The water temperature in the Bohai Sea varies with the seasons ( Figures 4a–d ). Influenced by the water depth, the coastal region warms up more rapidly in spring. The temperature is relatively high at the heads of Laizhou Bay, Bohai Bay, and Liaodong Bay, and low in the central region of Bohai Sea. In summer, the maximum water temperature of the Bohai Sea is about 29 °C. The temperature is slightly lower in the central Bohai Sea. In autumn, the coastal region is cooled faster than the offshore area, resulting in lower water temperature than the offshore area. In winter, the water temperature in the northern part of Liaodong Bay and the western part of Bohai Bay is below 0°C, while the temperature in the central region of the Bohai Sea and the Bohai Strait is about 4°C. This distribution is caused by a high-water temperature tongue that intrudes from the Yellow Sea through the northern Bohai Strait. The above seasonal variations in the water temperature given by the model are consistent with previous models and observations (Wang et al., 2008; Liu et al., 2003). It is worth noting that there is no sea ice module in this model. In winter, there is an area with floating ice in Liaodong Bay, but its impact on the water flux in the Bohai Strait is small (Zhang et al., 2019).

The salinity in the Bohai Sea is mainly affected by the Yellow River and Liaohe River ( Figures 4e–h ). The extension direction of the Yellow River plume varies with seasons. In winter, driven by the northerly wind, the Yellow River plume extends into Laizhou Bay. In spring, under the influence of tide-induced residual current, the low-salinity water from the Yellow River propagates northwestward to the southeastern Bohai Bay (Yu et al., 2021). In summer, influenced by the southerly wind, lower-salinity water expands northeastward to the central Bohai Sea. In autumn, when wind turns southward, low-salinity water moves southward along the coast of Laizhou Bay. The discharge of Liaohe River is largest in summer, inducing low salinity around the head of Liaodong Bay. Due to the increase in river discharge in summer, the salinity in the Bohai Sea is lowest in summer. The high salinity (>30 psu) area in the central Bohai Sea is larger in autumn and winter than in summer. Besides the river runoff, the salinity in the central Bohai Sea is also influenced by the intrusion of high-salinity water from the Yellow Sea via the northern Bohai Strait. The seasonal variations in the surface salinity given by the model are consistent with previous model results and observations (Wang et al., 2008; Liu et al., 2003).

The residual current in the Bohai Sea is affected by the monsoon ( Figures 4i–l ). In winter, the prevailing northwesterly winds over the Bohai Sea ( Figure 2a ) induce southwestward currents in the surface layer, and the current velocity is below 5 cm/s in most areas. The surface residual current flows out of the Bohai Sea through the southern channel of the Bohai Strait and into the Bohai Sea from the northern channel of the strait. In spring, the south-southwesterly winds prevail over the Bohai Sea ( Figure 2b ), generating east-northeastward surface residual currents over most of the Bohai Sea. Compared with winter, the circulation is enhanced in spring with a speed of about 6 cm/s in most areas and the surface flow is mainly eastward in the Bohai Strait. Influenced by the southeasterly winds ( Figure 2c ), the Yellow River plume extends northeastward in summer. Eastward residual currents exist at the southern channel and westward currents in the northern channel of the Bohai Strait. In autumn, the winds turn southward in the Bohai Sea, inducing southward residual current in the surface layer. The circulation in the Bohai Sea and Bohai Strait in autumn is similar to that in winter but its magnitude is stronger. Throughout the year, the eastward residual current in the southern strait is strongest in summer with a speed up to 10 cm/s.

In the Bohai Strait, the water temperature is vertically homogeneous in autumn and winter and stratified in the northern channel in spring and summer ( Figures 5a–d ). The water temperature is lowest in winter (-0.8°C) and highest in summer (26.7°C). Salinity is nearly vertically homogeneous except for the northern channel in summer ( Figures 5e–h ). Although the Yellow River discharge is not the largest in winter ( Figure 3 ), the salinity in the southern channel of the strait is the lowest (~ 28.7 psu) in winter ( Figure 5e ). Similarly, although the Yellow River discharge is highest in summer, the salinity in the southern channel is not the lowest (~ 30.5 psu) ( Figure 5g ). The structures of water temperature and salinity at the strait given by the model are basically consistent with the observations of Wu et al. (2019) and Zhang et al. (2010).

The residual current in the strait includes two parts: a westward current in the narrow area of the northern strait, and a two-layered current in the wide southern strait ( Figures 5i–l ). However, during the autumn season, the current in the southern strait is exclusively oriented eastward. The westward current in the northern strait exhibits considerable strength, with a maximum speed of ~31.6 cm/s, and demonstrates little seasonal variation. The two-layered current in the southern strait shows a strong outflow in the surface layer and a weak inflow in the bottom layer. The surface outflow is strongest in summer, with a maximum speed of 10.4 cm/s. The bottom inflow is at its peak in spring and weaker in summer and winter. This “north-in and south-out” water exchange structure is generally consistent with the previous modeling studies (Ji et al., 2019; Liu et al., 2021). The weak inflow at the bottom layer of the southern strait was observed in May by Wu et al. (2019).

In order to assess the seasonal variation of water flux through the Bohai Strait, we calculate the net water flux, outflow flux, and inflow flux through the Bohai Strait using the following formula during the model run, and then de-tide the hourly output of water flux.

Where u is the horizontal velocity that is oriented perpendicular to the Bohai Strait section, h is the bottom depth, η is the surface elevation, the integration in the y direction is from the south to the north along the full section across the Bohai Strait, σ is the sigma coordinate and the integration is from the sea surface to the sea bottom.

The volume transport of the outflow is strongest (9.49×10⁴ m³/s) in September and weakest in November (5.88×10⁴ m³/s), with an annual average of 7.09×10⁴ m³/s ( Figure 6a ). The volume transport of the inflow is similar, strongest (9.38×10⁴ m³/s) in September and weakest in November (5.65×10⁴ m³/s) ( Figure 6b ). The annually averaged transport of inflow is about 7.04×10⁴ m³/s which is slightly smaller than the annual mean of outflow. The net volume transport through the strait has an annual mean of 470 m³/s ( Figure 6c ). The seasonal variation of the net water flux through the strait is different from that of the outflow and inflow but bears similarity to that of sum of the river discharges into the Bohai Sea (red dashed line in Figure 3 ). The net water flux after 15-day running mean is largest (0.46×10⁴ m³/s) in July, and smallest (-0.39×10⁴ m³/s) in December. The half-month oscillation of the water flux in Figure 6 is caused by the fortnightly variation of tides.

In order to investigate the formation of the residual current structure in the Bohai Strait, we separate the residual current into the tide-induced residual current, wind-driven current, and density-driven current through five numerical experiments ( Table 1 ). Case 1 is the control case, whose results have been presented in Section 3. Case 2a is driven by tide only. In case 2a, the temperature is fixed at 10°C, the salinity at 32 psu, and both the residual current and surface elevation at the open boundary are fixed at 0. The results of Case 2a represent the tide-induced residual current. In Case 2b, the open boundary conditions are the same as those in Case 1, and the remaining conditions are consistent with Case 2a. Case 2b is used to be subtracted from Case 3 and Case 4 to obtain the corresponding currents. Case 3 adds the wind stress to Case 2b and the difference between Case 3 and Case 2b represents the wind-driven current under a barotropic condition. Case 4 restarts from the result of Case 1 at the beginning of February, May, August, and November, respectively, and is calculated for one month without wind stress. Consequently, the difference between Case 1 and Case 4 represents the wind-driven current under a baroclinic condition. Additionally, the difference between Case 4 and Case 2b primarily represents the density-driven current in the Bohai Sea.

In Case 2a, where tide is the only external forcing, the model result indicates that the seasonal variation of tide-induced residual current is small ( Figures 7a–d ). A strong westward current, with a maximum current speed of up to 29.88 cm/s, exists in the narrow area close to the northern strait. In the close south of this structure, an eastward current exists, with a maximum velocity of 3.98 cm/s, stronger in the bottom than in the surface layer. This current structure is likely associated with nonlinear effect near the cape. Weak outward currents can be found in the broad area of the southern strait. Consequently, the tide-induced residual current partly contributes to the flow pattern of “north in and south out” in the Bohai Strait.

The characteristics of wind-driven current under barotropic conditions ( Figures 7e–h ) and baroclinic conditions ( Figures 7i–l ) exhibit notable similarities, with the latter demonstrating a marginally greater intensity. In autumn and winter, the currents flow westward in the northern area and eastward in the southern area of the strait ( Figures 7e, h, i, and l ). This current structure is influenced by the prevailing northwesterly wind, which facilitates the movement of seawater from the Bohai Sea towards the southern region of the strait. This process subsequently generates an eastward current in the southern section and a compensatory westward current in the northern section of the strait (Wang et al., 2008). In spring, the current transitions to a two-layer structure, with outflow in the surface layer and inflow in the bottom layer ( Figures 7f, j ). The magnitude of velocity becomes a little stronger in spring than in winter. In summer, the wind-induced current is relatively weak ( Figures 7g, k ). The wind-driven current is the strongest in autumn and weakest in summer.

The density-driven current exhibits a more complex structure ( Figures 7m–p ). The current in the northern part of the strait is characterized by a “north in and south out” flow pattern, which is consistent with Wei et al. (2003). Moreover, it is strongest in summer and weakest in autumn. The current in the southern part of the strait is a two-layered structure in all seasons, which is outward in the surface layer and inward in the bottom layer. The outward current is stronger than the inward current and is strongest in summer and weakest in autumn. This current structure should be induced by the horizontal density gradient in the strait.

Consequently, we conclude that the inflow in the narrow area of northern strait is predominantly induced by the tide-induced residual current. The two-layered structure in the southern strait is primarily induced by the density-driven current. The wholly outward flow in the south in autumn is attributed to the wind-driven current.

We also calculate the monthly averaged water exchange flux through the Bohai Strait induced by the four factors ( Figure 8 ). Compared with the volume fluxes due to other processes, the tide-induced net water flux is small with the largest value of 322 m³/s in spring ( Figure 8a ); the outflow and inflow fluxes are large but with a weak seasonal variation ( Figures 8b, c ). The net water flux induced by wind-driven current under both barotropic and baroclinic conditions has the largest value (~1.50×10³ m³/s and ~1.88×10³ m³/s) in autumn. The net water flux induced by density-driven current is significantly stronger in summer (~4.36×10³ m³/s) than in other seasons, and it dominates the net water exchange volume in summer. The outflow and inflow fluxes induced by density-driven current are also greatest in summer, and are larger than fluxes induced by other factors. Consequently, the density-driven current in summer is critical to water exchange through the Bohai Strait.

Here, to investigate the response of the Bohai Strait to the Yellow River discharge during the WSRS in 2022, we carried out an additional numerical experiment (Case 5), which uses one tenth of the Yellow River discharge in 2022 but keeps the same other conditions as Case 1. The difference in Yellow River discharge between Case 1 and Case 5 (0.9 times YR discharge, green line in Figure 9a ) was largest in July, with a maximum difference of 3555 m³/s. Case 5 also runs for two years as Case 1.

The model result shows that the response of the net water flux through the Bohai Strait (dashed line in Figure 9a ) is almost synchronous with the variation in the discharge of the Yellow River between Case 1 and Case 5 (green line in Figure 9a ). The maximum difference of net flux between these two cases occurs in early July, consistent with that of the Yellow River discharge. However, the response of inflow/outflow is more complicated, and appears to be a combination of synchronous and asynchronous response with the variation of Yellow River discharge ( Figures 9b, c ). During the first 7 months of year 1, the difference in outflow (and to a less extent inflow) between Case 1 and Case 5 follows the difference in the discharge of the Yellow River (with a maximum in July). After the first 7 months, the difference in outflow/inflow shows a delayed response to the difference in river discharge. The difference in outflow/inflow shows a large increase in December of year 1, and then maintains at a high level with a peak value in March of year 2. In fact, the differences in outflow/inflow in the two years are quite different, suggesting that the differences can be mostly related to baroclinic instead of barotropic dynamics, likely the delayed response to Yellow River discharge.

The synchronous response of the net water flux through the Bohai Strait to the Yellow River discharge can be explained by the variation in the sea surface elevation. The sea surface elevation from the Yellow River mouth to the Bohai Strait is low during low Yellow River discharge period from January to May ( Figure 10 ). As the Yellow River discharge increases from late June, the sea surface elevation at the Yellow River mouth rises, and it quickly propagates to the Bohai Strait. Therefore, the immediate response of the net water flux through the Bohai Strait is affected by the barotropic adjustment. This immediate response of the net water flux also appears at the response of inflow/outflow at the Bohai Strait.

The lag in the response of inflow/outflow flux through the Bohai Strait to the variation in the discharge from the Yellow River can be explained by the seasonal behavior of the Yellow River plume. As shown in section 3.1, the Yellow River plume extends northeastward in summer ( Figure 4g ), and turns southward into Laizhou Bay in autumn ( Figure 4h ). In winter, the low-salinity water arrives at the northeast coast of Laizhou Bay and flows out through the southern Bohai Strait ( Figure 4e ). According to the variation of inflow/outflow flux difference (dashed lines in Figures 9b, c ), the low-salinity water starts to arrive at the Bohai Strait in second January, while the accumulated low-salinity water largely arrives in second March. Therefore, we know that it takes ~9 months for the strongest signal of variation in the discharge to arrive at the strait.

This modelled lagged phenomenon is also found in surveys around the Yellow River estuary. Researchers from Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, carried out field surveys around the Yellow River estuary from May 8-12, June 8-12, July 18–22 and November 5–11 of 2022, and February 2–7 of 2023. Surface salinity was measured at a depth of 2 meters. The spatial distribution of salinity around the Yellow River Estuary was plotted by linear interpolation ( Figures 11b–f ). In May and June, when the Yellow River discharge was relatively low (~500 m³/s, Figure 11a ), the Yellow River plume extended northward ( Figures 11b, c ). In July, as the river discharge increased, a corresponding decrease in salinity was noted around the river mouth, and the low-salinity water flows toward the northeast under the influence of the dominant southeasterly wind in summer ( Figure 11d ). In November, the low-salinity water extended southward into the Laizhou Bay ( Figure 11e ), and finally arrived at the southern strait in February ( Figure 11f ). The salinity at the southern strait is lowest in February, although the Yellow River discharge is not high in February. Due to the lack of observations in January and March, we conclude that the Yellow River water discharged in early July arrived at the southern strait until 8 months later in the following February.

To further examine this lagged phenomenon, we carried out a tracer numerical experiment. Due to the implementation of the WSRS, the discharge of the Yellow River surged on June 22, 2022. Based on the above model, we released passive tracer at the surface of the Yellow River mouth on June 22 for three days, with the tracer concentration of 1. The advection-diffusion Equation 1 was used to calculate the tracer concentration.

where N represents the tracer concentration, t means the time, V → is the velocity, K N represents the vertical turbulent mixing coefficient, and D N represents the horizontal diffusion term. The tracer was modelled for one year.

The model result shows that the tracer concentration in the strait is close to zero in July and August ( Figures 12a, b ), indicating that tracer has not yet reached the Bohai Strait. Little tracer arrives at the southern channel from September to November ( Figures 12c–e ). The highest tracer concentration is found in the southern channel in December and the following January ( Figures 12f, g ), indicating that the tracer flows out through the southern Bohai Strait at this time. After that, the tracer concentration gradually decreases ( Figures 12h–l ).

Time series of tracer concentrations at 24 stations from the Yellow River mouth to the strait (red triangles in Figure 1b ) show that the tracer is concentrated at stations 1–4 in July and August ( Figure 13 ). In September, tracer concentrations at stations 5–10 increase rapidly, indicating that tracer is moving along the coast of Laizhou Bay. The highest tracer concentrations in the Bohai Strait (No. 18) appear in December and January of the following year. A large amount of tracer arrives at the Bohai Strait, coinciding with the outflow volume increase in January ( Figure 9b ). Due to the short releasing duration (3 days), the tracer concentration does not show a second peak in March as that of outflow flux. Consequently, it can be concluded that the influence of the Yellow River discharge on the density-driven current through the Bohai Strait lags the discharge by ~7 months.