Characteristics of coastal trapped waves along the northern coast of the South China Sea during year 1990

Abstract

The structures and evolution of the coastal-trapped waves (CTW) along the northern coast of the South China Sea (SCS) in the year 1990 are studied using observed hourly sea level records collected from four sites around the northern SCS and a three-dimensional numerical model with realistic bathymetry and wind forcing. Analysis of the yearlong records of the observed sea level data indicates that the sea level variations are highly correlated between the stations and the sea level variability propagates southwestward along the coast. The sea level signals traveling from northeast to southwest along the coast with a propagation speed of 5.5–17.9 m s⁻¹ during both the typhoon season and the winter month show the characteristics of a CTW. The wave speed is faster between stations Shanwei and Zhapo than that between Xiamen and Shanwei. Sea level variations during both typhoon season and winter month are reasonably well represented by the numerical model. The model runs focused on the wave signals related to typhoons and winter storm show that the CTW propagating southwestward along the coast can be reinforced or decreased by the local wind forcing during its propagation and there are apparent differences in the propagation characteristics between the waves along the mainland and those traveling around Hainan Island. The abrupt change of the shelf width and coastline around Leizhou Peninsula and Hainan Island are responsible for strong scattering of CTWs from one mode into higher modes. The alongshore velocities across different transects associated with CTW are investigated to examine the vertical structures of the waves. The alongshore velocity structures at transects during different events are related to the combined effect of stratification and shelf profile, which can be estimated using the Burger number. The empirical orthogonal function analysis of alongshore velocity and nodal lines of the mode structure suggest mode two CTWs in transect S2 during typhoon season and mode 1 CTWs during winter. Sensitivity model experiments are also performed to demonstrate the effects of local wind and topography on the wave propagation.

1 Introduction

Coastal-trapped waves (CTW) exist on various continental shelves around the world, and these waves always travel to the right (left) along the coast when looking toward the propagation direction in the Northern (Southern) Hemisphere with the largest amplitude near the coast (Gill and Schumann 1974; Schumann and Brink 1990; Brink 1991; Ly 1994; Tang and Grimshaw 1995; Yankovsky 2009). Such waves with periods of a few days often play an important role in the variabilities on timescales between the inertial period and atmospheric weather changes over the continental margins (Brink 1991; Merrifield et al. 2002). The propagation features of CTW could be investigated using observed coastal sea level fluctuations and current structures (LeBlond and Mysak 1978). The alongshore component of the surface wind is often considered to be the main factor that generates the CTW which can deliver the response of the ocean in the alongshore direction during their propagation process (Brink 1991). The unique features of CTW have been given by Huthnance et al. (1986), and Brink (1991) also presented a thorough review on the observational and theoretical investigations of CTW on continental shelves.

In addition to the observational and theoretical studies of CTW, there have been many further investigations of the dynamic aspects of the CTW over different continental shelf and slope regions based on numerical models. Martínez and Allen (2004a, b) applied a hydrostatic primitive equation model to study the evolution of remotely forced CTW in the Gulf of California. Maiwa et al. (2010) did a thorough study of the propagation characteristics and spatial structures of CTW along the southern and eastern coasts of Australia based on a high-resolution ocean general circulation model and observed sea level data, and they also performed a series of sensitivity experiments using the Princeton Ocean Model. The large amount of energy injected into the coastal ocean by the strong winds associated with tropical cyclones often induced significant CTW (Eliot and Pattiaratchi 2010). There are also some researches focusing on the characteristics of the CTW generated by hurricanes (typhoons). Merrifield (1992) showed the low-frequency CTW event associated with tropical storms in the Gulf of California based on long-wave CTW theory. Eliot and Pattiaratchi (2010) clarified the propagation characteristics of the coastal trapped shelf waves using 10 years of tropical cyclones data and observed sea levels along the coast of Australia. They classified the tropical cyclones paths into six different types based on the amplitudes of the trapped shelf wave by analyzing the water level fluctuations and 10 years of tropical cyclone paths. Thiebaut and Vennell (2010) applied wavelet and cross-wavelet analyses of sea level records and described a fast continental shelf wave response along the east coast of Canada during Hurricane Florence. Moreover, numerical models are extensively used in the study of CTW associated with tropical storms. Ly (1994) have reported the CTW response to hurricane Frederic in the context of a numerical study. When CTW occurs along an island, the energy of the waves will be trapped around the island and CTW become island-trapped waves (ITW; Merrifield et al. 2002). Using a primitive equation model with real bathymetry, stratification, and wind forcing, Merrifield et al. (2002) performed three model experiments and reported the structure of the trapped waves generated by an extratropical cyclone around the Hawaiian Islands. On the continental shelf and slope on the eastern side of Sagami Bay, Igeta et al. (2007) used mooring observations of current and temperature together with numerical experiments to describe the generation and propagation of the CTW induced by typhoons. Based on two different horizontal resolutions of the HYbrid Coordinated Ocean Model forced by realistic winds, heat fluxes, rivers, and turbidity, Zamudio et al. (2010) studied the propagation of a hurricane-generated CTW inside the Gulf of California.

The South China Sea (SCS) is a large semi-enclosed marginal ocean basin with broad shelves in the western Pacific Ocean (Fig. 1). Connected with the East China Sea through the Taiwan Strait to the north, and adjoined with the Northwest Pacific Ocean by the Luzon Strait to the east, the SCS contributes significantly to the interactions between the Pacific Ocean and Indian Ocean (Hu et al. 2011). The SCS is influenced extensively by the East Asia Monsoon (Liang 1991). The southwest monsoon prevails from May to August, whereas the strong northeast winter monsoon runs from September through April. Tropical cyclone generated over the northwestern Pacific Ocean or inside the SCS is also a dominant weather phenomenon in the SCS (Wang et al. 2007). Observational studies have provided evidence for the CTW along the northern coast of the SCS generated by winter storms or tropical cyclones (Chen and Su 1987; Li 1989, 1993).

Fig. 1

Study area and bathymetry of the northern SCS. Contour value in meters. The transect used to illustrate the vertical structure of alongshore currents are shown in dashed lines. Sea level stations along the coast are indicated by black solid circle

Although the observational studies using sea level data in coastal region have already confirmed the presence of the CTW along the north coast of the SCS, comparatively few investigations have intensively examined the CTW around this region, especially modeling studies. Due to the limitation of observations and difficulties in simulating the CTW along the northern coast of the SCS using numerical models, the spatial structure and propagation process of the CTW still remain unsolved. Here, we examine the generation and propagation characteristics of the CTW along the northern coast of the SCS based on the observed sea level data and the unstructured grid, primitive equation, finite volume coastal ocean model (FVCOM) using realistic bathymetry and wind forcing. A set of numerical experiments were also performed to analyze the CTW propagation feature and sensitivity of the CTW to topography and local wind forcing. To our knowledge, this is the first modeling study of the CTW along the northern coast of the SCS with realistic wind stress and bottom topography. Given the fact that the SCS is under the influence of monsoon system and tropical cyclones originated in the Northwest Pacific Ocean, we focus on study of the CTW generated by winter storms and typhoons.

The rest of the paper is organized as follows: in Section 2, the observed data and the numerical model configuration are described. Section 3 briefly introduces the characteristics of the CTW associated with winter storm and typhoons based on the observed sea level fluctuations and wind field derived through cross-calibration and assimilation of ocean surface wind data from different satellites (Atlas et al. 1996, 2011). Section 4 presents the spatial structures and evolution of the CTW using a numerical model with realistic wind forcing and bathymetry. The sensitivity of the CTW to topography and local wind is examined by performing a series of model experiments in Section 5. The summary and conclusions are provided in Section 6.

2 Data and model configuration

2.1 Observed data

Observed sea level data records at hourly intervals at four tide gauge stations along the north coast of the SCS, obtained from University of Hawaii Sea Level Center were used for the CTW analysis and model validation. Locations of the tide gauges are shown in Fig. 1, including Xiamen (XM), Shanwei (SW), HongKong (HK), and Zhapo (ZP), extending a distance of more than 750 km off the north coast of the SCS. Hourly sea level data was detided using T_TIDE (Pawlowicz et al. 2002). The low-frequency water level time series at the stations were obtained by removing oscillations with frequencies higher than 1.29 cpd. The low pass-filtered result of the detided sea level data at station XM during typhoon OFELIA and PERCY is shown in Fig. 2. Yearlong records of the observed sea level data of 1990 were selected for the case study. Station HK and SW are located close to each other and the water level fluctuations at the two stations are of similar pattern. In addition, considering that the time series of water level fluctuations have broad peaks and it is not easy to estimate the time lags to within a short time, sea level records at XM, SW, and ZP were mainly used in the following analyses.

Fig. 2

Detided sea level record at XM station before (thin line) and after (thick line) low-pass filtering during typhoon OFELIA and PERCY

The surface atmospheric pressure data at 6-hourly interval extracted from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research reanalysis products provided by the NOAA–CIRES Climate Diagnostics Center, were used to adjust the observed sea level records for atmospheric pressure loading effects. The corrected sea level elevation is given by (Schumann and Brink 1990)

$$ \eta = 0.99{p_a} + {\eta_0} $$

(1)

where, p _a is the sea surface atmospheric pressure variation in millibars, η ₀ is observed sea level in centimeters, and η is the adjusted sea level elevation in centimeters. The 6-hourly surface pressure data with a resolution of 1° are interpolated to 1 h records using a linear method to match the sea level data. Omitting the errors in the air pressure data will indeed lead to a discrepancy of sea level fluctuations between model results and observations. The discrepancy induced by the errors in the air pressure data from NCEP is acceptable in our current research and more efforts will be made to quantify errors in the atmospheric pressure from NCEP reanalysis data in our future study.

The 6-hourly wind data at 10 m above the sea surface derived from the cross-calibrated multi-platform (CCMP; Atlas et al. 1996, 2011) are used for analysis and to force the numerical model. The CCMP wind covering the global ocean with a relatively high spatial resolution of 0.25° in both latitude and longitude is able to better capture the motions of tropical cyclones. The wind fields are decomposed into alongshore and cross-shore directions after interpolated to hourly records and low pass filtered in order to investigate the contribution of wind to coastally trapped signals. Southwestward is selected as the positive direction for the alongshore wind component. In addition, the tracks of typhoons are obtained from the best track archives of the Joint Typhoon Warning Center.

2.2 Model description

The unstructured grid, primitive equation, FVCOM (Chen et al. 2003, 2006a, b, 2007) is used in the modeling study, which employs a finite-volume discrete method using a system of irregular triangular grids (Chen et al. 2003) in the horizontal direction and a terrain-following σ coordinate in the vertical. A detailed description of FVCOM is given by Chen et al. (2003, 2006a, b). The vertical diffusion is derived from the Mellor and Yamada level 2.5 (MY-2.5) turbulent closure model (Mellor and Yamada 1982), while the horizontal diffusion is based on the Smagorinsky eddy parameterization method (Smagorinsky 1963). The bottom friction is based on the quadratic law and the wind stress is calculated from

(2)

where ρ _a is the density of air, V _w is surface wind speed, C _d is a drag coefficient dependent on wind speed and is computed by Large and Pond (1981).

The model domain covers the coastal region of the northern SCS extending from 13° to 28° N and from 105° to 128° E, with open boundaries placed far from the coastal region (Fig. 3). The horizontal grid resolution of the model varies from 5 km in the coastal region to 30 km in the open ocean. The resolution in coastal region is high enough to capture the coastally trapped signals. The triangular grid system is shown in Fig. 3, with 18,913 grid nodes and 36,692 triangular elements. In the vertical direction, 25 sigma layers are used, with 16 parallel levels set for the upper layer based on the parallel grid separation method (Pietrzak et al. 2002) to improve resolution in the surface Ekman layer. The upper 16 layers are divided as 2, 4, 8, 16, 20, 25, 25, 30, 30, 40, 50, 50, 50, 50, 50, and 50 m. The stratification below 400 m depth is not very significant and the depth of the continental shelf is less than 500 m, therefore we consider that the model construction is able to resolve the CTW in the coastal region. The water depths at all model nodes were determined using a combination of bathymetry data derived from China coastal sea chart database and topography data from DBDB5 (US Naval Oceanographic Office 1983) by interpolation of the depth data onto the model grid, with a minimum depth of 5 m applied at the coast.

Fig. 3

The model domain and horizontal unstructured grid used in the numerical model

A long gravity wave radiation boundary condition was applied for the open boundaries, and the standard nonslippery land boundary for the coast and bottom layer was used in the model. In addition, a sponge layer was also applied along the open boundaries to prevent energy accumulation along the boundaries to maintain model stable. In this study, the model external time step was 8 s, and the internal time step was 80 s determined by the Courant–Friedrichs–Levy numerical stability condition.

The ocean is set to be at rest at the initial state. The initial model stratification are horizontally uniform defined from winter (December) and summer (August) temperature and salinity field of Simple Ocean Data Assimilation (Carton and Giese 2008) with a pycnocline around 50–100 m depth for the region (Fig. 4). As Brink (1991) proposed that the CTW are mainly induced by alongshore winds, we use the numerical model to study the CTW response of the northern coast of the SCS to wind forcing. Therefore, the model is forced only by 0.25° horizontal resolution 6-hourly winds. No other forcing, such as surface atmospheric pressure, heat fluxes, tides, rivers, or flow is applied.

Fig. 4

Temperature and salinity profiles used in the model; a temperature, b salinity

The model ran for the time period of 1 August to 31 September and 10–31 December with 2 days’ ramp of model forcing. The model calculated sea surface elevation, horizontal current, and temperature. Data were stored every hour and used in the model results analysis. Two control model runs were examined: typhoon season run from 1 August through 31 September and winter month run from 10 to 31 December. Sensitive numerical experiments were also made for summer and winter month conditions. For summer case, a sensitive experiment was run by applying winds only within a certain area around the northern part of the model domain. For winter case, in addition to the sensitivity experiment of local wind, two additional model experiments were initiated by closing the Qiongzhou Strait and broadening the continental shelf around Hainan Island to diagnose the effects of topography on CTW propagation.

3 Analysis of the observed sea level fluctuation

3.1 Sea level fluctuations

Sea level fluctuations can be used to examine the coastally trapped signal (Schumann and Brink 1990). Figure 5a shows the low-passed time series of sea level variations at stations XM, SW, and ZP during the year 1990. The time variations of alongshore wind speed are also indicated in Fig. 5b. The low-passed sea level fluctuations dominated mainly by the weather system are quite similar along the north coast of the SCS from XM to ZP, especially between stations SW and ZP. Higher water level amplitudes mainly occur in summer and autumn with frequent tropical cyclone events. Significant surges are seen at stations ZP and XM with peak positive surges of 66 and 65 cm occurred in August, whereas the maximum surge level for SW is nearly 50 cm. We can note from Fig. 5b that the alongshore wind speed at the three stations are also similar during most of time period.

Fig. 5

a Time series of low frequency water level fluctuations and b the alongshore wind speed during year 1990. Southwestward is selected as the positive direction for the alongshore wind component

To examine the sea level propagation, we calculated the correlations between XM sea level variation and sea levels at SW and ZP (Table 1). The correlations between sea level variation and alongshore wind speed at the three stations were also calculated (Table 2). Similar to previous studies (Chen and Su 1987; Li 1993), the observed sea level variations are highly correlated between stations along the northern coast of the SCS. The correlation is equal to 0.89 between sea level signals at SW and XM with XM leading SW by 15 h, and 0.81 between ZP and XM with a lag of 23 h. The maximum correlation (0.96) occurs between SW and ZP when the sea level at ZP lags the sea level at SW by 6 h. The correlations between observed sea level at XM and observed sea level along the coast decrease gradually to the southwest from SW to ZP. This indicates that the sea level variability at XM propagates southwestward as coastal waves and the sea level signal is modified during the propagation process. Figure 5 and Table 2 reveal high coherence at low frequencies between observed sea level variations and alongshore wind speed at the observational locations, with correlations ranging from 0.75 to 0.80. The sea levels at tide gauge stations rise due to onshore Ekman transport when the alongshore wind is southwestward, whereas the observed sea levels drop as a result of offshore Ekman transport when the alongshore wind is northeastward.

Table 1 Maximum correlations and lags (hours) between observed water levels at different stations

Table 2 Maximum correlations and lags (hours) between observed water levels and corresponding alongshore wind component at the three stations

As can be seen from the low-frequency time series of sea level elevations shown in Fig. 5a, the water level fluctuations are highly related to the weather systems including tropical cyclones and winter storms. It is important to note that the sea level variations associated with winter storm from November to October and from January to February are quite different from the sea levels during typhoon season. It is apparent that the wave signals related to winter storm are more cyclical and persistent compared to the sea level signals in association with typhoons, mainly due to the periodical winter storm burst. In contrast, the sea level signals induced by typhoons show high variability from time to time, which are mainly related to the different intensity, traveling speeds, and landing locations of typhoons.

3.2 Sea level variations related to typhoons and winter storm burst

The analysis of the sea level variations in previous subsection led us to focus on sea levels during typhoon season and winter months. Here, we use the low-passed sea level variations related to typhoons and winter storms to examine the characteristics of the coastally trapped low frequency signal.

Figure 6a and b shows the time variations of low pass-filtered sea level and alongshore wind component at stations XM, SW, and ZP during August and September when tropical cyclones influence the SCS frequently. The passages of main typhoons attacking the north coast of the SCS during this period are also indicated in Fig. 6c. Large sea level fluctuations are present at the three stations related to typhoons’ passage. The sea level fluctuations are seen to be related with the alongshore wind at three stations, with sea level trough caused by negative values while large water level peak induced by positive values of alongshore wind speed. The amplitude of water level signal is estimated based on trough to crest measurements (Eliot and Pattiaratchi 2010). Large amplitude of about 80 cm occurs at ZP around 29 August when typhoon ABE and BECKY proceeding toward the SCS simultaneously. Higher amplitudes reaching 80 and 60 cm are also seen at XM and SW.

Fig. 6

a Time series of low frequency water level fluctuations, b alongshore wind component at three stations and c the tracks of typhoons during the period of 9 August–31 September 1990 (TC1 YANCY, TC2 ABE, TC3 BECKY, TC4 DOT, TC5 ED, TC6 GENE), the circles on the tracks represent the time interval of 6 h, d water level fluctuations during typhoon DOT, e water level fluctuations during typhoon ED

Note from Fig. 6a that there are apparent phase lags between the sea level responses at stations XM, SW, and ZP with XM leading SW and ZP, indicating that the wave signal propagates southwestward from XM to SW. The time lags are estimated from troughs and crests between stations by overlaying the time series of sea level at different stations in the same figure. The propagation speed of sea level variations is calculated using the lag time of sea level crests and distance between neighboring stations (Schumann and Brink 1990; Ly 1994). The travel speed of the peaks is estimated as 5.5–12.4 m s⁻¹ between XM and SW, and 8.3–17.9 m s⁻¹ between SW and ZP, respectively. It is noticeable that the sea level signal characterized by this range of travel speed and unidirectional propagation from northeast to southwest shows the feature of a CTW. However, it is difficult to separate the locally generated surge from the coastally trapped signal in the observed sea level data and the interaction between wave signal and storm surge generated by local wind forcing precludes the accurate estimation of propagation speed and amplitude of the CTW. This can be noticed clearly from the sea level variations during the time 1–24 September in Fig. 6a, where we can see that the surge level at SW and ZP is much higher than that of XM. It is supposed that the wave signal induced by the alongshore wind associated with typhoons propagated southwestward and interact with the local surge, causing higher surge levels.

It is also important to note that the peak of sea level variation shows propagation from XM to SW during 5–10 September as typhoon DOT progressed northwestward from Pacific Ocean and crossed the Taiwan Strait, as the sea level peak at SW seems not to be related to the local winds. Analysis of sea level data also shows that the amplitude of sea level fluctuation reaches up to about 50 cm at XM and decreases rapidly to about 10 cm when arriving at SW, and there is no clear sign of sea level peak at ZP. In addition, there are no apparent indications in the sea level disturbances propagating from SW to ZP, as the water level fluctuations in ZP seem to be mainly dominated by local winds.

Note from Fig. 6c that there are two representative types of typhoon tracks influencing the northern coast of the SCS significantly, with one type moving northwestward from the North Pacific Ocean and passing through over the Taiwan Strait and the other traveling eastward along approximately 18° N. To compare the differences in sea level response between the two types of typhoons, different sea level variations during typhoon DOT and typhoon ED are presented in Fig. 6d and e. Note from sea level fluctuations at the three stations that typhoon tracks make significant differences in the distribution of storm surge along the north coast of the SCS. High sea level of about 50 cm is located at station XM, which is related to the strong southwestward alongshore wind associated with typhoon DOT. After typhoon DOT made landfall, the alongshore winds are mainly northeastward, driving an offshore Ekman transport which weakened the surge level along the coast west of SW. We can see that the surge reaches only 10 cm at SW and no obvious sea level peak is seen at ZP. During typhoon ED, the situation is different, which can be noted from Fig. 6d. Sea levels of 10–15 cm are established, increasing slowly as the sea level signal moves westward along the coast. The increment is mainly related to the track of typhoon ED.

The sea level curves at three stations related to winter storm during December are plotted in Fig. 7a, and the alongshore wind components are also indicated in Fig. 7b. Unlike the time series of sea level data during typhoon season, no extremely large sea level fluctuation is found during this period. The amplitude of sea level variations ranges from 5 to 50 cm at all three stations, with largest amplitude appearing at XM. Similar to the sea level responses under the influence of typhoons, a significant phase lag between the stations along the coast can be seen in the water level signal. Comparing the sea level at XM from SW gives a time lag of about 11–13 h, while the sea levels at SW and ZP give a time lag of about 6–12 h. The sea level peaks and depressions are seen to propagate southwestward from XM to ZP as a signature of CTW with a wave period of about 3–4 days. The phase speed of wave signal between the stations is determined by tracing sea level maxima or sea level crest from the observed sea level fluctuations (Schumann and Brink 1990; Ly 1994). Using an averaged value of time lags and the distances between stations, the propagation speed is estimated to be about 5.5–11.1 m s⁻¹ from XM to SW and 9.7–17.9 m s⁻¹ from SW to ZP. It is also interesting to note that the time series of the observed sea levels are highly related to the alongshore wind and seem to be more periodic compared with the sea levels in typhoon season (Fig. 6a).

Fig. 7

Time series of low frequency a water level fluctuations and b alongshore wind speed during the period of 11–31 December 1990

Figure 8 shows the space–time contours of the low-passed fluctuations in the observed sea level anomaly at the three stations covering the periods of winter months and typhoon season in 1990. The propagation of the sea level variability is apparent along the coast both in the winter months and typhoon season. However, there are some differences of the propagation characteristics between the wave signals during the two periods. The amplitudes of wave signal are significantly higher under the influence of typhoons; however, the propagation of the signal is not always continuous from XM to ZP. On many occasions, the amplitude of some propagation signals associated with typhoons drops significantly during the propagation toward southwest along the coast (Fig. 8c,d), while some of the signal are strengthened as they arrive at station ZP due mainly to the local wind forcing. On the other hand, the propagation signals excited by the winter storm burst (Fig. 8a,b) seem to propagate all the way from XM to ZP on most occasions with a dominant wave period of about 3–4 days. The propagation speed of wave signals is estimated using the slopes by fitting lines along the contours. As can be seen from Fig. 8, the phase speed for water level signals in winter months are more consistent in comparison with the signals during typhoon season. The average propagation speed of the waves along the coast during typhoon season is estimated to be 10.9 m s⁻¹ while it is 10.7 m s⁻¹ during winter season. The waves seem to propagate faster during the typhoon season, since the stratification in summer or autumn would act to increase the phase speed (Schumann and Brink 1990; Brink 1991). It is also important to note that wave speed is faster between station SW and ZP than that between XM and SW as pointed out by one of the reviewer. We consider that the sea level peaks propagate westward mainly in the form of a forced wave along the northeastern coast while the free component of the waves becomes more important along the southwestern coast. As can be seen from the sea level fluctuations during different events, especially during winter, that the sea level peaks at XM are relatively larger than those at SW and ZP during most of the time, indicating that the sea level maxima at northwestern coast may cause a forced wave. In addition, the width of the continental shelf east of transect S1 is relatively narrower compared with the shelf east of S1 as can be noted from Fig. 1, which may be also responsible for the phase speed difference between the XM–SW shelf and SW–ZP shelf.

Fig. 8

Space–time contours of low frequency water level variability (centimeter) during winter months (a, b) and typhoon season (c, d)

The observed water level fluctuations at the three stations along the northern coast of the SCS are analyzed to study the propagation characteristics of coastally trapped signal. The wave signals are mainly dominated by weather systems during different seasons. According to the features of the sea level variations, the propagation signals are classified into two types: (1) wave signal related to typhoons and (2) wave signal induced by winter storm burst. Due to the limitation of the observed data, the spatial scale, and evolution of the CTW are not easily explored. Therefore, we use a numerical model to further investigate the characteristics of the CTW along the northern coast of the SCS in the next section.

4 Numerical study on wave structure and propagation

4.1 Typhoon season case

The first model run (case TS0) covering the period of August and September is used to illustrate the general structure and propagation features of the trapped wave along the coast associated with typhoon events. The model simulated time series of sea levels at the four stations are compared with the observed data to assess the model performance. The model–data comparison is given in Fig. 9. The model-calculated sea level fluctuations show reasonably good agreement with the observations. The observed curves of sea level are very similar to the modeled ones, and the coastally trapped signal can be clearly recognized in both model result and observations. The shelf waves are strongly related to the cyclone track (Fandry et al. 1984; Tang and Grimshaw 1995; Eliot and Pattiaratchi 2010) and there were mainly six typhoons generated in the western Pacific Ocean influencing the coastal regions of the north SCS (Fig. 6c) during this period. In order to study the differences of CTW response between these two types of typhoon tracks, the trapped wave signals associated with typhoon DOT and ED were selected for the case study. Typhoon DOT moved northwestward from the North Pacific Ocean and passed through over the Taiwan Strait with maximum sustained winds of ∼39 m s⁻¹, following the path shown in Fig. 6c, and finally made landfall on the west coast of the Taiwan Strait around 06:00 on 8 September 1990. Typhoon ED progressed westward after generation and during 14–18 September it followed a path approximately parallel to the north coast of the SCS after crossing the Luzon Strait. The maximum sustained winds reached up to ∼46 m s⁻¹ on 16 September.

Fig. 9

Time series of observed (solid lines) and modeled (dashed lines) sea level at Xiamen, Shanwei, HongKong, and Zhapo during August and September. The observed sea level data have been de-tided, corrected for atmospheric pressure loading effect and low-pass filtered. The locations of the four stations are indicated in Fig. 1

Figure 10 shows the evolution of the CTW generated by typhoon DOT, and the wind field vectors associated with the typhoon are also represented in Fig. 11. As typhoon DOT approached the Taiwan Strait on 7 September (Fig. 11a), strong southwestward alongshore winds associated with the typhoon caused an onshore Ekman transport and generated a significant sea level convergence on the west coast of the Taiwan Strait (Fig. 10a). Similar alongshore wind forcing continued to enhance the coastal convergence trough 12:00 on 7 September. The strong convergence caused a maximum surge level of more than 30 cm and generated a CTW propagating toward southwest (Fig. 10b–c). The alongshore and cross-shore scales of the CTW simulated by the FVCOM model were 780 and 100 km, respectively. The propagation speed of the wave was estimated to be 4.0–5.0 m s⁻¹ and the maximum near-shore surface currents associated with the CTW obtained 70 cm s⁻¹. In addition, the subsurface currents reached about 40 cm s⁻¹.

Fig. 10

Sea surface height anomaly (color contours in meter) and surface velocities around the northern SCS for six different times in September during typhoon DOT from typhoon season case with the numerical model. The scale bar was cropped in order to show more contrast in the figure

Fig. 11

Distribution of wind field vectors during typhoon DOT used in the model determined by CCMP data. The solid line denotes the typhoon track and the grid point is the current typhoon center position

After its generation, the CTW continued to propagate southwestward along the coast arriving around west of HK and weakened gradually as the southwestward alongshore wind decreased (Fig. 10d). After typhoon DOT made landfall on the mainland of China around 18:00 on 8 September, the northeastward alongshore winds prevailed throughout this region (Fig. 11e–f), and drove an offshore Ekman transport which weakened the wave propagation. The CTW decayed most rapidly by the upwelling favorable winds after passing HK and the wave signal characterized by amplitude of a few centimeters disappeared before arriving at ZP (Fig. 10f).

The generation and propagation of the CTW excited by typhoon ED on September 14–17 is given in Fig. 12. When the center of the typhoon was located east of the Luzon Strait (Fig. 13a and b), a negative sea surface height signal was seen to propagate southwestward along the coast, preceding the positive signal. When typhoon ED was approaching the Luzon Strait on September 14, the southwestward winds around the Taiwan Strait forced surface Ekman transport to the west coast of the Taiwan Strait, resulting in sea level convergence around the coast. The convergence raised the sea surface height 10–15 cm along the coast (Fig. 12c), and a CTW was generated along the west coast of the Taiwan Strait. The wave propagated southwestward with no major changes before arriving at ZP (Fig. 12d). The alongshore scale of the CTW was much larger than that of the cross-shore. Enhanced coastal currents of about 35 cm s⁻¹ associated with this CTW were also evident.

Fig. 12

Same as Fig. 10, but for eight different times in September during typhoon ED

Fig. 13

Distribution of wind field vectors during typhoon ED used in the model determined by CCMP data. The solid line denotes the typhoon track, and the grid point is the current typhoon center position

It is interesting to note that during its southwestward propagation the CTW was strengthened, especially around the coast west of ZP. Typhoon ED’s path is considered to be a main factor in the CTW enhancement. On September 16, typhoon ED continued to move westward with maximum sustained winds of 38.5 m s⁻¹ (Fig. 13e). Strong southwestward winds drove an onshore Ekman transport which further enhanced the CTW signal. The CTW along with onshore Ekman transport driven by alongshore winds raised sea surface height exceeding 20 cm and the winds forced the wave to continue to progress westward.

At the Qiongzhou Strait the wave split into two waves (Fig. 12f), with one wave continued propagating westward after passing through the Qiongzhou Strait, while the other wave was observed trapped by the Hainan Island and traveling anti-clockwise around the island in the model as an ITW (Fig. 12g). Both of the two waves entered the Gulf of Tonkin and met each other inside the gulf, causing the sea level to raise 10–15 cm, which could be seen in the fields of surface velocity and sea surface height anomaly (Fig. 12h).

Figure 14 shows the two-dimensional structure of the alongshore velocity over transect S1 when the CTW associated with typhoon DOT passed the transect. On September 7, 00:00, southwestward velocities of about 15–30 cm s⁻¹ occurred in the upper layer near the coast (Fig. 14a). Half day later, on September 7, 12:00 (Fig. 14b), the southwestward velocities began to strengthen. The strong alongshore velocities propagated downward and reached the bottom rapidly. The maximum alongshore velocity reached up to more than 40 cm s⁻¹ and the cross-shore scale stretched nearly 200 km in the surface layer. By September 8, 00:00, the alongshore velocities continued to intensify with maximum value obtaining about 70 cm s⁻¹ in the surface layer, and the alongshore velocities at the bottom reached 30 cm s⁻¹. After September 8, 00:00, the southwestward velocities began to decrease and the surface southwestward alongshore velocities decreased to about 20 cm s⁻¹ by September 9, 00:00 (Fig. 14f).

Fig. 14

Alongshore velocity (color contours in meter per second) for six different times in September during typhoon DOT simulated in the model over cross-transect S1 indicated in Fig. 1. Positive values indicate southwestward currents. Negative values are drawn as dashed lines and thick line indicates zero contour

The evolution of the alongshore velocity across transect S2 when the CTW induced by typhoon ED passed the transect is shown in Fig. 15. The alongshore current at the surface layer shows a southwestward flow reaching 30 cm s⁻¹ at 00:00 on 15 September. The southwestward alongshore velocity component was almost uniform above 10 m depth and it penetrated to 20 m depth in the region 100 km offshore (Fig. 15a). However, a northeastward countercurrent developed near the bottom next to the coast with maximum value reaching up to 20 cm s⁻¹. Six hours later, the surface southwestward alongshore velocity was intensified rapidly and the maximum value reached more than 35 cm s⁻¹. It is interesting to note that the core region of the northeastward flow propagated downslope along the bottom; and at 12:00 on 15 September, it reached around 60 m depth with decreased value of less than 10 cm s⁻¹. The strong southwestward alongshore velocity propagated slowly offshore (Fig. 15b–f) and gradually weakened. By the time 06:00 on 15 September (Fig. 15b), a southwestward alongshore current developed at the bottom next to coast behind the northeastward flow. The southwestward alongshore velocity was intensified with time and propagated downslope along the bottom. At 18:00 on 15 September, the core region of this southwestward alongshore velocity reached 40 m depth and the maximum velocity obtained 35 cm s⁻¹. It continued to propagate downslope and the magnitude was gradually decreased in the next 12 h (Fig. 15e–f).

Fig. 15

Alongshore velocity (color contours in meter per second) for six different times in September during typhoon ED simulated in the model over cross-transect S2 indicated in Fig. 1. Positive values indicate southwestward currents. Negative values are drawn as dashed lines and thick line indicates zero contour

4.2 Winter month case

Our next model simulation (case W0) focuses on the trapped wave signal related to winter storm burst. Figure 16 shows the time series of the observed and modeled sea levels at the four coastal stations. The modeled and observed sea levels are in good agreement during this period. It appears that the phase of the wave signal was well simulated in the model simulation. However, the model result underestimated the amplitude of the sea level fluctuations, which could be also seen in the typhoon season case run. The underestimation of wave amplitude could be due to the 6-hourly 0.25° resolution wind forcing and the inaccurate coastal bathymetry at tide gauge stations. In addition, excluding the interaction between wave signal and tide led to further discrepancy, as the characteristics of surge and wave were strongly influenced by the tidal amplitude and phase (Kim et al. 2008). Moreover, the errors in atmospheric pressure from NCEP data also affect the accuracy of the adjusted water level fluctuations.

Fig. 16

Time series of observed (solid lines) and modeled (dashed lines) sea level at Xiamen, Shanwei, HongKong, and Zhapo during winter. The observed sea level data have been de-tided, corrected for atmospheric pressure loading effect and low-pass filtered

The model-simulated sea surface height anomaly and surface current vectors during December are present in Fig. 17. The wind forcing used in the model for this case run is shown in Fig. 18. Note that the southwestward winds prevailed through December and favored convergence along the north coast of the SCS. On December 11 at 18:00 (Fig. 17a), a CTW characterized by a positive sea surface height with alongshore scale of 400 km and cross-shore scale of 70 km was induced along the west coast of the Taiwan Strait. During southwestward traveling along the coast, the alongshore scale and amplitude of the CTW were enlarged, which could be noticed from Fig. 17b. The wave continued its southwestward propagation until it arrived at the Qiongzhou Strait, where the wave was divided into two branches (Fig. 17c), with one branch passing the Qiongzhou Strait and continuing to travel along the coast of the Gulf of Tonkin, and the other propagating anti-clockwise around the Hainan Island in the form of an ITW. This is similar to the propagation pattern of the CTW induced by typhoon ED in the typhoon season case run (case TS0). We can also notice from Fig. 17e–g that a negative sea surface height signal followed the positive signal and also propagated southwestward, however, the negative signal decayed rapidly and disappeared before reaching station HK. After the negative signal vanished, a positive sea surface height was generated to the west coast of the Taiwan Strait (Fig. 17g), and a second CTW was excited due mainly to the southwestward periodic wind forcing.

Fig. 17

Sea surface height anomaly (color contours in meter) and surface velocities around the northern SCS for eight different times in December during winter storm burst case with the numerical model

Fig. 18

Distribution of wind field vectors during winter month used in the model determined by CCMP data

The structures of alongshore current over transect S3 simulated in winter month case are shown in Fig. 19. The velocity structures indicate that the southwestward alongshore current variability was trapped mainly within about 50 km of the continental shelf near the coast and in the layer shallower than 30 m depth. The maximum value of southwestward alongshore velocity reached up to 46 cm s⁻¹ at the surface layer near the coast and rapidly offshore decay of the alongshore velocity can be seen clearly. It is also interesting to note that the structures of alongshore velocity at transect S3 during winter is similar to that at S1 during typhoon DOT, and the structures are dominated by barotropic response for both events.

Fig. 19

Alongshore velocity (color contours in meter per second) for six different times in December during winter storm simulated in the model over cross-transect S3 indicated in Fig. 1. Positive values indicate southwestward currents. Negative values are drawn as dashed lines and thick line indicates zero contour

As can be seen from the cross-shelf structure of the alongshore velocity shown in Figs. 14 and 15, the stratification conditions for the two transects are nearly the same but the wave properties during the two events are different. We considered the difference of the cross-shelf structure between the two events to be related to the shelf profile of the two transects, as we can see that the continental shelf over transect S1 is narrower than that of S2 and the water depth is also shallower. In order to compare the CTW response between different events, the consistent transect S2 is selected and we calculated the cross-shelf structure of alongshore velocity during typhoon DOT at S2 (Fig. 20a–h). The results show that the cross-shelf structure over S2 during typhoon DOT is similar to that during typhoon ED (Fig. 20i–p). The cross-shelf structure of alongshore velocity in the same transect are similar.

Fig. 20

Alongshore velocity (color contours in meter per second) for different events simulated in the model over cross-transect S2 indicated in Fig. 1. Positive values indicate southwestward currents (a–h during typhoon DOT, i–p during typhoon ED, q–x during winter storm)

As we know that the wind stress term in primitive equation of momentum is divided by the total water depth. Thus, the effect of wind stress becomes significant as the water depth shallows (Flather 2001). The water depth along the shelf region in S1 is less than 40 m and the strong wind during typhoon DOT may influence the whole water column, so the cross-shelf structure of alongshore velocity shown in Fig. 14 seems to be a barotropic response. We also estimated the Burger number (Clarke and Brink 1985; Wilkin and Chapman 1990) to measure the strength of the stratification as one of the reviewer suggested. The Burger number is defined as Bur = NH/fL, where N is the Brunt–Vaisala frequency, f is the Coriolis factor, L is the cross-shelf distance from the coastline to deep ocean with a flat bottom, and H is the depth of the deep ocean. The estimated Burger number for transect S1 equals 0.14 ≪ 1 while the Burger number for transect S2 equals 0.85–1. According to Clarke and Brink (1985), the stratification effect is relatively more significant in transect S2. Therefore, barotropic response dominants the cross-shelf structure of alongshore velocity during typhoon DOT at S1, while the cross-shelf structure at S2 during typhoon ED is mainly baroclinic. The dynamics of the complex alongshore velocity structure at S2 need further investigation in future studies.

We also calculated the cross-shelf structure of alongshore velocity during winter at the same transect (Fig. 20q–x). The alongshore velocity structure is not as complex as in typhoon season and seems to be a barotropic response. The stratification is not obvious as can be noted from Fig. 4, and the Burger number for transect S2 during winter is estimated to be 0.04, which indicates that CTW response at transect S2 during winter is mainly barotropic. Note that the alongshore velocity structures at the transects during different events are related to the combined effect of stratification and shelf profile, which can be estimated using the product of Brunt-Vaisala Frequency and the average shelf slope (Clarke and Brink 1985; Wilkin and Chapman 1990; Johnson 1991). It is concluded that the cross-shelf structures of alongshore velocity are dominated by barotropic response during both typhoon events and winter storms if the stratification effect is not significant at a certain transect, whereas the structures of alongshore velocity at the transect is mainly a baroclinic response during typhoon season when the stratification effect is significant.

4.3 Free coastal trapped wave response

The general characteristics of free CTW are discussed by Allen (1975), Huthnance (1975, 1978), Clarke (1977), Wang and Mooers (1977), Brink (1982), and Battisti and Hickey (1984). To study the free waves properties along the north coast of the SCS, another model run is performed and the wind forcing is applied only in the northeastern corner of the model domain (Fig. 21a). The density stratification and topography in this model experiment are the same as typhoon season case run and winter month run. The wind forcing over the northeastern corner is abrupt in the model and lasts for a very short time. Under these conditions, the alongshore velocity component at transect S2 is calculated to examine the free wave response.

Fig. 21

Wind forcing in the free wave model run (a) and alongshore velocity structure (color contours in centimeter per second) for summer (b) and winter (c) over cross-transect S2. Positive values indicate southwestward currents

The cross-shelf structure of alongshore velocity at the arrival of the leading edge of the wave signal for summer and winter stratification is depicted in Fig. 21b–c. Note from Fig. 21b that the response of alongshore velocity for summer condition is mainly barotropic, taking the form of barotropic shelf waves. The results are in accordance with the analysis of Brink (1982) and Battisti and Hickey (1984). The response of alongshore velocity is strongest at the coast and decays gradually offshore, and there is no obvious decay with depth. The maximum current speed obtains 0.85 cm s⁻¹ near the coast. The model is also run with weak stratification in winter to examine the sensitivity of model simulated free wave structure and propagation to stratification variations. As can be seen from Fig. 21c, a similar depth-independent alongshore velocity structure is observed for winter condition. The phase speed is calculated based on the time lags for maximum correlation of the sea level fluctuations along the coast. The phase speed along the coast for free wave during summer is estimated to be 12.0 m s⁻¹, and the speed is not significantly affected by the stratification changes. The comparison between the free wave properties under different stratification conditions indicates that the cross-shelf structure of alongshore velocity and phase speed are not significantly affected by changes in stratification, which is consist with the result of Battisti and Hickey (1984).

4.4 The cross-shelf wave structure

In order to understand the cross-shelf structure of the CTW signals, the empirical orthogonal function (EOF) analysis is applied to the alongshore velocity anomaly at S2 during different events. EOF analysis is useful in separating organized signal from noise (Pizarro and Shaffer 1998). The EOF method has been used by oceanographers in the study of CTW over different continental margins (Battisti and Hickey 1984; Merrifield 1992; Pizarro and Shaffer 1998).

Figure 22 shows the spatial structure of EOF modes 1 and 2 for alongshore velocity at S2 during typhoon DOT, ED, and winter storm. The first and second EOF modes account for 48 and 32 % of the total variance during typhoon DOT, 42 and 30 % during typhoon ED, and 90 and 7 % during winter storm. It can be seen that EOF mode 1 during typhoon DOT is characterized by a two-layer structure (Fig. 22a). The maximum velocity amplitudes are found in the region about 140 km offshore, with core of positive values locating in 50 m depth and core of negative values locating in 20 m. Mode 2 during typhoon DOT is dominated by a three-layer structure with maximum positive amplitudes locating in 20 and 40 m depth (Fig. 22d). The spatial patterns of EOF mode 1 and 2 during typhoon ED mainly feature three-layer structures (Fig. 22b,e), and the structure of the second mode resembles that of mode 2 during typhoon DOT (Fig. 22d). The EOF analysis of alongshore velocity and nodal lines of the mode structure suggest mode 2 CTWs at transect S2 during typhoon season. The EOF mode 1 and 2 during winter are shown in Fig. 22c and f. As can be noted from the mode structure during winter that the amplitude of alongshore velocity is smaller than that during typhoon season. We can also see that the variability of alongshore velocity is trapped near the coast in the upper 40 m and the vertical structure is highly barotropic, suggesting the mode 1 CTW at S2 during winter.

Fig. 22

Spatial structure of EOF modes 1 and 2 of alongshore velocity at S2 during typhoon DOT (a, d), typhoon ED (b, e) and winter storm (c, f). Negative values are drawn as dashed lines and thick line indicates zero contour

5 Model experiments on CTW’s sensitivity to local wind forcing and topography

5.1 Sensitivity to local wind forcing

In order to investigate the effect of local winds on the CTW propagation, we applied the wind forcing only in the northern region of the model domain (Fig. 23, upper panel) based on the method of Maiwa et al. (2010). This region is chosen as the west coast of the Taiwan Strait is considered to be where the CTW are generated in the model domain. Wind forcing of typhoon season case and winter month case within the selected region are used to force the model and other model conditions are the same as the original runs. The two model runs forced by typhoon wind and winter storm within the particular region are referred to as case TS1 and case W1, respectively.

Fig. 23

Space–time contours of model-calculated sea level anomaly (color contours in centimeters) for a case TS0 and b case TS1. The wind forcing for case TS1 at 00:00 on 7 September is also shown in the upper panel

The space–time contours of model-calculated sea level anomaly at the nine stations in the model experiments are shown in Figs. 23 and 24. The propagation of the sea level variability from northeast to southwest coast of the SCS is apparent both in case TS0 (Fig. 23a) and case TS1 (Fig. 23b). However, the model experiment of case TS1 by applying wind only in the particular region shows some discrepancies in the propagation of the coastally trapped signal with case TS0. The propagation of the positive signal during August 18–20 is more continuous from station XM to station T5 for case TS1 than that for case TS0; however, the accompanying negative wave signal behind the positive signal seems to be weakened. This is mainly due to the omitting of offshore Ekman transport driven by local northeastward alongshore winds. On the other hand, the local wind forcing dominates the remote one during the time of August 25–30. As can be seen clearly in Fig. 23, the positive signal is greatly weakened when the local winds are ignored, especially around the coast west of HK. During this period, typhoon BECKY was moving westward across the north SCS, and the coastal region to the right of BECKY’s track was greatly affected by the onshore Ekman effect due to the local winds. Similar situation occurs during the time of September 14–19, when we can see that the local wind effect on the positive wave signal is more important than the remote one.

Fig. 24

Space–time contours of model-calculated sea level anomaly (color contours in centimeter) for a case W0, b case W1, c case W2, and d case W3

Figure 24a and b show the space–time contours of simulated sea level anomaly for case W0 and W1, respectively. It appears that the trapped wave signals simulated in case W1 are more evident than case W0. The amplitudes of positive wave signals are weakened for case W1 during December 10–20, and the propagation speed of the wave signals for case W1 is smaller than that of case W0, indicating that the local wind forcing enhanced the wave signals during their propagation. It is interesting to note that the positive wave signals are enhanced by only applying the remote wind forcing in case W1 during December 22–28. The positive wave signals propagate all the wave from station XM to T5 located southwest of Hainan Island. However, the positive wave signals in case W0 are not continuous along the coast. On the other hand, the negative signals during this period are weakened in case W1 compared with case W0. This indicates that the remote wind forcing dominates the positive wave signals whereas the local wind forcing dominates the negative signals during December 22–28.

5.2 Sensitivity to topography

Based on the simulation results of case W0 and case W1, it can be noticed that there is an abrupt drop in propagation speed of the CTW signals between the north coast of the SCS and the coast of Hainan Island. The propagation speed of the wave signals along the coast of China mainland was estimated to be 12.0 m s⁻¹ while this value reduced to 2.5 m s⁻¹ when the wave was trapped by Hainan Island after passing through the Qiongzhou Strait. In order to explain the change in the propagation speed of the wave, two additional numerical experiments were performed. Wind forcing used in the two model runs are same as case W1 by only considering the remote wind effect. In the first model experiment (case W2), the Qiongzhou Strait is closed so that the trapped wave cannot enter the Gulf of Tonkin. Another model experiment referred to as case W3 was conducted to examine the effect of continental shelf width on the wave propagation. In this case, the southeast continental shelf around Hainan Island was broadened to have similar width as that along the coast of the mainland.

Figure 24c shows the space–time contours of model-simulated sea level anomaly for case W2. The propagation speed of the ITW around Hainan Island is almost the same as that in case W1, and there is no obvious change in amplitude of the wave signal for case W2. The model experiments in case W1 and W2 indicate that the existence of the Qiongzhou Strait does not contribute to the abrupt decrease in propagation speed of the CTW. Figure 24d shows the simulation result for case W3. We can see that the propagation speed of ITW around Hainan Island simulated in this case does not decrease as much as in case W1 and W2. The propagation speed of the trapped wave signals after passing through the Qiongzhou Strait seems to be increased by widening the continental shelf width.

Large alongshore variations in coastlines and abrupt change of the shelf width may cause significant scattering of CTW energy from one mode into other modes as a result of mass and momentum conservation (Allen 1976; Wilkin and Chapman 1987, 1990; Webster 1987; Middleton and Wright 1988; Dorr and Grimshaw 1990; Johnson 1991; Middleton 1991, 1994; Yankovsky and Chapman 1995; Pizarro and Shaffer 1998). As can be noted from the topography of the north SCS shown in Fig. 1, the geography of this region is characterized by a sudden coastline change around Leizhou Peninsula and also the abrupt narrowing of the continental shelf around Hainan island. The coastline turns north–south when encountering Leizhou Peninsula. In the region offshore ZP, the shelf width is about 200 km which decreases rapidly to about 50 km to the southeast of Hainan Island. The abrupt change of the shelf width and coastline around Leizhou Peninsula and Hainan Island may stimulate strong scattering of CTWs. Note that the propagation speed of the CTW signals drops abruptly around Hainan Island, which has been discussed in previous paragraphs. The interaction of scattered CTW modes can strongly influence wave properties (Wilkin and Chapman 1987), and higher modes of CTWs travel slowly and are dissipated more rapidly by friction than lower modes (Merrifield 1992; Pizarro and Shaffer 1998). Further studies are needed to investigate the importance of scattering process of CTWs in the northern SCS where the coastline bends abruptly and the continental shelf narrows sharply.

6 Summary

Observed sea level data around the northern SCS and a three-dimensional numerical model with realistic topography and wind forcing are used to investigate the spatial structures and propagation characteristics of the CTW along the northern coast of the SCS.

The observed sea level fluctuations propagate southwestward with a traveling speed of 5.5–17.9 m s⁻¹ during the typhoon season and also winter month. The wave speed is faster between stations Shanwei and Zhapo than that between Xiamen and Shanwei. It is considered that the sea level peaks propagate westward mainly in the form of a forced wave along the northeastern coast of this region while the free component of the waves become more important along the southwestern coast. The observed sea levels during winter are highly related to the alongshore wind and seem to be more periodic compared with the sea levels in typhoon season. Based on the characteristics of the sea level variations, the propagation signals may be classified into two types: (1) wave signal related to typhoons and (2) wave signal induced by winter storm burst. Two model runs were conducted to examine the structure and propagation of the CTW associated with typhoons and winter storm burst. The strong convergence caused by onshore Ekman transport generated CTW propagating toward southwest along the coast. The CTW may be weakened (enhanced) by the offshore (onshore) Ekman transport due to local winds during the propagation process. The wave split into two parts at the Qiongzhou Strait, with one wave continuing to propagate westward, while the other one traveling anti-clockwise around the island as an ITW. The abrupt change of the coastline and shelf width around Leizhou Peninsula and Hainan Island may stimulate strong scattering of CTWs into higher modes. A brief discussion of CTW scattering in this region is present in the current study; however, further studies are needed to investigate the importance of scattering process of CTWs in the northern SCS where the coastline bends abruptly and the continental shelf narrows sharply.

Analysis of vertical structures of the alongshore velocities across different transects shows that the alongshore flow associated with the CTW propagated downslope along the bottom in the model run of typhoon season case, while southwestward alongshore current variability was confined mainly within about 50 km of the continental shelf near the coast and in the layer shallower than 30 m depth during the winter month case. The alongshore velocity structures at the transects during different events are related to the combined effect of stratification and shelf profile, which can be estimated using the Burger number. The EOF analysis of alongshore velocity and nodal lines of the mode structure suggest mode 2 CTWs in transect S2 during typhoon season and mode 1 CTWs during winter. Cross-shelf propagation of the wave signal during typhoon season can be noted from the cross-shelf structure of alongshore velocity shown in Fig. 20 as pointed out by one of the reviewers. However, the physical mechanism of the cross-shelf propagation requires further investigation. Moreover, inertial motion with period of nearly 1.5 days seems to be strong in the EOF time series.

We have examined the relative importance of local and remote wind forcing, together with geography and topography by designing sensitivity model experiments. The result is that local wind forcing is able to intensify or weaken the CTW signals through driving onshore or offshore Ekman transport. By performing model experiments in which the topography is changed, we also find that the scattering of CTW due to shelf width change be help explain the abrupt decrease in the propagation speed of the CTW in the model simulations.

As can be seen from the model results, the model calculated velocity fields near the west and north of Luzon Island seem to be problematic. It is thought to be related to the model construction, as the model was forced only by wind, and the initial model stratification was horizontally uniform. These factors will influence the model calculated velocity field near Luzon. However, we focus on the CTW in the coastal region in our current study, and the velocity field over the coastal seas seems to be normal. We also plan to improve the model construction in the future studies.