INTRODUCTION

The Bohai Sea is a semi-enclosed sea with shallow water (Figure 1a), which average water depth is only 18 m, surrounded by cities in the north Chinese Sea. In the Bohai Sea barotropic tides are the dominant circulation processes, having considerable amplitudes as well as momentum and energy fluxes. Because of the effects of enhanced bottom friction associated with shallow shelf topography, tides and tidal residual currents play an important role in affecting many other physical and biogeochemical processes in this region (Wei et al., 2003).

Figure 1.

(a) The bathymetry (depth in m) and positions of 14 tide-gauges in the Bohai Sea. Black stars show the location of tidal gauges. (b) The distribution of sea level rising trend (mm/yr) during 1993–2012 in the Bohai Sea

Accelerated economic development and large land reclamation have changed the coastline along the Bohai Sea. In the western Bohai Bay the large land reclamation of about 129.7 km² (SOAPRC, 2009), and to the northeast of Laizou Bay an artificial island of 35.2 km² was built, which both reconstructed the coastline. Since the shift of the Yellow River mouth has influenced the amphidromic points of M₂ to move (Wang et al., 2014), Huang et al. (2015) evaluated the influence of coastline modification in the Bohai Sea based on four different coastlines of 2000, 2008, 2010, and 2012, and found that the changed coastlines could move the amphidromic point and modify tide amplitudes, especially making the amphidromic point near the Yellow River estuary move towards south-east. Therefore it is important to use the newest coastline and accurate topography for tide models in the Bohai Sea.

It is an irrefutable fact that global warming causes sea level to rise. Accelerated sea level rise (SLR) can drastically affect coastal regions, such as submerging and increased flooding of lower-land. Except for these direct effect of increased high water level, on longer term scale SLR could influence tidal system (Pelling et al., 2013a; 2013b; Pickering et al., 2012; Zhang et al., 2013). The basic physical consequence to such changes is the variation in tidal dynamics (Chu-Agor et al., 2011; Muller et al., 2011; Pickering et al., 2012; Poulos et al., 2009; Snoussi et al., 2009; Ward et al., 2012). Some studies have shown that SLR has a direct effect on coastal tides. On the European shelf Pickering et al. (2012) found that tidal response of M₂ is nonlinear to future SLR with spatial variation in amplitude. Ward et al. (2012) studied the different effects of the way of SLR implemented in the model, flooding could intensify the response caused by SLR (Pelling and Green, 2013), the main difference of tidal response was found in the Bohai Bay and Liaodong Bay between flood and no-flood, but very small difference between flood and partial-flood (Pelling et al., 2013b). Gong et al. (2012) studied the effects of sea level rise on Yangtze estuary and found that tidal wave changed slightly in nearshore areas. Zhang et al. (2013) studied the tidal system changes due to sea level rise in China, and found that the enhanced amplitude was in the north to amphidromic point, while phase lags were increased to the eastern. The residual currents could be reduced by 20% caused by SLR change in narrow and shallow channels in Portuguese (Valentim et al., 2013). As a major forcing agent SLR could present a substantial influence on coastal erosion worldwide (Cooper and Pilkey, 2004; FitzGerald et al., 2008; Leatherman et al., 2000). To the Yellow River Delta tidal current was one of main factors causing coastal erosion (Ji and Jiang, 1994). All the results showed that future SLR has significant impacts on the tidal amplitudes, currents and associated tidal dissipation.

There have been many results about tide modeling in Chinese Sea (Bao et al., 2001; Fang et al., 2004; Kang et al., 2002; Lefèvre et al., 2000; Song et al., 2013; Wang et al., 2014; Yao et al., 2012; Yu et al., 2003). Some Chinese scientists have studied the effects of SLR on Chinese Sea (Kuang et al., 2014; Yu et al., 2003, 2007), but the conclusions were not consistent, especially the changes of tidal range and phase lags in local Bohai Sea. The influences of SLR on tides depend on local sea level rise and particular coast morphology. In the Bohai Sea from 1993 to 2012 the average satellite altimetry data show that mean sea level had a rising rate of about 3.8 mm/yr in the Bohai Sea, much faster than global average (Church and White, 2006) in Figure 1b. All these conclusions about effects of SLR on coastal tides are most based on a uniform value of SLR, however, there are few studies considering the spatial distribution difference of SLR. To evaluate the potential influence accurately caused by future sea level rise, in this study we use a hydrodynamic model to simulate the tide in Bohai Sea with newest coastline, and according the present sea level rising rate to assess the influence of SLR on tides and residual currents in the Bohai Sea in the future of one hundred years.

This paper is organized as follows: model configuration is described in detail in Section 2, and model results are shown in Section 3, and then followed a discussion and conclusion.

MODEL AND METHODS

Tidal energy flux and dissipation

The tidal energy flux was calculated according to (Greenberg 1979):

where ρ₀ is the density of seawater, taken as 1,026 kg/m³, h is the local depth in meters, η is the sea level fluctuations due to tides, u, v are the depth-averaged tidal currents components from the ROMS solutions and g is the gravitational acceleration, 9.8m/s². The integration is averaged over M₂ tidal period T (i.e., 12.42 h).

Mathematically, the tidal energy dissipation can be calculated following the scheme proposed by (Munk, 1997; Taylor, 1919):

Where C_d is the bottom friction coefficient taken as 0.0012 in our case, the other variables are the same as the above mentioned formula (1) for tidal energy flux. This formula is based on the quadratic bottom stress scheme, which is consistent with our ROMS model configurations.

Model validation

The basic validation was performed to ensure the model was correctly reproducing the observed tide. There were 14 sets of tidal harmonics for validation derived from tidal gauge and published scientific journals (Chen et al., 2011; Li et al., 2011; Wang et al., 2014; Yao et al., 2012; Figure 1a). Because semi-diurnal signal predominated in most parts of the Bohai Sea, we only showed the validation of M₂. Figure 2 showed the accuracy of our simulation. There were two amphidromic points located in Bohai Sea (Figure 2a): one at the offshore area of Qinhuangdao and one near the mouth of the Yellow River, which agreed well with previous publications (Bao et al., 2001; Fang et al., 2004; Yu et al., 2003), and with the new coastline, the changes of Yellow River Delta influenced its surrounding tidal wave and obstructed tidal energy here (Pelling et al., 2013a), the amphidromic point near Old Yellow River Mouth has moved to southeast (Hao et al., 2010). Figure 2b and 2c showed the linear-fit between simulations and observed amplitude and phase lag, respectively, and compared to previous studies (Bao et al., 2001; Song et al., 2013; Zhu and Liu, 2012) the average absolute error of amplitude in this paper is 3.6 cm, and phase error is 7.2°, we also used the variance to quantify the model results, where R_o is the root mean squared of observed values and R_m is the root mean squared difference between model and observations (Pelling et al., 2013b). The modeled M₂ amplitudes and phases both achieved a variance captured of 99.4%, which indicated that the errors are well controlled in the whole region, in general the established model of Bohai Sea could capture the tide correctly.

Figure 2.

Simulation verification. (a): Cotidal-chart of four main constituents (M_2, S_2, K_1, O₁), dashed line is for amplitude in meter, solid line is phase lag in degree; (b): Comparison between simulated and observed amplitude of M₂; (c): Comparison of phase of M₂

RESULTS

Changes of amplitude and phase

Figure 3 showed the responses of M₂ amplitude and phase to 1 m SLR. When the depth of Bohai Sea increased 1 meter, there exits certain distribution patterns in the differences between the amplitude and phase with different increment of sea level. Figure 3a displays obvious distribution in amplitude change of M_2, there are two areas where amplitude increases (shaded area), one is near the Yellow River Delta and the other in the Liaodong Bay, and the maximum increment of amplitude reached up to 5.5 cm. In the central Bohai basin, Laizhou Bay, Bohai Bay, and northeast of Liaodong Bay, SLR caused amplitude of M₂ to decrease, and the maximum decrement of 12cm appeared in the Laizhou Bay. The spatial distribution pattern of changed amplitude was similar to the result of Pelling et al. (2013b) with 2m SLR. However, compared to maximum decrement of 10 cm based on 2m SLR (Pelling et al., 2013b), the discrepancy was mainly caused by flooding. Flooding along the coast could increase energy dissipation, weaken the propagation of reflected tidal wave. The changes of M₂ phase showed a notable distribution. There are some regulations in changes of co-phases, it seems that on the western part near Qinhuangdao (site 7, marked in Figure 1a), co-tidal phase decreased anti-clockwise, while on the right phase lag increased clockwise (Figure 3b); and the same situation appeared in the Yellow River Delta, which was in most agreement with the theoretical model results (Yu et al., 2003), but inconsistent with previous conclusions (Yu et al., 2007), which showed that co-tidal phase changed in a same anti-clockwise direction.

Figure 3.

(a) Changes of amplitude of M₂ with SLR 1 meter (unit, cm), the shaded area are where amplitude increases. (b) Shift of co-phase lines near Qinhuangdao Island (black circle) due to different value of SLR and (c) changes near Yellow River Delta (unit: degree), black solid line is the present state, dashed line is SLR 0.5 m, and dot-line is SLR 1 m

Obviously SLR has changed the characteristics of tide, it can also influence the amphidromic point positions of tidal waves shift relatively to those of current tidal waves. In the shallow water, tidal wave propagated more quickly and wavelength increased with SLR increase, which would shift the amphidromic points. Table 1 showed the movements of amphidromic points under different SLR conditions. It was clear to see the migration of two amphidromic points, one amphidromic point near Yellow River Mouth moved to southeast due to SLR (Yao et al., 2012; Yu et al., 2007), and the other near Qinhuangdao moved to southwest (also shown in Figure 3b), which would change tidal phase lag.

Table 1.

The location of amphidromic point of M₂ constituent under different SLR conditions

Change of tidal energy

According to formula (1) we calculated the tidal energy flux distribution in Bohai Sea in different SLR scenario. The simulated current state (no SLR) of M₂ tidal energy flux (Figure 4a) reached a good agreement with results from Song et al. (2013) and Yao et al. (2012). The tidal energy flux came into the Bohai Sea along the 50 m isobaths through the Bohai Strait, which broke into two branches: one branch turns northward into the Liaodong Bay and the remaining moves westward into the Bohai Sea interior (Zhu and Liu, 2012). And in the Bohai Sea, the maximum tidal energy appeared in the Laotieshan Channel, less than 5 GW, far less than that of Yellow Sea (Yao et al., 2012). The mean tidal energy dissipation was also calculated using formula (2) and analyzed to study the changes of tidal energy dissipation in different SLR scenario. The spatial pattern of mean tidal energy dissipation of control run (0 m SLR) was also consistent with previous studies of tidal energy (Kang et al., 2002; Song et al., 2013; Yao et al., 2012), with the largest energy dissipation occurred near coast, especially where coastline was irregular (not shown). Specifically, three sections were chosen to evaluate the effects of SLR on tidal energy (Figure 4b), it was clear to see that with SLR tidal energy entered into the Bohai Sea was decreased by increased energy dissipation, the tidal energy that entered into the Bohai Bay and Laizhou Bay also decreased. At the same condition of SLR increment, tidal energy through the Strait decreased more than those entering into the bays, which implied that with the propagation of tidal wave, the SLR effects on tidal energy decreased gradually.

Figure 4.

(a) Tidal energy flux of M₂ and energy flux vectors are plotted every three grid points (unit: W m^−1, shown as logarithmic values base on 10). (b) Changes of tidal energy in three sections with different SLR, the positive values are energy flowing into Bohai Sea (blue solid line) or Bohai Bay (solid line) and Laizhou Bay (dashed line) with unit of GW, and tidal energy dissipation rate in A section (red dashed line, unit: W/m²⁾

Change of tidal current

The characteristics of tidal currents can be depicted by the depth-averaged tidal current ellipses (Figure 5a). In the Bohai Sea, the strongest tidal currents are seen in the Bohai Bay with a maximum speed of about 0.6 m s⁻¹ in west-east reversing flow. The weakest current occurs in the Laizhou Bay with a speed of only 0.1 ~ 0.2 m s⁻¹. The tidal currents in the center of Bohai Sea and Laizhou Bay behave as clockwise rotating currents rather than reversing ones appeared in Liaodong and Bohai Bays. And the tidal residual current has been recognized to play an important role influencing long-term sediment and other materials transport (Li et al., 2005; Wei et al., 2004). The mean residual currents in the interior of Bohai Sea are rather small, only of the order of a few cm s^−1, and larger residual currents appeared near coast, no more than 5 cm s⁻¹. In the Bohai Bay there was a weak, cyclonic gyre, and there was an anticyclone gyre southwest to Liaodong Peninsula, in the Bohai Strait, the mean tidal residual current flowed out the strait in the southern part and came into Bohai Sea in the northern (not shown). The simulation captured main characteristics of tidal currents.

Figure 5.

(a) Detail distribution of tidal current ellipsefor M₂, tidal ellipses are plotted every 6 grid points. The dashed (solid) ellipse shows the tidal ellipses rotate clockwise (counter-clockwise). (b) Tidal speed curves (m/s) from different SLR scenario at 4 ports. The five sea level scenarios are shown 0 m (black line), 1 m (red line), 2 m (mauve line), 3 m (green line), and 100 years (blue dashed line). Note that the ports are marked in Figure 1a

The changes in tidal energy act to influence tidal current as well. Four sites (where there was large human activity) were chosen to evaluate the changes caused by SLR (Figure 5b). It was clear to see that changes of tidal current was different in areas, in the Bohai Bay (site 8 and 9), influenced by sea level rise, tidal current speed was weakened, and there was a minor shift in time of maximum tidal current. In the Laizhou Bay (site 12) tidal current increased influenced by sea level-rise, and with SLR 3m scenario, tidal current could increased 5 cm/s, and in site 6 which located near Liaodong Bay, the effect of SLR on tidal current was small with little change in current speed.

DISCUSSION

Recently quick coastline changes caused by natural process and anthropogenic activity had influenced tidal system in the coastal zone (Huang et al., 2015; Pelling et al., 2013c; Wang et al., 2014). Compared to coastline changes SLR is a relative slow and imperceptible process, however, the long-time affection of sea level rise can not only increase the risk of extreme water level but also influence tidal dynamic system. As coastline change was mainly induced by anthropogenic reclamation, recent coastline was kept unchanged for future projection when evaluating the affection induced by SLR. In the shallow water equation, sea level rise increased water depth, which led to intensify the propagation of waves and modify the reflected and incident waves. The tidal amplitude responds to SLR in a spatially non-uniform manner, with substantial amplitude decreases and increases in different SLR scenarios. To get details we choose four sites (marked in Figure 1a with 6, 8, 9 and 12, respectively) to compare the effects of different SLR scenario (Figure 6). Detailed examinations show that the amplitude of M₂ responded appropriately linearly to uniform SLR (Figure 6a), but was not proportional to SLR. Influenced by 0.5 m SLR, the maximum of increased (decreased) M₂ amplitude was 3 (8) cm, the maximum increment changed to 5 cm with 1m SLR, 11 cm with 2 m SLR scenario, and 15 cm under 3 m SLR condition. However, with the combination effects of water depth and bottom friction, the tidal energy dissipation (Figure 6b) showed a nonlinear response to different increment of sea level, which is not consistent with amplitude changes.

Figure 6.

(a) M₂ amplitude response curves for station 6, 8, 9 and 12 (positions see Figure 1a); (b) The tidal energy dissipation at these four stations (shown as logarithmic values base on 10). The filled signals in the above two panels are values influenced by spatial distribution of SLR after one hundred years. (c) Water level curves (m) from different SLR scenario at 4 ports. The five sea level scenarios are shown 0 m (black line), 1 m (red line), 2 m (mauve line), 3 m (green line), and 100 years (blue dashed line)

The way of SLR implemented in the models could lead to qualitatively different results (Pelling et al., 2013a; Pelling and Green, 2013; Ward et al., 2012). Pickering et al. (2012) using a drying and flooding cell to study the effects of SLR with 2m and 10m on European shelf, found that the tidal amplitude effects was complex and non-linear to SLR. Most previous results used uniform SLR to study and predict its effects on coast in the future, neglected the spatial pattern of SLR in the domain. It was clearly to see that the effects of uniform SLR were much more different compared to effects of spatial pattern SLR (Figure 6a and b, marked with filled symbols). As Figure 1b showed, maximum rising trend of sea level was in Bohai Bay, from 5 mm/yr to 8 mm/yr, much larger than other areas of Bohai Sea. We assumed that the sea level trend keep constant, in the future after one hundred years the mean sea level in the Bohai Sea increased only 0.2 ~ 0.8 m and distributed spatially, simulation result showed that the effect was stronger than that of uniform SLR with 1 meter, even equivalent to effects of SLR with 2 meter, only considering amplitude changes (Figure 6a); and also in the migration of amphidromic points (Table 1), in the future the movement caused by spatial-distribution of SLR variation was farther than that caused by uniform SLR. Because tides in the Bohai Sea was forced by ocean tides from the Pacific, the wave frequency remains constant, as depth increased with the SLR the tidal wave propagates more quickly in the domain. With the spatial distribution of sea level-rise, tidal wave propagated into the Bohai Sea from adjoining sea, influenced by local changed depth, finally the accumulated results led to a complex and non-linear response to SLR (Figure 6c).

The changes caused by sea level-rise act to change tidal currents as well. As Figure 7a showed, there are three domains that residual currents changed dramatically, though maximum variance values are of the order of a few cm s⁻¹. The distribution of residual current change was similar to that of tidal energy change (not shown), which illustrated that the increment of tidal energy increased residual current. Compared Figure 7a and 7b, SLR with 1 meter mainly strengthened the effects caused by SLR 0.5 m, however, compared to the results between uniform SLR with 0.5m and spatial distrubiton-SLR after one hundred years (Figure 7a and 7c), the effects were intensified by spatial distribution of sea level rise, especially in Bohai Bay, where quicker rising rate of sea level increased local water level much more compared to other areas (Figure 1b), the local increased water depth would reduce incident waves and change reflected waves, which led to the increment of the residual current. Considering the spatial distribution of sea level variation, the influence of SLR was intenser than that of uniform variation. The migration of amphidromic points also showed the non-linear response between experiment case 0.5 and case100y (Table 1). As Zhou et al. (2015) confirmed that tidal current flow is indeed the main agent for transporting the fine sediment to the mud patch in the central South Yellow Sea, the changed tidal and residual currents caused by SLR were also related to the long-term transport of sediment in the Bohai Sea (Ji and Jiang, 1994; Li et al., 2005; Wei et al., 2004), for example near the Yellow River Delta weakened residual current may decrease the sediment transport outside and accumulate more sediment in the Delta. And in the Bohai Bay SLR decreased the residual currents, would increase the risk of port siltation.

Figure 7.

(a) Changes of tidal residual current between control run and uniform 0.5 m SLR run. (b) Changes of tidal residual current between control run and uniform 1 m SLR run. (c) Difference of effects from spatial distribution SLR run after one hundred years and uniform SLR 0.5 m. Values of both images are scaled by log₁₀ with unit of m s⁻¹

CONCLUSION

The influence of sea level rise on tides in the Bohai Sea was assessed by a series of numerical experiments using ROMS model. The scenario of spatial distribution of SLR case was projected in the future keeping the present sea level rising trend derived from altimeter data after one hundred years, and the results were compared with other cases under different SLR conditions of uniform increment of water level from 0.5 m to 3 m.

The modeled results show that with synchronous increment of sea level, changes of M₂ amplitude responded to SLR non-proportionally, and showed a non-linear response. The M₂ amplitudes increased only around the two amphidromic points influenced by sea level rise. Due to the shape of coastline (headland etc.), changed bottom friction affected tidal energy flux and moved the amphidromic points to deep water under sea level rise conditions. Rising sea level increased water depth, combined local effect of sea level, it indeed reduced/increased tidal currents and residual currents, especially along coasts, which would change long-term sediment transport and influence the coastal erosion (Li et al., 2005; Wei et al., 2004). Simulated results showed that the response of tide regime was complex to spatial distribution of sea level rise and stronger than that from uniform rise of sea level, which illustrated the importance of considering spatial distribution of sea level rising when evaluating the risk of SLR in the future.