Generation of diurnal K-1 internal ride in the Luzon Strait and its influence on surface tide in the South China Sea

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Generation of diurnal K

1

internal tide in the Luzon Strait and its

influence on surface tide in the South China Sea

Sen Jan,1,4 Ching-Sheng Chern,2,4 Joe Wang,2,4and Shenn-Yu Chao3

Received 3 November 2006; revised 20 January 2007; accepted 22 February 2007; published 21 June 2007.

[1] The predominance of diurnal surface tides over semidiurnal surface tides in the South

China Sea (SCS) has been attributed to the near-resonance response of the former in the SCS. Recent observations further revealed vigorous internal tides in the northern SCS. Conceivably, internal tides generated in the Luzon Strait could modify the surface tide in the SCS. We use a three-dimensional tide model of the East Asian seas to address this issue. With a typical summertime stratification of the SCS as the initial condition, energy budget indicates that one third of the incident K1surface tide energy is converted to

the baroclinic energy over topographic ridges in the Luzon Strait. In comparison with a global tidal model [Matsumoto et al., 2000], our numerical experiments that annihilated or reduced the K1 internal tide in the Luzon Strait led to up to 50% amplification of

the simulated K1 surface tide in the SCS. This suggests that the baroclinic energy

conversion substantially reduces the amplitude of K1 surface tide in the SCS. The

simulated phases in the SCS differ little from those calculated from Matsumoto’s tide model, suggesting that the modification is primarily on the amplitude. Two-dimensional surface tidal models lack baroclinic energy conversion in the Luzon Strait; the consequent overestimation of surface K1 tide can be reduced only through precise prescription of

sea levels in the Luzon Strait or assimilation of sea level data.

Citation: Jan, S., C.-S. Chern, J. Wang, and S.-Y. Chao (2007), Generation of diurnal K1internal tide in the Luzon Strait and its

influence on surface tide in the South China Sea, J. Geophys. Res., 112, C06019, doi:10.1029/2006JC004003.

1. Introduction

[2] The South China Sea (SCS), covering an area of about

3.5 106km2, is a semienclosed basin with depths of 3000 – 4000 m in the central basin and less than 200 m over most of peripheral shelves (Figure 1). There are five major passages connecting the SCS to surrounding seas. Both the Taiwan and Karimata straits are shallow passages (depth <100 m) to the East China Sea and the Java Sea, respectively. The Mindoro and Balabac straits are narrow passages to the Sulu Sea with limited water exchange. Among all passages, the Luzon Strait is the deepest and also the most important one connecting the SCS to the northwest Pacific Ocean.

[3] It is well known that the barotropic tides in the SCS

are dominated by diurnal constituents [Ye and Robinson, 1983; Huang et al., 1994; Mazzega and Berge, 1994; Yanagi et al., 1997]. Using a two-dimensional tide model, Yanagi and Takao [1998] verified that the quarter-wave resonant response of diurnal tides leads to the

predomi-nance. The cotidal chart plotted using harmonic constants derived from a two-dimensional global tide model with sea level data assimilation [Matsumoto et al., 2000, hereafter referred to as NAO.99] illustrates that the diurnal K1tide

with amplitude of about 20 cm propagates southwestward from the Pacific Ocean to the SCS mainly through the Luzon Strait (Figure 2a). The southwestward-propagating K1tide further amplifies to 40 cm over the deep basin of the

SCS. The K1tide is greatly amplified near heads of the Gulf

of Tonkin and the Gulf of Thailand due to the near-resonance diurnal response of the two gulfs [Fang et al., 1999]. By comparison, the semidiurnal M2 tide entering

through the Luzon Strait behaves as a decaying wave while propagating southwestward in the SCS. Its amplitude drops rapidly from 40 to 20 cm while passing through the Luzon Strait and further reduces to 10 – 20 cm in the central basin of the SCS [Ye and Robinson, 1983; Huang et al., 1994; Fang et al., 1999].

[4] Recently, dramatic internal tides and solitary waves

and bores with vertical isotherm displacements up to 100 m were observed near the Dongsha Island in the northern SCS [Lynch et al., 2004; Duda et al., 2004; Ramp et al., 2004]. Using a three-dimensional tide model, Niwa and Hibiya [2004] confirmed that the continental shelf/slope of the East China Sea and the prominent topographic ridges in the Luzon Strait are the major generation sites of the M2

internal tides in the northwest Pacific Ocean. They esti-mated that 25% of the M2 barotropic tide energy was

converted to baroclinic energy in the Luzon Strait.

Here for

Full Article

1

Institute of Hydrological Sciences, National Central University, Jung-li, Taiwan, Republic of China.

2

Institute of Oceanography, National Taiwan University, Taipei, Taiwan, Republic of China.

3

Horn Point Laboratory, University of Maryland Center for Environ-mental Science, Cambridge, MD, USA.

4

National Center for Ocean Research, Taipei, Taiwan, Republic of China.

Copyright 2007 by the American Geophysical Union. 0148-0227/07/2006JC004003$09.00

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[5] Of interest are the similarity and dissimilarity between

the Gulf of Mexico (GOM) and the SCS. The GOM is also semienclosed with passages to the Atlantic Ocean and the Caribbean Sea. Tides in the GOM are also predominantly diurnal rather than semidiurnal [Reid and Whitaker, 1981]. The amplitude of K1tide is about 10 cm in the entrance of

the GOM but increases to about 20 cm in the entire GOM

(Figure 2b). The amplification and predominance of the diurnal tide are attributed to the cooscillating tide response in the GOM [Zetler and Hansen, 1971]. The baroclinic tides, on the other hand, are seasonally modulated and are an order of magnitude smaller than the barotropic tides [He and Weisberg, 2002]. Not surprisingly, Clarke [1991] con-Figure 1. Bathymetry of our three-dimensional model domain, including the East Asian seas and

northwest Pacific Ocean. HC ridge represents the Heng-Chun Ridge extended from southernmost of Taiwan Island.

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cluded that the effects of baroclinic tides on the determi-nistic barotropic tides are negligible in the GOM.

[6] In contrast, internal tides in the SCS are remarkably

strong and may modify surface tides. The internal tides are being investigated extensively, but how they modify the surface tide is not clear. Previous barotropic tide studies using two-dimensional models mostly concentrated on the accuracy of modeled sea levels [e.g., Fang et al., 1999]. Recent three-dimensional numerical studies focused prima-rily on the generation, energetics, and evolution of the semidiurnal M2 internal tide in the Luzon Strait and

northern SCS [e.g., Niwa and Hibiya, 2004]; the investiga-tion on the diurnal tides was scarce. To investigate the potential influence of the diurnal internal tide created in the Luzon Strait on the characteristic of the surface tide in the SCS, we adopt a process-oriented numerical approach below. A three-dimensional tide model is used to simulate the K1 barotropic and baroclinic tides in the East Asian

seas. Harmonic constants analyzed from the model results are compared with those of NAO.99. Subsequent numer-ical experiments evaluate the modification of surface tide in response to the generation of internal tide in the Luzon Strait. The importance of topographic ridges in the Luzon Strait in generating internal tides is also investigated. For simplicity, we concentrate on the simulation of the major diurnal constituent, the K1.

2. Model Description

[7] Our tide model is a modified version of the Princeton

Ocean Model which was described in the work of Blumberg and Mellor [1987]. The model is a three-dimensional, nonlinear, primitive equation model with Boussinesq and hydrostatic approximations. We have added tidal forcing to facilitate this study. The vertical axis is transformed to thes coordinate by s = (z  h)/(H + h), where z is positive upward with the origin placed at the mean sea level,h is the

sea level fluctuation, and H is the mean water depth. The governing equations are as follows:

@UD @t þ ADVU f V D ¼  GRADxP 0þ DIF U þ gD@ðz bhÞ @x  r U  ð UÞD ð1Þ @VD @t þ ADVVþ f U D ¼  GRADyP 0þ DIF V þ gD@ðz bhÞ @y  r V  ð VÞD ð2Þ @P0 @s¼ r 0gD ð3Þ @h @tþ @UD @x þ @VD @y þ @w @s¼ 0 ð4Þ @8D @t þ ADV8¼ DIF8 ð5Þ

where (U, V ) are the horizontal velocity components in the x and y directions; w is the velocity component normal to s surface; D is the total water depth (D = H + h); t is the time; f is the Coriolis parameter; r0 is the perturbation density; P0 is the perturbation pressure; (ADVU, ADVV),

(GRADxP0, GRADyP0), and (DIFU, DIFV) are the advection,

pressure gradient, and diffusion terms, respectively, in the horizontal momentum equations (Mellor data available at http://www.aos.princeton.edu/WWWPUBLIC/htdocs.pom); b (= 0.94 for K1tide) represents the loading effect due to

ocean tides [Foreman et al., 1993]; g is the gravitational Figure 2. Harmonic constants (amplitude and phase) of K1tide in the (a) South China Sea and the

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acceleration; ð U ; VÞ represent depth-averaged horizontal velocities;8 can be the temperature (T) or salinity (S); and ADV8 and DIF8 are the advection and diffusion terms, respectively, in temperature and salinity equations. The non-linear interactions between internal tides and internal waves are parameterized by linear damping termsrðU  UÞ and rðV  VÞ in equations (1) and (2), respectively, where r is a damping coefficient which is set to 0.2 day1 as suggested by Niwa and Hibiya [2001, 2004]. The adjusted height of equilibrium tides (z ) is calculated using the formulation described in the study of Pugh [1987] (see Table 1 for details). Table 1 summarizes major specifications for the model.

[8] The initially motionless ocean has horizontally

homo-geneous but vertically stratified temperature field. Figure 3 shows the initial temperature profile which was obtained by Chen et al. [2006] at a station in the northern SCS (118.5°E, 19°N) in July 1999. Salinity is assumed to be homogeneous because it varies vertically by less than 3% in deep reaches of the SCS where the density stratification is dominated by the vertical temperature variation. Subsequently, the model is driven by prescribed tidal sea levels on all open ocean boundaries through a forced radiation condition similar to that adopted by Blumberg and Kantha [1985]. The tidal sea levels on the open boundaries are computed using the harmonic constants of NAO.99. The depth-averaged tidal current velocity normal to the open boundaries is determined by the following equation:

unB¼ u2Dþ C hB hpre

 

=H ð6Þ

where u2Dis calculated from a fine-tuned, two-dimensional

tide model of Jan et al. [2004], C(=pffiffiffiffiffiffiffigH) is the phase speed of a shallow water gravity wave, hB is the sea level

calculated by the three-dimensional tidal model, andhpreis

the prescribed tidal sea level on open boundaries. A flow relaxation scheme described by Engedahl [1995] is applied to the internal mode velocity and temperature in a 1° wide strip adjacent to open boundaries to eliminate artificial reflections.

[9] It takes 8 – 10 days for the first vertical mode of

internal tide to propagate from the source to open bound-aries of the model. The basic model run is therefore set to 15 days. Hourly model results of the last three tidal cycles of K1 tide are analyzed subsequently. To retain the

dyna-mics of tidal waves as much as possible, the control run neither fine-tunes the model parameters nor assimilates the

Table 1. Model Specification

Parameter Specification

Range of domain 99.25° – 135.25°E and 2.25° – 43.25°N (Figure 1) Horizontal resolution 1/12° ( 9.17 km near equator)

Vertical resolution 51s layer with uneven s spacing (sk= 0, 0.002, 0.004, 0.006, 0.008, 0.01, 0.012, 0.014, 0.018, 0.022, 0.026, 0.03, 0.034, 0.037, 0.045, 0.053, 0.061, 0.069, 0.077, 0.085, 0.1, 0.116, 0.132, 0.148, 0.179, 0.211, 0.243, 0.274, 0.306, 0.337, 0.369, 0.4, 0.432, 0.464, 0.495, 0.527, 0.558, 0.59, 0.621, 0.653, 0.684, 0.716, 0.748, 0.779, 0.811, 0.842, 0.874, 0.905, 0.937, 0.968, and 1 as k varies from 1 to 51)

Topography (depths) (1) 1-min depth archive in the region between 105° – 135°E and 2° – 35°N, and

(2) 2-min gridded global depths database ETOPO2 (U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Geophysical Data Center data available at

http://www.ngdc.noaa.gov/mgg/fliers/01mgg04.html) elsewhere Adjusted equilibrium

tides in equations (1) and (2) z¼ fK1HK1cos ½wK1tþ Vð 0þ mÞ þ l , where fK1is nodal factor,wK1is K1tidal frequency, V0is initial

phase angle of the equilibrium tides,m is nodal angle, l is longitude, and HK1= 0.104 sin2ffor K1

tide (f: latitude)

Horizontal viscosity and diffusivity Smagorinsky’s [1963] formulation

Vertical viscosity and diffusivity Mellor and Yamada’s [1982] level 2.5 turbulence closure scheme Bottom stress Cz[U2+ V2]0.5(U, V), where Cz= MAX[k2/{ln[(1 +s50)H/z0]2,

0.0025] (k= 0.4 is the von Karman constant, and z0= 0.01 m is the bottom roughness length)

Figure 3. Typical temperature profile of the SCS in summer. Data were obtained at (118.5°E, 19°N) in July 1999 by Chen et al. [2006].

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observed sea levels into the model interior to improve accuracy.

3. Results

3.1. Barotropic Tide

[10] Figure 4 illustrates the cotidal chart and depth-averaged

tidal current ellipses of the simulated K1barotropic tide in the

SCS. The simulated cotidal patterns capture essential features of K1 tide presented in earlier model results [Yanagi and

Takao, 1998; Fang et al., 1999; Matsumoto et al., 2000]. The cophase distribution indicates that incident waves from the northwest Pacific propagate into the SCS through the Taiwan and Luzon straits and subsequently enter the Gulf of Tonkin and Gulf of Thailand. The amplitude in the central SCS is twofold of that in the northwest Pacific Ocean. Comparing to the harmonic constants of NAO.99, the amplitudes are about 20 cm overestimated between Vietnam and Malay Peninsula; the phases lag NAO.99 by approximately 10° in the central SCS but lead NAO.99 by 10° over the Sunda Shelf (cf. Figure 2a). The phase discrepancy suggests that the simulated surface tide propagates slower than that from NAO.99 in the central SCS. In consequence, the simulated tidal wave has to speed up over the Sunda Shelf to meet the prescribed tidal phase across the southern open boundary. In addition, the different levels of topographic representation between our model and NAO.99 and the emergence of internal tides in our model may also contribute to the phase discrepancy. The root mean square difference between our model and NAO.99 results is 3.2 cm for tidal sea levels in regions deeper than 1000 m. Notably, sinuous oscillations of the cophase line around the Luzon Strait and northern SCS are possibly caused by the internal tide because their length scale is comparable to the horizontal wavelength of the K1internal tide.

[11] Figure 4b shows relatively weaker tidal currents in the

northwest Pacific Ocean and the main portion of the SCS. Tidal currents strengthen in the Luzon Strait (20 – 50 cm/s), the Gulfs of Tonkin and Thailand ( 50 cm/s), and the Sunda Shelf ( 20 cm/s). Moving eastward over the Sunda Shelf, the tidal amplitudes increase but tidal currents decrease considerably in the region from the southern tip of Vietnam to the West Coast of Malay Peninsula. This is indicative of an antinodal band for a standing wave. In contrast, smaller amplitudes and stronger tidal currents in the Luzon Strait are indicative of a nodal band. [12] We also compared simulated barotropic tidal currents

with observations conducted under the Asian Seas Interna-tional Acoustics Experiment (ASIAEX) near the Dongsha Island [see Lynch et al., 2004 for an overview of the project]. Figure 5 shows the depth-averaged tidal current ellipses from our model results and corresponding ones observed at five acoustic Doppler current profiler (ADCP) stations of ASIAEX [Table 5 in the paper of Beardsley et al., 2004]. Locations of the five ADCP stations are marked in the right panel of Figure 5. On average, the modeled barotropic tidal currents are about 15% stronger than those observed. Discre-pancies between the simulated and observed major tidal axis orientation are less than 10°. The truncation error of local topographic structure is likely a major source causing the discrepancy. Further fine-tuning without better topography resolution may further improve the model performance in this locale, but it may not serve the major interest of this basin-wide process-oriented study.

3.2. Baroclinic Tide

[13] Figure 6 shows instantaneous sea surface elevations

and vertical isopycnal displacements relative to 150 m depth at days 14 and 14.5. The tidal phase difference between the two instants is approximately 180°. The surface elevations in the SCS and the northwest Pacific Ocean are nearly out of phase by 180°. The vertical isopycnal displacement indicates pronounced internal tides in the northwest Pacific Ocean (between 24° and 16°N) and the northern SCS. The horizontal internal tide pattern is complex in the southern SCS due to the interference with reflection waves from the Sunda Shelf. The vertical density (st) distribution and the bottom depth contour

along 20°N in Figure 7a demonstrate that the isopycnal excursion (twofold of the internal tide amplitude) is larger than 45 m immediately west of the Hengchun Ridge, about 20 m just east of the Dongsha Island and 10 – 20 m on the Pacific side of Luzon Strait. The Luzon Strait seems to be the center of action, as oscillations decrease in amplitude with distance away from it. The corresponding excursions near Dongsha Island during ASIAEX, after harmonic analysis, were 10 m in neap tide and 50 m in spring tide [Duda et al., 2004]. Thus the modeled excursion appears to be reasonable even though we adopt the hydrostatic approxi-mation and include only the K1tide. Note that an observed

vertical isotherm excursion of more than 100 m in the northern SCS [Ramp et al., 2004] is normally a mixture of internal tides, nonlinear internal waves, and solitary waves and bores, of which the last three are mostly excluded by our hydrostatic model.

[14] The horizontal wavelength of the internal tide,

esti-mated by the distance between two successive wave crests (or troughs) in Figure 6, is about 400 km in the Pacific Ocean around 20°N, 300 – 350 km in the northern SCS, and 240 km in the southern SCS. Changing water depths ( 5000 m in the northwest Pacific, 3000 m in the northern SCS, and 1500 m in the southern SCS) are mostly responsible for the difference. The corresponding propagation speed (wavelength divided by K1tide period) is

4.6 m/s in the Pacific Ocean, 3.4 – 4.0 m/s in the northern SCS, and 2.8 m/s in the southern SCS. These estimates are consistent with phase speeds of the first baroclinic mode.

[15] Relative to waves generated in the Luzon Strait,

Figure 6 also reveals shorter internal tide wavelengths (100 – 150 km) in the Celebes Sea and the Pacific Ocean south of 10°N. A zonal transect along 4°N (Figure 7b) pro-vides an explanation. Comparing Figure 7b with Figure 7a, one sees much more complex topographic structure south of 10°N, and the separation distances between ridges could provide wavelengths of choice for local internal tides. Several prominent meridional ridges reside between south of Palau and east of the Celebes Sea (Figure 1) and, not surprisingly, internal tide wavelengths are comparable to topographic wave-lengths ( 100 km) in these regions (Figures 6 and 7b). A further dynamical investigation beyond the foregoing description is beyond the present scope but merits study.

4. Discussion

[16] The major feature of K1 tide in the SCS is the

twofold amplification, which leads to the predominance of diurnal over semidiurnal tides. Using the coamplitude and cophase patterns in Figure 4a as a guide, one can idealize

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Figure 4. (a) Cotidal chart and (b) depth-averaged tidal current ellipses for the simulated K1tide. The

open square AE at about (117°E, 22°N) in the top panel represents the study site of ASIAEX [Lynch et al., 2004].

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the setting for the following theoretical analysis. Imagine the SCS as a long and narrow channel with open ends at the Luzon Strait and over the Sunda Shelf. One can also idealize the shoaling bottom between the deep SCS basin and Sunda Shelf as a step-like topography with water depths of H1( 2000 m) over the former and H2( 100 m) over the

latter. Dean and Dalrymple [1991] derived transmission and reflection coefficients of a linear frictionless long channel wave propagating over the step as kt¼ 2

1þ ffiffiffiffiffiffiffiffiffiffiH2=H1 p and kr¼ 1 ffiffiffiffiffiffiffiffiffiffiH2=H1 p 1þ ffiffiffiffiffiffiffiffiffiffiH2=H1

p , respectively [section 5.5 in the book of Dean and Dalrymple, 1991]. Since H2<< H1, the reflection and

transmission coefficients at the topographic step are approx-imately 0.7 and 1.7, respectively. Notably, the northward reflection from the Sunda Shelf causes the K1surface tide to

behave as a partial standing wave in the central SCS. The behavior is consistent with our model results (section 3.1). Given a mean depth of 2000 m for the SCS, the wavelength of the barotropic K1tide (l) is about 12,000 km. Fixing the

antinode of the partial standing wave at the topographic step (Sunda Shelf), the Luzon Strait is about 3000 km or l/4 away. Thus the SCS is close to being a quarter-wave resonator for K1tide with the Luzon Strait serving as a nodal

point. The twofold amplification (20 cm in the Luzon Strait versus 40 cm in the SCS), small phase variation ( 20°), and stronger tidal currents in the Luzon Strait are all indicative of quarter-wave resonance in the SCS. Moreover, the diurnal tide period is close to the first mode of free oscillation period of the SCS if one treats SCS as a harbor and Luzon Strait as the harbor mouth. Let L ( 3000 km) be the distance between Luzon Strait and Karimata Strait and H ( 2000 m) be the mean depth of SCS. The gravest mode of free oscillation period, 4L/(gH)1/2, is 23.8 hours, resulting in nearly resonant response of K1tide in the SCS.

[17] The resonant oscillation in an idealized rectangular

harbor has been extensively studied both theoretically and experimentally in 1960s [e.g., Miles and Munk, 1961]. These studies essentially pointed out the sensitivity of wave behavior to the width of entrance and the incident wave condition. Since the internal tide generation in the Luzon

Strait must extract tidal energy from the incident surface tide, it could in turn modify K1surface tide in the SCS to

some extent. This subject is analytically intractable and has rarely been examined in literature. We analyze the energy budget from our model results below to address this issue. [18] Following Niwa and Hibiya [2004], Table 2 lists

essential formulae for calculating the barotropic and clinic tidal energy. Figure 8 shows depth-integrated baro-tropic energy flux, barobaro-tropic-to-baroclinic energy conversion rate, and baroclinic energy flux averaged over one K1tidal

period. The distribution of barotropic energy flux in Figure 8a suggests that K1 surface tide enters the SCS through the

Luzon Strait and thereafter progresses southwestward. Table 3 summarizes the barotropic tidal energy budget in the SCS. The barotropic energy integrated along the east section of the Luzon Strait (122.5°E or L1 in Figure 8a) and north section of the Taiwan Strait (25°N or L2 in Figure 8a) is 34.2 GW (1 GW = 109 watt) westward and 0.6 GW southward, respectively. After propagating through the deep basin of SCS, the barotropic energy integrated along 10°N (L3 in Figure 8a) becomes 15.7 GW southward. Colors in Figure 8a indicate the barotropic-to-baroclinic energy con-version rate, which resides mostly in the Luzon Strait. We also find minor baroclinic energy conversion rate near Dongsha Island and over shallow reaches in the center and southeast of the SCS. The area-integrated barotropic-to-baroclinic energy conversion in the Luzon Strait (rectangular box in Figure 8a or 8b) is 12.4 GW, which is far greater than the similar conversion elsewhere in the SCS (1.0 GW in the vast area bounded by 10°N, 25°N, and the west boundary of Luzon Strait).

[19] The depth-integrated baroclinic energy flux in

Figure 8b shows both westward and eastward propagation of K1internal tide energy in the Luzon Strait. Figure 8b also

indicates some baroclinic energy generation near the island in central SCS and some northward reflection of baroclinic energy from islands in the southeastern SCS and northern edge of Sunda Shelf. The net outward baroclinic energy fluxes from Luzon Strait (rectangular box in Figure 8b) are 2.5 and 1.1 GW across the east and west sections, respec-Figure 5. Observed [Beardsley et al., 2004] and modeled K1barotropic tidal current ellipses at (a) five

acoustic Doppler current profiler stations and (b) relative locations of the five stations in an area indicated by the square AE in Figure 4a.

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tively. The estimation of the total energy budget indicates considerable barotropic energy ( 5.6 GW) dissipation by bottom and lateral frictions in the SCS beyond 10°N and in the Luzon Strait. About 36% of the input barotropic energy is converted to the baroclinic energy for K1tide in the Luzon

Strait. In comparison, similar conversion is only 25% for M2

tide in the same region [Niwa and Hibiya, 2004].

[20] The aforementioned simulation is the control run. To

assess the modification of K1 surface tide caused by the

36% of barotropic energy loss to baroclinic energy in the Figure 6. Instantaneous sea surface elevations (left panels) and vertical isopycnal displacements relative

to 150 m depth (right panels) at (a) day 14 and (b) day 14.5. Also superimposed on left panels are instantaneous depth-averaged tidal currents.

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Luzon Strait, five more numerical experiments with various stratification, topography, or sea level boundary condition are analyzed and discussed below. Table 4 lists the basic model configurations for control run and the five cases (A,

B, C, D, and E). The ocean is homogeneous in cases A and B; case B assimilates observed sea level data but case A does not. In case B, sea level composed from harmonic constants of NAO.99 is assimilated into the model domain

Table 2. Formulae for the Calculation of Barotropic and Baroclinic Tidal Energy [Niwa and Hibiya, 2004]

Tidal Energy Formulation

Depth-integrated barotropic energy flux in the x and y directions



URHh ðgr0ðz bhÞ þ P0Þdz

 

andVRHh ðgr0ðz bhÞ þ P0Þdz,

respectively, wherer0represents the initial background density stratification, and angle brackets denote time average over one K1tidal period

Depth-integrated baroclinic energy flux in the x and y directions

Rh

HðU0P0Þdz

 

andRHh ðV0P0Þdz, respectively, where (U0, V0) are the baroclinic velocity components in the x and y directions

Depth-integrated barotropic-to-baroclinic energy conversion rate averaged over one tidal period g

Rh Hr0wbtdz   , where wbt ¼ U s@D@xþ@h@x   þ Vs@D@yþ@h@yþ s @h@tþ@h@t

is the Cartesian vertical velocity relevant to the barotropic flow

Figure 7. Instantaneous vertical density (st) distribution and corresponding close-up of upper 300 m at

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Figure 8. (a) Depth-integrated barotropic energy flux and barotropic-to-baroclinic energy conversion rate and (b) baroclinic energy flux. All quantities are averages over one K1tide period.

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in areas deeper than 2000 m according to the succeeding formula:

h¼ ð1  eÞhcalþ ehNAO:99 ð7Þ

where hcalis the model-calculated sea level, hNAO.99 is the sea level composed from harmonic constants of NAO.99, ande(= 0.15) is a constraint factor. In cases C, D, and E, the ocean is stratified as in the control run. In case C, both topographic ridges in the Luzon Strait are reduced by 50% in height relative to 3000 m depth. To distinguish the role of each ridge, the 50% height reduction is restricted to the west ridge (Hengchun Ridge) in case D and to the east ridge (Luzon Island Arc) in case E. Model results are discussed below.

[21] Figure 9 plots calculated harmonic constants along

the major axis of the SCS (P-Q in Figure 4a) and a zonal section extending eastward from the Luzon Strait to the Pacific Ocean (Q-R in Figure 4a) for each case. Harmonic constants from NAO.99 are also plotted as a reference. As expected, the horizontal length scales of the fluctuations in amplitude and phase from the control run are close to the wavelengths of internal tides in the Pacific Ocean and the SCS. Similar modulation in the simulated barotropic M2

tide has been verified by the comparison with TOPEX/ Poseidon altimeter data [Niwa and Hibiya, 2004]. Leaving oscillations induced by internal tides aside, all six simula-tions lead to harmonic constants close to NAO.99 on the Pacific Ocean side. On the SCS side, the results differ significantly from NAO.99 except for case B; this is understandable because case B assimilates NAO.99 into the model. The control run produces much smaller amplitude of harmonic constants than its homogeneous counterpart (case A) on the SCS side. Apparently, the energy-extracting internal tides in the Luzon Strait greatly reduce the ampli-tude of the simulated surface K1tide in the SCS. Without

the barotropic-to-baroclinic energy conversion, the simulated amplitude is overestimated by 20 – 50% in the SCS. In other words, the amplification of surface K1tide caused by

quasi-quarter-wave resonance is much reduced in the SCS due to the barotropic energy loss in the Luzon Strait. The ridge height reduction (in cases C, D, and E) also enhances the amplitude of K1 surface tide on the SCS side because of

reduced blocking and consequently reduced internal tide generation by the ridges. Without stratification (in cases A and B), the spatial variation of phase remains almost un-changed compared to that of NAO.99. With ridge height reduction in cases (C, D, and E), the K1 surface tide

propagates faster in the Luzon Strait because of the depth

increase. In consequence, the phase of transmitted wave in the SCS is advanced. The most severe ridge height reduction is case C, in which the phase is advanced by about 20° relative to NAO.99 in the SCS. Relative to case C, height reduction of either east ridge or west ridge causes smaller phase advance. East ridge reduction causes larger phase advance than does the west ridge reduction. This is conceiv-able because east ridge is, when averaged meridionally, higher than the west ridge and the consequent 50% height reduction is more severe. The close match between case B and NAO.99 points out the importance of data assimilation in tide prediction if one uses a tidal model without the gener-ation of internal tides in the Luzon Strait.

[22] Ridge height reduction not only reduces the

barotropic-to-baroclinic energy conversion rate in the Luzon Strait but also changes the influx of barotropic tidal energy from the Pacific Ocean. In the control run, 36% (12.4 GW) of the barotropic influx from the Pacific Ocean (34.2 GW) is converted to baroclinic energy in the Luzon Strait (rectangular box in Figure 8a). The corresponding conversion rate is 27% (9.1 GW) of the barotropic influx (33.6 GW) in case D and 14% (6.7 GW) of the barotropic influx (47.2 GW) in case E. Apparently, east ridge height reduction (case E) decreases the barotropic-to-baroclinic conversion rate more because of the reason that it is the major ridge between the two. In other words, the east ridge in its present-day condition is the major source of internal K1tide in the SCS.

5. Concluding Remarks

[23] Entering the SCS, the K1barotropic tide becomes a

partial standing wave in a near-resonance state. The gener-ation of vigorous internal tides in the Luzon Strait thus considerably modifies the characteristic of the transmitted K1barotropic tide. With a typical summertime stratification

of the SCS as the initial condition, model results indicate that the depth-integrated rate of the barotropic-to-baroclinic energy conversion amounts up to 36% of the K1barotropic

tide energy influx (12.4 GW of 34.2 GW). The internal tides excited over the topographic ridges in the Luzon Strait propagate both eastward into the Pacific Ocean and west-southwestward into the SCS. Additional internal tides created over the shelf and slope regions in the southern SCS present wave interference pattern. Numerical experi-ments that eliminate or reduce the K1 internal tide in the Table 3. Barotropic Energy Budget of the Control Run in the SCS

Bounded by Sections L1, L2, and L3 in Figure 8aa Sectional BT Energy

BT-to-BC Energy

Conversion Rate Dissipations Dueto Friction

L1 L2 L3 Luzon Strait SCS

+34.2 +0.6 15.8 12.4 (36% of L1) 1.1 5.6 a

The L1, L2, and L3 (see Figure 8a for their locations) are sections to the east of the Luzon Strait, north of the Taiwan Strait, and south of the SCS, respectively. BT means barotropic while BC means baroclinic. Units are in GW.

Table 4. List of Numerical Experiments

Case Initial Stratification

Sea Level Assimilation

Topographic Ridges in Luzon Strait Control run Typical SCS

summer profile

No Realistic

A None No Realistic

B None Yes Realistic

C Typical SCS summer profile No 50% reduction in height relative to 3000 m D Typical SCS summer profile No 50% reduction in height relative to 3000 m for Heng-Chun Ridge only

E Typical SCS

summer profile

No 50% reduction in height relative to 3000 m for Luzon Island Arc only

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Luzon Strait further suggest that the baroclinic energy conversion reduces the amplitude of K1 surface tide by

about 30%. Our investigation also explains why a two-dimensional model without data assimilation or precisely prescribed sea levels around the Luzon Strait commonly overestimates amplitudes of diurnal tides in the SCS.

[24] The oceanographic condition around the Luzon Strait

is far more complex than the present model setting. In this light, the influence of the seasonally varying Kuroshio on K1tide warrants further studies. Furthermore, the seasonal

variation of the stratification in the SCS adds yet another complication to the generation of K1internal tide and the

subsequent modification of K1 surface tide; this also

deserves future attention. More comprehensive field obser-vations, especially on the Pacific Ocean side of Luzon Strait, are also needed for the validation of model results.

[25] Acknowledgments. This study is funded by Taiwan’s National Science Council under grant NSC95-172611-M-008-004-MY3. S.-Y. Chao is supported by the U.S. Office of Naval Research, Code 322 PO, under contract N00014-05-1-0279. C.-C. Chen at NTNU kindly provided CTD data. R.-C. Lien at APL of UW provided constructive suggestions on the analyses of our model results. Two anonymous reviewers contributed substantially to the explanation and presentation of our results. This is NCOR contribution 118.

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S.-Y. Chao, Horn Point Laboratory, University of Maryland Center for Environmental Science, P.O. Box 0775, Cambridge, MD 21613-0775, USA.

C.-S. Chern and J. Wang, Institute of Oceanography, National Taiwan University, P. O. Box 23-13, Taipei 10617, Taiwan, Republic of China.

S. Jan, Institute of Hydrological Sciences, National Central University, 300 Jung-da Road, Jung-li 32001, Taiwan, Republic of China. (senjan@ cc.ncu.edu.tw)

數據

Figure 3. Typical temperature profile of the SCS in summer. Data were obtained at (118.5°E, 19°N) in July 1999 by Chen et al

Figure 3.

Typical temperature profile of the SCS in summer. Data were obtained at (118.5°E, 19°N) in July 1999 by Chen et al p.4
Table 3 summarizes the barotropic tidal energy budget in the SCS. The barotropic energy integrated along the east section of the Luzon Strait (122.5°E or L1 in Figure 8a) and north section of the Taiwan Strait (25°N or L2 in Figure 8a) is 34.2 GW (1 GW = 1

Table 3

summarizes the barotropic tidal energy budget in the SCS. The barotropic energy integrated along the east section of the Luzon Strait (122.5°E or L1 in Figure 8a) and north section of the Taiwan Strait (25°N or L2 in Figure 8a) is 34.2 GW (1 GW = 1 p.7
Table 2. Formulae for the Calculation of Barotropic and Baroclinic Tidal Energy [Niwa and Hibiya, 2004]

Table 2.

Formulae for the Calculation of Barotropic and Baroclinic Tidal Energy [Niwa and Hibiya, 2004] p.9
Figure 7. Instantaneous vertical density (s t ) distribution and corresponding close-up of upper 300 m at day 14 along (a) 20°N and (b) 4°N.

Figure 7.

Instantaneous vertical density (s t ) distribution and corresponding close-up of upper 300 m at day 14 along (a) 20°N and (b) 4°N. p.9
Figure 8. (a) Depth-integrated barotropic energy flux and barotropic-to-baroclinic energy conversion rate and (b) baroclinic energy flux

Figure 8.

(a) Depth-integrated barotropic energy flux and barotropic-to-baroclinic energy conversion rate and (b) baroclinic energy flux p.10
Table 4. List of Numerical Experiments

Table 4.

List of Numerical Experiments p.11
Figure 9. Harmonic constants along P-Q-R section in Figure 4a from the control run and cases A, B, C, D, and E

Figure 9.

Harmonic constants along P-Q-R section in Figure 4a from the control run and cases A, B, C, D, and E p.12

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