Development History of the Numerical Simulation of Tides in the East Asian Marginal Seas: An Overview

Abstract

As a ubiquitous movement in the ocean, tides are vital for marine life and numerous marine activities such as fishing and ocean engineering. Tidal dynamics are complicated in the East Asian marginal seas (EAMS) due to changing complex topography and coastlines related to human activities (e.g., land reclamation and channel deepening) and natural variability (e.g., seasonal variations of ocean stratification and river flow). As an important tool, numerical models are widely used because they can provide basin-scale patterns of tidal dynamics compared to point-based tide gauges. This paper aims to overview the development history of the numerical simulation of tides in the EAMS, including the Bohai Sea, the Yellow Sea, the East China Sea, the East/Japan Sea, and the South China Sea, provide comprehensive understanding of tidal dynamics, and address contemporary research challenges. The basic features of major tidal constituents obtained by tidal models are reviewed, and the progress in the inversion of spatially and temporally changing model parameters via the adjoint method are presented. We review numerical research on how a changing ocean environment induces tidal evolution and how tides and tidal mixing influence ocean environment in turn. The generation, propagation, and dissipation of internal tides in the EAMS are also reviewed. Although remarkable progresses in tidal dynamics have been made, nonstationary tidal variations are not fully explained yet, and further efforts are needed. In addition, tidal influences on ocean environment still receive limited attention, which deserves special attention.

1. Introduction

Tides are periodic sea level oscillations originated from the gravitation of the moon and the sun [1]. Tides are ubiquitous in the global ocean, and the accurate prediction of tides is essential and necessary for marine activities such as fishing, ocean transport, and ocean engineering [2]. East Asian marginal seas (EAMS), including the Bohai Sea, the Yellow Sea, the East China Sea, the East/Japan Sea, and the South China Sea, have complicated topography and coastlines that induce complex tidal dynamics [3,4]. In most locations in the EAMS, the strongest tidal constituent is M₂ with a period of 12.4206 h. Other significant semi-diurnal tides include S₂ (12 h), K₂ (11.9672 h), and N₂ (12.6583 h). In minor locations such as the Gulf of Tonkin, diurnal tides like K₁ (23.9345 h) and O₁ (25.8193 h) are stronger than M₂ tides. Because of relatively shallow water depth, tidal ranges in the EAMS are significantly larger than those in deep seas, for example, at Incheon in the Yellow Sea, the local tidal range can exceed 10 m [5,6]. Furthermore, due to the rapid development of economy and thus increasing human activities, such as harbor construction, land reclamation, and channel deepening, local coastlines and topography have been significantly changed, which contributes to local tidal evolution [7,8,9].

Based on tide gauges, satellite altimeter observations and numerical models, numerous studies have been conducted in the EAMS, revealing basic features of major tidal constituents and exploring multi-time scale tidal evolution [10,11,12,13]. The purpose of this paper is to overview the development history of the numerical simulation of tides in the EAMS, provide comprehensive understanding of tidal dynamics, and address contemporary research challenges. Compared to point-based tide gauge observations, numerical models can provide basin-scale patterns of tidal dynamics. Before the 1990s, due to the limitation of computer power, ocean tide models were mainly two-dimensional (2D), and their resolution was relatively low. High-resolution three-dimensional (3D) tidal models have gradually become common since the 1990s as the result of improved computer power. The rapid increase of satellite observations since the 1990s popularized the assimilated tidal models, which significantly improved the accuracy of tidal models in the sea area with rare tide gauges [14,15]. Alongside simulating accurate tidal constants, numerous studies also focus on exploring nonstationary tidal amplitudes/phases’ changes caused by human activities and natural variability (e.g., seasonal variations of ocean stratification and river flow). As a typical nonstationary tide, internal tides receive lots of attention, especially in the South China Sea [16,17,18]. In addition, recent studies indicate the importance of tides and tidal mixing on influencing the ocean environment and global climate [19,20,21].

The structure of this paper is as follows. In Section 2, we review numerical research on stationary tides in the EAMS via 2D and 3D models without data assimilation. In Section 3, we review numerical studies using an assimilated tidal model and the progress in the inversion of spatially and temporally changing model parameters. The interactions between the ocean environment and tides is discussed in Section 4 and Section 5. Numerical studies on internal tides are described in Section 6. Summary and conclusions are given in Section 7.

2. Tidal Modeling without Data Assimilation

In early numerical studies, due to lack of computer resources, most research simulated tides using 2D tidal models. Numerically simulated M₂ tides in the Bohai and Yellow Seas (BYS) indicated that bottom friction is vital in shallow water, and semi-diurnal tides in the coast of the Korean Peninsula are noticeably larger than those in the coast of China [10] (Figure 1). Via numerical modeling, Shen [5] obtained the co-tidal charts of M₂, S₂, K₁, and O₁ tides in the East China Sea which are consistent with observations. As shown in Figure 1, for the M₂ tide, there exist four amphidromic points in the BYS: two amphidromic points located in the Bohai Sea, one near Qinhuangdao (labeled as Q in Figure 1), and another located in the Yellow River delta (labeled as Y); two amphidromic points located in the Yellow Sea, one located in the north of Chengshantou (labeled as C), and another located in the east of Jiangsu coast (labeled as J). For the K₁ tide, there are only two amphidromic points in the BYS, one is located in the Bohai Strait (labeled as B in Figure 2), and the other lies in the middle of the South Yellow Sea (labeled as S).

Fang [22] modeled the tides and tidal currents in the Taiwan Strait using 2D nonlinear hydrodynamic equations and concluded that most of the energy flux of semi-diurnal tides in the Taiwan Strait is from the East China Sea. Fang and Yang [23] simultaneously simulated semi-diurnal, diurnal, and shallow-water tidal constituents as well as tidal currents in the Bohai Sea based on 2D tidal wave equations. Fang [24] proposed a finite difference–least square technique to solve tidal wave equations and applied this technique to model the M₂ tide in the Yellow Sea. Via numerical modeling, Fang [25] gave the charts for tides and tidal currents in the marginal seas adjacent to China. In fact, these experiments were performed in 1970s, but the results remained unpublished for many years because of the fact that the publication of Chinese scientific journals had been halted during that time. Fang and Yang [26] computed semi-diurnal and diurnal tides and tidal currents in the Korea Strait and proposed a method for large-area tides and tidal currents’ prediction.

Odamaki [27] explored the generation mechanism of tides in the East/Japan Sea by means of a one-dimensional tidal model. He found that semi-diurnal and diurnal tides in the East/Japan Sea are generally weak, and most tidal energy was from the Korea Strait (Figure 3). Cao and Fang [28] simulated diurnal and semi-diurnal tides and tidal currents in the Gulf of Tonkin and gave the distribution of the tidal energy flux, the residual tidal current, and the residual tidal elevation. As displayed in Figure 4, K₁ amplitudes in the Gulf of Tonkin can reach 80 cm, while the maximum of M₂ amplitudes is only about 30 cm. Choi and Fang [29] reviewed earlier numerical studies of the Bohai, Yellow, and East China Seas (BYECS) and discussed the utilization of numerical models to study tidal mixing, tidal circulation, and tidal sedimentation. Zhao et al. [30] discussed the characteristics of tidal residual currents in the BYECS and found that the directions of tidal residual currents are consistent with the coastal current system in most areas. Fang et al. [31] simulated principal tidal constituents in the South China Sea and confirmed that a clockwise rotating M₂ amphidromic point located in the southeast of the Gulf of Thailand (labeled as M in Figure 5) and a counterclockwise rotating K₁ amphidromic point lied in the south of the Gulf of Thailand (labeled as K in Figure 4).

Figure 1. Cotidal chart for M₂ in the BYS based on the EOT20 model [32], in which the color and white lines represent the amplitude and phase lag, respectively.

Figure 1. Cotidal chart for M₂ in the BYS based on the EOT20 model [32], in which the color and white lines represent the amplitude and phase lag, respectively.

Figure 2. Same as Figure 1, but for the K₁ tide.

Figure 2. Same as Figure 1, but for the K₁ tide.

Figure 3. Cotidal charts for M₂ (a) and K₁ (b) tides in the East/Japan Sea.

Figure 3. Cotidal charts for M₂ (a) and K₁ (b) tides in the East/Japan Sea.

Using a 2D finite element model, Lin et al. [33] indicated that the anomalous amplifications of semi-diurnal tides along the western coast of Taiwan (Figure 6) are caused by resonance. Jan et al. [34] found the importance of the abrupt step in the topography to the amplification of semi-diurnal tides in the Taiwan Strait based on numerical experiments and theoretical analysis. Teng et al. [35] considered the effects of self-attraction loading and internal tide dissipation to M₂ and S₂ tides in the BYECS and found that 80% of tidal energy was dissipated via bottom friction and the remaining 20% was dissipated via internal tide dissipation. Zhang et al. [36] designed a schematized numerical tidal model to investigate the generation of tidal current system in the Yellow Sea and concluded that Poincare modes were necessary for the existence of the radial tidal current.

Since the 1990s, with significant improvement in computing power, 3D tidal models are more common. Zhu and Fang [37] simulated the vertical structure of tidal currents in the Gulf of Tonkin with less computer time by combing 2D and 3D models. Guo and Yanagi [38] presented the vertical distribution of tidal currents in the BYECS for M₂, S₂, K₁, and O₁ constituents using a high-resolution three-dimensional numerical model (with 12.5 km resolution in the horizontal and 20 layers in the vertical). Wang et al. [39] computed M₂ tides and tidal currents in the BYECS by means of a new 3D semi-implicit numerical model and revealed that the current-amphidromic points at different layers were located at the same horizontal position. Based on the Regional Ocean Model System (ROMS [40]), Wu et al. [41] established a high-resolution ocean model with two-way nesting to simulate tides in the Zhoushan Archipelago waters and found that M₄ and M₆ tides mainly originate from advective nonlinearity, not bottom friction. Chu et al. [42] investigated tidal duration asymmetry induced by higher harmonics of the main constituents (M₄, MS₄, M₆, and MS₆) in the Zhoushan Archipelago using the Finite-Volume Coastal Ocean Model (FVCOM [43]). Their numerical results indicate that tides are flood-dominant in the Zhoushan Archipelago, and tidal asymmetry is enhanced from the open sea to coastal areas.

3. Tidal Modeling with Data Assimilation

Since the launch of the TOPEX/Poseidon (T/P) satellite in 1992, satellite altimeter data have been assimilated into tidal models and significantly improved their accuracy. The flowchart for tidal modeling with the adjoint assimilation method is displayed in Figure 7. Han et al. [44] optimized the open boundary conditions (OBCs) by assimilating T/P observations to the adjoint tidal model for the East China Sea. He et al. [45] established a numerical adjoint model assimilating T/P data to investigate the shallow water constituents (M₄, MS₄, and M₆) in the BYS. Wu et al. [46] considered the equilibrium tides, optimized the OBCs, and assimilated T/P observations to the Princeton Ocean Model (POM [47]) for the South China Sea. Book et al. [48] assimilated moored ADCP, tide gauges, and altimeter records to a numerical model to optimize OBCs and obtained accurate barotropic tides in the Korea Strait. Jan et al. [49] used variational data assimilation to inverse the OBCs in a 3D ocean model for the Taiwan Strait. Lv and Zhang [14] derived spatially varying bottom friction coefficients (BFCs) in the BYECS via a 2D adjoint tidal model. To reduce the number of control variables and avoid the ill-posedness of the inverse problem, Lv and Zhang [14] used the independent point (IP) scheme, which meant that BFCs at the selected IPs were treated as independent parameters and that values at rest grid points were obtained by interpolation. Zu et al. [50] assimilated T/P data into a barotropic tide model for the eight main constituents in the South China Sea. They indicated that the response of tides in the South China Sea is closely related to the propagating directions of the tides from the Pacific, the wavelengths, the coastline, and the topography.

Zhang and Lu [51] simulated the 3D tidal currents in the BYS by assimilating satellite altimetry. Zhang et al. [52] studied the similarities and the differences between linear and nonlinear bottom friction parameterizations in the BYS using a 2D adjoint tidal model. Zhang and Wang [53] proposed a feature points method for inversion of periodic OBCs in the adjoint tidal model. Gao et al. [12] added a parameterized internal tide dissipation term in the adjoint tidal model to investigate tidal dynamics in the South China Sea and indicated that internal tide dissipation mainly occurred in the Luzon Strait and the central deep basin of the South China Sea. Pan et al. [2] proposed an improved IP scheme which used the Spline interpolation to replace the Cressman interpolation in the traditional IP scheme. Practical experiments in the BYS indicated that the misfits between modeled results and observations were smaller when the improved IP scheme was applied [2]. The improved IP scheme has been used to optimize spatially varying BFCs in the Bohai Sea [15] and smoothly varying OBCs in the northern South China Sea [54]. Zheng et al. [55] developed a dynamically constrained interpolation methodology based on the adjoint method and successfully obtained an accurate M₂ cotidal chart in the BYECS. Qian et al. [56] assimilated multi-mission satellite observations to the adjoint tidal model and further improved the model’s performance in the BYECS. Wang et al. [57,58] estimated spatially and temporally varying BFCs in the BYECS and indicated that BFCs are significantly related to the current speed and water depth.

Generally, most previous studies used the adjoint method to iteratively optimize the model parameters. Although the adjoint method is powerful, it is computationally expensive and technically demanding. Therefore, there exist a few studies using another assimilating method. Li et al. [59,60] used an artificial neural network to estimate optimal OBCs for regional tidal models. Moon et al. [61] applied a new method which used Green’s function approach to optimize modal parameters and noticeably improved the accuracy of tidal simulation for the EAMS. Wei et al. [62] proposed an improved Nudging assimilation scheme and successfully applied it to simulate the M₂ constituent in the Northwest Pacific based on POM. Zhu et al. [63] assimilated coastal acoustic tomography observations to FVCOM via an Ensemble Kalman Filter scheme and studied the dynamics of tidal currents in the Jiaozhou Bay.

4. Changing Tides under Natural Variability and Human Activities

Due to non-astronomical perturbations such as river flow, sea ice, coastline, and water depth change related to human activities and sea level rise, tides show multiscale nonstationary changes [64,65]. Figure 8 displays the observed tides in the Yangtze river estuary (YRE) which are typical nonstationary tides. Tides are basically stationary and slightly influenced by river flow at Tianshenggang, located in the entrance of YRE. As tides propagate landward to Zhenjiang, they are significantly suppressed by river flow, especially in the flood season. Previous studies reviewed in Section 2 and Section 3 all focus on modeling stationary tides which means that tidal amplitudes and phases are constant, thus, they ignore potential tidal evolution which is the main focus of recent tidal studies.

Pelling et al. [11] discussed the impact of rapid coastline changes to the M₂ tide in the Bohai Sea and found that M₂ amplitudes changed up to 20 cm in some parts. Lu et al. [66] explored tidal propagation, tidal distortion, and tidal damping in the YRE during the dry season using Delft-3D [67]. Zhang et al. [68,69] explored the seasonal variation of a tidal prism and energy in the YRE via the TELEMAC-2D model [70]. They indicated that tidal discharge showed a noticeable decreasing trend with the increase of river discharge rate while the tidal storage volume was insensitive to river discharge. Zhang et al. [71] quantified the tide–surge interaction in the east coast of the Leizhou Peninsula, South China Sea via POM and pointed out that the largest amplitudes of the tide–surge interaction can reach 1 m during typhoon events.

Zhang et al. [72] investigated seasonal interactions between tides and river flow in the YRE by Delft-3D and indicated that in the downstream reach of a tidal river, increasing discharge can reduce semi-diurnal amplitudes but amplify diurnal amplitudes. Zhu et al. [7] systematically explored the influences of changes in topography and coastline related to reclamation and coastal erosion on tidal systems, tidal currents, and tidal fluxes in the Bohai Sea from 1987 to 2016. They considered coastline changes in the Liaodong Bay that occurred in the 2010s, which was ignored by Pelling et al. [11]. It is found that the changes in M₂ amplitudes in the Bohai Sea are between −23.3 and 17.2 cm, while the variations in K₁ amplitudes range from −0.9 to 3.1 cm. Devlin et al. [73] found that seasonal tidal variability in the seas of Southeast Asia was correlated to the western North Pacific monsoon index. Via the model perturbation approach, Devlin et al. [73] indicated that seasonal tidal variability in the southern Gulf of Thailand and near Singapore was caused by the combined effects of geostrophic and wind-driven Ekman currents. Feng et al. [8] quantified the influence of satellite-based sea level trends on tidal changes in the Yellow Sea via FVCOM. They indicated that a significant decrease in tidal range laid in the northern shelf of the Yellow Sea, while the increase of tidal range was mainly located in the southern shelf.

Phan et al. [74] explored tidal wave propagation along the coast of the Mekong delta using Delft-3D, and their results indicate that wind monsoon climate can change tidal amplitudes along the Mekong deltaic coast about 2–3 cm. Zhang et al. [75] investigated the potential influence of sea ice on tides in the Bohai Sea via FVCOM. They found that sea ice almost did not alter M₂ phases but reduced M₂ amplitudes up to 1 cm. Guo et al. [76] employed Delft-3D to explore long-period tidal behaviors under changing river flow in the YRE. They indicated that estuaries act like a frequency filter, where long-period tidal waves damp at a smaller rate and propagate more upward than short-period tidal waves do. Wang et al. [13] discussed the seasonal tidal variability in the Bohai Sea via the Massachusetts Institute of Technology General Circulation Model (MITgcm [77]) and pointed out that seasonally the mean sea level, changing stratification, and vertical eddy should be responsible for seasonable tidal variability at Dalian. Zhao et al. [78] numerically investigated the potential influence of planned intense reclamation on the tides along the open coast in southeastern Zhejiang using the MIKE21 model. It was found that the tidal ranges were reduced, tidal directions were altered, and tidal refraction effects were weakened after land reclamation. Choi et al. [79,80] explored the tide–wave–surge interaction in the Yellow Sea via numerical models.

Feng and Feng [81] explored the influence of coastline changes and a rising sea level on tidal asymmetry along the coast of Jiangsu and found that the interactions between M₂/M₄ and M₂/S₂/MS₄ were most sensitive to coastline changes and contributed the largest part to tidal distortion. Using ROMS, Lin et al. [9] studied the tidal response to changes in coastline and water depth related to land reclamation and waterway dredging in the Pearl River Estuary (PRE). They indicated that coastline changes reduced the water area and volume in the PRE, which caused a decrease of 17.1% (11.3%) in the tidal prism during neap (spring) tides and induced a noticeable reduction of 19.0% in the tidal energy flux propagating into the PRE. Zhu et al. [82] explored decadal tidal changes caused by morphological and sedimentary evolution in the YRE via Delft-3D. They found that tidal damping increased in the mouth zone of the YRE since 1997, mainly because of stronger effective bottom roughness related to local engineering projects. They also indicated the dual influences of reduced sediment supply on tides: it strengthened tides in the South Branch through its effects on morphology but dampened tides via its effects on bottom friction.

5. Tidal Influence on the Ocean Environment

In Section 4, the impact of the changing ocean environment related to human activities and natural variability on tidal evolution is reviewed. In fact, tides can also change the ocean environment in turn. Numerous studies have indicated the important role of tides and tidal mixing on ocean circulation, the ocean ecosystem, and the global climate based on in situ and satellite observations [20,21,83]. It is found that satellite-derived sea surface temperature observations in the coastal waters of Hong Kong show significant spring-neap cycles which are vital indicators for tide-induced mixing [20]. Noticeable spring-neap signals which can change satellite-derived chlorophyll-a concentrations up to 12–33% are observed in the East China Sea and South China Sea [21]. Fortnightly cycles in satellite-observed sea surface temperature in the Indonesian seas show seasonal and interannual modulation that is related to the monsoon and El Niño Southern Oscillation (ENSO) [83].

There are also many studies which used numerical models to quantify the influence of tides on the marine environment. Lee et al. [84] investigated the influence of tides on the intermediate water in the East/Japan Sea by means of an eddy-resolving ocean model and indicated that tides enhanced vertical mixing and brought simulated water mass features closer to observations. Zhang et al. [85] quantified the tidal impact on the distribution of river discharge in the YRE by means of a 2D hydrodynamic model and found that tides can change the river discharge division by ~12% to 22% at Xuliujing bifurcation with river flows changing from 30,000 to 20,000 m³s⁻¹. Ji and Zhang [86] explored the tidal influence on the evolution of river hydraulic geometry in the PRE via a 2D numerical model and indicated that the nonlinear tide–river interplay can create a water level setup which influences the discharge division at tidal bifurcations while the net tidal effect generally attenuates the inequality in the discharge division.

It is well-known that continental shelf circulation simulated by numerical models cannot display a reasonable vertical thermohaline structure in the absence of tides. Adding additional tidal forcing on the open boundary is a common method to include the influences of tidal mixing, however, this method is computationally expensive because the time scale of ocean tides is significantly smaller than that of ocean circulation. Therefore, Wei et al. [19] developed harmonic analyzed parameterization of tide-induced (HAT) mixing for ocean circulation models as an alternative to avoid running an independent tidal model. Differently from previous tidal mixing parameterization schemes which only consider spatial mixing coefficients, HAT additionally considers temporal changes of the tide-induced mixing coefficient caused by typical semi-diurnal and diurnal periods of tidal fluctuations. Figure 9 displays the results of a series of comparative numerical experiments in the BYECS with and without HAT via ROMS. Figure 9a is the result of a control experiment which adds explicit tidal forcing on the open boundary (Experiment 1), while Figure 9b shows the results without tidal forcing on the open boundary (Experiment 2). Figure 9c displays the results without tides but considering HAT (Experiment 3). It is clear that HAT successfully reproduces vertical temperature structures, similarly to the results obtained by directly adding tidal forcing on the open boundary, while HAT is computationally cheap.

6. Numerical Studies of Internal Tides

Internal tides are internal waves with tidal frequencies which are generated in the stratified ocean when barotropic tides interplay with topography and play a vital role in deep ocean mixing and energy dissipation of barotropic tides [17]. Internal tides are ubiquitous in East Asian marginal seas and especially significant in the South China Sea. Thus, the South China Sea is a hot spot for the research of internal tides. Yuan et al. [87] developed a three-layer tidal model to investigate the generation of internal tides in the northeastern South China Sea. Their results showed that M₂ internal tides were mainly generated in the shelf break south of the Taiwan shoal, while K₁ internal tides were mainly generated in the shelf break southeast of the Yitong shoal. Fang et al. [88] developed a layered 3D tidal model whose surface can simultaneously simulate barotropic and baroclinic tides, and successfully simulated internal tides in the northwestern South China Sea. Combined with the observational feature of internal tides in the sea area around the Nansha Islands, Cai et al. [89] used a two-layer ocean model to investigate the generation of internal tides in the shelf break. It was found that internal tidal amplitudes can be influenced by the source depth of barotropic tides, nonlinear effects, and wind stress.

Jan et al. [16] investigated the spatial and seasonal variability of internal tides in the Luzon Strait using POM and indicated that there was no noticeable seasonal variation of baroclinic tidal energy, but the propagation speed of internal tide waves was about 10% slower in the winter than in the summer. Miao et al. [90] developed a three-dimensional isopycnic-coordinate ocean model for internal tides and applied it to the South China Sea. They found that the K₁ internal tides generated in the Luzon Strait propagated away in two distinct branches: one branch propagated southwestward into the South China Sea with a beam width of ~250 km; the other branch propagated eastward into the Pacific with a beam width of ~450 km. Wang et al. [91] explored the generation of internal tides in the Luzon Strait via POM and found that the diurnal modulation of semi-diurnal internal tides was induced by the interplay between the linear internal waves and barotropic diurnal tidal currents. Wu et al. [92] discussed the seasonal variability of M₂ and K₁ internal tides in the northern South China Sea using MITgcm. Their numerical results indicated that ocean mixing caused by internal tides in the summer was weaker than those in the winter in the northern South China Sea.

Guo et al. [93] explored how the seasonal variations of ocean stratification influenced the generation of internal tides in the Luzon Strait. They indicated that the seasonal changes of ocean stratification influenced the wavelength of internal tides and the interference of local topography within internal tides, which finally altered baroclinic energy conversion in the Luzon Strait. Based on mooring observations, Yan et al. [18] found that internal tides in the northwestern South China Sea were strong in the summer but negligible in the winter. Their numerical results indicated that the seasonal changing ocean stratification controlled the seasonality of internal tides. In the summer, due to strong stratified layers, baroclinic tides can be generated locally or remotely and easily propagated across the shelf, while in the winter, internal tides dissipate at the shelf break because of the disappearance of ocean stratification caused by uniformly vertical mixing. Guo et al. [94] employed the Coastal and Regional Ocean COmmunity (CROCO) model to investigate the impact of internal tides originating from the Luzon Strait on the local generation of internal tides on the continental slope in the South China Sea. It was found that remote internal tides can noticeably change the phases and amplitudes of the pressure perturbation on the continental shelf, thus, influence the local generation of internal tides.

Wang et al. [95] explored the reflection of the K₁ internal tides at the continental shelf break in the northern South China Sea via MITgcm. K₁ internal tides originated from the Luzon Strait propagate westward into the northern South China Sea with energy of 3.54 GW and then, 0.31 GW of energy are reflected by the shelf break. There exist two reflected beams caused by the complicated bottom topography. The southeast one is dominant and can spread across the deep basin of the South China Sea, consistent with satellite altimeter observations. The other one propagating eastward to the Luzon Strait is weak and absent in altimeter observations due to its low intensity. Li et al. [96] discussed the modulation of internal tides caused by turbulent mixing in the South China Sea using MITgcm and indicated that turbulent mixing altered horizontal density in the South China Sea and then increased the incoherence of internal tides.

In recent years, the internal tides in the Yellow Sea and the East/Japan Sea receive more and more attention. Jiang and Lv [97] studied the basic feature of M₂, S₂, K₁, and O₁ internal tides in the BYECS via a 3D layered tidal model. They found that internal tides are mainly generated in the Okinawa Trough and are stronger in the winter than in the summer. Jeon et al. [98] used an eddy-resolving high-resolution ocean model to investigate the seasonal variability of semi-diurnal internal tides in the East/Japan Sea. Their results indicated that due to the seasonality in ocean stratification near the southwestern East/Japan Sea, baroclinic energy conversion varied seasonally with minima in March (ranging from 0.11 to 0.16 GW) and maxima in September (ranging from 0.48 to 0.52 GW). The seasonal and spatial variations of M₂ internal tides in the Yellow Sea are studied by Liu et al. [17] via ROMS. They found that seasonal ocean stratification, induced by the East Asian monsoon, seasonal ocean circulation, and Yangtze river flow, controls the seasonal variations of the generation, propagation, and dissipation of M₂ internal tides in the Yellow Sea. Lin et al. [99] investigated M₂ internal tides in the northern Yellow Sea in the summer via ROMS and moored current observations. They indicated that internal tides are mainly generated in the shelf break regions near the Korean Peninsula with a restricted regional propagation.

7. Summary and Prospect

Tides play an important role in numerous economic sections such as coastal engineering, maritime logistics, and fishery [1]. Significant progresses in tidal dynamics in the EAMS have been made over the past few decades mainly due to ample water-level observations (especially satellite altimeter data) and improved numerical models with data assimilation [3,4,5,6,7,8,9,10]. The basic characteristics of barotropic tides in the EAMS are very clear, and the accuracy of ocean tide models is generally satisfactory. The focus of tidal research is gradually changing from stationary tides to nonstationary tides (such as river tides, internal tides) which show significant non-astronomical variations caused by natural variability and human interference. It is found that tides show multi-time scale variations (from seasonal to multi-decadal), which are not fully understood [100]. There are only few publicly accessible long-term (more than 20 years) tide gauges in the EAMS, which is not conducive to our understanding on secular tidal evolution. The impact of tides and tidal mixing on the ocean environment and climate is a potential hotspot. Tidal influences on the ocean ecosystem and climate modes have been reported based on observations, but detailed physical mechanisms are still unclear and can be further explored by means of numerical models. Furthermore, the nascent artificial intelligence methods, such as deep learning, provide an unprecedented opportunity to help tidal researchers analyze water-level data. The combination of artificial intelligence and ocean tidal models is another potential hotspot.