Tidal flux and resonance in the Gulf of Tonkin

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Description of the Gulf of Tonkin


The Gulf of Tonkin (16o10ÕÐ21o30ÕN, 105o40ÕÐ110o00ÕE; Figure 1.1) is a shallow, tropical, crescent-shape, semi-enclosed basin located in the northwest of the Vietnam East Sea/South China Sea (VES/SCS), which is the biggest marginal sea in the Northwestern Pacific Ocean. Bounded by China and Vietnam to the north and west, the Gulf of Tonkin is 270 km wide and about 500 km long, connecting with the Vietnam East Sea/South China Sea through the south of the gulf and the Qiongzhou Strait (Quynh Chau strait; also called Hainan strait). This strait is about 20 km wide and 100 m deep in between the Hainan Island and the Qiongzhou Peninsula (mainland China). The southern Gulf of Tonkin is a NW-SE trending shallow embayment from 50 to 100 meters in depth. Many rivers feed the gulf, the largest being the Red River. The Red River flows from China, where it is known as the Yuan, then through Vietnam, where it mainly collects the waters of the Da and Lo rivers before emptying into the gulf through 9 distributaries in its delta. It provides the major riverine discharge into the gulf, along with some smaller rivers along the north and west coastal area. The Red River, annually transporting 100 million tons of sediment (van Maren, 2004), flows into a shallow shelf sea. The river plume is then advected to the south by coastal current.
There are topographic dataset available for the Gulf of Tonkin, like ETOPO2 (global digital bathymetry 2-minute resolution), DEM (digital elevation model 15-minute resolution) from Vietnamese navigation chart, GEBCO_08 (30-second resolution global bathymetry), Smith&Sandwell version 14 (1-minute resolution global bathymetry). GEBCO_08 is chosen here for our simulations because of its higher resolution and the fact that it contains data provided by the International Hydrographic OrganizationÕs (IHO) Member States for shallow water areas shallower than 300m. One of the focuses of IHOÕs technical assistance efforts is in the Vietnam East Sea/South China Sea. They contracted a study of shipping traffic patterns in the area and have been assessing the status of hydrographic surveying in the region (according to a report of improved global bathymetry by UNESCO, 2001).

Tidal forcing

According to Wyrtki (1961), the four most important tidal constituents in the Vietnam East Sea/South China Sea give a relatively complete picture of the tidal pattern of the region and are sufficient for a general description. These tides, with their periods T in hours are shown below in Table 1.1
Tides in the Vietnam East Sea/South China Sea have been studied since the 1940s. The co-tidal and co-range charts (maps of tidal phase and amplitudes of the main tidal constituents) that were drawn by various researchers before the 1980s revealed large discrepancies over the shelf areas. The discrepancies among the published charts were reduced since the 1980s, when a number of numerical models were developed to improve the accuracy of tides and tidal current predictions. Recent examples are mostly Chinese: the two-dimensional, depth-integrated shallow water model of Fang et al. (1999) and the three-dimensional tidal models of Cai et al. (2005), Zu et al. (2008) and Chen et al. (2009). Zu et al. (2008) used data assimilation of TOPEX/POSEIDON altimeter data to improve predictions while Cai et al. (2005) explored the sensitivity of shelf dynamics to various model parameters and forcing. With a relatively coarse resolution (quarter degree) model, Fang et al. (1999) and Zu et al. (2008) showed that tides in the Vietnam East Sea/South China Sea are essentially maintained by the energy fluxes of both diurnal and semidiurnal tides from the Pacific Ocean through the Luzon Strait situated between Taiwan and Luzon (Luzon is the largest island in the Philippines, located in the northernmost region of the archipelago). The major branch of energy flux is southwestward passing through the deep basin. The branch toward the Gulf of Tonkin is weak for the semidiurnal tide but rather strong for the diurnal tide. The M2 tidal amplitude is reduced while the O1 amplitude is amplified after they pass through the Luzon strait. The results show that the M2 amplitude is generally small (<0.2m) at the entrance of the Gulf of Tonkin but the K1 and O1 amplitude are about 0.3m (Figure 1.3).
Vietnamese scientists, e.g., Nguy!n Ng »c Th#y (1984), have also studied tides in the Vietnam East Sea/South China Sea since the 1980s, but the high-resolution dynamics of the Gulf of Tonkin remain poorly estimated. What is known is that the tidal regime of the Gulf of Tonkin is diurnal, with large amplitudes in the north decreasing in the south. Tidal currents are strong and complex. Tides in bays generally have larger amplitudes than in the open ocean but with similar anticlockwise propagation around the coasts (northern hemisphere). The propagation is also much slower consistent with the shallower water. In such small bodies of water, the effects of gravitational forcing acting directly on the water body are small compared with the indirect effects of open-ocean forcing. Therefore, tides in coastal seas and bays are driven primarily by the open ocean tide at the mouth of the bay. In some cases, this can lead to large amplitudes, by at least two processes. One is simply focusing: if the bay becomes progressively narrower along its length, the tide will be confined to a narrower channel as it propagates, thus concentrating its energy. The second process is resonance by constructive interference between the incoming tide and a component reflected from the coast. If the geometry of the bay is such that it takes one-quarter period for a wave to propagate its length, it will support a quarter-wavelength mode at the forcing period, leading to large tides at the head of the bay. Tidal waves enter the Gulf of Tonkin from the adjacent Vietnam East Sea/South China Sea, and are partly reflected in the northern part of the Gulf. The geometry of the basin causes the diurnal components O1 and K1 to resonate. Therefore, the amplitude of these components increases northward along the North Vietnamese coastline, where they reach their highest values in the whole of Vietnam East Sea/South China Sea (exceeding 90 cm for O1 and 80 cm for K1; Fang et al., 1999). The strongest diurnal tidal current occurs in the Hainan Strait.
More specifically, if we consider the Gulf of Tonkin as an ideal rectangular gulf of length L and constant water depth h, which communicates with a deep ocean at the open end, we can compute a solution for resonant modes (Taylor, 1922). For that, we assume that the gulf is sufficiently narrow for the Coriolis force to be neglected, and omit for simplicity the friction effects. In this case, the linear, non-rotating, one-dimensional shallow water equations (under the assumption that at the closed end of the gulf the normal velocity is vanishing) take a solution in the form of a standing wave:
The length of the Gulf of Tonkin is about 500 km and its average depth is 50 m. Therefore the resonance would occur for a tidal forcing period of T = 25.1 hours, which is close to the period of O1 (Fang et al., 1999).
However, neglecting the Coriolis force may not be appropriate (Van Maren et al., 2004). The incoming diurnal tidal waves tend to be deflected to the right by Coriolis forcing and reflect against the northern enclosure of the gulf. The reflected waves propagate southward and are partly dissipated by friction. The result is a mixture of a standing wave, a northward-propagating wave in the eastern part, and a southward-propagating wave in the western part. This suggests a wide range of phase relationships between tidal currents and high/low tides (as opposed to propagating waves, in standing waves currents are out of phase by 90¡ with water level). Coriolis forcing also produce a frequency shift of the resonant wave. Taylor (1922) and van Dantzig and Lauwerier (1960) proposed a general expression for this frequency shift, again for a rectangular basin. Jonsson et al. (2008) added a useful simplification for narrow bays (if the width is no more than half the length):
W is the width of the basin (270 km for the Gulf of Tonkin) and F is the Coriolis frequency (~0.5 10-4 s-1 at 20¡N). The period after correction for rotation is 23.4 hours, which is shorter than the period of O1 and closer to K1. However, we cannot expect the crude estimate of treating the Gulf of Tonkin as a flat-bottomed rectangular gulf to yield an accurate result. We will use our numerical model to provide a better estimate of the optimal resonant period under the influence of complex bathymetry and coastlines and of the Hainan Strait opening in the north.

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Meteorological conditions


According to the literature, dynamical processes in the Vietnam East Sea/South China Sea are governed to a large extent by the Asian monsoon system. In this monsoon system a distinction can be made between the North East (NE) monsoon (also called winter or dry monsoon) and the South West (SW) monsoon (also called the summer or wet monsoon). This system follows the annual cycle (Wyrtki, 1961):
• From September to April the NE monsoon prevails. This monsoon is fully developed in January (8.0 Ð 10.7 m/s), prevails over the entire Vietnam East Sea/South China Sea. From February onwards, the NE monsoon weakens but prevails until April.
• From May to August the NE monsoon is succeeded by the SW monsoon. During May the NE winds over the Vietnam East Sea/South China Sea collapse and a SW wind succeeds. Its force increases over the following months, reaching full development in July and August (5.5 Ð 7.9 m/s). From September onwards, however, NE winds occur over the North East Sea and prevail over the entire Vietnam East Sea/South China Sea from October.
This annual cycle is illustrated in Figure 1.4 by monthly-mean wind stress fields for February and August (the NE and SW monsoon highs). These fields are obtained from QuikSCAT monthly climatology. They clearly show the inverted NE and SW monsoon wind directions. Also, it can be observed that during the NE monsoon the wind magnitude is essentially uniform over the entire Vietnam East Sea/South China Sea basin.
Figure 1.4: Monthly-mean surface wind stress for February (left) and August (right). Obtained from Monthly mean wind stress based on the QuikSCAT monthly climatology with magnitude in shaded [N/m2].
Figure 1.5 shows the wind-stress for the Gulf of Tonkin. This data is QuikSCAT monthly climatology and represents the area-averaged conditions over [16¡10ÕÐ 21¡30ÕN, 105¡40ÕÐ110¡00ÕE]. A maximum wind stress is observed around December/January, when the NE monsoon is high. A second maximum is observed June/July, when the SW monsoon is high. April/May and August/September are periods of transition between monsoons.


The precipitation in the Vietnam East Sea/South China Sea is mainly controlled by the winter and summer monsoons. Most of the rainfall occurs during the summer monsoon (May-September), in the mountain areas it can reach up to more than 2000 mm (Figure 1.6).
Figure 1.6: Annual mean precipitation [mm/year] from Tropical Rainfall Measuring Mission (TRMM_3B43) observations between 1998 and 2011.

Surface heat flux

Qsw and Qlw are the heat fluxes due to solar short wave and long wave radiation respectively, Qlat is the latent and Qsen the sensible heat flux. The Vietnam East Sea/South China Sea lies between the equator and the Tropic of Cancer where the incident sunlight is practically vertical to the sea surface. The solar short wave radiation reaches its maximum in April because of the least cloud cover and the vertical incidence of sunlight. In winter Qsw is lowest but due to the tropical position of the VES/SCS the annual range of values is mild. The latent heat transport Qlat reaches its maximum in winter, due to the strong northeast monsoon with its cold, dry air. The latent heat flux has minimal during the transition periods between monsoons. As a result, the oceanic net heat gain Qnet reaches a maximum in April, drops quickly in May and is negative from October to February. The VES/SCS can store a large amount of heat energy and would exert a large influence on the atmospheric circulation and synoptic systems in eastern Asia. The sudden changes of Qsw, Qlat, Qnet in April-May reflect the quick adjustment of atmospheric circulation before the onset of summer SW monsoon. The VES/SCS acts as a source of heat and vapour to maintain the monsoon. It is the water evaporation and convective heating caused by the strong air-sea interactions that influence the local synoptic systems over the VES/SCS. There is also considerable spatial variability. The Gulf of Tonkin in particular is less affected by the summer monsoon winds than southern Vietnam (Figure 1.4).
The annual variation of SST in the VES/SCS is lowest in winter and rises swiftly after February (Figure 1.7). SST maximum does not appear in April while the surface net heat flux in the ocean is maximum, but lags by about one to two months. Then the SST drops with the decrease of Qnet. This implies that it is the surface net heat gain Qnet (not oceanic transport) that drives seasonal SST variations at regional scale (Yang, 1999).

Ocean Climatology

Sea Surface Temperature patterns

During the NE monsoon (winter), the combined effect of surface heat flux and wind-driven basin-scale circulation contributes to the formation of a tongue of cold water along the northwest coast of the gulf. These processes contribute to seasonal amplitudes of over 6oC in the northwest gulf.
Figure 1.8 shows monthly-mean Sea Surface Temperature (SST) fields for February and August, these months were identified as the maximum of the NE and SW monsoons, respectively. They show that the largest seasonal amplitudes are located in the coastal zones, particularly in the Gulf of Tonkin.
The Gulf of Tonkin is connected to the Vietnam East Sea/South China Sea and has a tropical climate with monsoon winds. It is semi-enclosed with an average water depth of 50 m. During the winter monsoon, the wind blows from the northeast generating a southward flow. During the dry season the southward flow dominates and is described by an anticlockwise rotating cell. During the wet season, the southern monsoon winds are weak in the gulf and become minimal in August. Then, there are two circulation cells, which diverge near the coastline of the Red River Delta.
Figure 1.9: Residual flow in the Gulf of Tonkin during the dry season (February) and the wet season (August), based on the Vietnam National Atlas (1996). The 50, 200, and 2000 m depth contours are shown for reference.

Table of contents :

Chapter 1: Description of the Gulf of Tonkin
1.1 Geography
1.2 Tidal forcing
1.3 Meteorological conditions
1.3.1 Winds
1.3.2 Precipitation
1.3.3 Surface heat flux
1.4 Ocean Climatology
1.4.1 Sea Surface Temperature patterns
1.4.2 Subtidal circulation
Chapter 2: Methods
2.1 Description of the Regional Ocean Modeling System (ROMS)
2.1.1 Equations of continuity and momentum balance
2.1.2 Vertical boundary conditions.
2.1.3 Terrain-following coordinate systems
2.1.4 Horizontal curvilinear coordinates
2.1.5 Open boundary conditions
2.1.6 Time-stepping
2.1.7 Sigma-coordinate errors: The pressure gradient and diffusion terms
2.1.8 Turbulent closure
2.1.9 Nesting
2.2 Lagrangian modeling: Ariane
2.3 Data for model verification
2.3.1 Tide gauges
2.3.2 Altimetry data
2.4 Harmonic tidal analysis: Detidor
2.5 Tidal energy budget: COMODO-energy
Chapter 3: Model validation and sensitivity analysis in the Gulf of Tonkin
3.1 Previous modeling work
3.2 Model setup
3.2.1 Grid generation
3.2.2 Surface fluxes
3.2.3 Initial and boundary conditions
3.3 Model validation
3.3.1 Tidal gauges
3.3.2 Satellite altimetry
3.4 Model sensitivity
3.4.1 Sensitivity to bottom stress formulation
3.4.2 Sensitivity to the horizontal resolution
3.4.3 Comparison of two- and three-dimensional model solutions
3.4.4 Sensitivity to bathymetry
3.5 Conclusion
A.1 Comparison of altimeter and tide gauge measurements
A.2 Relative errors
A.3 OTIS forcing
Chapter 4: Tidal flux and resonance in the Gulf of Tonkin
4.1 Tidal energy flux
4.2 Tidal resonance
4.2.1 The rectangular bay model
4.2.2 Numerical simulations
Chapter 5: Residual transports
5.1 Tide-induced residual current and transport
5.1.1 Eulerian residuals
5.1.2 Tide-induced Lagrangian residual current
5.2 Subtidal residual flow
5.2.1 Wind-driven circulation
5.2.2 Density circulation
5.3 Connectivity to Ha-Long bay
5.4 Conclusion
Chapter 6: Heat budget
6.1 Coastal cooling in winter
6.2 Frontogenesis in spring-summer


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