Tidal-Driven Water Residence Time in the Bohai and Yellow Seas: The Roles of Different Tidal Constituents

Abstract

Water residence time (WRT) is a crucial parameter for evaluating the rate of water exchange and it serves as a timescale for elucidating hydrodynamic processes, pollutant dispersion, and biogeochemical cycling in coastal waters. This study investigates the tidal-driven WRT patterns in the Bohai and Yellow Seas (collectively known as BYS) by employing a tidal model in conjunction with an adjoint WRT diagnostic model and explores the influence of tidal constituents on WRT. The findings indicate that the tidal-driven WRT in the BYS is approximately 2.11 years, exhibiting a significant spatially heterogeneous distribution. The WRT pattern shows a strong correlation with the pattern of tidal-driven Lagrangian residual currents (LRCs). Semidiurnal tides have a more pronounced effect on WRT than diurnal tides. Semidiurnal tides significantly reduce WRT across the entire BYS, while diurnal tides predominantly influence WRT in the Bohai Sea (BS). The M₂ tidal constituent is the most influential in decreasing WRT and enhancing water exchange, owing to its dominant energy contribution within the tidal system. In contrast, the S₂ tidal constituent has a minimal effect; however, its interaction with the M₂ tidal constituent plays a significant role in reducing the WRT. The K₁ and O₁ constituents exert more localized effects on WRT, particularly in the central BS, where their energy ratios relative to M₂ are relatively high. Although the amplitude of the S₂ constituent exceeds that of K₁ and O₁, its contribution to LRC—and consequently to WRT—is limited due to the overlapping tidal wave with M₂. This research contributes to a deeper understanding of the influence of tidal dynamics on long-term water transport and associated timescales, which are vital for enhancing predictions of material transport and ecosystem dynamics in tidal-dominated environments.

1. Introduction

Water residence time (WRT) is defined as the time required for a water parcel to leave the region of interest for the first time [1,2,3] and serves as a pivotal timescale parameter for understanding ocean hydrodynamics and marine biogeochemistry cycling [4,5]. In coastal regions, nutrient cycling, primary production, pollutant dispersion, and ecosystem resilience are highly related to the WRT [5,6,7]. A short WRT promotes water renewal, which limits pollutant accumulation but may restrict nutrient retention, potentially inhibiting primary production. Conversely, a longer WRT enhances nutrient retention and organic matter sedimentation, thus supporting productivity and increasing the risks of eutrophication and hypoxia [7,8,9]. Furthermore, WRT can provide insights into ecosystem connectivity and resilience, which is critical for understanding how ecosystems respond to anthropogenic pressures and climate change [5]. Given its significant implications for marine ecology and environmental management, investigating the variability of WRT in coastal waters and its underlying dynamic mechanisms is essential [10,11].

The variability of WRT in coastal waters is influenced by various physical processes and their interactions. For example, seasonal and interannual variations in WRT in the Chesapeake Bay are primarily driven by fluctuations in river discharge and wind [12], with gravitational circulation also playing a significant role [13,14]. Research has indicated that the distribution and seasonal changes of water residence time (WRT) in the BS and Subei Coastal waters are primarily influenced by tidal and wind forces [9,15]. Furthermore, it has been suggested that wind-driven coastal currents and their interactions with tides play a significant role in determining WRT in the eastern shelf seas of China [16]. Tides, as substantial components of coastal hydrodynamics, play essential roles in the hydrodynamic processes and water exchange in coastal regions [17,18,19,20,21]. While previous studies have primarily focused on the overall patterns of WRT influenced by all physical processes in coastal waters, the characteristics of WRT solely driven by tidal forces have not been fully elucidated. In particular, the contributions of various tidal constituents and their differing roles in WRT remain unclear. Due to rising sea levels and changes in the coastline resulting from land reclamation, the coastal tidal system is undergoing significant transformations [22]. Different tidal constituents exhibit varying responses to these changes [23]. Understanding the tidal-driven WRT and the roles of tidal constituents is crucial for assessing the potential future alterations in water exchange capacity in coastal regions, as well as the subsequent impacts on the marine environment and ecology.

This study aims to investigate the patterns of tidal-driven WRT in the Bohai and Yellow Seas (collectively known as BYS), which are typical enclosed shelf seas, and to elucidate the roles of various tidal constituents through three-dimensional tidal simulations and a diagnostic model of WRT. The structure of this paper is organized as follows: Section 2 introduces the tidal simulation methodology, the WRT diagnostic model, and the numerical experimental designs. Section 3 presents the results of the tidal-driven WRT in the BYS and examines the influence of different tidal constituents on WRT. Section 4 discusses the formation of the WRT patterns and the contributions of various tidal constituents by analyzing the tidal-driven Lagrangian residual currents (LRCs). Finally, Section 5 provides a concise conclusion.

2. Methods

2.1. Study Area

The Bohai and Yellow Seas (collectively known as BYS), characterized by a mean water depth of approximately 40 m and bordered by China and the Korean Peninsula, are typical semi-enclosed coastal seas (Figure 1). The BYS features a strong and complex tidal system, including semidiurnal constituents (M₂, S₂) and diurnal ones (K₁, O₁), significantly influencing hydrodynamics and water exchange processes [16,24]. Previous studies utilizing hydrodynamic models have explored the seasonal and spatial variations in WRT driven by various dynamic processes within the BYS. For instance, substantial seasonal fluctuations in WRT in the BS, influenced by wind, tidal forces, and river discharge, were revealed through three-dimensional modeling [15]. Moreover, it has been shown that the WRT pattern and its variability in the BYS as well as the coastal waters of the Yellow Sea (YS) are significantly affected by the interactions between tides and wind, based on a hydrodynamic model considering complete dynamic processes [9,24]. By comparing various hydrodynamic processes, a previous study by Lin et al. (2020) suggested that tides are the predominant factor influencing the WRT in the BYS [16]. Nonetheless, the patterns of tidal-driven WRT and the roles of different tidal constituents in the BYS remain poorly understood.

2.2. Tidal Simulation by the MERF Model

The hydrostatic and barotropic versions of the Marine Environment Research and Forecasting (MERF) ocean model [25] were employed in this study to simulate the tidal process. MERF employed the three-dimensional, primitive, non-hydrostatic equations governing the ocean dynamics, using the Boussinesq approximation and the terrain-following σ-coordinate system [25]. The two-equation turbulence closure model (MY2.5) [26] was implemented in the model to determine the values of the vertical viscosity coefficient and diffusion coefficient.

As shown in Figure 1, the model domain covers the entire BYS. The domain was discretized into a 333 × 333 grid horizontally with a resolution of approximately 3 km (1/30 degree) and into 21 σ-levels vertically. A time step of 30 s was adopted. The model was forced by tidal elevation at the open boundaries, which were calculated based on the tidal amplitudes and epochs of 8 tidal constituents (M₂, S₂, K₁, O₁, N₂, K₂, P₁, and Q₁). Data for these 8 tidal constituents were obtained from the global ocean tides model TPXO8-atlas TOPEX/Poseidon (https://www.tpxo.net/tpxo-products-and-registration, accessed on 13 June 2022). The tidal model was run for 396 days, starting from 2 December 2019. The simulation results from the last 366 days were output for tidal harmonic analysis and used to drive the WRT model. The amplitudes and epochs of the four primary tidal constituents (i.e., M₂, S₂, K₁, and O₁) were validated using data from the 36 tide gauge stations (https://www.chaoxibiao.net/, accessed on 17 August 2023). In the absence of observational data for tidal currents during the simulation period, validation of the modeled tidal currents was conducted by comparing tidal current ellipses with data from the TPXO8 atlas. Meanwhile, given the strong correlation between tidal elevations and currents, validating tidal amplitudes and epochs can serve as an indicator of the accuracy of the modeled tidal currents. Model outputs—including water depth, velocity, and diffusion coefficients—were saved at 30 min intervals and used to drive the WRT model introduced in Section 2.3.

2.3. Diagnosis of Water Residence Time

In this study, WRT is diagnosed using the adjoint method [2] under the framework of the constituent-oriented age and residence time (CART) theory [2,27,28]. By solving the adjoint problem associated with tracer transport, the WRT equation is derived as follows [2]:

$${\displaystyle \frac{\partial \overline{\theta }}{\partial t}}+{\delta }_{\omega }\left(x\right)+\mathit{V}\cdot \nabla \overline{\theta }+\nabla \cdot \left[K\cdot \nabla \overline{\theta }\right]=0,$$

(1)

where $\overline{\theta }$ represents the WRT, $V$ denotes the three-dimensional velocity field, $K$ is the diffusion tensor, ${\delta }_{\omega }\left(x\right)$ represents the characteristic function of the control region $\omega$, and ${\delta }_{\omega }(x)=\left\{\begin{array}{l}1 \forall x\in \omega \\ 0 \forall x\notin \omega \end{array}\right.$. The adjoint method enables the calculation of spatiotemporal variations in WRT through a single backward model run.

Based on the adjoint Equation (1), a WRT diagnosis model [29] was applied to determine the spatiotemporal distribution of the WRT in the BYS based on the adjoint method. This model functions as a submodule of the Marine Environment Research and Forecasting model. The governing equations are solved using the finite-difference method, maintaining consistency in grids and vertical layers with the hydrodynamic model. This model has been successfully applied to study WRT in multiple regions, including Jiaozhou Bay [29], the BS [15], the eastern shelf seas of China [16], and the Subei Coastal Water of the YS [9]. These studies showed the high reliability of the WRT model.

In the calculation, the closed boundary is set to $\overrightarrow{n}·\left(\nabla \overline{\theta }\right)=0$, with $\overrightarrow{n}$ as the outgoing unit vector normal to the boundary. For the open boundary (red lines in Figure 1), a homogeneous Dirichlet boundary condition ($\overline{\theta }=0$) is imposed, representing the time required for a water parcel to leave the control region for the first time [2,30,31]. The WRT model was executed for a 10-year spin-up period using water depth, velocity, and diffusion coefficients derived from the tidal model. This duration ensured the attainment of a stable WRT variation in the BYS, effectively eliminating the influence of initial conditions on the WRT [12,31]. The WRT values of the 10th year were subsequently utilized for analysis.

2.4. Numerical Sensitivity Experiments

To investigate the impact of different tidal constituents on WRT in the BYS, we conducted two groups of numerical sensitivity experiments. In each experiment, one or several tidal constituents were removed from the tidal model, and then the WRT result was calculated by the WRT model driven by the changed tidal model. Then, the WRT results from different experiments were compared with the control run (i.e., the calculation including all eight tidal constituents) to quantify the impact of various tidal constituents on the WRT in the BYS. In the first group of experiments, we excluded either the semidiurnal or diurnal tidal constituents from the tidal model, separately, and calculated the corresponding WRT for the two cases (hereinafter referred to as “NoSemidiurnal” and “NoDiurnal” cases, respectively). In addition, we, respectively, excluded the M₂ + S₂ and K₁ + O₁ constituents from the tidal model individually to examine the effect of interaction between the primary semidiurnal or diurnal tidal constituents (hereafter referred to as “NoM₂S₂” and “NoK₁O₁” cases, respectively). In the second group of experiments, we, respectively, excluded the M₂, S₂, K₁, and O₁ constituents from the tidal model individually and then calculated the corresponding WRT values for the six cases (hereafter referred to as “NoM₂”, “NoS₂”, “NoK₁”, and “NoO₁” cases, respectively).

2.5. Lagrangian Residual Currents

In coastal waters, the Lagrangian residual currents (LRCs) have been recognized as determinants of long-term water transport [32,33,34]. The tidal-driven Lagrangian residual currents (LRCs) in the BYS were diagnosed and analyzed to help understand the role of tides on the WRT. The LRC is defined as the net displacement of a labeled water parcel over one or multiple tidal cycles, divided by the corresponding time interval, which is calculated using the following equation [32,33]:

$$u_L\left(X, \tau ; t_0\right)=〈u\left[X_0+\xi \left(t; \tau \right), t; \tau \right]〉={\displaystyle \frac{{\xi }_{nr}}{nT}},$$

(2)

where $u_L$ represents the LRC; $X$ denotes the position vector; $X_0$ represents the initial position vector; t and τ represent the intra-tidal process-independent time and the inter-tidal process-independent time, respectively; $t_0$ is the initial time at which the water parcel is tracked; $u\left(X_0+\xi \left(t; \tau \right)\right)$ is the instantaneous velocity, where $u={\displaystyle \frac{\partial \xi }{\partial t}}$; $\xi \left(t; \tau \right)$ is the displacement of the water parcel, where $\xi =X-X_0$; ${\xi }_{nr}$ represents the net displacement of the water parcel over n tidal cycles; and T is the tidal period.

Based on Equation (2), we implemented a particle tracking model to determine the net displacement of particles after a period of 30 days (one month). The particle tracking model utilized in this study is derived from open-access code that has been previously employed in other studies, including the calculation of the LRC [15,35]. In the particle tracking model, a spatial linear interpolation method was implemented to derive velocity values at the particle locations, facilitating a smooth transition of velocity values between grid nodes and reducing the discontinuities of the current field. The LRC was calculated by dividing this net displacement by 30 days. At the initial time step, particles were released at the center of each grid cell of the tidal model. We computed the LRC for the sensitivity experiments in Section 2.3 and analyzed the LRC characteristics of tidal constituents. Although we lack data to validate the LRC, the correspondence between the LRC and the WRT presented below may offer some evidence supporting the model’s validity.

3. Results

3.1. Validation of the Tidal Simulation

The cotidal charts of the four principal tidal constituents (M₂, S₂, K₁, and O₁) in the BYS obtained from the tidal model are shown in Figure 2. The simulation results of our tidal model are consistent with the marine atlas of the BS and YS [36], the observations of the satellite altimeter [37], and numerical simulations [38,39,40], particularly showing high agreement in terms of amphidromic point locations and amplitude distribution. Furthermore, we validated the simulated tidal amplitudes and epochs of the tidal model against observations from tide gauge stations (Figure 3), which show high consistency with each other. The root mean square errors (RMSEs) of the amplitude for the M₂, S₂, K₁, and O₁ tidal constituents are 7.4 cm, 4.5 cm, 1.9 cm, and 2.1 cm, respectively, and the RMSE values of the epoch for these constituents are 10.6°, 9.2°, 5.1°, and 5.8°, respectively. Meanwhile, the modeled tidal current ellipse demonstrates strong consistency with the data from the TPXO8-atlas (Figure 3c,d). Therefore, the tidal model of the BYS established in this study can well represent the tidal characteristics and be reliable for simulating the tidal dynamic processes in the BYS.

3.2. Tidal-Driven WRT in the BYS

Driven by the tides in the BYS, the WRT was diagnosed using the WRT model. The spatially averaged WRT for the BYS, the BS, and the YS are 2.11 years, 2.40 years, and 2.05 years, respectively. Influenced by the tidal cycles, the spatially averaged WRT in the BYS exhibits a semidiurnal tidal variation (Figure 4a) and a spring–neap tidal cycle on a monthly scale (Figure 4b). However, these tidal variations are only approximately 4–6 days, which is small compared to the average WRT of 2.11 years for the BYS. Similarly, although there are significant differences in the WRT values across different experiments, the tidal variation within each experiment is negligible (Figure 4c).

In space, the WRT in the BYS exhibits significant inhomogeneity (Figure 5). Overall, the WRT is longer in the BS and relatively shorter in the YS. Specifically, the central and southern areas of BS, the central YS, and the southern waters off the Korean Peninsula are characterized by longer WRTs, reaching up to 3 to 6 years in the central BS and central YS. This indicates a lower rate of water exchange in these areas. In contrast, the coastal waters of the YS—particularly those of the Liaodong Peninsula, the northwestern side of the Korean Peninsula, the eastern side of the Shandong Peninsula, and along the southern waters of the Jiangsu coast—have shorter residence times, approximately 1 to 2 years, suggesting a faster water exchange in these regions.

3.3. Effects of Tidal Constituents on the WRT

Using the sensitivity experiments, the effects of different tidal constituents (semidiurnal tides, diurnal tides, and the four primary tidal constituents) on the WRT are investigated. In the NoSemidiurnal case, the average WRT values are 5.71 years in BYS, 3.86 years in BS, and 6.10 years in YS (

Table 1. The spatially averaged WRT in various regions for different sensitivity experiments.

Region	Control Run	NoSemidiurnal	NoDiurnal	NoM2S2	NoK1O1	NoM2	NoS2	NoK1	NoO1
BYS (year)	2.11	5.71	2.29	4.92	2.24	3.68	2.20	2.16	2.13
BS (year)	2.40	3.86	3.09	3.42	2.93	3.08	2.40	2.73	2.67
YS (year)	2.05	6.10	2.12	5.24	2.09	3.80	2.15	2.04	2.01

). Compared to the control run, the spatially averaged WRT in the BYS increases by 170% (Figure 6a). Figure 6b shows that the absence of semidiurnal tides leads to a significant increase in WRT across most areas of the YS and the center and south of the BS, with increases of up to approximately 3 years. This finding suggests that the semidiurnal tides significantly reduce the WRT and, thus, enhance water exchange in the BYS. In addition, the NoM₂S₂ case shows similar WRT and changes to those observed in the NoSemidiurnal case (Table 1 and Figure 6e,f), indicating that the two primary semidiurnal constituents, M₂ and S₂, could play major roles in the role of semidiurnal tides on the WRT.

In contrast, the NoDiurnal case with WRT values of 2.29 years in BYS, 3.09 years in BS, and 2.12 years in YS (Table 1) in the respective regions has a relatively small difference from the control run. The spatially averaged WRT in the BYS increases by only 8.5% compared to the control run. The spatial distribution of WRT in the NoDiurnal case (Figure 6c) is generally similar to that in the control run (Figure 5). The difference distribution (control run–NoDiurnal, Figure 6d) shows that in the NoDiurnal case, the change in WRT mainly occurs in BS. The change in BS is comparable to that in the NoM₂ case. The diurnal tides increase the WRT by 1 to 2 years in the central BS and decrease the WRT by about 3 years in the northwest of the BS. Overall, the semidiurnal tides have a more pronounced effect on the WRT than the diurnal tides, which is related to the stronger amplitude of the semidiurnal tides, while the effect of diurnal tides is mainly in the BS. Similarly, the two primary semidiurnal constituents, K₁ and O₁, play major roles in the role of diurnal tides on the WRT (Table 1 and Figure 6g,h).

The WRT results of the second group of numerical experiments are shown in Figure 7. In the NoM₂ case, the WRT in the BYS significantly increased, with a spatial average of 3.68 years, representing a 74.4% increase compared to the control run (Figure 7a). This increase is particularly pronounced in the central YS, where it reaches approximately 3 years. The WRT difference between the control run and the NoM₂ case (Figure 7b) further shows that the presence of the M₂ tidal constituent significantly reduces the WRT in most areas of the BYS, especially highlighting its crucial role in accelerating the water exchange of the YS. In the NoS₂ case, the spatially averaged WRT is 2.20 years, and the spatial distribution of the WRT (Figure 7c) is very similar to that of the control run. The WRT difference between the control run and NoS₂ (Figure 7d) further reveals no significant changes in WRT, suggesting a minimal impact from the S₂ tidal constituent. In the NoK₁ and NoO₁ cases, the spatially averaged WRT values are 2.16 and 2.13 years, respectively, and the spatial distributions of WRT are nearly identical (Figure 7e,g). Their differences with the control run (control run—NoK₁, Figure 7f; control run—NoO₁, Figure 7h) showed that the effects of the K₁ and O₁ tidal constituents are relatively strong in the BS, but weak in the YS.

Furthermore, the combination of the two experimental groups indicated that the WRT in the NoM₂S₂ case (4.92 years) is significantly longer than the WRT observed in both the NoM₂ (3.68 years) and NoS₂ (2.20 years) cases (see Table 1 and Figure 6 and Figure 7). This finding suggests that the interaction between the two primary semidiurnal constituents, M2 and S2, may also be critical in influencing WRT. Overall, the effects of the tidal constituents on the WRT in the BYS exhibit significant differences. The M₂ tidal constituent leads to a substantial decrease in the WRT, while the S₂, K₁, and O₁ tidal constituents have relatively minor effects on the WRT. The influence of the K1 and O₁ tidal constituents is primarily confined to the central and northern parts of the BS, while the S₂ tidal constituent has the least impact on water exchange in the BYS.

4. Discussion

4.1. Comparison with Previous Studies

In contrast to previous studies that examined water residence time (WRT) patterns or seasonal variations influenced by various dynamic processes, including tides, wind, and river discharge (e.g., Luo et al. [15]; Lin et al. [16]), the present study specifically investigates the WRT pattern driven solely by tidal forces, with a focus on the roles of different tidal constituents. Although this study employed the same WRT diagnostic methodology as the prior research, it utilized a different boundary for the calculations. Luo et al. [15] and Lin et al. [16] defined their boundaries at the Bohai Strait and the shelf break of the eastern shelf seas of China, whereas this study established its boundary at the interface between the Yellow Sea (YS) and the East China Sea. The variation in boundary definitions is likely to result in differing WRT estimates.

For instance, Lin et al. [16] reported average WRTs of 11.60 years in the Bohai Sea (BS) and 4.95 years in the YS, which are substantially longer than the WRTs found in this study (2.40 years and 2.05 years, respectively). Luo et al. [15] calculated an annual mean WRT of 3.43 years in the BS, slightly higher than the values reported here. This discrepancy may be attributed to the stratification present in the Bohai Sea, which may limit bottom water mixing and exchange, thereby prolonging the WRT.

Moreover, while the tidal-driven WRT exhibited similar values in the BS and YS in this study, Lin et al. [16] observed a significantly higher WRT in the BS compared to the YS. This finding suggests that other hydrodynamic processes, such as wind-driven currents, contribute to the increased disparity in WRT between the YS and BS. In the YS, strong wind-driven coastal currents and the warm current of the Yellow Sea facilitate water exchange. In contrast, in the BS, wind-driven currents may be hindered by shallower water depths and considerable bottom resistance, resulting in a much longer WRT compared to that in the YS [16].

4.2. Formation Mechanism of the Tidal-Driven WRT Pattern

The tidal-driven LRC in the BYS, which represents long-term transport by the tidal currents [33,34], is analyzed to understand the spatial patterns of the tidal-driven WRT. A comparison of the LRC (Figure 8) and the WRT (Figure 5) shows a significant spatial correlation. The LRC (Figure 8) is relatively weak in the central BS and the central YS, with flow speeds generally below 0.005 m/s, corresponding to the higher WRT observed in these areas (Figure 5). The weaker LRC in these regions facilitates water retention, thereby leading to a longer WRT. In contrast, coastal regions, such as the Liaodong Peninsula, Shandong Peninsula, Korean Peninsula, and the Jiangsu Coast, exhibit stronger LRCs, with local speeds reaching up to 0.02 m/s or more, corresponding to a lower WRT. Stronger LRCs in the coastal regions accelerate the water exchange rate, thereby reducing the WRT. In addition, the direction of the LRC also influences the WRT in the BYS. In the central BS and the central YS, the LRC exhibits eddy structures (Figure 8). These LRC eddies could trap the water inside the eddies to some extent and, thus, significantly extend the WRT in these regions (Figure 5). In nearshore regions, the LRC generally flows outward toward the open sea, such as along the coasts of the Liaodong and Shandong Peninsulas and Jiangsu. The LRC exhibits along-shore flow patterns that facilitate the transport of coastal waters offshore, thereby reducing the WRT in these regions.

Other processes, such as tidal pumping and tidal dispersion, may also influence water transport, particularly in proximity to topography. In the majority of this study, the terrain is relatively flat, which likely confines their effects primarily to the coastal regions. Furthermore, the spatial scale of the study area is approximately 1000 km, with a mean lateral residual current (LRC) of approximately 0.01 m/s (Figure 8). Consequently, the estimated water residence time (WRT) induced by the LRC is approximately 3.2 years, which closely aligns with the modeled WRT value. This suggests that the LRC is the predominant factor influencing the WRT within the overall system.

4.3. Roles of Different Tidal Constituents on the WRT

In the sensitivity experiments, the changes in the LRC for different tidal constituents can explain the changes in the WRT well. Compared to the control run results (Figure 8), the intensity of LRC in almost the entire BYS weakens in the NoSemidiurnal case (Figure 9a), with the most pronounced reduction occurring in the coastal regions, where the decrease reaches up to 0.02 m/s. The LRC reduction induces a slower water exchange rate and longer WRT (Figure 6a). The LRC induced by the semidiurnal tides (i.e., LRC in control run–NoSemidiurnal, Figure 9b) shows the strong currents along the coast of the BYS, indicating that the semidiurnal tides could facilitate the water export in the BYS mainly by inducing the coastal water transport. In the NoDiurnal case, the LRC is weakened in the central BS, while the LRC in the YS is generally similar to those in the control run (Figure 8 and Figure 9c). The difference in the LRC (control run–NoDiurnal, Figure 9d) indicates that the diurnal tide has a significant effect on the LRC in the BS, especially on the LRC eddy, and a minimal effect on the LRC in the YS. The diurnal tides enhance the LRC intensity in the coastal BS (Figure 9d), thereby reducing the WRT in the coastal BS. However, the diurnal tides also enhance the LRC eddy in the central BS, which exacerbates the trapping of the water in the central BS and, thus, increases the WRT in the central region (Figure 6d). In summary, both the semidiurnal and diurnal tidal constituents exert an influence on the LRC in the BYS. The semidiurnal tides primarily affect the intensity of the LRC along the coasts of the BYS, as well as the eddy structures in the central BS, thereby influencing the WRT in these regions. In contrast, the diurnal tides have a significant impact on the LRC intensity and eddy structures in the central BS, with minimal effects in other regions.

The significant influence of the interaction between M₂ and S₂ on the WRT is also supported by the stronger LRC in the NoM₂S₂ case compared to both the NoM₂ and NoS₂ cases. The superposition of M₂ and S₂ generates the spring–neap tidal cycle. During spring tides, the tidal currents are significantly intensified, leading to enhanced residual currents and water exchange. Although the tidal currents and water exchange are diminished during neap tides, the strengthening effect of spring tides on the water exchange may surpass the weakening effect of neap tides, indicating a non-linear interaction among tidal constituents that influences long-term water transport and WRT.

The LRCs of the NoM₂, NoS₂, NoK₁, and NoO₁ sensitivity experiments are shown in Figure 10a,c,e,g, respectively. By subtracting the LRCs of the sensitivity experiments from that of the control run, we can obtain the LRCs induced by M₂, S₂, K₁, and O₁ (Figure 10b,d,f,h), respectively. In comparison, M₂ induces strong LRCs along the coasts of the BYS and in the central BS (Figure 10b), suggesting the critical role of the M₂ tidal constituent in driving water exchange along the coasts of the BYS and in the central BS. Therefore, M₂ plays an important role in the long-term water transport and WRT pattern in the BYS. The S₂ tidal constituent has a relatively weak influence on the LRC in the entire BYS (Figure 10d) and, thus, a weak influence on the WRT. The K₁ and O₁ tidal constituents mainly influence the LRC in the BS (Figure 10f,h) and, thus, the WRT in the BS.

The different roles of the tidal constituents on the LRC and WRT could be related to their different tidal energies, as demonstrated by the significant correlation between the tidal energy and change in WRT (Figure 11a). The tidal energy (quantified using the square of the tidal amplitude [41]) of M₂ is mainly concentrated in the nearshore and shallow regions of the BYS (Figure 11b), which induces strong coastal tidal currents and LRCs and, thus, facilitates the water export of the BYS. The tidal energies of S₂, K₁, and O₁ are significantly lower than that of the M₂ constituent (Figure 11c–e). Because the M₂ constituent dominates the tidal energy and dynamics of the BYS (Figure 2 and Figure 11), exerting a primary influence on the WRT. Due to the tidal wave overlap of the S₂ with M₂, the contribution of the S₂ constituent on the LRC and WRT is limited, although the amplitude of S₂ is stronger than K₁ and O₁ (Figure 2). On the contrary, although the amplitudes of K₁ and O₁ are relatively small, they have a relatively high energy ratio to M₂ in the BS, particularly in the central BS around the M₂ amphidromic points (Figure 2 and Figure 11) and, thus, they can modulate the LRC in the BS, which can explain the pronounced effects of K₁ and O₁ on WRT in the BS.

5. Conclusions

This study examines the tidal-driven WRT in the BYS, elucidating the influence of various tidal constituents, including semidiurnal and diurnal tides, on WRT. We determined that the tidal-driven WRT values for BYS, BS, and YS are 2.11 years, 2.40 years, and 2.05 years, respectively. The tidal-driven WRT exhibits a significant spatially heterogeneous pattern, which correlates with the distribution of the tidal-driven LRC. Our results indicate that semidiurnal tides exert a greater influence on WRT compared to diurnal tides. Specifically, semidiurnal tides substantially decrease WRT across the entire BYS, whereas diurnal tides primarily affect WRT in the BS. The various tidal constituents have distinct effects on the spatial distribution of WRT. The M₂ tidal constituent is the most influential in reducing WRT and facilitating water exchange due to its predominant energy contribution within the tidal system. In contrast, K₁ and O₁ have more localized effects on WRT, particularly in the central BS, where their energy ratios relative to M₂ are relatively high. Although the amplitude of the S₂ constituent is greater than those of K₁ and O₁, its contribution to LRC and, consequently, to WRT is limited due to the overlapping tidal wave effects with M₂. This research enhances the understanding of the impact of tidal dynamics on long-term water transport and its associated timescales, which are crucial for improving our understanding and predictions of material transport and ecosystem dynamics in tidal-dominated environments.