The Yellow River Delta is characterized by high sediment load, fast accretion and frequent avulsions ( Figure 1A ). Over the last 2000 years, the sediment delivered by the YR was 1–1.1 × 10⁹ t/a (Milliman and Syvitski, 1992; Ganti et al., 2014). The lower course of the YRD has shifted more than 1593 times from 602BCE to 1938CE (according to the Yellow River Conservancy Commission). Since 1855, the modern YRD has prograded seaward at an average rate of approximately 150 m/a (Vangelder et al., 1994), accompanied by over 50 shifts of deltaic river courses (Zheng et al., 2017). Currently, three large artificial diversions of the main channel in the YRD were implemented since 1953. The deltaic channel has migrated from Shenxiangou (SXG) course (1953-1964) and Diaokouhe (DKH) course (1964-1976) to Qingshuiogu (QSG) course (1976-present). The active delta lobe has expanded seaward consistently since 1976, forming a spit-like feature extending 20 km seaward (Pelling et al., 2013).

The Bohai Sea is a semi-enclosed continental shelf sea situated in the northeastern region of China. Adjacent to megacities and hosting significant oil fields, it acts as a focal point for extensive economic and maritime activities (Tian et al., 2020; Wang et al., 2021). There are five regions in the BS: Liaodong Bay (LDB), Bohai Bay (BHB), Laizhou Bay (LZB), the central area, and Bohai Strait, which connects the BS to the northern Yellow Sea ( Figure 1C ). It spans approximately 555 km from northeast to southwest and about 350 km from west to east, covering a total area of 77000 km² with an average depth of 18 m (Wang et al., 2022). The tidal regime in the BS is dominated by irregular semi-diurnal tides, with the M₂ constituent being the principal tidal component (Lu et al., 2022). The tidal dynamics are relatively weak, characterized by an average tidal amplitude of 2 m and an average tidal flow velocity of 0.5–1.0 m/s (Wu et al., 2023a).

The dataset of daily flow and sediment load at the Lijin station (the most downstream hydrological station on the YR) was measured and provided by the Yellow River Conservancy Commission (YRCC). The shoreline and bathymetry data since 1962 were obtained and digitized from marine charts published by the Navigation Guarantee Department of the Chinese Navy Headquarters. The shoreline and bathymetry data in 1855 were digitized from the bathymetric maps studied by Wang and Huang (1988). These data were georeferenced and corrected to the same datum (corresponding to the low tide line). The static shoreline representation omits the differences between high and low tide lines. The mean width of intertidal zones along the YRD is approximately 2 km (Fan et al., 2018; Wang et al., 2020; Cao et al., 2023), spanning about one cross-shore grid cell at the model resolution. Considering the basin-scale focus of this study, the impact of using static shorelines on the overall tidal response is limited. This approach provides a consistent and measurable boundary for long-term modeling. Additionally, data of the delta land area was culled from the literature, which was extracted from remote-sensing satellite images and bathymetric surveys (Tang et al., 2020; Fu et al., 2021).

The water level and velocity (speed and direction) data used for model validation were collected through a field survey conducted during July 13-16, 2003. These datasets were obtained at three stations, O1 (117.73°E, 38.88°N), O2 (118.12°E, 38.85°N), and O3 (118.12°E, 38.58°N) ( Figure 1C ). Measurements were taken using a Conductivity-Temperature-Depth (CTD) and an Acoustic Doppler Current Profilers (ADCP), respectively. Tide levels at TG (117.78°E, 38.98°N) and QHD (119.62°E, 39.92°N) were obtained from tide tables during November 15-17, 2012.

To investigate how tide propagates in the bay under the influence of delta expansion, a theoretical model is established. The bay is idealized as a system with a constant width and water depth. Under the small-amplitude and Boussinesq assumptions, and neglecting the Coriolis force, conservation of mass and momentum equations are as Equations 6, 7

where Q = b h u is the tidal discharge, b is the width, u is depth averaged velocity, h is water depth, A is the cross-sectional area, η is the water level, g is gravity, F ~ C d u | u | is the frictional resistance, and C d is drag coefficient. In the absence of convective acceleration and friction, conservation of mass and momentum equations are as Equation 8

where L is the length of the basin, λ is the tidal wavelength. Further incorporating the friction into the analysis, the amplification ( A * ) with friction which has been linearized (Talke and Jay, 2020) as Equations 9-11

where λ 0 = T g h is the tidal wavelength, ω = 2 π / T is angular frequency, r = 3 π C d U / 8 h is the linearized friction coefficient, U is the velocity.

To investigate the overall impact of the delta expansion on the tidal regime in the BS, tidal flux during spring and neap tides were quantified across four profiles (P1-P4, as shown in Figure 1C ). The temporal variations of tidal flux in each profile are illustrated in Figure 4 , expressed as relative changes compared to the 2003 value. With the continuous advancement of the YRD coastline since 1855, tidal flux in the major bays exhibited an increasing trend. However, this trend is projected to reverse under future scenarios. The most significant changes occur in the LZB. As the delta coastline continues to advance after 2003, tidal flux is projected to rise by 6-10% in the initial decades, reaching its maximum under scenario R2. It subsequently begins to decline, with the largest reduction of 8.9% under scenario R4 relative to the 2003 levels. In the BHB, tidal flux reached the peak in 1981, and has since shown a decrease, with a maximum projected reduction of 11.5% under scenario R4. Similarly, the expansion of the delta after 2003 leads to a gradual decline in tidal flux in the LDB, with a maximum reduction of 6%. Tidal flux through the Bohai Strait under future scenarios also exhibits fluctuations, with a reduction of approximately 1%. Overall, the bays in the BS exhibit similar trends in tidal flux variation, with an initial increase followed by a decline. The LZB and BHB, which are adjacent to the YRD and have relatively smaller basin sizes, experience more pronounced variations. In contrast, the LDB, located farther from the delta and occupying a larger area, shows smaller fluctuations in tidal flux.

The spatial distribution of changes in maximum tidal flow velocity (V _max) under different delta coastline conditions during spring tides are shown in Figures 4E, F . Relative to 2003, changes in V _max under scenario R2 ( Figure 4E ) exhibit spatial inconsistency, ranging from -0.24 to 0.29 m/s. In the LZB, V _max shows a general increasing trend, with the greatest increase reaching up to 0.29 m/s. In contrast, both the BHB and LDB experience decline in V _max, with maximum reductions of 0.31 and 0.06 m/s, respectively. A slight increase is observed in the Bohai Strait, with the maximum increase of 0.04 m/s. The difference between scenarios R2 and R4 ( Figure 4F ) suggests that regions with enhanced flow velocities become spatially confined. While the LZB continues to exhibit increasing V _max, with a maximum increase of 0.25 m/s, most other regions of the BS experience further decline, with reductions of up to 0.37 m/s. The largest decrease occurs along the western margin of the YRD. These results indicate that the continued expansion of the delta induces a widespread reduction in tidal flow velocities throughout the BS, including the BHB, LDB and the central area, consistent with the changes in tidal flux. Conversely, the LZB experiences sustained intensification of tidal flow velocities. This localized enhancement is primarily attributed to the morphological shrinkage of the bay, which amplifies local hydrodynamics by concentrating flow within a reduced spatial domain (Hallock et al., 2003). Nevertheless, despite the amplified velocities, the concurrent reduction in bay area ultimately results in a net decrease in tidal flux through the LZB ( Figure 4A ).

Tidal dynamics play a crucial role in controlling sediment deposition and transport processes in the delta, and have also been altered by the delta expansion. Figure 5 illustrates the spatial evolution of tidal sediment transport capacity (T_s ) in response to historical and projected shoreline changes. During the initial stage in 1855, when the delta shoreline exhibited a smooth configuration, T_s in the estuarine region remained generally low ( Figure 5A ). The subsequent formation of distinct deltaic lobes through sediment deposition created morphological protrusions that modified local hydrodynamic conditions. These geomorphic changes accelerated tidal currents and enhanced T_s near the deltaic lobes. Specifically, the diversion of the deltaic river into the SXG course led to the formation of a new delta lobe by 1962, inducing localized increase in T_s nearshore ( Figure 5B ). This effect of coastline advancement became more pronounced by 1982, when the shoreline in the northern delta extended seaward by approximately 20 km due to the formation of the DKH lobe, resulting in markedly enhanced T_s along the northern delta front ( Figure 5C ). Subsequently, the evolution of the QSG lobe by 2003 resulted in a new center of high T_s in the southern delta front ( Figure 5D ). The tidal dynamics near the DKH lobe remain stronger than the QSG lobe, consistent with observed records (Wang and Liang, 2000).

Under future scenarios ( Figures 5E–H ), the continuous seaward progradation of the QSG lobe is projected to further intensify T_s near the active river mouth. In contrast, abandoned lobes in the northern delta exhibit a continuous decline in T_s , despite no additional shoreline modification being imposed on those areas. This spatial divergence highlights the non-uniform tidal responses to deltaic evolution, where modifications to one segment of the shoreline can influence tidal dynamics throughout the system. Additionally, while the use of different bathymetry data sources may introduce local discrepancies in tidal magnitude, the tidal evolution patterns observed in this study can be supported by previous studies. Specifically, Bai et al. (2019) simulated flow patterns near the YRD over the past 60 years, demonstrating high-flow-velocity zones closely related to the formation of sand spits in the river mouth; Zhan et al. (2020) indicated that tidal currents off the active delta lobe increased significantly with the progradation of the river mouth since 1976. Similarly, Wang et al. (2015a) revealed the strong tidal current areas shifted from the abandoned to the active river mouth after 1996, with increased flow velocities near the active mouth and a decline near the abandoned lobe. These studies can support the spatial divergence and changing trends captured in this study, that further highlight the feedback between deltaic morphological evolution and tidal dynamics.

Here, the propagation of M₂ tide, the dominant tidal constituent in the BS, is investigated by the theoretical model. Figure 6 illustrates the variation of amplification as a function of normalized length ( L / λ 0 ) and friction ( r / ω ) in the idealized bay. Resonance within the basin is identified at the peaks of the amplification lines. Changes in bay length make the basin approach or move away from the resonance. For basins with a length below the resonant frequency, tidal amplification increases with basin length. Conversely, for systems above this threshold, increasing length would decrease the amplification. The approximate positions of the historical and current YRD within this parameter space of M₂ constitute are shown in Figure 6 . Since 1855, expansion of the YRD into the BS has effectively shortened the tidal basin, thereby moving the system closer to resonance. However, the current YRD appears to lie near the threshold point. Further seaward expansion of the delta might shift the system beyond the resonant state, resulting in a gradual decrease of the tidal amplification. It indicates the nonlinear relationship between tidal dynamics and delta coastline evolution, consistent with the numerical simulations. Furthermore, beyond delta evolution, large-scale land reclamation also modifies the shoreline and constrains the bay geometry, producing impacts on tides. Zhu et al. (2018); Liu et al. (2023a), and Wu et al. (2023b) suggested that the land reclamation reduced tidal currents and tidal flux within the BS, leading to increase in residence time and decrease in water exchange capacity. Similar patterns have been observed in other estuary systems. In China’s Lingdingyang Bay, large-scale land reclamation projects have reduced tidal flux and weakened tidal currents (Chu et al., 2022). In contrast, the Ems Estuary of Germany has experienced enhanced tidal dynamics due to similar interventions (Chernetsky et al., 2010). These divergent responses are primarily driven by differences in their resonance state ( Figure 6 ). While this geometric control is fundamental, resonance in more physically realistic systems, however, is influenced by additional factors including depth variations, width convergence and bottom friction (Ralston et al., 2019; Larson et al., 2020; Gao et al., 2024). Changes in depth and width influence the progradation speed of tidal waves and frictional damping, thereby altering the resonant frequency and maximum amplification (Roos and Schuttelaars, 2011; Ensing et al., 2015). As shown in Figure 6 , changes in water depth (h) could modify both friction ( r / ω ) and tidal wavelength ( λ 0 ), and increased friction ( r / ω ) reduces the maximum amplification. Despite the simplifications used in the model, it still provides valuable insights into how the resonance might be altered by geometry changes (Talke and Jay, 2020), as it captures the dominant tidal constituent and characteristic scales of the BS.

Furthermore, the simulation results reveal an intensification of local tidal dynamics near the active deltaic lobe and in the adjacent LZB. As the active delta lobe shoreline protrudes seaward, the convex shoreline geometry accelerates tidal currents in the nearshore regions. This process is analogous to flow around a bluff body, where fluid passing a body with a broad cross-section experiences flow separation and local acceleration due to pressure gradients and streamline deflection (Bearman, 1984). Similarly, the advancing delta lobe acts as a bluff obstacle in the tidal flow field, enhancing nearshore velocities.

The YRD evolves under changing tidal conditions. The YR has discharged into a shallow embayment following the shift of the river mouth from the DKH to QSG course in 1976. Weak tidal currents near the river mouth have favored sediment accumulation on the delta plain and accelerated the infilling of the shallow embayment for land building (Zhang et al., 2018). Previous studies examined that over 70% of the sediment delivered by the YR was deposited within the nearshore region (Zhou et al., 2020), exceeding the 50–60% deposition rate observed at the abandoned lobes (Dong, 1997), where the tidal currents were stronger. Tidal dynamics and sediment transport capacity near the active QSG lobe are projected to enhance with the continued progradation of the river mouth. However, it should be noted that such intensification depends on the elongation of the river mouth, which could elevate the base level of the perched lower YR and increase the risk of overbank flooding (Shi et al., 2019; Zheng et al., 2019). Meanwhile, tidal dynamics near the abandoned DKH lobe weakens with the expansion of the active lobe. There is an alternative flow path within the DKH lobe, which could potentially replace the current QSG course or serve as a flood diversion channel (Qian et al., 2023). However, the decline in tidal currents might hinder sediment dispersal and promote further sedimentation in the standby river mouth. This trend poses challenges to the long-term morphological stability of the delta and may affect its resilience to future changes.

Furthermore, the progressive seaward expansion of the YRD acts as a protruding boundary that disrupts the propagation and reflection of tidal waves. This morphological evolution is projected to diminish tidal currents and reduce tidal flux across the major bays. The BHB, where major ports like Caofeidian and Huanghua are located, shows a significant decline in tidal currents. The weakened tidal dynamics could reduce natural sediment flushing and dispersal in navigation channels (Song et al., 2013; Huang et al., 2023), accelerating siltation in port basins and increasing reliance on dredging operations, thus elevating maintenance costs (Fuller et al., 2024; Deng et al., 2025). In addition, diminished tidal dynamics could increase the water residence time within the basin (Wisha et al., 2018; Wu et al., 2023b). This prolonged retention directly elevates the risk of eutrophication by allowing nutrients from riverine inputs and coastal activities to accumulate (Mundaca et al., 2025) and fueling persistent phytoplankton blooms (Ouyang et al., 2023), including harmful algal blooms (Song et al., 2016). Meanwhile, the accumulation of pollutants such as heavy metals and microplastics might also be exacerbated, posing chronic threats to marine organisms and ecosystem health (Li et al., 2018). Moreover, the loss of tidal mixing could promote stratification of the water column and reduce vertical exchange of oxygen, increasing the likelihood of hypoxic or even anoxic conditions in bottom waters (Zhang et al., 2022a; Wu et al., 2025). The hypoxic emerges as a major threat to marine biodiversity, leading to mass death of benthic organisms and disrupting the structure and function of marine ecosystems (Rakocinski et al., 2023; Thompson et al., 2023). Reduced growth and reproduction linked to poor water conditions also lead to substantial declines in fishery yields and economic losses for coastal communities (Huang et al., 2010; Liu et al., 2023b). Given the limited environmental capacity and ecological vulnerability of the BS, tidal weakening induced by delta expansion warrants attention in coastal management.

To evaluate the robustness of the simulation results, an uncertainty analysis was conducted focusing on key parameters including friction (quantified by Manning coefficients) and grid resolution. Manning coefficients were varied from 0.014 to 0.020 relative to the baseline value of 0.0165. Water levels and tidal flow velocities during spring tide were analyzed at three representative sites for comparison (LZ, BH, and LD; see Figure 1C ). Variations in Manning coefficients primarily affected the magnitude of water levels and tidal currents, with increased friction leading to reduced tidal dynamics ( Figures 7A–F ). Meanwhile, minimal phase shifts were observed, indicating little impact on the simulated trend in tidal responses. To examine spatial resolution sensitivity, simulations were performed using both the original 1.5 km grid and a refined 0.75 km grid. The refined mesh resulted in only minor differences in tidal currents, with the RMSE values for simulated velocities below 0.015 m/s ( Figures 7G–I ). These results suggest that the baseline grid resolution is adequate for capturing the basin-scale tidal dynamics.

This study estimates the tidal evolution across the BS to long-term expansion of the YRD. While the findings offer valuable insights into geometry-tidal feedbacks and their implications for coastal sustainability, certain limitations regarding the method should be acknowledged. First, the use of static shorelines neglects short-term morphological changes, which may affect nearshore hydrodynamics at finer spatial scales (Cao et al., 2023). Second, the analysis focuses solely on tidal dynamics, whereas other processes such as wind-waves, especially during winter storms, could temporarily enhance water levels and currents in estuaries (Zhao et al., 2025). In addition, the two-dimensional model does not account for density-stratification effects which may influence sediment deposition processes in the river mouth during flood events (Wu et al., 2023a). These factors operate at distinct spatiotemporal scales and are worth being considered in future work to achieve a more comprehensive understanding of coupled estuarine dynamics.