133-·1 48 , Marc , h 1996 Semi-Diurnal Tide on the Shelf Break in Northeast of Taiwan

On the shelf break in northeast of Taiwan, a b. uoy-mounted, upward looking Acoustic Doppler Current Profiler (ADCP) was moored at 270 m to record the current velocity above it. The obtained data was used to study the vertical structure of the semi-diurnal tidal current and its temporal variations. The deployment duration was from September 28 to November 27, 1991 for 59 days. Both barotropic and first baroclinic semi-diurnal tides were found to be important in this area. The nodal point of the first baroclinic tide was located at 110 m-130 m. The Kuroshio intrusion, which occurred in mid­ October, had a relatively small impact . on the barotropic tide but a large one on the baroclinic tide. The speed of the barotropic and baroclinic tides were comparable before the intrusion, but subsequent to the intruded, the baroclinic tide accelerated, and its tidal ellipses showed considerable change in its orientation and eccentricity. In contrast, the difference in barotropic tidal ellipses before and after the intrusion were small. Changes in local water stratification and background low-frequency cur­ rent induced by the intrusion of the Kuroshio ma)1 have been responsible for the observed variations in the vertical structure of the semi-diurnal tide. (


INTRODUCTION
As part of the Kuroshio Edge Exchange Process (KEEP) program, an upward look ing Acoustic Doppler Current Profile� (ADCP) was moored on the shelf break northeast of Ta iwan , measuring the ocean current in the upper 240 m of the water column.Although these measurements were primarily focused toward a study of the vertical structure of low frequency current variations (Tang and Yang,19 93), they a]so enabled an investigation of the semi-diurnal tide on the shelf break.Gene.rally, the semi-diurnal tidal energy on the con tinental she.If is concentrated in the barotropic and lowest baroclinic modes (Baines,19 86).The baroclinic (or internal) tide on the shelf has been found in many observations, for exam ple, Hayes and Halpern ( 19 76) observed of internal tides and waves off the Oregon Coast .
Further, since the barotropic tide does not convert al l of its energy into the baroclinic tide (Wunsch, 1975), it usually remains at a significant amplitude on the shelf.Rosenfeld and Beards le)' ( 1987) and Rosenfeld ( 1990) found that both barotropic and first baroclinic 17Vf 2 tides are important .onthe shelf off northern California.
The generation and propagation of an internal tide on the shelf region has been stud ied using various analytical and numerical models.Zeilon ( 19 12) first suggested that the generation mechanism for internal tides is the interaction of long \\i'aves and bottom topog raphy.Subsequent theoretical and numerical model studies are numerous (Rattra) ' et al.,   1969; Sandstorm, 197 6; Max worthy, 1979).A general review of the theory and observ•ation of inte.maltides in the ocean and on the shelf we.re given by Wunsch (1975) and Baines ( 1986), respectively.An internal tide could be generated as a barotropic tide propagating across the bottom topography from the ope.n sea to the continental shelf.The generation process is strongest at or near the shelf break (Baines, 1982), and local water stratification is one crucial factor.
On the continental shelf� northeast of Taiwan , Chem and Wang ( 1990) examined the temperature and salinity vertical profiles over a 24-hour period and found that the internal semi-diurnal tide amplitude could be as large as 40 m.They inferred that the internal tidal current was a primary source of the ve.rtical water mixing on the shelf.However, the short data records did not allow conclusive re.suits, and many characteristics of the semi-diurnal tide on the shelf region northeast of Taiwan remain a myste.ry.Accordingly, in the preser1t study: an attempt is made to explore some of these characteristics using current measurements 0\1er the water column between 30 m and 240 m.Special attention is paid to the variation of the semi-diurnal tidal current before and after the Kuroshio intrusion.
The pape14 proceeds as fo llows.Section 2 describes the kinematics of the semi-diurnal tidal current before and after the Kuroshio intrusion \XJith the total record di\1ided into three segments.A brief review of the background of the low-fr equency current, previously de-.scribed b )1 Tang and Yan g ( 1993 ), is al so given.In Section 3, a coherence anal)1sis is applied to study the vertical structure of the semi-diurnal tidal current and its temporal variation.Sec tion 4 discusse.sthe characteristics of the barotropic and first baroc1inic semi-diurna] tides.The separation of the.se tides is made by assuming that the \1ertical integration of baroclinic tidal velocity is zero.The potential error due to this assumption and a discussion are pro\1ided in Section 5. Section 6 summarizes the finding and presents the conclusions of this paper.

BACKGROUND AND DATA DESCRIPTION
The mooring location (25 °25'N1 122 °24'E) and surrounding bathymetry on the shelf� break northeast of Taiwan are sho\\i•n in Figure 1.The local water depth was 386 m; the ADCP current meter was moored at 270 m, and the current above it was measured.The mooring \vas deployed for 59 days, fr om September 28 to November 27, 1991, with samples taken at half-hour intervals.A detailed description of the mooring and data retrieval can be fo und in Tang and Yang (1993).The acquired data was linearly interpolated fr om 30 rn to 240 m, and vertical profiles were resampled at fixed 10-m intervals.
Figure 2  Depth contour labels are in meters.(after Tang and Yang, 1993).

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the record to mid-October.After which the current abruptly turned northwestwardly.This action initially occurred in the surface layer and then gradually extended to the deeper layer.
Below the depth of 170 m, the current resumed its southwest ftow.Tang and Yang (199 3) concluded that this abrupt change of current direction in the upper ocean was related to the Kuroshio intrusion.
The same current data is used here to study the temporal and vertical structure varia tions of the semi-diurnal .tidal current.A truncated Fourier transfonn was applied to each original velocity time series to remove fluctuations outside of the semi-diurnal tidal frequency band.The frequency bandwidth was 6.60 x 10-3 cycle per hour (cph) and was centered at 8.05 x 10-2 cp h.Figures 3a and 3b show a representative band-pass filtered velocity time series at 30 m, 80 m, 130 m, 180 m and 230 m for the east component velocity, U, and the north component velocity, V, respectively.The variation of the tidal current in the upper ocean showed different characte.ristics before and after the middle of October, coinciding with the Kuroshio intrusion.The U component had a smaller amplitude in the upper water c. olumn than in the lower one before mid-October, but then., the U component amplitude was nearly constant over the entire water column.This vertical distribution suggests that more than a single mode dominated in U before mid-October, but a barotropic tide dominated thereafter.The V component a1s o showed a different vertical structure before and after the middle of October.Before mid-October, the amplitude of V was smallest in the upper ocean and increased generally with depth.Afterward, the amplitude was smallest at mid-depth and increased with distance from that depth in both directions.Such vertical distribution indicates that a mixed tidal mode and a first baroclinic tide were respectively important before and after mid-October.The Kuroshio intrusion thus appeared to had a significant impact on the semi-diurnal tidal current.In addition to the.spatial variation, the semi-diurnal tidal current also showed a temporal variation (oscillation) of nearly 2 weeks� apparently related to the.neap and spring tides. • In order to study the variation of the vertical structure of the semi-diurnal tidal current before and after the intrusion of the Kuroshio, the original time series was divided into three segments.A similar method was used by We isberg et al. ( 1987) to study the 1\12 tidal current variation on the equatorial Pacific Ocean.The length of each segment was 456 hours (19 days).Segment I was from 9/29 to 10/17 , Se. gment II was from 10/18 to 11/15, and Segment III \\'as from 1116 to 11 /24.Segment I represented the tidal current before the intrusion, while.Segments II and III represented it after the intrusion.A rotary spectra was applied to calculate the hodograph ellipse centered upon the lvf 2 tidai frequency at each of the 22 depths for the three segments.These ellipses are shown in Figure 4.Each column indicates the ellipses over the \:\later column between 30 m and 240 rn in each segment.The tidal ellip • se \\1as the largest in Segment II.In the Jower water column (deepe-r than 140 m), the ellipses did not change notably with time.Their orie-ntations, sizes and senses of rotation

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were the same over the three segments.The amplitude of ellipse generally increased with depth.The orientation (around 0.757r) and the sense of rotation (clockwise) were consistent with depth.In contrast with those in the lower water column, the ellipses in the upper water column did vary with time.The ellipse orientation in Segment I varied anti-clockwise with depth from the uppermost depth to around 60 m.Below that, the major elliptical axis was directed NW-SE.Unlike the ones in Segment I� the orientations of the ellipses in Segments II and III did not vary with depth in the upper ocean but abruptly changed at mid-depth and rotated clockwise around ?T 12 at around 110 m, where the size of the ellipse was the smallest.Below or above this mid-depth, the size of the ellipse increased with distance.This vertical distribution of tidal ellipses in Segments II and III was similar to the vertical structure of the first baroclinic semi-diurnal tide.

COHERENCE ANALYSIS
The coherence-squared and phase between tidal current velocities were calculated over all depth pairs in each segment.The central frequency and bandwidth used in the calcul .ation were 8.05 x io-2 cph and 6.6x 10-3 cph, respectively.The number of degree of freedom was 13 and the corresponding 90% significance level for the null hypothesis on coherence squared was 0.35.
Fig. 4. The semi-diurnal tidal ellipses at each ot' 22 depths from 30 m to 240 m for Segments I, II and III.With the exception of those mark with a plus sign, all of the ellipses are polarized clockwise.
Figures 5 to 7 show the coherence-squared and phase between the U components over all depth pairs as a function of depth for the three segments.In Segment I, the coherence squared values decreased with the distance bet\veen two depths in the upper water column and were high in the lower water column.There was incoherence between the upper and lower water columns and the phase lag was small over the whole.Unlike that in Segment I, the U components in Segments II and III were highly cohe14ent over the whole water column.The phase lag increased with distance between t\vo depths.The maximum phase lag, between the uppennost and bottom depths, was around -Jr/2.In Segment I, results from the coherence analysis did not indicate any single mode predominating in U, thus, a mixed tidal mode must be considered.Although the high coherence-squared values over the entire water column in Segments II and III suggest that a barotropic semi-diurnal tide.dominated in U, their corresponding phase distribution did not support such a hypothesis.Again, a mixed tidal mode was indicated.
Between the upper and lower water columns, the V components were coherent but out-of phase.The distribution of coherence-squared in Segment I was similar to those in Segments II and III, but the phase distributions were different.No single dynamic tidal mode was suggested in .Segment I, and at least two tidal modes must be used to explain its vertical structure .The vertical distributions of coherence-squared and phase in Segments II and III, however, clearly indicated a first baroclinic tide dominating V with a nodal point near 100 m .
Coherence analysis indicated that both barotropic and first baroclinic tides are important.The Kuroshio intrusion had a significant impact on the vertical structure of the tidal current.
After the intrusion, the first baroclinic tide was much more visible in both U and V. Its nodal point was located around I 00 m.This result is similar to that found in the tidal ellipse analysis.

BAROTROPIC AND BAROCLINIC TIDES
The assumption that the vertical integration of baroclinic velocity over the water column between 30 m and 240 m is zero was applied in treating the depth average of U and V as the barotropic velocity.A similar method had been applied in a number of studies (Rosenfeld and Beardsley, 1987; Siedler and Paul, 1991 ).The potential error due to this assumption is discussed in the next section.The resultant barotropic hodograph ellipses fo r the three segments are shown in Figure 11.Although the se-mi-major axes and orientations of the barotropic tidal ellipses in the three segments had very similar values, they were still slightly different after the intrusion of the Kuroshio.Table 1 shows the values of the semi-major axes, orientation and phase lag between U and V. Before the intrusion, the amplitudes of U and V were comparable.The minor axis value was smallest in Segment I, since the phase lag between U and V was close to one Jr.The orientation rotated from about 0.87r in Segment I to 0.9n in Segment III, meaning that the barotropic tidal current in V was reduced after the  142 TAO, Vol. 7, 1Vo.l, March 1996 Ta .
ble 1.The semi-major axis, orientation and phase lag betwee.n the U and V com ponents of the barotropic tidal ellipses in Segments I, II and III.
. _I Il ill Amplitude (cn1 s-1) To subtract the depth a\1erage velocit)' from U and V at each depth, the residual velocity time series was treated as the ba1• oclinic tidal current whose hodograph ellipses are shown in Figure 12.The influence of the Kuroshio intrusion is easily seen in this figure.After the intrusion, the.ellipse \\.'as enlarged and its orientation changed from about 0.757r to 0.57r.
The amplitude of V increased significantly and was large.r than the amplitude of U.Although the ellipse at each depth did show visible change after the intrusion, its vertical structure remained nearly the same.all three segments, the ellipses were smallest at mid-depth (around 110 m-130 m) but increased with the distance fr om that depth.The largest ellipses occurred both at the uppermost and bottom depths.The orientation varied rapidly at mid depth (around 110 m-130 m).Such a v•ertical structure indicated that a first baroclinic mode was dominant in the residual velocity field.

+ + +
� 0 f.1ig•.12.The baroclinic •tidal ellipses at each of 22 depths between 30 m and 240 m in Segments I, II and III.All ot� the ellipses are polarized clockwise.
To further examine the vertical structure, a frequency domain Empirical Orthogonal Functions (EOF) was used to decompose the residual U and V separately into a set of orthogonal EOF modes (Wallace and Dickinson, 1972).The same central frequency and bandwidth were used.Cross-spectral matrices were constructed and their eigenvalues and eigenfunctions were calculated.The eigenvalues partition variance in orthogonal modes and the eigenfunctions give the spatial distribution of amplitude and phase for each mode (Tang   et al., 1988).
In all three segments, the first EOF mode for both U and V contained over 90o/o of variance.Their vertical structures were also similar, indicating that only one mode was important.Figure 13 shows the vertical distributions of amplitude and phase for these six first mode eigenfunctions.The smallest amplitude was around 110 m-130 m, where the phase changed rapidly .There was no phase difference in the water column above or below the mid depths.The phase difference between these two sections of the water column, however, was 7r.A first baroclinic mode was obviously responsible for this vertical structure.The first EOF mode, which contained over 90% of variance, therefore, represented the first baroclinic mode.
The baroclinic tidal current in V was enlarged significantly •after the Kuroshio intrusion. ..-...
It is concluded that both the.barotropic and first baroclinic tides were important in this area.The barotropic tidal current had a larger amplitude in U, while the baroclinic tidal current had a larger amplitude in V.The nodal point of the first baroclinic tidal current was around 110 m-130 m.After the Kuroshio intruded, the first baroclinic tide was enlarged, especially in V, but its vertical structure did not sho�' a significant change.The barotropic tide was slightly diffe rent.The amplitude of V was reduced, and the phase between U and V changed.

DISCUSSION
By assuming that tidal motions are linear, hydrostatic, viscid, and Boussinesq approx imations, the governing equation for the vertical velocit)' •uJ on an f plane (Roberts, 1975) • is: where x, y and z are the east, north and \1ertical directi ons, respectively, while f is the inertial freque.ncy.If N, buoyancy frequency, is a fu nction of z only, the abo\'e equation can be separated into two others.One is a function of x, y and t, \\1hi1e the other is a function of z only.The latter can be written as: where ' LL' is a function of z.only, and /\7i is a separation constant (eigen\1alue).This equation ( where Kn is the horizontal tidal wave number, • and w . . is �.tidal frequency.By taking the derivative of z, the vertical structure of the horizontal yeloe it y can be obtained.Figure 14 shows the vertical profiles of N and the corresponding ve i.tjcal structure of horizontal velocity for the first baroclinic mode, before and after the Kuroshio intrusion.The N profiles were calculated using CTD measurement casts after the moorit} g _was done and then retrieved.A vertical convolution average was applied for smoothing.• Th� computed nodal points of the first baroclinic mode before and after the intrusion were located at 115 m and 140 m.This result agreed with previous findings, where the depth •of nodal point was around 100-130 m.It is noted that the depth of the nodal point descended 25 m after the Kuroshio intrusion occurred.A similar feature was found in the EOF result, but it was only seen in Segment II.By substituting the corresponding eigenvalue into Eq.( 3), the first baroclinic tidal wave number was obtained.The relative phase and group velocities were also computed.The computed wavelength, phase velocities and group velocities before and after the intrusion were 54 km, 120 cm s-1 and 97 cm s-1 and 59 km, 132 cm s-1 and I 07 cm s-1 , respectively.This comparison shows only a small change among these physical characteristics before and after the intrusion of Kuroshio, which this small change was also found by considering the historical CTD measurements in the surrounding area of the ADCP mooring.The depth range of the nodal point of the calculated first baroclinic mode was 130±25 m.The corresponding eigenvalues varied ± 13% from their mean.The conclusion, then, can be made that the depth of the nodal point of the first baroclinic mode, which was estimated directly from the current measurement, agrees with its theoretical value, which was calculated from the CTD measurement.
In section 4, the barotropic tidal velocity was calculated by taking the vertical average of the current measurements over the water column between 30 m and 240 m.Three assumptions were implicitly imposed on this c.alculation.The first was the rigid lid surface boundary condition ( u1 = 0).The error due to this assumption is negligible.The second was the zero vertical velocity at bottom.Wunsch (1969) found that this assumption is likely applicable as long as the local bottom slope is also far from an apex.Although the bottom slope in here was not flat, it was far from an apex.The error due to this assumption should have therefore b�en negligible, too.To apply these two boundary conditions, the integration of the horizontal velocity of baroclinic tidal modes over the whole water column was assumed to be zero.Unfortunately, the present current measurement did not record the velocity over the whole water column, which meant the third assumption had to be applied.This assumption is that the incomplete vertical integration of horizontal baroclinic velocity was zero over the water column between 30 m and 240 m, which is acceptable as long as the greater part of the water column is considered.To estimate the potential error owing to the third assumption, a residual velocity was computed by averaging the horizontal velocity between 30 m and 240 m from the calculated first baroclinic mode.Using the first baroclinic modes in Figure 14 as an example, the amplitudes of this residual velocity were equivalent to 8% and 13% of the first barocJinic velocity at 30 m before and after the Kuroshio intrusion. of error on the barotropic tidal current or could shift the nodal point of the first baroclinic tidal current up or down by 20 m-30 m.However, this amount of error would not have seriously distorted the characteristics of the semi-diurnal tide described above.
Magnell et al. (1980) studied the relationship between low-frequency current and the amplitude of the semi-diurnal tidal current at the sloping north edge of Georges Bank and found a nonlinear mechanism linking the tidal and low-frequency current.Likewise, the abrupt change in the low-frequency current in the present study area before and after the Kuroshio intrusion had a significant impact on the local tidal current.

SUMI\1ARY AND CONCLUSIONS
In the present study, the.vertical structure and temporal variation of the semi-diurnal tidal current on the shelf break northeast of Taiwan were examined.It was found that the vertical distribution of tidal current had different characteristics before and after the intrusion of the Kuroshio which occurred in mid-October (Tang and Yan g, 1993).The observed velocity time series was divided into three segments, each one I 9 days in length.The first segment contained the \i1elocity series before the Kuroshio intruded, while the other two segments contained the velocity time series afte.r the Kuroshio intrusion.
By examining the ''ertical distribution of tidal ellipses over the three segments, it was found in the present study that the tidal ellipses had similar characteristics in the lower water column but differe.nt in the upper water column before and after the intrusion of the Kuroshio.Before the Kuroshio intruded, Segme.nt I \1aried slowl)1 with depth from the uppermost to 60 m.After the intrusion, in Se. gments II and III the orientation of tidal ellipse remained the same in the upper and lower water columns, but a rapid phase change was found at mid-depths, which in fact showed the sm allest ellipse.These results indicate that the first baroclinic tide dominated after the Kuroshio intrusion.The calculated coherence values over all de.pth pairs indicated no single mode dominated the semi-diurnal tide in the U component and suggested the first baroclinic tide was important in the V fie.Id, especially, after the intrusion.According to tidal ellipse and coherence analysis� the barot1• opic and first baroclinic modes were important in the studied a1• ea.
The barotropic tidal velocity was obtaine.d by assuming that the vertical integration of the baroclinic tidal v•elocity between 30 m and 240 m \�as zero.The orientation and semi major axis of the barotropic tide changed slightly over the three segments.The amplitude of the semi-major axis varied from around 29 to 24 cm s-1 .Before the Kuroshio intrusion, the amplitudes of U and V were.comparab]e with V decreasing after the intrusion.
The baroclinic tidaJ velocit)' was obtained by subtracting the barotropic tidal velocity from the original band-pass-fi ltered tidal velocit)' at each depth.The vertica1 structure of the baroclinic tidal el lipses were.similar in the three segments.The smallest tidal ellipse was at around 1I0 m-130 m, where the orientation c. hanged rapidly.The baroclinic tidal ellipse had a similar vertica] structure in each of the three segments, its orientation and size varied with time.The ellipses were.smallest before the Kuroshio intrusion after which they enlarge.d.A frequency domain EOF was applied to further decompose the baroclinic tidal velocity time serie.s.Only one EOF mode contained over 90% of variance in all three segments for both U and V.The six first EOF modes had very similar vertical structures.The nodal point was at around 110 m-130 m, which again was consistent \\1ith previous results.
The results frotn the above three different analytical methods were consistent.Both barotropic and first baroclinic tides were important on the shelf break northeast of Taiwan.The first baroclinic tide had its nodal point around 110 m-130 m. • •Its vertical structure was generally stable with time, while its amplitude and phase c•hanged after the Kuroshio intrusion.
Before the intrusion, the• barotropic and baroclinic tides were comparable, but afterwards, the baroclinic tide was enlarged and projected more energy onto its north component velocity.
Combining changes in both barotropic and baroclinic components, the tidal current showed a different vertical distribution before and after the Kuroshio intrusion.The variation in local water stratification and low-frequency background current, induced by the intrusion of the Kuroshio, may have been responsible for the change in the semi-diurnal tidal current ..
Fig;. 3. (a) The band-passed filtered east component velocity (U) time series.The uppermost to the bottom panels show the U at 30 m, 80 m, 130 m, 180 m and 230 m, respectively.(b) The band-passed filtered north component ,,.elocity (V) time series.The .upper1nost to the bottom panels show the V at 30 m, 80 m, 130 m, 180 rri and 230 m, respectively.
Fig�. 5. Coherence-squared (left panel) and phase (right panel) between east com ponents of velocity in Segment I, calculated over all depth pairs between 30 m and 240 m.

Fig. 6 .
Fig.6.Coherence-squared (left panel) and phase (right panel) between east com ponents of velocity in Segment II, calculated over all depth pairs between 30 m and 240 m.
Fig;. 7. Coherence-squared (left panel) and phase (right panel) between east com ponents of velocity in Segment III, calculated over all depth pairs between 30 m and 240 m.

Fig. 8 .Fig. 9 .
Fig. 8. Coherence-squared (left panel) and phase (right panel) between north com ponents of velocity in Segment I, calculated over all depth pairs between 30 m and 240 m.

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Fig. _ 11 . .The barotropic tidal ellipses in Segments I, II, III.The ellipse of Segment I, mark with a plus sign, is polarized anti-clockwise.

Fig. 13 .
Fig. 13.The distribution of amplitude. (left panels) and phase (right panels) for the first eigenfunction, calculated from the residual velocity time series.The upper two panels are for east component velocity, and the lower two panels are for n .orth component velocity.The solid line represents Segment I, the.dashed line Segment II, an d the dashed-dotted line Segment III.

Fig. 14 .
Fig. 14.The vertical distribution of N (left) and the horizontal velocities of the first baroclinic mode (right) before and after the Kuroshio intrusion.The solid and dashed lines represent the results before and after the intrusion.
can be sol-v •ed numerically b]' imposing a rigid lid surface boundary and a flat rigid bottom I no flow penetrating into the flat bottom.The solution, is =1h0 suDi.: • :of ... a • set ;of orthogonal dynamical modes, with each one c0r1esponding to an eigenvalue which can •be • Tang & Da Wei Lee 147 It could induce 18% TA 0., vol.7, l\J o. l, lVI a. 1•cl1 1996