Numerical Analysis of the Influence of Runoff Input on Salinity Distribution and Its Mechanisms in Laizhou Bay

Abstract

This study employs the MIKE 3 Flow Model, incorporating forcing conditions such as inflow from 18 major rivers along the Bohai coast, wind, precipitation, evaporation, and solar radiation, to develop a hydrodynamic and temperature-salinity model for the Bohai Sea, using a finer mesh for more detailed simulation in Laizhou Bay. The residual current in the surface layer primarily flowed eastward, exhibiting coastal transport characteristics in the southern region, leading to the formation of a large low-salinity region. The bottom salinity distribution closely mirrored that of the surface, with the isohaline shifting shoreward due to the high-salinity Bohai Sea water transported by the residual current. By grouping major runoff sources according to river outlet locations and residual current patterns, the study analyzed the impact of freshwater plumes formed by runoff from different directions on the salinity distribution in Laizhou Bay. The results indicate that the influence of freshwater inputs on both the mean salinity and the area of low-salinity zones in Laizhou Bay, ranked from greatest to least, is as follows: the Yellow River, the southwest, and the southeast. The variation in the area of low-salinity regions is closely related to factors such as runoff volume, residual currents, and the selection of boundaries for the low-salinity regions.

1. Introduction

Laizhou Bay, one of the three major bays of the Bohai Sea, is located in the northwestern corner of the Shandong Peninsula. This bay includes several critical ecological and economic zones, such as national nature reserves, special marine protection areas, designated aquaculture zones, and germplasm resource conservation areas. Several rivers, most notably the Yellow River and Xiaoqing River, discharge substantial volumes of freshwater and nutrients into the bay, making it a vital spawning and aquaculture site within the Bohai Sea [1,2,3]. Consequently, investigating the variations in key indices of Laizhou Bay is of significant importance. Recently, factors such as the resurgence of Yellow River runoff and increased precipitation in the Bohai Sea region have notably altered the salinity distribution in both the Bohai Sea and Laizhou Bay [4,5,6]. Salinity is a critical environmental factor that influences the spatial distribution of plankton in coastal waters. Variations in low-salinity regions can significantly affect both the composition and abundance of plankton [7,8,9]. Furthermore, the community structure of fish eggs and larvae is closely linked to salinity levels, with larval fish demonstrating a strong propensity to migrate toward water flow in low-salinity regions. The increased influx of freshwater and sediment from runoff is essential for replenishing fishery resources [10,11].

Substantial research on temperature and salinity distribution in the Bohai Sea and Laizhou Bay regions has been conducted using satellite remote sensing, numerical simulations, and other methods. Zhao et al. investigated the distribution characteristics of low-salinity regions in the Bohai Sea using monthly mean salinity data from quarter-degree grids, explaining the occurrence and evolution of two distinct types of low-salinity regions [12]. Lin et al. analyzed nearly 40 years of survey data, identifying the rate of change in annual average sea surface temperature and salinity [13]. Yu et al. examined observed salinity data, which included sea surface and bottom salinity measurements, to determine annual salinity fields and identified decadal trends in Bohai Sea salinity since the 1950s [14]. Meng et al. combined satellite data with measured surface water samples to analyze the biogeochemical changes in Laizhou Bay caused by heavy rainfall-induced flooding, emphasizing that increased flood runoff introduces large quantities of terrestrial materials rich in suspended matter, phosphorus, and organic matter, enhancing the offshore spread of low-salinity water plumes and fronts [15]. Xing et al. utilized Landsat images to analyze the impact of submarine groundwater discharge on temperature and salinity distribution in Laizhou Bay, identifying the link between groundwater discharge and algal blooms occurrence [1]. Shi et al. employed the FVCOM model to analyze the correlation between salinity in Laizhou Bay and multi-year Yellow River runoff, identifying variation patterns in the vertical salinity gradient [16]. Li et al., using the MIKE model, considered input from 16 major rivers along the Bohai coast to study changes in temperature and salinity distribution in the Bohai Sea in 2010 [17]. Qin et al. applied the FVCOM numerical model to study the characteristics and differences in salinity distribution near the Yellow River Estuary during the wet and dry seasons of 2020, highlighting that Yellow River runoff volume and wind speed are key factors affecting salinity distribution in the Yellow River Estuary and adjacent sea areas [18].

Current salinity simulations for the Bohai Sea primarily depend on earlier data, which fail to accurately reflect recent changes in salinity distribution resulting from variations in runoff and climate change [4,19,20,21,22,23]. Most existing studies focus predominantly on the runoff from the Yellow River, often overlooking the contributions of several other rivers in Laizhou Bay, each with an annual average runoff exceeding 100 million cubic meters. This study incorporates various forcing conditions, including wind fields, heat radiation, and relative humidity, and considers freshwater inputs from 18 major rivers along the Bohai Sea coast. We conducted three numerical experiments to evaluate the impact of these freshwater sources on salinity distribution in Laizhou Bay. The findings provide valuable insights into environmental protection and resource management in the region.

2. Models and Methods

2.1. Model Description

MIKE is a suite of water environment management software developed by the Danish Hydraulic Institute. Its unstructured mesh model employs a cell-centered finite volume method, which allows for accurate representation of complex shorelines. This model provides significant advantages in numerical simulations of estuaries, bays, and coastal regions. It is based on the three-dimensional incompressible Reynolds-averaged Navier-Stokes equations, incorporating the Boussinesq assumption and the hydrostatic pressure approximation [24].

The local continuity equation and the two horizontal momentum equations for the x- and y-components are presented as follows:

$${\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}+{\displaystyle \frac{\partial w}{\partial z}}=S$$

(1)

$${\displaystyle \frac{\partial u}{\partial t}}+{\displaystyle \frac{\partial u^2}{\partial x}}+{\displaystyle \frac{\partial uv}{\partial y}}+{\displaystyle \frac{\partial wu}{\partial z}}=fv-g{\displaystyle \frac{\partial \eta }{\partial x}}--{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial p_a}{\partial x}}-{\displaystyle \frac{g}{{\rho }_0}}{\displaystyle {\int }_z^{\eta }\frac{\partial \rho }{\partial x}}dz-{\displaystyle \frac{1}{{\rho }_{0}h}}\left({\displaystyle \frac{\partial s_{xx}}{\partial x}}+{\displaystyle \frac{\partial s_{xy}}{\partial y}}\right)+F_u+{\displaystyle \frac{\partial }{\partial z}}\left(v_t{\displaystyle \frac{\partial u}{\partial z}}\right)+u_{S}S$$

(2)

$${\displaystyle \frac{\partial v}{\partial t}}+{\displaystyle \frac{\partial v^2}{\partial y}}+{\displaystyle \frac{\partial uv}{\partial x}}+{\displaystyle \frac{\partial wv}{\partial z}}=fu-g{\displaystyle \frac{\partial \eta }{\partial y}}--{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial p_a}{\partial y}}-{\displaystyle \frac{g}{{\rho }_0}}{\displaystyle {\int }_z^{\eta }\frac{\partial \rho }{\partial y}}dz-{\displaystyle \frac{1}{{\rho }_{0}h}}\left({\displaystyle \frac{\partial s_{yx}}{\partial x}}+{\displaystyle \frac{\partial s_{yy}}{\partial y}}\right)+F_v+{\displaystyle \frac{\partial }{\partial z}}\left(v_t{\displaystyle \frac{\partial u}{\partial z}}\right)+v_{S}S$$

(3)

where $t$ is the time; $x$, $y$, and $z$ are the Cartesian co-ordinates; $\eta$ is the surface elevation; $d$ is the still water depth; $h=\eta +d$ is the total water depth; $u$, $v$, and $w$ are the velocity components in the $x$, $y$, and $z$ direction; $f=2\mathrm{\Omega }\sin \varphi$ is the Coriolis parameter ($\mathrm{\Omega }$ is the angular rate of revolution and $\varphi$ the geographic latitude); $g$ is the gravitational acceleration; $\rho$ is the density of water; $s_{xx}$, $s_{xy}$, $s_{yx}$, and $s_{yy}$ are components of the radiation stress tensor; $v_t$ is the vertical turbulent (or eddy) viscosity; $p_a$ is the atmospheric pressure; and ${\rho }_0$ is the reference density of water. $S$ is the magnitude of the discharge due to point sources and $\left(u_S,v_S\right)$ is the velocity by which the water is discharged into the ambient water. The horizontal stress terms are described using a gradient–stress relation, which is simplified to:

$$F_u={\displaystyle \frac{\partial }{\partial x}}\left(2A{\displaystyle \frac{\partial u}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left[A\left({\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}}\right)\right]$$

(4)

$$F_v={\displaystyle \frac{\partial }{\partial x}}\left[A\left({\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}}\right)\right]+{\displaystyle \frac{\partial }{\partial y}}\left(2A{\displaystyle \frac{\partial v}{\partial y}}\right)$$

(5)

where A is the horizontal eddy viscosity.

The transport of temperature, $T$, and salinity, $s$, follow the general transport–diffusion equations as:

$${\displaystyle \frac{\partial T}{\partial t}}+{\displaystyle \frac{\partial uT}{\partial x}}+{\displaystyle \frac{\partial vT}{\partial y}}+{\displaystyle \frac{\partial wT}{\partial z}}=F_T+{\displaystyle \frac{\partial }{\partial z}}\left(D_v{\displaystyle \frac{\partial T}{\partial z}}\right)+\stackrel{⌢}{H}+T_{S}S$$

(6)

$${\displaystyle \frac{\partial s}{\partial t}}+{\displaystyle \frac{\partial us}{\partial x}}+{\displaystyle \frac{\partial vs}{\partial y}}+{\displaystyle \frac{\partial ws}{\partial z}}=F_s+{\displaystyle \frac{\partial }{\partial z}}\left(D_v{\displaystyle \frac{\partial s}{\partial z}}\right)+s_{S}S$$

(7)

where $D_v$ is the vertical turbulent (eddy) diffusion coefficient. $\stackrel{⌢}{H}$ is a source term due to heat exchange with the atmosphere. $T_S$ and $s_S$ are the temperature and the salinity of the source. $F$ is the horizontal diffusion terms defined by:

$$(F_T,F_S)=\left[{\displaystyle \frac{\partial }{\partial x}}\left(D_h{\displaystyle \frac{\partial }{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(D_h{\displaystyle \frac{\partial }{\partial y}}\right)\right]\left(T,s\right)$$

(8)

where $D_h$ is the horizontal diffusion coefficient. The diffusion coefficients can be related to the eddy viscosity

$$D_h={\displaystyle \frac{A}{{\sigma }_T}},D_v={\displaystyle \frac{v_t}{{\sigma }_T}}$$

(9)

where ${\sigma }_T$ is the Prandtl number.

2.2. Computational Domain and Parameter Settings

The software version used in this study is MIKE Zero 2021. The computational domain of the model encompasses the entire Bohai Sea. Bathymetric data were obtained from nautical charts provided by the Navigation Guarantee Department of the Naval Headquarters of the People’s Liberation Army of China. In the three-dimensional case, a layered mesh is used. In the horizontal domain, an unstructured mesh is used, while in the vertical domain, a structured mesh is used. The vertical mesh is based on sigma coordinates. The elements are perfectly vertical, and all layers have identical topology. The unstructured mesh for the Bohai Sea region was generated using a Surface Water Modeling System (SMS), consisting of 39,467 grid cells and 20,283 control points. The mesh has a minimum interior angle of 30°, a maximum interior angle of 120°, and a maximum slope of 0.1. The element area change rate is 0.5, with each element connected to up to eight neighboring elements. In the refined area of Laizhou Bay, the maximum grid cell size is limited to 1 km, with the smallest grid size being 300 m. In non-refined regions of the Bohai Sea, the maximum grid cell size does not exceed 3 km. Vertically, the domain is discretized into six sigma layers. The sigma coordinate system is suitable for hydrodynamic and water-quality simulations in scenarios with complex terrain, shallow water regions, and where high-precision vertical resolution is required [24]. A hydrodynamic and thermohaline model of the Bohai Sea was developed using high-order solution techniques. The time step interval used in the simulations is 3600 s. The critical Courant–Friedrich–Lévy (CFL) number for this model is 0.8, with a minimum time step of 0.01 s and a maximum time step of 30 s. The turbulence is modeled using an eddy viscosity concept. The turbulence model is based on a standard k-ε model, with buoyancy extension. This model uses transport equations for the turbulent kinetic energy (TKE), k, and the dissipation of TKE, ε, to describe the turbulence [24,25,26,27]:

$$CF{L}_{HD}=\left(\sqrt{gh}+\left|u\right|\right){\displaystyle \frac{\mathsf{\Delta }t}{\mathsf{\Delta }x}}+\left(\sqrt{gh}+\left|v\right|\right){\displaystyle \frac{\mathsf{\Delta }t}{\mathsf{\Delta }y}}$$

(10)

where $h$ is the total water depth, $u$ and $v$ are the velocity components in the x- and y-direction, respectively, $g$ is the gravitational acceleration, $\mathsf{\Delta }x$ and $\mathsf{\Delta }y$ are a characteristic length scale in the x- and y-direction, respectively, for an element, and $\mathsf{\Delta }t$ is the time step interval. The characteristic length scale, $\mathsf{\Delta }x$ and $\mathsf{\Delta }y$, is approximated by the minimum edge length for each element, and the water depth and the velocity component are evaluated at the element’s center.

Based on the 2022 runoff changes in major rivers within Laizhou Bay, May and September were chosen as representative periods for analyzing the dry and wet seasons of that year [19,20,28,29,30,31,32,33]. In the remainder of this paper, the terms “dry season” and “wet season” specifically refer to the months of May and September, respectively. All analyses related to salinity distribution and low-salinity zones are based on the statistical mean salinity data calculated using the MIKE model for these representative months.

The open ocean boundary conditions are forecasted using the global tidal model from the MIKE 21 Toolbox, incorporating eight principal tidal constituents: M2, S2, K1, O1, N2, P1, K2, and Q1. For external forcing conditions, wind fields, precipitation, evaporation, and radiation data are sourced from ERA5 (ECMWF Reanalysis v5) with a resolution of 0.25° × 0.25°. Initial conditions for temperature and salinity, as well as open boundary data, are derived from HYCOM, which provides a resolution of 0.08° × 0.04° [25,34].

Freshwater input from 18 major rivers along the Bohai Sea coast is considered, as depicted in Figure 1. Among these, seven major rivers along the Laizhou Bay coast are selected, including the Yellow River, Guangli River, Xiaoqing River, Mi River, Bailang River, Weihe River, and Jiaolai River, each with an average annual runoff exceeding 100 million cubic meters. Flow data are obtained from various sources, including the Yellow River Sediment Bulletin, China River Sediment Bulletin, Song–Liao Basin Water Resources Bulletin, Haihe Basin Water Resources Bulletin, the National Water, and Rainfall Information Platform (http://xxfb.mwr.cn, accessed on 6 May 2024), and relevant references [19,20,28,29,30,31,32,33]. The locations of the river mouths are illustrated in the figure.

2.3. Model Calibration and Validation

This study conducts regression analysis on the reliability of calibration and validation results using the Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Nash-Sutcliffe Model Efficiency Coefficient (NSE), and Index of Agreement (d) [35,36,37,38,39]. Values for MAE and RMSE that are closer to zero indicate smaller errors and better simulation performance, with both MAE and RMSE having units consistent with the analyzed data [35,36,37,38]. The values of d and NSE are dimensionless. The Index of Agreement (d) ranges from 0 to 1 and is used to assess the degree of agreement between simulated and observed values; the closer d is to 1, the more consistent the trends of simulated and observed values are [39,40,41,42]. The NSE value ranges from negative infinity to 1, with values closer to 1 indicating higher simulation accuracy. An NSE value between 0.65 and 1 is considered to indicate excellent model fit, while an NSE value between 0.5 and 0.65 indicates a good model fit [35,36,39,43].

$$\mathrm{MAE}={\displaystyle \frac{1}{N}}{\displaystyle {\sum }_{i=1}^N\left|M_i-O_i\right|}$$

(11)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N{\left(M_i-O_i\right)}^2}}{N}}}$$

(12)

$$\mathrm{NSE}=1-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N{\left(M_i-O_i\right)}^2}}{{\displaystyle {\sum }_{i=1}^N{\left(O_i-\overline{O}\right)}^2}}}$$

(13)

$$d=1-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N{\left(M_i-O_i\right)}^2}}{{\displaystyle {\sum }_{i=1}^N{\left(\left|M_i-\overline{O}\right|+\left|O_i-\overline{O}\right|\right)}^2}}}$$

(14)

$M_i$ represents the model-simulated value at the $i$-th time step; $O_i$ represents the observed value at the $i$-th time step; $\overline{O}$ is the average of all observed values at the station across all time steps; and $N$ is the total number of time steps.

2.3.1. Hydrodynamic Calibration and Validation

The distribution of hydrological observation stations used in this study is illustrated in Figure 1, with detailed information provided in

Table 1. List of hydrodynamic observation stations.

Station Name	Longitude (°, E)	Latitude (°, N)	Time
A1	120.8592	39.9093	20 April 2021–20 May 2021
A2	120.7558	40.2174	20 April 2021–20 May 2021
A3	120.4231	39.9501	20 April 2021–20 May 2021
A4	120.0580	39.9886	20 April 2021–20 May 2021
T1	119.5275	38.1407	18 April 2022–3 May 2022
T2	119.7739	38.0718	18 April 2022–3 May 2022
B1	119.8094	37.8439	27 November 2023–1 December 2023
B2	119.7014	37.6763	27 November 2023–1 December 2023

. The calibration of the model’s surface elevation, current velocity, and direction was performed using data from stations A3, A4, and B2. After calibration, the bed roughness height was set to 0.001 m, and the horizontal eddy viscosity was calculated using the Smagorinsky formulation with a constant value of 0.28. The vertical eddy viscosity was modeled using the k-ε formulation. Model validation was conducted using data from stations A1, A2, T1, T2, B1, and B2, with station B2’s calibration and validation employing data from different time periods.

Figure 2 and Figure 3 present validation curves for surface elevation, current speed, and current direction at selected stations, with detailed results outlined in

Table 2. Evaluation criteria for hydrodynamic model and validation results.

Name of Station	Validation Target	MAE	RMSE	NSE	d
A1	Surface Elevation	0.12	0.15	0.88	0.96
	Surface current speed	0.02	0.03	0.98	1.00
	Middle current speed	0.03	0.03	0.98	0.99
	Bottom current speed	0.04	0.05	0.89	0.98
	Surface current direction	4.20	7.10	0.99	1.00
	Middle current direction	7.58	13.12	0.98	1.00
	Bottom current direction	8.94	16.65	0.97	0.99
A2	Surface Elevation	0.13	0.16	0.91	0.97
	Surface current speed	0.05	0.06	0.92	0.98
	Middle current speed	0.03	0.03	0.97	0.99
	Bottom current speed	0.04	0.05	0.87	0.97
	Surface current direction	13.51	18.92	0.96	0.99
	Middle current direction	4.20	7.10	0.99	1.00
	Bottom current direction	15.49	18.79	0.96	0.99
T1	Surface Elevation	0.11	0.13	0.76	0.92
T2	Surface Elevation	0.11	0.14	0.78	0.93
B1	Surface Elevation	0.05	0.06	0.96	0.99
	Surface current speed	0.04	0.05	0.71	0.91
	Middle current speed	0.03	0.04	0.78	0.93
	Bottom current speed	0.03	0.04	0.74	0.91
	Surface current direction	14.96	18.75	0.96	0.99
	Middle current direction	14.34	17.98	0.97	0.99
	Bottom current direction	15.70	19.87	0.96	0.99
B2	Surface Elevation	0.05	0.06	0.95	0.99
	Surface current speed	0.06	0.07	0.71	0.90
	Middle current speed	0.05	0.06	0.74	0.91
	Bottom current speed	0.05	0.06	0.71	0.90
	Surface current direction	22.59	25.94	0.94	0.98
	Middle current direction	17.94	21.55	0.96	0.99
	Bottom current direction	15.91	19.80	0.97	0.99

. These results suggest that the model established in this study adequately represents the tidal and current conditions within the computational domain, providing a reliable basis for subsequent analyses using this hydrodynamic field.

2.3.2. Salinity Validation

The distribution of salinity observation stations used in this study is shown in Figure 1. The validation of surface and bottom-layer salinity for the dry and wet seasons of 2022 is presented in Figure 4.

Table 3. Salinity calculation indicators in different water layers during dry and wet seasons.

Water Layers-Seasons	MAE (PSU)	RMSE (PSU)	d
Surface salinity in dry season	0.41	0.50	0.90
Bottom salinity in dry season	0.16	0.20	0.99
Surface salinity in wet season	0.60	0.72	0.71
Bottom salinity in wet season	0.54	0.66	0.77

shows the validation results of salinity. The validation stations are situated near the Yellow River, where the MAE and RMSE between the simulated and measured values during the dry season remain within 0.5 PSU. Although the error slightly increases following the rise in runoff during the wet season, the index of agreement (d) also remains above 0.7, while the simulation results for both the dry and wet seasons are still considered relatively accurate [39,40,41,42].

3. Simulation and Analysis

The salinity distribution in Laizhou Bay was simulated using the MIKE 3 Flow Model, incorporating various forcing factors such as runoff, wind fields, precipitation, evaporation, solar radiation, relative humidity, and atmospheric temperature. The resulting simulation data were then analyzed in conjunction with tidal currents to identify the key factors influencing salinity distribution.

3.1. Flow Field Analysis

Tidal current variations within the bay significantly influence seawater transport and salinity distribution. Figure 5 illustrates the flow field conditions at key moments on the surface of the Bohai Sea. Throughout a tidal cycle, the tidal currents in Laizhou Bay generally flow from southwest to northeast. During the maximum flood, the northwestward tidal flow entering the bay is notably deflected southward, creating a prominent clockwise circulation near the Yellow River estuary and forming high-speed regions. As the tidal flow continues to deflect, it deflects westward in the southwestern part of Laizhou Bay and southward in the southeastern part. At flood slack, the tidal flow entering the bay from the north turns westward, resulting in westward flow in the southwestern part and southwestward flow in the southeastern part, which generates high-speed regions in the southern part of the bay.

During the maximum ebb, eastward and northeastward currents in the southwestern and southern parts of Laizhou Bay are deflected northward in the central area. The flow in the eastern part turns northeastward, with a counterclockwise circulation emerging near the Yellow River Delta, accompanied by high-speed regions. As the flow exits, it gradually shifts from eastward to northwestward, exiting to the northwest of the Yellow River estuary. During the ebb slack, the flow in the southwestern and southern parts of Laizhou Bay, as well as at the bay entrance, is predominantly eastward. Upon reaching the nearshore area in the east, the flow turns northward, merging with the northeastward tidal flow at the bay entrance and forming a band of high-speed regions in the eastern part of Laizhou Bay.

3.2. Salinity Distribution and Residual Current Analysis

As a semi-enclosed sea, the Bohai Sea has a poor water exchange capacity, and tides are the main driving force in this region. Due to factors such as friction, bathymetric features, and boundary shapes, tidal currents in nearshore areas flow in a nonlinear manner, with the resulting residual currents being the primary driving force affecting material transport and distribution throughout the Bohai Sea [44]. To study the material transport involved in the formation of salinity distribution in Laizhou Bay, Lagrangian residual currents were used to analyze the dynamic transport processes in Laizhou Bay [45,46,47,48,49]. The equations are as follows:

$$\overrightarrow{U_L}=\overrightarrow{U_E}+\overrightarrow{U_S}$$

(15)

$\overrightarrow{U_L}$ represents the Lagrangian mean velocity, $\overrightarrow{U_E}$ represents the Eulerian residual velocity, and $\overrightarrow{U_S}$ represents the Stokes drift velocity, expressed as:

$$\overrightarrow{U_S}=\langle {\displaystyle {\int }_{t_0}^{t_0+nT}\overrightarrow{U}}\left(x_0,t\right)dt\cdot \left(\nabla \overrightarrow{U}\left(x_0,t\right)\right)\rangle$$

(16)

$\overrightarrow{U}\left(x_0,t\right)$ represents the tidal current velocity at a specific point, and $\langle \cdot \rangle$ denotes the time average, expressed as:

$$\langle \cdot \rangle ={\displaystyle \frac{1}{nT}}{\displaystyle {\int }_{t_0}^{t_0+nT}\cdot dt}$$

(17)

The simulated surface and bottom salinity, along with the residual current distribution during the dry and wet seasons in Laizhou Bay, are depicted in Figure 6. Low-salinity regions in Laizhou Bay are primarily concentrated near the southern coast and around the Yellow River estuary in the northwest. Prominent freshwater plumes are evident at the mouths of three rivers, creating distinct low-salinity regions [5]. The influx and diffusion of freshwater from these rivers significantly affect the salinity distribution in Laizhou Bay. The distribution and variation of these low-salinity regions correspond with interannual changes in runoff volume [3,15,16,50,51]. Overall, the salinity distribution in Laizhou Bay is characterized by lower salinity in the southwest and higher salinity in the northeast, reflecting the influence of river runoff and the intrusion of high-salinity water from the Bohai Sea. The isoline patterns reveal three distinct low-salinity cores in Laizhou Bay, located in the northwest, southwest, and southeast, each associated with river inputs from different directions as modeled.

Lü et al. analyzed the annual salinity field of the Bohai Sea from 1958 to 2000 based on measured salinity data, indicating that the overall salinity of the Bohai Sea has shown an increasing trend since the 1950s. However, in the 1960s, due to the occurrence of wet years and the increase in average runoff of the Yellow River, there was a significant decrease in salinity [52]. The interannual variation of salinity in the Bohai Sea shows a negative correlation with runoff and precipitation [13,14,16]. In 2022, the Bohai Sea and Laizhou Bay experienced significantly higher-than-average runoff and precipitation. Surface water resources in the Liao River, Hai River, and Yellow River basins exceeded the annual norm by 35.1%, 13.8%, and 0.9%, respectively. Shandong Province had an exceptionally wet year, with the Yellow River’s runoff increasing by 70.6% compared to the average from 1987–2016 [19]. Weifang City’s total water resources increased by 132.6% relative to the long-term average, with the city’s seawater inflow rising by 275.0% compared to 2021. Additionally, total water resources in Dongying and Yantai surpassed long-term averages by 99.3% and 130.7%, respectively. In 2022, precipitation in Northeast China and North China exceeded the annual average by 24% and 8%, respectively, with the Liaohe, Haihe, and Yellow River basins experiencing increases of 35%, 14%, and 4.1% above the norm [21]. The distribution of simulated salinity contour lines is in good agreement with the observed and simulated results from previous studies during wet years [12,15,52]. In Laizhou Bay, salinity exhibits a distribution characteristic of lower values in the southwest and higher values in the northeast, with a significant low-salinity region occurring in the nearshore waters at river estuaries.

During the dry season, reduced runoff during this period allows high-salinity water from the Bohai Sea to penetrate southward into the central and southern parts of Laizhou Bay. Isohalines near the southern coast run parallel to the shoreline, while near the bay mouth, they generally follow depth contours. Surface salinity distribution during the dry season is heavily influenced by runoff. Surface residual currents predominantly flow eastward, aligning the salinity contours near the bay mouth, as well as southern and eastern regions, with the direction of these currents. Water from the northwest, southwest, and southeast of Laizhou Bay is transported eastward along the coastline under the influence of residual currents, creating a low-salinity, high-speed region in the eastern nearshore area.

In contrast, the influence of runoff on the bottom layer during the dry season is weaker compared to the surface layer. The low-salinity region near the Yellow River estuary shrinks considerably, although fan-shaped low-salinity regions persist at the mouths of rivers in the southwest and southeast. The direction of bottom layer residual currents shifts from southwestward at the bay mouth to southeastward in the southern parts, with westward, southward, and eastward flows in the western, central, and eastern regions, respectively. The increased inflow of high-salinity water from the Bohai Sea pushes the high-salinity isohalines closer to shore, maintaining a distribution pattern similar to that of the surface layer.

During the wet season, increased runoff during this period causes low-salinity regions near river mouths to expand, with freshwater plumes extending further into the bay. Isohalines become more tightly packed and shift northeastward compared to the dry season. Near the bay mouth, the isohalines generally follow bathymetric contour lines, but near the mouths of the Yellow River and rivers in the southwest and southeast, they bend oceanward due to the influence of freshwater runoff.

During the wet season, surface salinity distribution continues to be significantly affected by runoff, with surface residual currents predominantly flowing eastward. Isohalines at the bay mouth, as well as southern and eastern regions, generally align with the direction of the residual currents. In the eastern nearshore area of Laizhou Bay, isohalines are more densely packed compared to the dry season, with higher flow velocities and a northward shift in the outflow direction. The distribution of isohalines in the bottom layer during the wet season mirrors that of the surface layer, and the patterns of isohalines and residual currents are consistent in both layers during the dry season.

3.3. Profile Analysis

The profile location is shown in Figure 1, and the salinity distribution of the profile is shown in Figure 7. Profile A originates in the shallow coastal waters of southwestern Laizhou Bay, approximately 5.6 km from the Bailang River estuary, and extends northeast toward the bay’s mouth, with the bathymetry gradually deepening. Profile B begins at Diaolongzui and stretches to the Old Yellow River estuary, characterized by shallow waters at both ends and deeper waters in the middle. Salinity stratification is observed near the coast and at the bay mouth, resulting from the influence of freshwater input from the river and the influx of high-salinity water from the Bohai Sea.

Profile A demonstrates that low-salinity water from river input significantly affects the vertical salinity distribution in shallow coastal waters, creating a distinct low-salinity zone and forming a halocline (a layer with a sharp salinity gradient). During the wet season, the halocline’s influence expands as runoff increases. In the central part of Laizhou Bay, the direct impact of riverine freshwater on the vertical salinity distribution decreases, resulting in a more uniform salinity profile. However, near the bay’s mouth, a weaker halocline reemerges. Profile A indicates that during the dry season, the salinity near the coastline can differ by more than 5 PSU compared to the wet season, with this difference diminishing progressively to approximately 0.1 PSU at the bay mouth. Flow field and residual current analyses indicate that the surface layer at the bay mouth is influenced by the tidal transport of water from the Yellow River and internal freshwater within the bay, while the bottom layer is affected by the intrusion of high-salinity water from the Bohai Sea, leading to the formation of a halocline at the bay’s mouth [5,53,54].

Profile B displays lower salinity in the nearshore areas at both ends and higher salinity in the central region. The salinity profile during the dry season is typically approximately 0.5 PSU higher than that observed in the wet season. The low-salinity seawater in the nearshore shallow waters is primarily influenced by residual currents. Near the Old Yellow River estuary, the water is affected by the southward flow of diluted Yellow River water, while near Diaolongzui, it is influenced by the eastward movement of low-salinity water from the southern part of the bay. The distribution of low-salinity zones and haloclines in these nearshore shallow waters closely aligns with previous analyses of residual currents and the transport of low-salinity water.

4. Discussion

Based on river outlet locations and residual current patterns, the freshwater outputs from the major rivers in Laizhou Bay were consolidated into three distinct freshwater plumes: the Yellow River plume, dominated by freshwater from the Yellow River; the southwest plume, influenced by the Guangli River, Xiaoqing River, Mi River, and Bailang River; and the southeast plume, shaped by the Weihe River and Jiaolai River. To assess the impact of terrestrial freshwater input on salinity distribution in Laizhou Bay, three experimental scenarios were designed, each excluding one freshwater plume while keeping other parameters constant.

The analysis of tidal currents and salinity distribution in Laizhou Bay under the control group reveals that runoff input has a more pronounced influence on the surface layer. The low-salinity water, driven by residual currents, significantly affects the horizontal salinity distribution at the surface. In contrast, the bottom layer is less influenced by runoff and is primarily affected by high-salinity water from the Northeastern Bohai Sea, transported by tidal currents, showing a consistent distribution pattern under various conditions. During the analysis of salinity distribution in the control group and various scenarios, it was found that the influence of riverine freshwater input on salinity distribution diminishes with increasing bathymetry, and the isohaline patterns in the bottom layer are generally consistent with those at the surface, showing similar trends across scenarios. Therefore, to avoid redundancy in figures and descriptions and to highlight the core findings, the subsequent presentation and discussion will primarily focus on the surface layer.

4.1. Scenario 1: Removal of the Yellow River Runoff Input

The simulated salinity distribution and residual current patterns are illustrated in Figure 8. After removing the runoff input from the Yellow River, the mean surface salinity in Laizhou Bay increased by 2.29 PSU during the dry season and 1.78 PSU during the wet season, with the isohalines shifting significantly shoreward. The isohaline movement was most pronounced in the southwestern direction of Laizhou Bay. During the dry season, the 27 PSU isohaline advanced inland by over 50 km in the southwestern region of Laizhou Bay, whereas during the wet season, it moved inland by approximately 20 km in the same area. The ring-shaped low-salinity region and high-velocity areas around the Yellow River estuary disappeared. In Experimental Scenario 1, the isohalines during the dry season were generally parallel to those under normal conditions, though they were more densely packed near the southern estuary. The distribution of residual currents remained largely consistent with normal conditions, predominantly flowing eastward, with slightly higher current speeds in the south and enhanced eastward transport. The residual currents near the Northwestern Yellow River estuary shifted southeastward. During the wet season, the isohaline variation patterns were similar to those in the dry season. Compared to normal input, the significant eastward transport of residual currents at the bay mouth was absent, with southeastward currents dominating the west side of the bay mouth and northeastward currents on the east side. The residual current distribution in the southern part of the bay remained generally consistent with normal conditions, primarily flowing eastward, turning clockwise at Diaolongzui, and then moving northeastward along the coastline. Under this experimental scenario, low-salinity regions were mainly concentrated in the southern part of Laizhou Bay, followed by the eastern nearshore areas.

4.2. Scenario 2: Removal of the Southwest Runoff Input

The simulated salinity distribution and residual current patterns are illustrated in Figure 9. After removing the southwest runoff input, the mean surface salinity in Laizhou Bay increased by 0.55 PSU during the dry season and 1.16 PSU during the wet season. During the dry season, the isohaline distribution largely remained parallel to the pattern observed under normal conditions, except for a notable bend towards the shore near the southwestern river mouth. The displacement of the 27 PSU isohaline was minimal, staying mostly within 1 km. In contrast, the 26 PSU isohaline showed the most significant variation, with a maximum displacement exceeding 5 km. After the removal of the southwestern runoff input, the 24–27 PSU isohalines in the central region of Laizhou Bay shifted outward to some degree along the southwest–northeast axis. The residual current distribution was similar to normal conditions, predominantly flowing eastward. In the wet season, the isohalines were consistent with those under the control group, though the southern isohalines contracted toward the southwestern shore, maintaining a roughly parallel alignment with the coastline. The residual current direction largely remained unchanged, with a slight southward deflection in the southern part of the bay, continuing along the eastern coastline after merging with the nearshore flow. Under these conditions, low-salinity regions were primarily concentrated in the northwest and southeast parts of Laizhou Bay, with additional low-salinity regions observed in the eastern nearshore areas.

4.3. Scenario 3: Removal of the Southeast Runoff Input

The simulated salinity distribution and residual current patterns are illustrated in Figure 10. After removing the southeast runoff input, the mean surface salinity in Laizhou Bay increased by 0.13 PSU during the dry season and 0.58 PSU during the wet season. During the dry season, the isohaline pattern generally remained parallel to that observed under normal conditions, with a noticeable bend toward the shore near the southeastern river mouth. The residual current distribution was similar to normal conditions, predominantly flowing eastward. In the wet season, the isohalines were consistent with those under normal conditions, though the southern isohalines contracted toward the southeastern shore, maintaining a roughly parallel alignment with the coastline. The variation trend and magnitude of the isohaline closely resemble those observed under Scenario 2. The residual current direction largely remained unchanged, with a slight southward deflection in the southern part of the bay, continuing along the eastern coastline after merging with the nearshore flow. Under these conditions, low-salinity regions were primarily concentrated in the northwest and southwest parts of Laizhou Bay, with additional low-salinity regions observed in the eastern nearshore areas.

4.4. Comparative Analysis of Experiment Results

The concept of a low-salinity region refers to areas of the ocean where salinity is relatively low, without a standardized quantitative classification or reference to specific sea areas. Scholars set different isohalines as boundaries for diluted water based on the salinity characteristics of their target areas, thereby defining various low-salinity regions. For instance, Xiao et al. examined changes in the extent of low-salinity zones in the nearshore waters of the Yellow River from 2004 to 2009, using the 27 isohaline as the boundary to distinguish the Yellow River’s diluted water from that of other rivers flowing into Laizhou Bay [55]. Similarly, Wang et al. studied the impact of variations in the Yellow River’s runoff due to water-sediment regulation on salinity distribution outside the estuary, employing isohalines of 28, 27, and 26 to mark the Yellow River diluted waterfront during different water–sediment regulation events [5]. Moon et al., investigating the influence of Changjiang diluted water on the thermal structure of the Northern East China Sea during summer, used the 26 PSU isohaline to delineate the freshwater intrusion area and describe the spatiotemporal distribution of low-salinity water [56].

As illustrated in Figure 6, in the control group, the 28 PSU isohaline spans the entire entrance of Laizhou Bay, with salinities within the bay ranging from 20 to 27 PSU. Salinity decreases towards the south, where the 20 PSU isohaline approaches the estuarine plume, mixing with riverine freshwater to form a fan-shaped low-salinity region with salinities below 10 PSU near the estuary. This study identifies eight isohalines, ranging from 20 to 27 PSU, to delineate various low-salinity regions. The effects of freshwater inputs under different scenarios on the extent of these low-salinity regions in Laizhou Bay are also examined.

Table 4. Monthly runoff volume.

Runoff Input	Monthly Runoff during the Dry Season/108 m3	Monthly Runoff during the Wet Season/108 m3
Yellow River Runoff Input	9.85	17.95
Southwest Runoff Input	0.98	5.17
Southeast Runoff Input	0.64	5.58

presents the monthly runoff volumes from different directions in Laizhou Bay during the dry and wet seasons, while

Table 5. Area of low-salinity regions (km²).

Groups	Seasons	20 PSU	21 PSU	22 PSU	23 PSU	24 PSU	25 PSU	26 PSU	27 PSU
Control Group	Dry Season	292.69	514.32	772.33	1146.69	1674.20	2833.78	4610.77	5813.37
	Wet Season	1549.83	1795.01	2158.74	2823.67	3973.82	4551.92	5253.72	5908.90
Scenario 1	Dry Season	107.55	152.36	231.06	400.91	640.50	969.00	1425.31	2167.95
	Wet Season	955.42	1197.27	1484.28	1734.84	2079.28	2812.58	4360.28	5501.16
Scenario 2	Dry Season	65.87	93.20	323.99	748.89	1263.72	2406.09	4693.52	5818.40
	Wet Season	1103.46	1376.71	1743.85	2310.91	3672.51	4609.44	5275.11	5992.33
Scenario 3	Dry Season	240.69	434.32	662.82	1058.29	1702.94	2906.68	4656.73	5675.38
	Wet Season	1201.72	1599.45	2108.12	2679.15	3854.17	4589.44	5280.88	6003.17

details the areas of low-salinity zones under various conditions.

Variations in runoff volume, surrounding topography, and geographic orientation result in different freshwater inputs generating distinct plumes that have varying impacts on salinity distribution. Figure 11 demonstrates the rate of change in the area of low-salinity regions compared to the control group under different conditions, time frames, and water layers, visually depicting the extent to which these varying plumes influence salinity changes in these regions.

Based on earlier simulation results, the removal of the three directional runoff inputs results in a significant increase in the mean salinity of Laizhou Bay. The increase follows an order based on impact, with the removal of the Yellow River runoff having the largest effect, followed by the southwest and southeast runoff inputs. Changes in the area of low-salinity regions are influenced not only by the runoff volume of these inputs but also by the choice of boundary salinity values.

During the dry season, the change rates of low-salinity regions under three different conditions overlap to some extent based on various defined standards. When considering the overall change rates of low-salinity regions within the 20 to 27 PSU range, the Yellow River runoff exerts the greatest influence on the low-salinity regions in Laizhou Bay. The average rate of change in the area of low-salinity regions is −66.01% after excluding the Yellow River runoff input. When the southwest runoff is removed, the average rate of change decreases to −36.23%, and after eliminating the southeast runoff input, the average rate of change is −6.54%. However, when using 20 and 21 PSU as boundaries, the increase in low-salinity region within the bay exceeds 10% after the removal of the southwest runoff input compared to the Yellow River runoff. Based on prior salinity distribution and residual current conditions, the reduction in low-salinity regions is primarily concentrated around the river estuaries in the southwest of Laizhou Bay, a phenomenon mainly shaped by local topography. As Yellow River freshwater flows into Laizhou Bay from the south, it mixes with the surrounding high-salinity water, causing salinity to rise to around 26 PSU upon entry. In contrast, the southwest runoff has estuaries within Laizhou Bay, forming estuarine plumes that significantly reduce salinity and create low-salinity zones [57,58,59,60,61,62]. As tides mix with ocean water outside the bay, this influence gradually diminishes, significantly reducing the area of low-salinity regions above 21 PSU, though its impact is less than the Yellow River’s due to the latter’s larger runoff volume. The southeast runoff impacts the bay similarly to the southwest runoff, but because its volume is smaller during the dry season and the southern part of Laizhou Bay is influenced by tides, the freshwater transport pathway within the bay is diverted. Thus, the removal of the southeast runoff input results in a relatively moderate change in the low-salinity region [54].

During the wet season, the overall mean salinity in Laizhou Bay decreases by more than 2 PSU compared to the dry season. Among all low-salinity regions, the Yellow River runoff exerts the most significant influence, followed by the southwest runoff, while the southeast runoff has the least impact. The average change rate in the area of low-salinity regions is −31.41% following the exclusion of the Yellow River runoff input. When the southwest runoff is excluded, this rate changes to −11.75%, and upon removing the southeast runoff input, it further shifts to −5.11%. As the mean salinity decreases, the phenomenon observed in the dry season, where the southwest runoff leads to larger changes in low-salinity regions, no longer occurs. Furthermore, due to increased runoff and lower mean salinity, the envelope area of low-salinity regions in Laizhou Bay expands during the wet season, resulting in smaller area change rates across all three conditions compared to the dry season.

In Scenarios 2 and 3, there is a slight increase in the area of low-salinity regions (above 24 PSU), primarily in the western and northwestern parts of Laizhou Bay. Analysis of the incremental changes in salinity distribution and residual current transport reveals that this increase is largely due to the Yellow River runoff. This phenomenon is linked to the weakening of the eastward residual current in the southern part of Laizhou Bay after the removal of the southwest and southeast runoff inputs. Normally, freshwater from the Yellow River, which enters Laizhou Bay from the south, would follow the residual current eastward along the coastline, moving towards the northeast. However, in Scenarios 2 and 3, the weakening of this eastward current causes some of the Yellow River freshwater to flow southeastward, shifting the isohaline line closer to the shore and slightly expanding the low-salinity region.

5. Conclusions

• The surface salinity distribution in Laizhou Bay is significantly influenced by both freshwater runoff and residual currents. The salinity isohalines at the bay’s entrance, southern, and eastern regions generally align with the direction of the residual currents. Within the bay, the residual currents predominantly flow eastward, with a pronounced coastal transport feature in the southern region. Freshwater inputs from various directions converge near the southern coast of Laizhou Bay, creating an extensive low-salinity region. The bottom salinity distribution largely mirrors that of the surface layer. As water depth increases, the influence of runoff gradually weakens, and the isohalines shift shoreward under the influence of high-salinity water transported by the residual currents from the Bohai Sea.
• In 2022, the area surrounding the Bohai Sea experienced either a normal or exceptionally wet year. By comparing the salinity simulation results with historical multi-year salinity distribution data of the Bohai Sea, it was found that the salinity level in Laizhou Bay that year was close to that of historical wet years and showed significant differences compared to dry years. Following the removal of the Yellow River runoff, the surface mean salinity in Laizhou Bay increased by 2.29 PSU during the dry season and 1.78 PSU during the wet season. The removal of southwest runoff resulted in salinity increases of 0.55 PSU and 1.16 PSU for the dry and wet seasons. Similarly, the removal of southeast runoff led to salinity increases of 0.13 PSU and 0.58 PSU for the dry and wet seasons, respectively. The main freshwater input pathways in Laizhou Bay, such as runoff and precipitation, are influenced by seasonal and interannual variations and exhibit relatively sensitive responses in salinity distribution [5,6].
• In this study, the seven major runoffs entering Laizhou Bay are classified into three directional runoff inputs: the Yellow River, the southwest, and the southeast. Their effects on the mean salinity and the extent of low-salinity regions in Laizhou Bay, from most to least significant, are as follows: the Yellow River runoff, the southwest runoff, and the southeast runoff. Changes in the size of low-salinity regions are influenced by runoff volume, residual currents, and the definition of low-salinity boundaries. Under the boundary conditions of the 20 and 21 PSU isohalines, the southwestern runoff affects the change in the area of the low-salinity region by over 10% compared to the Yellow River runoff, even though the Yellow River has a significantly larger runoff volume. Additionally, variations in runoff input can influence nearshore residual currents, potentially causing an expansion rather than a reduction of the low-salinity region with salinity levels above 24 PSU, even when freshwater inflow decreases.

The terrain of Laizhou Bay is complex, and the residual currents generated by tidal forces play a critical role in the transport and distribution of materials in this marine area. Furthermore, the numerous coastal rivers and substantial runoff inputs significantly influence the hydrodynamic conditions and material transport processes within the bay, making them essential parameters in numerical simulations. Freshwater input from runoff is a critical factor influencing the distribution of salinity and the dynamics of low-salinity regions in coastal waters. Studies have indicated that reduced runoff can lead to increased salinity and the contraction of low-salinity regions, resulting in significant declines in plankton populations and fishery yields, which can instigate substantial changes in the marine ecosystem. Therefore, utilizing numerical simulations to monitor the salinity changes and distribution of low-salinity regions caused by runoff input is crucial for marine environmental protection and resource management [7,8,9,10,11]. Early studies, constrained by limited data, limited computational resources, and outdated datasets, often considered only the influence of the Yellow River. This narrow focus resulted in limitations in the salinity simulations for Laizhou Bay, hindering accurate and timely reflection of salinity distribution and changes within the bay. Future research on simulating salinity in the Laizhou Bay area must account for residual current transport within the bay and incorporate runoff inputs as comprehensively as possible.