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Home , Amphidromic point, Bohai Bay, China Seas, Coastline of China, Gulf of Tonkin, Korea Bay

Journal of Coastal Research 00 0 000–000 Coconut Creek, Florida Month 0000 Influence of Potential Future -Level Rise on in the Sea Cuiping Kuang†*, Huidi Liang†, Xiaodan Mao†, Bryan Karney‡, Jie Gu§, Hongcheng Huang†, Wei Chen†, and Honglin Song†

†College of Civil Engineering ‡College of Civil Engineering §College of Marine Sciences Tongji University University of Toronto University Shanghai 200092, China Toronto M5S 1A4, Canada Shanghai 201306, China

ABSTRACT

Kuang, C.; Liang, H.; Mao, X.; Karney, B.; Gu, J.; Huang, H.; Chen, W., and Song, H., 0000. Influence of potential future sea-level rise on tides in the China Sea. Journal of Coastal Research, 00(0), 000–000. Coconut Creek (Florida), ISSN 0749-0208.

This study investigates the diurnal and semidiurnal tidal responses of the entire China Sea to a potential rise in of 0.5–2 m. A modified two-dimensional tidal model based on MIKE21 is primarily configured and validated for the present situation; then, three (0.5, 1, 2 m) sea-level rise (SLR) scenarios are simulated with this model. The predicted results show that the principal lunar semidiurnal (M2) and diurnal (K1) tidal constituents respond to SLR in a spatially nonuniform manner. Generally, changes of M2 and K1 in shallow are larger than those in the , and significant tidal alterations mainly occur in the Bohai and Yellow , Jianghua , Bay, Taiwan , River , Pearl River estuary, and Beibu Bay. Possible mechanisms further discussed for these changes mainly relate to bottom friction decreasing, migration, and resonant effect change. Additionally, simulated changes in M2 and K1 amplitudes in response to three SLR scenarios imply that M2 changes are proportional to the magnitude of SLR, whereas this proportionality does not hold for K1 amplitudes. Identifying the response of tides in the China Sea to SLR not only increases our knowledge of tidal systems, but also assists in setting conservation requirements and management plans in coastal areas.

ADDTIONAL INDEX WORDS: Tidal regime change, migration of amphidromes, numerical simulation.

INTRODUCTION m global rise in sea level as a pragmatic range for a A rising sea level related to climate change is likely to temperature rise of 48C. redistribute tidal and to influence coastal areas SLR has been identified as a major threat to coastal habits strongly. Ocean thermal expansion and loss are and communities worldwide. On one hand, SLR itself could the two dominant contributors to global mean sea-level rise greatly increase flood risk and erosion of beaches by elevating (SLR) (Church et al., 2013). The observed average rate of global levels (Bacopoulos and Hagen, 2014; Brunel and SLR was 1.8 mm/y from 1961 to 2003, but accelerated to 3.1 Sabatier, 2009; Kont, Jaagus, and Aunap, 2003; Snoussi et mm/y from 1993 to 2003 according to the Fifth Assessment al., 2009; Testut et al., 2016) in coastal areas, affecting Report (AR5) of the Intergovernmental Panel on Climate , destroying coastal habitats (Kuang et al., 2014; Change (IPCC; Church et al., 2013). Although there has been McInnes et al., 2003; Xie et al., 2015), and endangering the almost 2000 years of moderate fluctuation in sea level, the and property of coastal dwellers. On the other hand, SLR could expected global SLR is unprecedented (Ward, Green, and interact with tides and storm surges, which are expected to Pelling, 2012). Specifically for the China Sea, an average rate of alter tidal regimes (Passeri et al., 2015; Pelling and Green, 2014; Pickering et al., 2012), contribute to extreme water levels þ3 mm/y was observed from 1980 to 2014 (State Oceanic (Arns et al., 2015; Smith et al., 2010; Warner and Tissot, 2012), Administration, 2015), and sea level in 2012 reached its and have other effects related to saline water intrusion (Chen et maximum at 122 mm higher than the average. This SLR is al., 2016) and coastal structures (Cheon and Suh, 2016; Xie et expected to continue to rise through the 21st century, but its al., 2015). Moreover, morphological changes in barrier islands, value varies with spatial scale and climate change scenario. , and beaches (Biria et al., 2015; Kuiry, Ding, and Without considering the contributions of sheets and glacier Wang, 2014; Nicholls and Cazenave, 2010; van der Wegen, melting, the sea level in the (BS), (YS), 2013) may be strongly affected by SLR. and (ECS) will rise about 0.12 to 0.2 m (Chen et In practice, the influence of SLR interacting with tides, which al., 2014; Cheng, Xu, and Zhang, 2015). Although global SLR changes tidal dynamics and energy, is more profound than that projections to the late 21st century by the IPCC AR5 range from of SLR itself. A number of modeling studies have been 0.52 to 0.98 m, Nicholls et al. (2010) advocated using a 0.5–2.0- conducted into how past or future SLR interacts with the global tides. On the European Shelf, principal lunar semidiur- DOI: 10.2112/JCOASTRES-D-16-00057.1 received 2 April 2016; nal (M2) tidal amplitude responds to SLR in a spatially accepted in revision 31 May, 2016; corrected proofs received 21 July 2016; published pre-print online 1 September 2016. nonuniform manner with substantial amplitude increases *Corresponding author: [email protected] and decreases as SLR (Pickering et al., 2012), and permanent ÓCoastal Education and Research Foundation, Inc. 2016 flooding of new significantly alters the response of the 0 Kuang et al.

Figure 1. Study domain of the entire China Sea and positions of 39 gauges used for model validation. tides to SLR (Pelling and Green, 2014; Ward, Green, and induced circulation and complex bottom topography (Zu, Gan, Pelling, 2012). Specifically, significant increases in extreme and Erofeeva, 2008). For these reasons, researchers have often water levels and of extreme coastal storm surge divided the China Sea into ECS and SCS for numerical analysis events are relative to SLR in both the United Kingdom and of the corresponding tides (Pelling, Uehara, and Green, 2013; Germany (Arns et al., 2015; Lowe, Gregory, and Flather, 2001). Zu, Gan, and Erofeeva, 2008) and have generally agreed on the In SE Louisiana, the increase of surge is as much as double and ECS tidal regime (Cheng, Xu, and Zhang, 2015; Fang, 1986; triple the SLR over broad areas and as much as five times the Lin et al., 1997; Shen, 1980; Wang, Fang, and Feng, 1999; Ye SLR in isolated areas (Smith et al., 2010). Dynamic flooding and Mei, 1995; Ye and Robinson, 1983; Yu and Zhang, 1987; (considered the interaction between tides and SLR) outweighs Zhang, 2005). However, the spatial characteristics of the static flooding (only SLR) by a factor of 4/3–5/3 in Apalachicola amplitude, phase, and amphidromic points in the SCS are still Bay, Florida (Bacopoulos and Hagen, 2014), and the occur- disputed (Fang et al., 1999; Li et al., 2002; Shen et al., 1985; Ye rences of tidal flooding also increase with SLR in (Kruel, and Robinson, 1983; Yu, 1984), particularly the number and 2015). In the China Sea, the effect of SLR on tides has been distribution of amphidromic points associated with the of investigated in BS (Pelling, Uehara, and Green, 2013) and ECS Thailand. The domains in those studies didn’t cover the entire (Gao, 2008; Yan, Zuo, and Chen, 2010). However, little China Sea, and because their open boundaries are relatively systematic has been done on the entire China Sea (Figure close to the study area, there is a risk that the boundary 1), which is the goal of the current study. conditions may have unduly influenced the simulation. The entire China Sea (Figure 1) comprises the BS, YS, ECS, Recently, Zhang et al. (2013) developed a numerical model of and Sea (SCS). The SCS links with the in the NW Pacific, including the entire China Sea, to study both the south, with the through several narrow channels the tidal system and the tidal changes due to a 0.9-m SLR in the between the Philippine Islands, and directly with the Pacific marginal seas near China. Because only one SLR scenario was through the highly energetic Luzon Strait in the south of considered, the effects of continually changing sea level were Taiwan (Green and David, 2013). The BS has special not considered. Although considerable published work sug- characteristics, being semienclosed by the , Liao- gests that tidal changes are often proportional to SLR, neither dong, and Korean peninsulas and exchanging energy with YS this assumption nor that of spatial uniformity can be clarified through the Bohai Strait. The regional tidal dynamics in those with a single SLR scenario. Because morphological adjust- areas are complicated because of the different local - ments were rarely simulated (Pelling, Uehara, and Green,

Journal of Coastal Research, Vol. 00, No. 0, 0000 Influence of Sea-Level Rise on Tides in China Sea 0

2013) and the bottom friction coefficient was usually assumed to be constant (Pelling and Green, 2014; Ward, Green, and Pelling, 2012), other uncertainties were not addressed. This study assesses the potential effect of future SLR on the China Sea, in the first instance by assessing the effect of SLR on the semidiurnal M2 tidal constituent and its diurnal (K1) counterpart. The second objective is to capture the tidal responses along the coastline around Chinese mainland and to evaluate the linearity of the response. To address these objectives, a high-resolution two-dimensional (2D) tidal model based on MIKE 21 Flow Model is developed. The simulation assumed the 0.5-m SLR value, which is a high-probability event and is often taken as the lower limit of possible SLR changes in this century; 1 m is next taken as middle or most likely scenario, and the 2-m change is taken as the upper limit to cover a reasonable range of possible changes over this century. These scenarios are used first to capture the potential tidal changes and to assess the linearity of the tidal response to Figure 2. Computational mesh in the study domain. SLR. The next section describes the numerical tidal model and its validation, and the following two discusses the predictive to 418 N and from 998 E to 1288 E, covering the entire China results. Finally, both the mechanisms of tidal changes and Sea, the , the Sulu Sea, the Luzon Strait, and potential influences of SLR on the main coastal ports of China portions of the western Pacific Ocean. An unstructured mesh is are discussed. used to avoid the ‘‘staircase’’ problem at (Jones and METHODS Davies, 2007; Quinn, Atkinson, and Wells, 2012), and divides the into 12,491 nodes and 23,205 triangle elements A two-dimensional depth-averaged barotropic tidal model (Figure 2). The finest mesh length is ,1 km (associated with based on the MIKE 21 model suite of the Danish Hydraulic the mesh refinements in the PRE, YRE, and BS), and the Institute (DHI) is established to study tidal response of the maximum is approximately 110 km at the eastern open China Sea to potential future SLR. boundary. The bathymetric data, interpolated into the model Numerical Model mesh, was obtained from two sources, including ETOPO5 data MIKE 21 Flow Model is a state-of-the-art numerical provided by National Geophysical Data Center with 10 modeling system developed by DHI for complex application resolution and high-resolution nautical charts in shallow within oceanographic, coastal, and estuarine environments. waters. This system is based on numerical approximation of two- The model was driven by the astronomic tidal level derived dimensional incompressible Reynolds-averaged Navier–Stokes from a global tidal model (Cheng and Andersen, 2011) equations invoking the assumptions of Boussinesq and hydro- implemented in MIKE 21. In this model, eight major tidal static pressure (DHI, 2013). The spatial discretization of the constituents (M2,S2,K1,O1,N2,K2,P1,Q1) are prescribed at all governing equations is performed using a cell-centered finite open boundaries, which accounted for most of the tidal energy method. The spatial domain is discretized into in the diurnal and semidiurnal tides. nonoverlapping triangular or quadrilateral elements. MIKE 21 Flow Model has been successfully applied from local to Parameter Settings regional scales, with studies based on it in the past including The model solves the shallow-water equations for surface the characteristics of the routes of the tidal current and its tidal elevation (g) and depth-averaged current vector (u), and regime in ECS (Liu, 2012), the hydrodynamic influence of SLR performs discretization in solution domain using a cell- in YRE (Chen et al., 2016; Kuang et al., 2014), the tidal regime centered finite volume method. The governing equations are in the China Sea (Zhang, 2007), and effect of SLR on storm given by: surge in the (Arns et al., 2015). MIKE 21 Flow Model ]g þ Ñ ðDuÞ¼0 ð1Þ is able to model coupled processes, e.g., coupling among ]t currents, , and , which has been applied to study the hydro-sedimentological interactions in Lianyungang ]Du þðu ÑÞDu þ kf 3 Du ¼gDÑg c juju þ A DÑ2 ð2Þ Harbor (Xie, Zhang, and Guo, 2010) and fine-grained ]t d h transport in the southern YS (Xing, Wang, and Wang, 2012; Xu where t is time; Ñ is the horizontal gradient operator; D¼Hþg et al., 2016). Further information concerning MIKE 21 can be is water depth, in which H is the undisturbed depth; f is the found online (DHI, 2016). parameter; k is the vertical unit vector; g is the 2 1/3 Model Setup gravitational constant; cd ¼ g/(M D ) is the bottom friction To minimize deviation of model results from the approxima- coefficient in inverse proportion of water depth D and Manning tion of open boundary conditions and incorporate more number M; and Ah is the horizontal coefficient. adjacent seas, the model domain (Figure 1) extends from 38 N The horizontal eddy viscosity is herein specified by the

Journal of Coastal Research, Vol. 00, No. 0, 0000 0 Kuang et al.

Table 1. Parameter settings in the numerical model. Two different approaches induce SLR into simulations: changing the boundary conditions and increasing mean sea Parameters Setting Value level by changing the . The former is the most Time Step (s) 0.0001–30 widely used method for simulating responses of tidal dynamic Manning number (m1/3/s) 50–100 Smagorinsky coefficient 0.28 to SLR (Huang et al., 2015; Qiu and Zhu, 2015; Yang et al.,

hdry (m) 0.005 2015; Zhang et al., 2013; Zhou et al., 2013); Pickering et al. hflood (m) 0.05 (2012), especially, induced the SLR into the model covering the hwet (m) 0.1 whole European Shelf by increasing the boundary tidal levels. This study assumed that the SLR induced from the deep sea Smagorinsky formulation, with the Smagorinsky coefficient and the SLR across the domain was nonuniform, so the specified at its default value of 0.28. To better describe bed simulations were made by only adding 0.5, 1, and 2 m to the roughness, a spatially varied Manning field for the bottom open boundaries. The model used a cold start, with 0, 0.3, 0.6, friction is calculated by an empirical formula of water depth in and 0.9 m as four initial conditions, respectively, at the first shallow water. More specifically, the Manning number varies step. This method involves increasing the water depth but not 1/3 over the range 50–100 m /s in shallow water. allowing new areas to flood, assuming that the land boundaries The Courant Friedrich Levy (CFL) number is defined as of the basin are maintained by coastal defense works. To better isolate the pure effects induced by SLR and to avoid random pffiffiffiffiffiffiffi Dt pffiffiffiffiffiffiffi Dt CFL ¼ð gD þjujÞ þð gD þjvjÞ ð3Þ interference, the wind factor was not invoked. All the Dx Dy simulations started from 29 April 2009 for the available where u and v are the velocity components in the x and y validation data. The Tidal Analysis of Heights (the program directions, Dx and Dy are characteristic length scales in the x for the analysis of tidal heights comprised by the MIKE 21 and y directions for an element, and Dt is the time step. The Toolbox) was used to conduct harmonic analysis to extract tidal water depth and velocity components are evaluated at the constituent amplitudes and phases. The model was run for 360 center of each element. The numerical scheme is stable if CFL days, with the first 10 days for initiation and the harmonic , 1.0. The self-regulated time steps range from 0.0001 to 30 analysis performed on the last 350 days. seconds, so that the CFL restriction is met for all computational Model Validation nodes and time steps. Computed values of M2 and K1 amplitudes and phases at the To reproduce the intermittent appearance of the tidal flat 39 tidal gauges are compared with observed values from while maintaining accuracy, wet-dry moving boundaries are Admiralty Tide Tables (Zhang, 2005) in Figure 3. The average adopted. Depth thresholds in each element are used to classify absolute deviations between computed and observed ampli- each element as drying, flooding, and wetting (DHI, 2013), with tudes of M2 and K1 are 0.09 and 0.06 m, respectively, whereas threshold depths of 0.005, 0.05 and 0.1 m, respectively (Kuang the deviations of the M2 and K1 phases are 108 and 68, et al., 2014). Parameter settings are summarized in Table 1. respectively. There is generally good agreement for both

Figure 3. Correlation of harmonic constants (amplitude and phase of M2 and K1) between observed and computed values at 39 gauges.

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Table 2. Comparison of the locations of M2 amphidromic points under Table 3. Comparison of the locations of K1 amphidromic points under PSL. PSL. Location of Location of Sea Amphidromic Point Reference Coordinates Sea Amphidromic Point Reference Coordinates BS Bohai Strait Shen (1980) 388050 N, 1208450 E BS Near Shen (1980) 398450 N, 1208300 E Fang (1986) 388100 N, 1208500 E Fang (1986) 398400 N, 1208100 E Zhang (2005) 388130 N, 1208440 E Zhang (2005) 398580 N, 1198550 E This study 388250 N, 1208500 E This study 398500 N, 1208200 E YS North Sea Shen (1980) 348300 N, 1228100 E Outside the entrance Shen (1980) 388200 N, 1198100 E Fang (1986) 338500 N, 1238000 E of the Fang (1986) 388050 N, 1198000 E Zhang (2005) 348130 N, 1238390 E Zhang (2005) 388070 N, 1198080 E This study 348150 N, 1238140 E This study 388140 N, 1198080 E YS Outside Shen (1980) 378400 N, 1238100 E River, and two others are outside the cities of Chengshanjiao Chengshanjiao Fang (1986) 378300 N, 1238050 E Zhang (2005) 378350 N, 1238120 E and Lianyungang, respectively. (These positions are shown in This study 378500 N, 1238080 E Figure 1.) In the Gulf of Thailand a degraded amphidromic Outside Lianyungang Shen (1980) 348400 N, 1218200 E point can be observed; however, whether the amphidromic 0 0 Fang (1986) 34840 N, 121840 E point is degenerate has been debated (Fang et al., 1999; Li et al., Zhang (2005) 348340 N, 1218260 E This study 348370 N, 1208390 E 2002; Yu, 1984). Diurnal tides K1 and O1 have similar distribution features; that is, two amphidromic points are formed in the central areas amplitude and phases of M2 and K1 tides. The correlation of the BS and YS, respectively, and no amphidromic point is coefficients of M2 amplitude, M2 phase, K1 amplitude, and K1 phase are 0.96, 0.98, 0.93 and 0.98, respectively, showing an found in the SCS. The relatively high amplitude zones appear in , , Jianghua Bay, Beibu Bay, and the overall robust relation (.0.90). North Gulf of Thailand. The maximum amplitudes of K and O The locations of the amphidromic points can be obtained by 1 1 occur in the North Gulf of Thailand, with a value of 0.58 m, and interpolation based on the positions of the minimum tidal in Beibu Bay, with a value of 0.45 m. It is noteworthy that in amplitude. Tables 2 and 3 list the locations of amphidromic the SCS the tidal amplitude increases gradually toward the SW points of M and K obtained from different studies (Fang, 2 1 after passing through the Luzon Strait from the Pacific. 1986; Shen, 1980; Zhang, 2005). Clearly the locations of the The modeled distributions of amplitudes, phases, and amphidromic points under present sea level (PSL) in this study amphidromic points of M ,S,K,andO are consistent with are reasonable, a validation that generally supports the 2 2 1 1 previous studies (Fang, 1986; Lin et al., 1997; Shen, 1980; applicability of the tidal simulation in the China Sea. Wang, Fang, and Feng, 1999; Ye and Mei, 1995; Zhang, 2005). Specifically, the tidal regimes in the SCS are also identified by RESULTS Zu, Gan, and Erofeeva (2008). These consistencies demonstrate To study the effects of SLR on the China Sea tides, the water that our model nicely captured the tidal regimes in China Sea level at the open boundary is raised by 0.5, 1, and 2 m, under PSL, which is a reasonable basis for predicting the tides respectively; the associated shape of the tides at the open under different SLR scenarios. boundary is independent of SLR, and other conditions were kept the same as used in the PSL scenario. Detailed results Migration of Amphidromic Points of M2 and K1 from first show the tidal constituents regime under PSL then Potential Future SLR demonstrate the migration of M2 and K1 amphidromic points The locations of amphidromic points would change under the and changes of M2 and K1 amplitude and phase due to SLR. SLR scenarios. Hence, this section focuses on the migration of Finally, the results elucidate the linearity of the amplitude M2 and K1 amphidromic points, which represent semidiurnal responses and the effect on ports. tide and diurnal tide, respectively. Figure 5 shows the amphidromic point locations of M2 in BS M2,S2,K1, and O1 Tidal Constituents of the China Sea and YS under PSL (the base situation), as well as three other under PSL SLR scenarios (0.5, 1, and 2-m SLRs). Under the 0.5-m SLR To further test model results and obtain detailed tidal scenario, the amphidromic points change little compared with characteristics, we extracted the harmonic constants of M2, the base situation. However, the amphidromic points outside S2,K1,andO1 over the entire study domain for the PSL the entrance of the Yellow River and the city of Chengshanjiao condition, which are shown in the cotidal charts in Figure 4. move to the east, reaching up to the maximum migration of 200 The M2 and S2 amplitudes are generally smaller (,0.4 and 0.2 (29 km) under the 2-m SLR scenario. Meanwhile, the m, respectively) in the central part of the SCS, whereas the amphidromic points near Qinhuangdao and outside Lianyun- tidal amplitudes across the are larger in gang move SW and NE, respectively, but their displacements Korea Bay, Jianghua Bay, South Jiangsu Sea, YRE, Hangzhou are ,50 (17 km).

Bay, coastal areas, and the . The Figure 6 presents the amphidromic point locations of K1 in maximum amplitudes of M2 and S2 can reach 2.8 and 0.9 m, BS and the North Jiangsu Sea under PSL and three SLR respectively, in the concave coastlines of Jianghua Bay. Of the scenarios. The amphidromic point in the Bohai Strait initially four amphidromic points in the China Sea, one is near the city moves to the east under the 0.5-m SLR but migrates no farther of Qinhuangdao, one is outside the entrance of the Yellow with greater values of SLR. The amphidromic point in the

Journal of Coastal Research, Vol. 00, No. 0, 0000 0 Kuang et al.

Figure 4. Cotidal charts of the M2,S2,K1, and O1 tidal constituents in PSL. Patches give amplitude (m), solid lines with values indicate phase (8).

North Jiangsu Sea generally moves SE relative to its current that the amphidromic points generally moved to the east, position. Although the displacements of the two points are except the amphidromic point near the city of Qinhuangdao. It small (,50), even such small displacements of amphidromic is expected that this eastward migration might well lead to a points can cause strong spatial variation of tidal amplitude and coherent amplitude change along the coastline. phase. Effects on the Amplitude and Phase of M and K from The comparison of the changes in M and K amphidromic 2 1 2 1 Potential Future SLR points in response to the 0.5, 1, and 2-m SLR scenarios shows Not surprisingly, tidal magnitudes are sensitive to the magnitude of SLR, and the associated changes of the amplitude

and phase of K1 and M2 are shown in Figures 7 and 8, respectively. The effect of SLR on tides is clearly spatially variable, because tidal changes are much more effective on the shelf (depth , 200 m) than in the deep sea. A notable decrease

in K1 amplitude can be detected in the Liaodong Bay, BS, and

YS, as well as YRE and . An increase in K1

Figure 5. Locations of M2 amphidromic points under PSL and three SLR Figure 6. Locations of K1 amphidromic points under PSL and three SLR scenarios. scenarios.

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Figure 7. Changes of K1 amplitude (a, b, and c) and phase (d, e, and f) in the China Sea. (a, d) 0.5-m, (b, e) 1-m, and (c, f) 2-m SLR scenario responses. amplitude can be detected in the Taiwan Strait, PRE, Beibu scenario) along the of the Korean peninsula. The phase

Bay, Sulu Sea, and the northern Gulf of Thailand. The changes of K1 (Figure 7) are also remarkable in the ECS amplitude decreases outward from the amphidromic point, amphidromic system. Generally the negative changes in phase reaching the largest decrease (0.04 m in the 0.5-m SLR indicate an earlier arrival of K1, with accelerated speeds

Figure 8. Changes of M2 amplitude (a, b, and c) and phase (d, e, and f) in the China Sea. (a, d) 0.5-m, (b, e) 1-m, and (c, f) 2-m SLR scenario responses.

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Figure 9. Amplitude change ratios (%) of M2 associated with a 2-m SLR with respect to PSL. The solid triangles denote sampled locations. The letters A–P indicate 16 ports (, , Qinhuangdao, , Huanghua, Figure 10. Amplitude changes in M2 and K1 along the coastline at 114 , Weihai, , Lianyungang, Shanghai, Zhoushan, Taizhou, points. , Zhuhai, , and Beibu Bay from north to south along the coastline). strong tendency to increase, indicating a later arrival of M2. Under the 1-m SLR scenario, amplitude generally increases associated with larger water depths. Taking zero value for the with SLR but decreases in Hangzhou Bay. The most significant cophase line in ECS as a dividing line, the phase changes are increase of amplitude and decrease of phase are more than 0.2 negative for the east (implying earlier mand168, respectively. An interesting finding is that changes arrival of K ), whereas along the west coast of the Korean 1 in M tidal amplitude are roughly proportional to the SLR Peninsula, the changes are positive, indicating a later arrival. 2 value. In the 2-m SLR scenario, changes in the M amplitude The areas of significant effect in the 1 and 2-m SLR scenarios 2 and phase are certainly greater, but the distribution of the are qualitatively the same as those for the 0.5-m SLR scenario, amplitude and phase changes of M is consistent with that of but the quantitative changes are larger. The largest K 2 1 the 0.5 and 1-m SLR scenarios. The largest change in amplitude changes in 1 and 2-m SLR scenarios both occur in amplitude occurs in Jianghua Bay, with a value of 0.4 m, Korea Bay, reaching 0.06 and 0.08 m, respectively, whereas the which is beyond the color bar limits. The largest phase largest decreases of phase in 1 and 2-m SLR scenarios occur in alterations, about 358, lie in , which means that the SW corner of the Indochina Peninsula—more than 128 and the M tide arrives 73 min (T ¼ 12.42 h) earlier there under 248, respectively. The change of phase demonstrates an earlier 2 M2 the 2-m SLR scenario. time of tidal arrival, t, which can be calculated by Comparing Figures 7 and 8, the spatial responses of tides to SLR in K and M show some common characteristics. The t ¼ Dg=360 3 TK1 ð4Þ 1 2 amplitudes increase in the southern ECS and SCS, and where Dg is the variation and TK1 is the period of the K1 tidal localized increases of M2 and K1 tidal amplitude can be seen constituent (the maximum Dg ¼ 24, T ¼ 23.93 h, t ¼ 95 min ). K1 in Beibu Bay and Taiwan Strait. Responses of tides to SLR are The earliest arrival of the K tidal constituent is 95 min in the 1 spatially variable, but in Bohai Bay, Korea Bay, Jianghua Bay 2-m SLR scenario. and YS, they are restricted by the amphidromic points. In the 0.5-m SLR scenario, the M amplitudes in the BS, 2 Amplitude in the YRE and the PRE increases with increasing Korea Bay, Jianghua Bay, the eastern YS, Taiwan Strait, SLR; however, it clearly decreases in Hangzhou Bay. Beibu Bay, and the Gulf of Thailand display an increasing tendency, in which Jianghua Bay captured the most significant Linearity of the Responses and the Effect on Ports increase of amplitude with a value about 0.1 m. Decreased To investigate the influence of SLR on China’s coastline and amplitudes are found in Hangzhou Bay and the YS near to examine whether the amplitude of tidal changes are Jiangsu Province. The changes of phases in most areas of the proportional to SLR values, amplitude changes are compared study domain are negative. Significant decreases occur in the at 114 coastal points in China, including the largest 16 ports shallow and coastal areas, such as BS, YS, Taiwan Strait, (Dalian, Yingkou, Qinhuangdao, Tianjin, Huanghua, Yantai, Beibu Bay, the Gulf of Thailand, eastern coastal areas of the Weihai, Qingdao, Lianyungang, Shanghai, Zhoushan, Taiz- Malay Peninsula, partial areas in the northern YS, and coastal hou, Xiamen, Zhuhai, Hong Kong, and Beibu Bay, from north areas of and provinces. The Bay, to south) (Figures 9 and 10). The largest M2 change ratios near the amphidromic point, experiences the most significant occurred near amphidromic points and are sensitive to small phase decrease (ca. 88). The phase change in the deep sea is amplitude changes (Pickering et al., 2012), whereas tides in the generally weaker, but in the Sulu Sea, phase change shows a coastal area with the largest absolute amplitude changes tend

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Table 4. M2 amplitude under PSL, and its change and change ratio in the Table 5. K1 amplitude under PSL and its change and change ratio in the 0.5, 1, and 2-m SLR scenarios. 0.5, 1, and 2-m SLR scenarios.

M Amplitude M Amplitude Change K Amplitude K Amplitude Change M 2 2 K 1 1 2 Change (cm) Ratio to PSL (% ) 1 Change (cm) Ratio to PSL (% ) Amplitude (cm) Amplitude (cm) Location PSL 0.5 1 2 0.5 1 2 Location PSL 0.5 1 2 0.5 1 2 Dalian 33 2 4 8 6 12 25 Dalian 23 2 3 4 8 13 17 Yingkou 60 3 6 14 5 11 23 Yingkou 54 4 6 9 8 12 16 Qinhuangdao 12 0 0 0 1 1 4 Qinhuangdao 39 3 4 5 7 10 13 Tianjin 71 3 6 10 5 8 14 Tianjin 49 2 4 6 5 8 12 Huanghua 62 3 5 10 4 8 16 Huanghua 48 3 5 6 6 10 12 Yantai 34 2 5 11 6 14 32 Yantai 23 2 3 4 7 12 17 Weihai 32 2 4 10 6 13 32 Weihai 27 2 3 4 7 11 16 Qingdao 73 1 3 8 1 4 11 Qingdao 42 2 3 4 4 7 9 Lianyungang 51 2 4 9 3 8 17 Lianyungang 42 2 3 4 5 8 10 Shanghai 67 5 10 20 7 14 29 Shanghai 19 1 3 6 7 14 30 Zhoushan 97 2 4 7 2 4 7 Zhoushan 30 0 1 1 2 2 2 Taizhou 149 3 4 3 2 3 2 Taizhou 22 2 3 4 9 14 17 Xiamen 167 1 2 3 1 1 2 Xiamen 36 0 0 1 1 1 2 Zhuhai 40 1 1 1 1 2 3 Zhuhai 37 0 0 0 0 0 0 Hong Kong 41 1 2 3 2 4 6 Hong Kong 38 0 0 1 0 1 2 Beibu Bay 26 1 2 4 5 8 14 Beibu Bay 54 1 2 4 2 4 8 to display small relative changes (Figure 9). This kind of tional simulations. However, for larger SLR (.2 m) scenarios, characteristic can be seen in Jianghua Bay and in the Taiwan linearity needs further validation. Strait. Figure 10 shows the difference in coastal amplitude changes induced by 0.5, 1, and 2-m SLRs. The K1 and M2 tidal DISCUSSION amplitudes alter in a variable manner along the coastline, and The simulated results show that the M2 and K1 tidal the changes increase with increasing SLR. Most of the changes amplitudes respond to SLR in a spatially nonuniform manner. in M2 amplitude are positive, but changes in K1 amplitude are Generally, the changes of M2 and K1 amplitude in shallow negative in BS, YS, and northern ECS, while remaining waters are larger than those in the deep sea; significant tidal positive in southern ECS and SCS. The large amplitude alterations mainly occur in the BS, YS, YRE, PRE, and Taiwan changes mainly occur at port locations, indicating these areas Strait. Possible mechanisms for these changes relate to a will be the first to suffer from tidal changes and flood risks decrease of bottom friction, migration of amphidromic points, caused by SLR. The values given in Tables 4 and 5 summarize and changes in effects (Arns et al., 2015; Pelling, Green, and Ward, 2013; Pickering et al., 2012). the changes in M2 and K1 tides associated with the 0.5, 1, and 2- Results on continental shelf exhibit substantial amplitude m SLR scenarios. Substantial changes in M2 amplitude (.10 cm in the 2-m SLR scenario) occur at Yingkou, Tianjin, changes. Many researchers explained these differences from the aspect of bottom friction effects (Arns et al., 2015; Pelling Huanghua, Yantai, Weihai, and Shanghai. The three largest and Green, 2013; Pickering et al., 2012), which is closely related M amplitude change ratios are 32% at Yantai and Weihai and 2 to tidal and plays an important role in the tidal 29% at Shanghai. The four largest K amplitude changes are in 1 phenomenon (Lu and Zhang, 2006; Mayo et al., 2014). In tidal the vicinity of Yingkou, Tianjin, Huanghua, and Shanghai, but models, the bottom friction effect is parameterized by the bed the absolute change values are only between 6 and 9 cm. friction coefficient, which varies with water depth. According to The M amplitude changes in the 1 and 2-m SLR scenarios 2 the depth dependency of the bottom friction coefficient [c ¼ g/ compared with those in the 0.5-m SLR scenario are plotted in d (M2D1/3)], the bottom friction coefficient decreases if water Figure 11a. Comparisons of these datasets show that M 2 depth increases, resulting in a decrease in bottom friction and amplitude changes in the 1-m SLR scenario increase propor- tidal energy dissipation. As tides propagate into shallow tionally by a factor of 2.1 compared with those in the 0.5-m SLR waters, the magnitude of tidal variation is especially sensitive scenario, and the factor between the 2-m and the 0.5-m SLR to the bottom friction coefficient (Kumar and Balaji, 2015). The scenarios proportionally increases to 4.1, which indicates that bottom friction coefficient is expected to decrease significantly the responses of M2 amplitude turn out to be roughly linear to as the result of SLR, which reduces tidal dissipation and tends SLR values. However, in Figure 11b, K1 amplitude changes in to increase tidal amplitudes. To investigate the effects of the 1-m SLR scenario increase by a factor of 1.6 compared with bottom friction coefficients on tidal amplitude change, we those in the 0.5-m SLR scenario, and the factor is 2.3 when increased the Manning number by 50% of the current level over comparing K1 amplitude changes in the 2-m SLR to those in the whole domain—which means the bottom friction coefficient 0.5-m SLR scenarios. Both regression factors in Figure 11b decreased as a result—and ran the model again at PSL. Figure indicate that the amplitude changes in K1 are disproportional 12 shows that M2 and K1 amplitudes basically increase as to SLR values. Therefore, the proportionality of M2 tidal bottom friction coefficients decrease, and that the M2 tide is amplitude changes to the SLR scenario means the flood risk more sensitive to decreasing bottom friction coefficients than assessment for limited climate change scenarios (0.5–2-m SLR) the K1 tide. From Figure 12 it can be expected that decreasing can be simply interpolated without having to perform addi- bottom friction coefficients could cause increasing amplitudes.

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Figure 12. Amplitude response to 50% Manning number increase in (a) M2 tide and (b) K1 tide. Figure 11. Regression of amplitude changes in the 1-m SLR and 2-m SLR scenarios compared with those in the 0.5-m SLR scenario in (a) M2 tide and (b) K1 tide. bottom friction, the speed of a tidal wave c can be approximated by pffiffiffiffiffiffiffi M2 amplitude increases significantly in the Taiwan Strait, c ¼ gH ð5Þ YRE, and PRE; meanwhile, the tendency for the K1 amplitude to change in the Taiwan Strait, YRE, PRE, and Beibu Bay is in Equation (5) highlights that the tidal wave speed c only accordance with Figures 7a–c. Therefore, Figure 12 indicates depends on the water depth H and gravitational acceleration g. decreasing bottom friction from SLR contributes to the change Thus, it is concluded that as depth increases with SLR, waves in amplitude in these sea areas. propagate more quickly. In this case, the (k¼c3T) However, comparing Figure 8c with Figure 12a, decreasing increases with SLR, resulting in the displacement of standing M amplitudes are found in , Hangzhou Bay, and 2 waves and amphidrome, which can cause significant changes to YS near Jiangsu Province. Meanwhile, K amplitude changes 1 tidal amplitude and phase. (Figure 7c) from SLR in BS, YS, Jianghua Bay, and Hangzhou The results in Hangzhou Bay exhibit substantial decreases Bay are also opposite the result in Figure 12b, which shows because of SLR, which is somewhat out of this study’s that amplitude changes on the continental shelf are affected expectation that increasing results are found in the macrotidal not only by decreasing bottom friction. To explain these differences, we focused on the propagation of tides and shape embayment. The response in Hangzhou Bay to an increasing of the bay. Manning number is also obviously very different from that of In semiclosed rectangular bays like BS and YS, as the tide SLR, and it is suggested here that this is due to changes in the propagates from the sea and then reflects at the land-sea resonant properties of Hangzhou Bay, which occurs when its boundary, standing waves tend to occur where the two waves length (L) is a quarter of the wavelength of the incoming tide interfere. Because of the , the amphidrome forms (Pelling, Green, and Ward, 2013): from the standing waves at distances k/4 and 3k/4 (where k is pffiffiffiffiffiffiffi the wavelength) from the solid boundary. The motion of tide k gH L ¼ ¼ T ð6Þ belongs to the class of long gravity waves, and neglecting 4 4

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increasing mean sea level and amplitude could destroy flood defenses and threaten urban safety, so upgrades in embank- ments in the estuaries will be required to cope with SLR. A possible mechanism of tidal changes may relate to decreased bottom friction from increased water depth because of SLR, migration of amphidromic points, and changes in resonance effect. To track the mechanism of changes in amplitude, an analysis by Manning number showed a 50% increase over the whole domain in the PSL model. Results show

M2 and K1 amplitudes basically increase as bed friction Figure 13. The basin length, L ¼ [(gH)1/2/4)T], as a function of water depth coefficients decrease, but the M2 tide is more sensitive to required for K1 and M2 resonance in (a) Hangzhou Bay and (b) Jianghua Bay. bottom friction coefficients than the K1 tide. M2 amplitudes in The dash line indicates the natural basin length. the Taiwan Strait, YRE, and PRE, as well as K1 amplitude changes in the Taiwan Strait, YRE, PRE, and Beibu Bay, are in Because the wavelength increases with SLR while the basin accordance with SLR, which indicates decreasing bottom length is unchanged, the increase in the quarter wavelength friction from SLR contributes to the change of amplitude in tends to move it closer to the basin length (L), causing a larger these sea areas. However, in semiclosed rectangular bays, like tidal amplitude. A move away from resonance thus results in BS and YS, changes in the amplitude response to SLR on the an overall decrease in . The length of Hangzhou continental shelf are not dominated by decreasing bed friction, but the increasing wavelength results in displacements of Bay in the model bathymetry in this study is 85 km, and the standing waves and amphidromes. In resonant areas (i.e. present mean water depth is 9 m. Figure 13a shows that Hangzhou Bay and Jianghua Bay), amplitude change is the increasing the water depth in Hangzhou Bay will move the result of changes in resonant properties. With SLR, Hangzhou basin further from resonance; thus, the decreased resonance is Bay will move farther from resonance, which contributes to an likely to contribute to a decreased amplitude. Jianghua Bay amplitude decrease, whereas Jianghua Bay will move closer to has the largest tidal range in Korea, and its amplitude change resonance in M , causing a large amplitude increase, but will also could be explained by resonant mechanisms (An, 1977). 2 move the system away from resonance in K , inducing an Our results suggest that SLR scenarios draw the embayment 1 amplitude decrease. (L ¼ 100 km, present mean depth ¼ 5.4 m) closer to resonance Additionally, it is noted that the tidal changes not only in M , causing a large amplitude increase (Figure 13b), 2 influence the associated physical and sedimentary process, whereas this change moves the system away from resonance resulting in saltwater intrusion and coastline evolution, but in K1. This analysis is in good agreement with the amplitude also affect both biological and ecological processes, influencing change in Figures 7 and 8. the future vulnerability and viability of nesting habitats. Therefore, environmental, societal, and economic assessments, CONCLUSIONS such as design recommendations for coastal flood defenses, This study investigates the diurnal and semidiurnal tidal availability of tidal energy, and safeguarding habitats of responses in the entire China Sea to a potential of endangered species, are necessarily because of potential 0.5–2 m by a modified 2D tidal model based on MIKE 21. alterations to tidal dynamics with SLR. Despite the flood risk Comparing the 0.5–2-m SLR scenarios with the PSL scenario, associated with tidal changes (,17% of the SLR value), the the M2 and K1 tides are found to respond to SLR in a spatially largest contributor to flood risk comes from SLR itself. nonuniform manner. Generally, the changes in M2 and K1 Therefore, managers should strengthen action in coastal areas amplitude in shallow waters are larger than those in the deep in BS, YRE, PRE, Taiwan Strait, and Beibu Bay, which are sea, and significant tidal alterations mainly occur in BS, YS, shown to be potentially most vulnerable to future tidal dynamic Taiwan Strait, and shallow-water areas. The mean absolute alterations, while assessing and enforcing measures of flood alteration in M2 amplitude along the coastline is 0.016 m with a defense regularly. 0.5-m SLR, 0.032 m with a 1-m SLR, and 0.067 m with a 2-m SLR, respectively, whereas the mean absolute K1 amplitude ACKNOWLEDGMENTS changes are less significant, ranging from 0.014 to 0.032 m for This research was financially supported by National Key the 0.5–2-m SLR scenarios. Additionally, the simulated Basic Research Program of China (2012CB957704), Marine changes in M2 and K1 amplitude in response to three (0.5, 1, Public Welfare Program of China (201305003), and Key and 2-m) SLR scenarios imply that changes in M2 amplitude Subject Foundation of Shanghai Education Committee are proportional to the magnitude of SLR, whereas this (J50702). proportionality does not hold for K1 amplitudes. Comparing amplitude changes at 114 coastal points in LITERATURE CITED

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