.
- Cook, S.; Price, O.; King, A.; Finnegan, C.; van Egmond, R.; Schafer, H.; Pearson, J.M.; Abolfathi, S.; Bending, G.D. Bedform characteristics and biofilm community development interact to modify hyporheic exchange. Sci. Total Environ.
**2020**, 749, 141397. [Google Scholar] [CrossRef]

**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