Diurnal coastal-trapped waves on the eastern shelf of Sakhalin in the Sea of Okhotsk and their modification by sea ice

ARTICLE IN PRESS

Continental Shelf Research 28 (2008) 697–709 www.elsevier.com/locate/csr

Diurnal coastal-trapped waves on the eastern shelf of Sakhalin in the Sea of Okhotsk and their modification by sea ice Jun Onoa,, Kay I. Ohshimaa, Genta Mizutab, Yasushi Fukamachia, Masaaki Wakatsuchia a

Institute of Low Temperature Science, Hokkaido University, Kita-19, Nishi-8, Kita-ku, Sapporo 060-0819, Japan b Graduate School of Environmental Science, Hokkaido University, Sapporo, Japan Received 25 May 2007; received in revised form 8 November 2007; accepted 21 November 2007 Available online 4 December 2007

Abstract From July 1998 to June 2000, the first long-term mooring measurements were carried out off the east coast of Sakhalin. Using these data, we examined the characteristics of the tidal heights and currents. The tidal heights and currents are dominated by the diurnal variability with fortnightly modulation over the northern part of the shelf. The K 1 and O1 tidal current ellipses are clockwise with their major axes along the isobaths and their signal propagates with the coast on the right with phase speeds of 3.4 and 3:8 m s1 , respectively. The diurnal tidal currents are almost uniform in the vertical direction except for the bottom Ekman layer. The thickness of the bottom Ekman layer caused by the diurnal tidal currents is larger in the region of stronger tidal currents, reaching 20–30 m over the northern part of the shelf. The diurnal tidal currents over the northern part of the shelf can be explained by the first-mode diurnal coastal-trapped waves (CTWs). The diurnal CTWs are almost independent of the seasonal variability of density stratification and contribute significantly to diurnal currents, but only slightly to sea-surface heights. The diurnal tidal currents over the southern part of the shelf are significantly smaller than those over the northern part. This is because the diurnal CTWs cannot exist south of 52 N from the dispersion relation. The diurnal tidal currents are significantly reduced over the northern shelf, where the diurnal CTWs exist, during the high sea-ice concentration periods. From this result, we propose the scenario that the CTWs are damped by the spin-down effect due to the Ekman layer that would occur underneath the sea ice. r 2007 Elsevier Ltd. All rights reserved. Keywords: The Sea of Okhotsk (a marginal sea in the Northwestern Pacific); Diurnal tidal currents; Coastal-trapped waves; Sea ice; Bottom Ekman layer

1. Introduction It has been shown, from a barotropic numerical simulation of tide, that the Sea of Okhotsk is a region of large tidal heights and strong tidal currents at the diurnal periods (Suzuki and Kanari, 1986; Kowalik and Polyakov, 1998; Nakamura et al., 2000). This is because the period of the natural oscillation in the Sea of Okhotsk, 26.3 h, is close to the diurnal periods (Kowalik and Polyakov, 1998). In addition, the diurnal tidal currents are enhanced in some local regions of the wide shelf and steep slope; Kashevarov Bank (Kowalik and Polyakov, 1998, 1999; Polyakov and Martin, 2000; Ohshima et al., 2002; Martin et al., 2004; Ono et al., 2006) Kuril Islands (Kovalev and Rabinovich, Corresponding author. Tel.: +81 11 706 5483; fax: +81 11 706 7362.

E-mail address: [email protected] (J. Ono). 0278-4343/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2007.11.008

1980; Yefimov and Rabinovich, 1980; Nakamura et al., 2000; Rabinovich and Thomson, 2001; Ohshima et al., 2002; Katsumata et al., 2004) the northeastern coast of Hokkaido (Odamaki, 1994), and the eastern coast of Sakhalin (Rabinovich and Zhukov, 1984; Ohshima et al., 2002; Shevchenko et al., 2004) (see Fig. 1 for these locations). Amplified diurnal tidal currents associated with a topographic wave were first identified in current meter records over the Hebrides Islands shelf off Scotland (Cartwright, 1969; Cartwright et al., 1980) and observed over the shelf and slope in the world such as regions off the west coast of Vancouver Island (e.g., Crawford and Thomson, 1982, 1984) and east coast of Australia (e.g., Freeland, 1988). Over the eastern shelf of Sakhalin, it has been shown that amplified diurnal tidal currents can be explained by the first-mode diurnal shelf waves (SWs), from the comparison of the observations and the

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698

60N

55N

50N

45N

140E

145E

150E

155E

160E

Fig. 1. A map showing locations of moorings (circles). A cross near M1 denotes tide gauge location for tidal harmonic constants of Nakano (1940) used in Fig. 10b. Contours indicate isobaths based on the General Bathymetric Chart of the Oceans (GEBCO) data.

barotropic SW solution (Rabinovich and Zhukov, 1984; Ohshima et al., 2002; Shevchenko et al., 2004). Thus these regions are very interesting locations from the viewpoint of the geophysical fluid dynamics. However, so far drifter and mooring observations were limited to the surface or a single depth and their durations were short. Thus the seasonal variability and the vertical structure of tidal currents have not been fully clarified. Further, the effects of stratification and mean flow on the tidal currents have not been considered. Recently, Mizuta et al. (2005) showed that the subtidal variability of the East Sakhalin Current (ESC) can be explained by the coastaltrapped waves (CTWs). However, they did not focus on the tidal variability. The Sea of Okhotsk is the southernmost sea with a sizeable seasonal ice cover in the northern hemisphere. It is interesting to investigate the relation between tides and sea ice. From the observation in western Hudson Bay, Prinsenberg (1987) showed that sea ice damps the amplitudes of tidal heights and currents and changes their phases. Prinsenberg (1988) also revealed the mechanism for the damping and phase change of the tide caused by the sea ice in Hudson Bay. In the Sea of Okhotsk, the sea ice over Kashevarov Bank, which is a region of strong diurnal tidal currents, is affected by the tidal currents (Polyakov and Martin, 2000; Martin et al., 2004; Ono et al., 2006). Polyakov and Martin (2000) showed, from a coupled ice-

ocean model, that oceanic heat flux from below caused by the residual upward current and tidal mixing results in seaice melting, forming and maintaining the polynya over Kashevarov Bank. Martin et al. (2004) showed, from satellite imagery, that the polynya area varies diurnally and fortnightly. From high-quality radar ice-velocity data, Shevchenko et al. (2004) examined the sea-ice motions off the northeastern coast of Sakhalin. They revealed that ice drift over the Sakhalin shelf is governed by two major mechanisms: diurnal tidal currents and wind-induced surface drift. These studies prompt us to investigate the relation between tides and sea ice based on the direct current observation. The first long-term mooring experiments were carried out off the east coast of Sakhalin in 1998–2000 under the joint Japanese–Russian–U.S. study of the Sea of Okhotsk. We successfully obtained continuous long-term velocity and sea-surface height data for nearly one year, including the ice-covered season. The present data set, which consists of three lines in the alongshore direction (Fig. 1), is much more extensive one than those of the previous observations. The purposes of this study are to clarify the detailed characteristics of tidal currents and heights off the east coast of Sakhalin based on the observations, and to interpret the observed results by the application of the CTW theory. Furthermore we examine how tidal currents are affected by sea ice.

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2. Data Fig. 1 shows the mooring sites. From July 1998 to June 2000, the mooring measurements were carried out along the three lines; a line extending northeastward from the northern end of Sakhalin (line A), lines along 53 N (line B) and 49:5 N (line C) off the east coast of Sakhalin. Mooring sites M1, M5, M8, and M9 were located in the shelf region, M2, M3, M6, and M7 were in the slope region, and M4 was in the offshore region. Table 1 lists the detailed information about the mooring measurements (modified from Table 1 in Mizuta et al., 2003). At the four mooring sites in the shelf regions, an Acoustic Doppler Current Profiler (ADCP) (RD Instruments Workhorse Sentinel 300 kHz) for measuring the vertical profile of velocity and the sea-surface height was used, except at M1 in 1999–2000. The ADCPs were housed in a trawl resistant bottom mount (Flotation Technologies AL-200) to avoid damage by fishing activities. In the slope and offshore regions, the moorings consisted of ADCPs (RD Instruments BroadBand Self-Contained 150 kHz) and current meters (Union Engineering RU-1). The deployment and recovery of instruments were performed by R/V Professor Khromov of Russian Far Eastern Regional Hydrometeorological Institute. The ADCP provides velocity data in 4- or 8-m bins. In this study, velocity data in the shallower layers were not used because the data contain errors especially during the winter (Mizuta et al., 2003). The accuracy of the flow speed is less than 0:01 m s1 for ADCPs and 2% of actual speed for current meters. Seasurface height was processed according to Visbeck and Fischer (1995) with a correction based on sea-level pressure data of the European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data. The mooring data were recorded with 30- or 60-min sampling intervals. The vertical profiles of density stratification in

699

summer and winter were obtained from CTD measurements (Fukamachi et al., 2004) and profiling floats (Ohshima et al., 2005), respectively. In this study, we used the daily sea-ice concentration with the spatial resolution of 25  25 km, derived from the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave Imager (SSM/I), on the basis of an algorithm of Kimura and Wakatsuchi (1999). 3. Results As an example of observational results, time series of the tidal components for the east–west and north–south velocity at a depth of 44 m at M1 are shown in Fig. 2, where the tidal components were obtained by subtracting the data filtered with a tide-eliminating filter of 10 days (Thompson, 1983) from the raw data. The tidal components of the velocity are dominated by the diurnal signal with fortnightly modulation. The amplitude of the tidal components for the north–south velocity reaches 0.4–0:6 m s1 during the tropical tide that corresponds to the time of maximum lunar declination. An interesting feature to note is that the amplitudes of the tidal components are apparently reduced in January–March. This indicates that sea ice influences the tidal components of the velocity. This will be discussed in Section 3.3. Also at M5, M8, and M9 over the shelf, the velocity is dominated by the diurnal variability with fortnightly modulation (not shown). 3.1. Tidal analyses To clarify the characteristics of tidal currents and heights at all mooring sites, a harmonic tidal analysis with nodal corrections (Foreman, 1977, 1978) was performed for the time series of velocity and sea-surface height anomaly.

Table 1 Mooring site, location, instrument type, bottom and nominal instrument depths, mooring period, and length of good data Site

Lat. (1N)

Lon. (1E)

Type

M7

54.9

143.9

M8 M9 M1 M2

54.7 54.5 53.0 53.0

143.5 143.0 144.0 144.4

M3

53.0

144.8

M4

53.0

145.5

M5 M6

49.5 49.5

144.5 146.5

ADCP CM ADCP ADCP ADCP/CM CM CM ADCP CM CM CM/ADCP CM ADCP ADCP CM CM

Depth (m) 480 110 90 100 480 970

1720 130 790

Dnom (m)

Period

Length (days)

200 430 110 90 100 200 430 190 460 870 180 470 130 180 480 740

September 1999–June 2000

291 291 101 179 349 689 689 406 406 233 689 686 348 663 548 587

September 1999–June 2000 September 1999–June 2000 July 1998–June 2000 July 1998–June 2000 July 1998–September 1999

July 1998–June 2000 August 1998–September 1999 August 1998–June 2000

Acronym CM indicates a current meter. Acronyms ADCP/CM and CM/ADCP indicate an ADCP for July 1998–September 1999 and a current meter for September 1999 and a current meter for September 1999–June 2000 and vice versa. Mooring sites are listed from the north.

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700

(m s−1)

0.5 0 −0.5

(m s−1)

0.5 0 −0.5 AUG

SEP

OCT 1998

NOV

DEC

JAN

FEB

MAR

APR 1999

MAY

JUN

Fig. 2. Time series of the tidal components of (a) east–west and (b) north–south velocity at a depth of 44 m at M1.

Table 2 Tidal current ellipse parameters for K 1 , O1 , and M 2 constituents Site

Measured depth (m)

Tidal constituents O1

K1

M7 M8 M9 M1 M2 M3 M4 M5 M6

145 50 28 44 203 140 199 73 152

M2

L

S

Or

Ph

Ro

L

S

Or

Ph

Ro

L

S

Or

Ph

Ro

0.15 0.30 0.36 0.21 0.05 0.05 0.04 0.12 0.07

0.03 0.11 0.08 0.10 0.02 0.00 0.01 0.02 0.03

101 102 127 97 52 69 103 111 103

61 70 63 246 347 356 25 30 19

CCW CW CW CW CW CCW CCW CW CW

0.17 0.21 0.30 0.20 0.04 0.04 0.04 0.10 0.06

0.03 0.06 0.06 0.08 0.02 0.00 0.01 0.02 0.03

103 104 127 93 48 58 109 113 105

21 15 19 171 267 294 347 350 339

CCW CW CW CW CW CCW CCW CW CW

0.07 0.05 0.05 0.03 0.02 0.02 0.03 0.05 0.05

0.00 0.01 0.00 0.00 0.00 0.01 0.01 0.00 0.02

112 42 12 105 85 136 115 109 67

309 264 272 230 233 278 255 236 214

CCW CCW CW CW CW CCW CW CW CW

L and S are the length of the major and minor axes of the tidal currents ellipses ðm s1 Þ. Or is orientation (deg.) defined by the angle from the east to the major axis in the counterclockwise direction. Ph is the phase (deg.) defined by the time when flow speed reaches a maximum at a mooring location after a virtual heavenly body culminates at the Greenwich meridian. Ro is the rotation direction of the tidal currents ellipses. CW (CCW) indicates clockwise (counterclockwise) rotation.

Depths of the instruments moored at M7 changed twice, because the mooring was advected about 20 km southward by strong currents. Thus a harmonic analysis at M7 was performed only for the velocity data in September– November before the first depth change. At all mooring sites, K 1 and O1 are prominent tidal constituents (Tables 2 and 3). Strong diurnal tidal currents over the northern shelf are qualitatively similar to the results of the observation (Rabinovich and Zhukov, 1984) and the numerical model (Kowalik and Polyakov, 1998). The amplitudes of the semidiurnal tidal currents, which are dominated by M 2 constituent, are 1=2–1=6 of those of the diurnal tidal currents (Table 2), except for 3/4 at M4. Fig. 3a shows the observed K 1 tidal current ellipses at all mooring sites. In the shelf region (M1, M5, M8, and M9), the K 1 tidal current ellipses are clockwise with their major axes along the isobaths. Their major axis lengths reach 0.11–0:34 m s1 and decay in the southward direction. In the slope (M2, M3, M6, and M7) and offshore (M4) regions, the amplitudes of K 1 tidal current ellipses are

Table 3 Amplitudes (A) and phases (Ph) for the K 1 , O1 , and M 2 constituents of the sea-surface height over the shelf Site

Tidal constituents O1

K1

M8 M9 M1 M5

M2

A (m)

Ph (deg.)

A (m)

Ph (deg.)

A (m)

Ph (deg.)

0.39 0.26 0.28 0.15

280 98 83 85

0.31 0.24 0.31 0.19

219 61 50 51

0.18 0.13 0.15 0.05

298 303 304 123

much smaller than those over the shelf. Thus significant K 1 tidal currents are confined to the shelf regions. These features are also observed for the O1 tidal current ellipses (Fig. 3b). From the Greenwich phases of the K 1 and O1 tidal current ellipses at M9 and M1 and distances between these mooring sites, the phase speeds of K 1 and O1 were

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701

55N

55N

53N

53N

B

N

N E

E

0.1 m s−1

0.1 m s−1 51N

51N

M6

M5

49N

49N 142E

144E

146E

148E

142E

144E

146E

148E

Fig. 3. (a) K 1 and (b) O1 tidal current ellipses at mooring sites; M1 (at a depth of 44 m), M2 (203 m), M3 (140 m), M4 (199 m), M5 (73 m), M6 (152 m), M7 (145 m), M8 (50 m), and M9 (28 m) from the harmonic analysis. Solid lines within ellipses denote the Greenwich phase. The rotation directions of tidal current ellipses are indicated by thick and thin ellipses for clockwise and counterclockwise rotation, respectively, in addition to arrowheads. The 100-, 200-, and 1000-m isobaths are superimposed by thin lines.

Tidal current ellipse 0

Major Axis

Minor Axis

Orientation

Gr.Phase

N E

0.1 m s−1 20

Depth (m)

40

K1

O1

60

80

100 0

0.1

0.2

(m s−1)

0

0.1 (m s−1)

0.2

0

180 (deg.)

360

0

180

360

(deg.)

Fig. 4. Vertical structure of tidal current ellipses for the K 1 and O1 constituents and their parameters (solid curves for K 1 and dashed curves for O1 ) constituents at mooring site M1. Solid lines within tidal current ellipses denote the Greenwich phase. All the tidal current ellipses are clockwise, which are shown by arrowheads. Results at 8-m interval from 44 to 96 m are shown. A horizontal line indicates the bottom depth (102 m).

estimated. Assuming that the diurnal tidal currents propagate with the coast on the right, the K 1 and O1 constituents propagate with phase speeds of 3.4 and 3:8 m s1 between M9 and M1, respectively. The phase

speed for K 1 ðO1 Þ is close to those of 3.9 (4.3) and 4:0 ð4:2Þ m s1 of SWs calculated numerically by Rabinovich and Zhukov (1984) and Shevchenko et al. (2004). The observed shapes, rotation directions, and phase speeds for

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702

Depth (m)

the K 1 and O1 tidal current ellipses suggest the excitation of the diurnal SWs. In Section 3.2, we will interpret these observed results by a CTW solution. The K 1 and O1 tidal current ellipses along the line B show that the Greenwich phases nearshore lead those offshore (Table 2). This is consistent with the theory that bottom friction causes offshore phase lags for SWs, demonstrated by Brink and Allen (1978). Along the lines A and C, such phase lags in offshore direction are not observed (Table 2). Fig. 4 shows the vertical profiles of tidal current ellipses, major and minor axis lengths, orientation, and Greenwich phase for the K 1 and O1 constituents observed at M1. The lengths of major and minor axis of K 1 and O1 tidal current

ellipses decrease near the bottom. Also their velocity vectors are rotated counterclockwise with the depth near the bottom. These features suggest the formation of the bottom Ekman layer. This will be discussed in Section 3.4. 3.2. Application of a CTW solution To interpret the observed results a linear, inviscid CTW solution (Brink and Chapman, 1987) was applied. Fig. 5 shows the vertical profiles of realistic bottom depth and density stratification used in the CTW solution. Using density stratification in summer and bottom topography along three lines (A, B, and C), dispersion curves for firstand second-mode CTWs were calculated (Fig. 6a). It is

0

0

200

200

400

400

600

600

800

800

1000

1000 0

1

2

N2 (x10−4 s−2)

1200 1400 1600 0

100 200 Offshore distance (km)

300

Fig. 5. (a) Cross-shelf depth profiles along the lines A (long-dashed curve), B (solid curve), and C (short-dashed curve). (b) Vertical profiles of the squared buoyancy frequency along the line B in summer (solid curve) and winter (dashed curve).

1

M1 M2 M3

0

M4

200 400 K1 O1

0.6 0.4

Depth (m)

 /f

0.8

600 800 1000 1200

0.2

1400 1600

0 0

0.1

0.2 l (×10

-4

0.3 m-1)

0.4

0

100

200

300

Distance (km)

Fig. 6. (a) Dispersion curves for the first- (thick curves) and second- (thin curves) modes CTW computed for the summer stratification and depth profiles along the lines A (long-dashed curves), B (solid curves), and C (short-dashed curves). Horizontal thin lines indicate the normalized frequencies of the K 1 and O1 along the line A. A dispersion curve for the barotropic SW calculated with depth profile along the line B is superimposed by a dash-dotted curve. (b) The cross-shelf modal structure of alongshore velocity of the first-mode CTW at K 1 period for the line B. Amplitudes are arbitrary. The solid and dashed curves indicate positive and negative values, respectively.

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703

M8 M7

M9

M9

M8

M7

55N

M1 M2

M2

M3

M4

M4

53N M3

N E

M1

0.1 m s−1

142E

144E

146E

Fig. 7. Comparison of K 1 tidal current ellipses between (a) the observation and (b) the CTW solution along the lines A and B. Solid lines within ellipses denote the Greenwich phase. Along the line A (B), the calculated phase at M9 (M1) shown in (b) is fitted to the observed Greenwich phase at M9 (M1) shown in (a) and the relative phases are represented for the other. As in Fig. 3, the directions of rotation are indicated by thick and thin ellipses, respectively, in addition to arrowheads. In the left figure, the 100-, 200-, and 1000-m isobaths are superimposed by thin lines.

line A

line B

line C

6 Phase speed (m s−1)

found that the first-mode diurnal CTWs can exist at bottom topography along the lines A and B but not along the line C. The cross-shore modal structure of alongshore velocity for the first-mode CTW at K 1 period along the line B is presented in Fig. 6b. We find that the structure of the CTWs was nearly barotropic. The nearly barotropic structure of the CTWs was also valid at O1 period and along the line A (not shown). These structures agree with the observed results. However, since this CTW solution does not include the effects of friction, the structure of the bottom Ekman layer as shown in Fig. 4 is not captured. Fig. 7 shows the K 1 tidal current ellipses from (a) the observation and (b) the CTW solution. The rotation directions and shapes of the tidal current ellipses over the shelf (M1, M8, and M9) derived from the CTW solution are similar to the observed ones. Fig. 8 shows alongshore variation in phase speeds for the first-mode diurnal (K 1 and O1 ) CTWs calculated using the ETOPO5 bottom-depth data. The mean phase speed and wavelength of K 1 (O1 ) constituent between the lines A and B from the CTW solution are 3:4 m s1 and 290 km (3:7 m s1 and 340 km), respectively. These phase speeds coincide well with the observed speed of 3.4 ð3:8Þ m s1 for K 1 (O1 ). From the dispersion relation, the diurnal CTWs cannot exist at the bottom depth south of 51:8 N. This means that the diurnal CTWs can only propagate up to

O1 K1 4

O1 K1 No CTWs

2

0 55

54

53 52 Latitude (N)

51

50

Fig. 8. Alongshore variation in phase speed of the first-mode diurnal CTWs computed from the ETOPO5 bottom-depth data. Dashed lines denote the phase speeds between lines A and B estimated from the observations.

51–52 N. These results are consistent with Ohshima et al. (2002) and Shevchenko et al. (2004): the diurnal CTWs cannot exist at the south of 51–52 N because the shelf is narrow and the slope is gentle. Using the mean phase speed of the diurnal CTWs, it takes 1:0 day for the diurnal CTWs to propagate from the line A to the southern end

ARTICLE IN PRESS J. Ono et al. / Continental Shelf Research 28 (2008) 697–709

M1 M2 M3

M4

0 Velocity (m s−1)

ð51:8 NÞ of the region where the diurnal CTWs can exist. The above comparison between the observation and the CTW solution suggests that the first-mode diurnal CTWs can explain the diurnal tidal currents over the northern part of the eastern shelf of Sakhalin. The dispersion curves calculated using density stratification in summer and winter are almost identical with each other (not shown) along the lines A and B. As in the case of the subtidal CTWs demonstrated by Mizuta et al. (2005), effects of the seasonal change in density stratification on the diurnal CTWs are found to be small. A dispersion curve of the first-mode SWs for the depth profile along the line B is superimposed on Fig. 6a. A dispersion curve of the SWs in this area is not so different from that of the CTWs with stratification. To investigate the seasonal variation in the phase speeds of K 1 and O1 from the observational data, we decomposed the time series of velocity observed at M9 and M1 into the periods in summer–fall and in winter and then performed a harmonic analysis. Summer–fall and winter periods are 1 August–31 October and 1 January–31 March for M1, and 19 September–30 November and 1 January–15 March for M9. To remove the influence of seasonal modulation by the tidal potential, unresolved tidal constituents due to the shorter periods are inferred by assuming the amplitude ratios and phase differences of neighboring constituents from the results of longer analysis periods at the same mooring sites (Foreman, 1978); specifically, the components of P1 (24.07 h) and K 2 (11.97 h) are inferred from the K 1 and S 2 constituents, respectively. This process can reduce the influence of modulation caused by the neighboring constituents. The observed phase speeds in summer–fall and in winter are 3.3 (3.8) and 3:5 ð4:0Þ m s1 for K 1 (O1 ) constituent, respectively. The phase speeds of the K 1 and O1 increase by 0:2 m s1 in winter. This increase in phase speeds is close to that of the ESC that attains a maximum in winter (Mizuta et al., 2003), implying effects of advection by the ESC. To examine the effects of the mean flow on the seasonal variation in the phase speed of the SWs, we applied a SW solution in the presence of a mean flow because the first-mode diurnal CTWs are almost barotropic as shown in Fig. 6a. Fig. 9a shows the depthaveraged north–south velocity components in summer (July) and winter (January) observed at four mooring sites along the line B and their approximate quadratic curves. The computed dispersion curves for SWs with the mean flow in summer and winter are compared in Fig. 9b. The phase speeds of K 1 and O1 increase by 0:2 m s1 in winter compared with those in summer. This suggests that the observed increase of phase speeds in winter can be explained by the advection due to the ESC. We estimated the contribution of the diurnal CTWs to the tidal heights. From the pressure (p) of the first-mode CTWs based on the major axis lengths of tidal current ellipses observed at M1 and M9, the amplitudes of seasurface height ðZÞ of CTWs at K 1 and O1 frequencies are calculated by Z ¼ p=rg, where r ð¼ 1025 kg m3 Þ is density

−0.1 −0.2 −0.3 −0.4 0

100

200

300

Distance (km)

1

0.8

K1 O1

0.6  /f

704

0.4

0.2

0 0

0.1

0.2 l (× 10

−4

m

0.3

0.4

s−1)

Fig. 9. (a) The observed mean north–south velocity components of the ESC in summer (crosses) and winter (circles). Quadratic curves fitted to the observation are also shown. (b) Dispersion curves for a barotropic SW solution with the mean velocity in summer (solid curve) and winter (dashed curve). These dispersion curves are calculated with the method similar to that in Ohshima (1987). Horizontal lines indicate the normalized frequencies of K 1 and O1 along the line B.

and g is the acceleration of gravity. Fig. 10 shows the amplitudes of sea-surface height from the observation (Table 3) and the CTW solution along the lines (a) A and (b) B. The amplitudes of K 1 and O1 tidal heights observed by the ADCP along the line A, which increase toward M8 from M9, cannot be explained by the CTW solution (Fig. 10a). From the barotropic tidal model (e.g., Kowalik and Polyakov, 1998), it has been shown that an amphidromic point is formed off the northernmost part of Sakhalin. It is likely that the complicated tidal heights and currents fields are formed through the processes such as the scattering and diffraction of waves around line A where isobaths bend sharply. The K 1 and O1 amplitudes of the sea-surface height observed along the line B decrease by 0.1 m from the coast to M1, which can be explained by the diurnal CTW solution (Fig. 10b). However, the observed K 1 and O1

ARTICLE IN PRESS J. Ono et al. / Continental Shelf Research 28 (2008) 697–709

M9

M8

M7

0.4

 (m)

0.3 0.2 0.1 0 0

100 M1 M2 M3

200

300

200

300

M4

0.4

 (m)

0.3 0.2 0.1 0 0

100 Distance (km)

Fig. 10. Comparisons of sea-surface height between the observation and the CTW solution for the K 1 (circles and solid line) and O1 (crosses and dashed line) constituents along the lines (a) A and (b) B. We used the tidal harmonic constants of Nakano (1940) for the values at the coast in (b).

amplitudes themselves are much larger than those by the diurnal CTW solution. This indicates the contribution other than the diurnal CTWs. One possible candidate for this is a barotropic Kelvin wave, as suggested by Rabinovich and Zhukov (1984). However the scale of the Kelvin wave (the Rossby radius of deformation is 1000 km in the Sea of Okhotsk) is comparable to that of the Okhotsk Sea, which is unfavorable condition for the existence of the Kelvin wave. The sea-surface height and velocity of the Kelvin wave should be in phase theoretically. At M5, where the diurnal CTWs cannot exist, the phase difference between the sea-surface height and the tidal current ellipses for K 1 (O1 ) constituent is 55 ð299 Þ and not in phase at all (Tables 2 and 3). At least, the observed sea-surface height cannot be explained simply by the Kelvin wave. 3.3. Effect of sea ice on the tidal currents Fig. 2 shows that the amplitude of the tidal currents is relatively small in January–March. In this subsection we examined the effects of sea ice on the tidal currents. The time series of velocity observed at M1 in 1998–1999 are divided into the eight segments with 42-day periods and then the harmonic analyses are performed for each period. Figs. 11a and b show the time series of the vertical profiles of major axis lengths for the K 1 and O1 tidal current ellipses, respectively. Fig. 11c shows the time series of the

705

sea-ice concentration averaged over the area enclosed by the thick lines in Fig. 11d. It is found that the major axis lengths for the K 1 and O1 tidal current ellipses at all depths significantly decrease in January–March, which roughly coincides with the period with sea-ice concentration larger than 80% (Fig. 11c). To investigate the impacts of sea ice on the tidal currents, we compared the tidal currents during the ice-covered season with those during the ice-free season at all mooring sites, except for M7 and M8 where data were not sufficiently long to perform harmonic analysis. From the time series of mean sea-ice concentration around each mooring site (not shown), we divided the time series of velocity at each mooring site into two- to three-month periods for the ice-covered and ice-free seasons (see Table 4 for the periods) and then carried out harmonic analyses. Table 4 shows ratios of the major axis length for the K 1 and O1 tidal current ellipses during the ice-covered season to those during the ice-free season. It is interesting to note that both K 1 and O1 tidal currents decrease significantly during the ice-covered season only at M1 and its reduction ratios are 30%. The K 1 and O1 tidal currents at M9 decrease slightly, but their reduction ratios are insignificant. Why does the significant reduction of the diurnal tidal currents during the ice-covered season occur only at M1? It is likely that the diurnal CTWs controlling the diurnal tidal currents at M1 are attenuated. If the sea-ice concentration is close to 100% and the sea-ice motions are limited, the seaice bottom possibly causes the same effects of spin down by friction as the sea bottom does. Thus it is suggested that the damping of the diurnal CTWs caused by spin down due to the friction at both the sea-ice and ocean bottoms results in the significant reduction of the diurnal tidal currents during the ice-covered season only at M1. In contrast, amplitudes of both K 1 and O1 tidal currents observed at other mooring sites except at M1 and M9 are large during the ice-covered season (Table 4). However, this is not likely significant since time series of tidal currents at these sites have relatively small signal-to-noise ratios (not shown). 3.4. Bottom Ekman layer Fig. 4 suggests that the bottom Ekman layer with respect to tidal currents is formed over the shelf. In this subsection we estimate the bottom Ekman layer thickness of oscillatory currents from the observed results, following the method by Maas and Haren (1987). In their method the horizontal components of tidal velocity, u and v, at frequency s are expressed with a complex velocity w, and are decomposed into two counterrotating components, w ¼ u þ iv ¼ w eist þ wþ eist ,

(1)

w ¼ W  eiy ;

(2)

wþ ¼ W þ eiyþ .

Here the asterisk denotes the complex conjugate, t is time, and W þ ðW  Þ and yþ ðy Þ are the amplitude and phase of the anticlockwise (clockwise) component. The vertical

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Depth (m)

60

0.26

70

0.24

80 0.22

90

0.20 Depth (m)

50

0.18

60

0.16

70 80

0.14

90

Length of major axis (m s−1)

0.28

50

0.12 100

M7 M8 M9

(%)

80 60 40

M3 M4

20 M1 M2

0 A

S

O 1998

N

D

J

F

M A 1999

M

J

M5

M6

Fig. 11. Time series of the vertical profiles of the major axis lengths for the (a) K 1 and (b) O1 constituents, from the ADCP data, at mooring site M1, and (c) the sea-ice concentration averaged over the area enclosed by thick lines in (d). (d) Shows the SSM/I grids (25  25 km) and the mooring sites. The 200and 1000-m isobaths are superimposed by thin lines. Table 4 Ratios of the major axis lengths of K 1 and O1 tidal current ellipses during the ice-covered season to those during the ice-free season Site

Measured depth (m)

K1

M9 M1 M2 M3 M4 M5 M6

28 44 203 140 199 73 152

0.98 0.77 1.48 1.00 1.12 1.15 1.08

O1 (0.006) (0.055) (0.018) (0.000) (0.005) (0.017) (0.005)

0.93 0.66 1.22 1.03 1.09 1.06 1.03

(0.022) (0.082) (0.008) (0.001) (0.003) (0.006) (0.002)

The differences ðm s1 Þ of the major axis lengths of K 1 and O1 tidal current ellipses obtained by subtracting the values during the ice-free season from those during the ice-covered season are shown in parentheses. The periods during the ice-free and ice-covered seasons are 1 August (3 August at M6)–31 October and 1 January–31 March, respectively. The periods at M9 are 19 September–30 November and 1 January–15 March for ice-free and ice-covered seasons, respectively.

profiles of W  and y are shown by dots in Figs. 12a and b, respectively. Then the observed wþ and w are fitted with an analytic solution of the Ekman layer   coshða z=HÞ w ðzÞ ¼ w 1  , (3) cosh a þ ða =sÞ sinh a a ¼ ð1  iÞðH=d Þ.

(4)

Here z is the vertical coordinate measured upward from the top of the bottom boundary layer, H is local bottom depth, wþ and w are complex amplitudes in the interior, s ð¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rH=KÞ is the stress parameter and d (¼ 2K=ðjf  sjÞ) is the bottom Ekman layer thickness of each rotating components, where K is vertical eddy viscosity, r is bottom friction velocity, and f is the Coriolis parameter. Using a least-square method, we determine s and d by fitting solution (3) to the observation (dots in Fig. 12). Then, K and r are obtained. An effective combined Ekman layer thickness, d (Soulsby, 1983) is calculated by d¼

W þ dþ þ W  d . Wþ þ W

(5)

It is found that the observed vertical profiles of the amplitudes of diurnal tidal currents are well explained by the Ekman layer theory of oscillating currents (Fig. 12a). The vertical profiles of the phases are also roughly consistent with the Ekman layer theory (Fig. 12b). The bottom Ekman layer thickness induced by the diurnal tidal currents is estimated to be 20–30 m over the northern part of the shelf, and the corresponding vertical eddy viscosity and bottom friction velocity are 100–400  104 and 4–8  104 m s1 , respectively (Table 5). An interesting feature to note is that the bottom Ekman layer thickness and, hence, vertical eddy viscosity are larger in regions of stronger tidal currents, specifically in the vicinity of the source area of the CTWs.

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707

0 M1 W+

20

M5 W+

W−

M9

M8

W−

W−

W+

W+

W−

Depth (m)

40 60 80 100 120

0.1

0

0.2

0

(m s−1)

0.1

0.2

0

(m s−1)

0.1

0.2

0

(m s−1)

0.1

0.2

(m s−1)

0 M1

M5

M8

M9

20

Depth (m)

40 60 80 100 120

240

300 (deg.)

60

120 (deg.)

0

60 120 180 (deg.)

300

360 (deg.)

Fig. 12. Vertical profiles of (a) the amplitudes and (b) the phases of the anticlockwise ðWþ ; yþ Þ and clockwise ðW ; y Þ components observed from ADCPs at M1, M5, M8, and M9 indicated by dots. Curves are best-fit curves of the Ekman layer solution. Horizontal lines indicate bottom depths. Table 5 The effective combined bottom Ekman layer thickness d (m), vertical eddy viscosity K (104 m2 s1 ), and bottom friction velocity r (104 m s1 ) induced by K 1 and O1 tidal currents Site

Tidal constituents O1

K1

M8 M9 M1 M5

d

K

r

d

K

r

31 29 21 13

306 307 119 60

5.0 5.0 3.8 3.1

32 30 20 14

385 345 127 73

7.7 7.4 4.4 3.5

1990). The values of T f for K 1 (O1 ) constituent is calculated to be 2.8 (1.8) and 1.9 (1.6) days for bottom topography along the lines A and B, respectively. As mentioned in Section 3.2, it takes 1:0 day for the diurnal CTWs to propagate from the line A to the southern limit of the region where the diurnal CTWs can exist. Thus, the dissipation of the diurnal CTWs by bottom friction is significant. The major axis lengths of K 1 and O1 tidal current ellipses over the shelf decrease by 30–40% from M9 to M1 (Table 2). This damping seems to be caused partly by the spin-down effect of the bottom friction. 4. Concluding remarks

From the solution of the CTWs and the values of the bottom friction velocity r in Table 5, the frictional decay time of the diurnal CTWs, T f , can be estimated (Brink,

The first long-term mooring measurements were carried out off the east coast of Sakhalin from July 1998 to June 2000. The tidal heights and currents are dominated by the

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diurnal variability (K 1 and O1 ) with fortnightly modulation over the northern part of the eastern shelf (M1, M8, and M9) of Sakhalin (see Fig. 2 for the tidal currents). The structures of K 1 and O1 tidal currents are almost uniform in the vertical direction except for the bottom Ekman layer (Fig. 4). The thickness of the bottom Ekman layer estimated from the observations is much thicker over the northern part, where the diurnal tidal currents are strong, than over the southern part of the eastern shelf of Sakhalin (Table 5). This suggests that energy of diurnal CTWs is effectively dissipated in the thicker bottom Ekman layer in regions of stronger tidal currents. Thus, in modeling the tidal fields in the region where the diurnal CTWs exist, parameterization of vertical eddy viscosity should be adequately modified. The K 1 and O1 tidal current ellipses over the shelf are clockwise with their major axes along the isobaths (Fig. 3) and their signal propagates with the coast on the right with phase speeds of 3.4 and 3:8 m s1 , respectively. From the application of a CTW solution (Brink and Chapman, 1987), the diurnal CTWs can exist for the depth profile over the northern part but not over the southern part of the shelf (Figs. 6a and 8). Over the northern part of the shelf, the structures of the observed K 1 and O1 tidal current ellipses are similar to those of the CTW solution (Fig. 7). These results reveal that the diurnal tidal current fields over the northern part of the shelf can be explained by the firstmode diurnal CTWs. The frictional damping time of the diurnal CTWs are estimated to be 1.6–2.8 days. Thus, the effects of the bottom friction on the diurnal tidal currents over the northern shelf are significant. The diurnal CTWs are almost independent of the effects of the seasonal variability in density stratification and contribute slightly to the sea-surface heights. The observed increase (0:2 m s1 in winter) in the phase speeds of K 1 and O1 tidal currents can be explained by the advection due to the ESC (Fig. 9b). The diurnal tidal currents are significantly reduced during the ice-covered season only at M1, where the diurnal CTWs exist (Fig. 11 and Table 4). The following scenario can be inferred from these results; if sea-ice concentration is close to 100% and the sea-ice motions are limited, the diurnal CTWs are effectively damped by the spin down due to friction underneath the sea ice, leading to the reduction of the diurnal tidal currents. In reality, sea ice occasionally moves even if sea-ice concentration is very high, as demonstrated by Shevchenko et al. (2004). On the other hand, the roughness underneath the sea ice is thought to be larger than that over the sea bottom. Although the sea ice likely causes the spin-down effect qualitatively, its quantitative evaluation is difficult. No significant reduction of the diurnal tidal currents during the ice-covered season can been seen at M9, where the diurnal tidal currents associated with the CTWs are dominant. Two reasons can be considered for this. One is that sea ice moves more freely at M9 than at M1 because isobaths sharply bend around M9. The other is the propagation distance of the diurnal CTWs from the source

area: M9 is very close to the source area, while M1 is at a distance from the source and thus the CTWs are damped more effectively by the sea ice there. To verify this scenario, further theoretical studies and numerical experiments are necessary. Acknowledgments We would like to thank Humio Mitsudera, Masahisa Kubota, and Tomohiro Nakamura for their useful discussion. We are deeply indebted to captain and crew of R/V Professor Khromov and Far Eastern Regional Hydrometeorological Research Institute (Director Yuri N. Volkov), Russia, for their support in the observations. This study was carried out under the Joint Japanese–Russian–U.S. study of the Sea of Okhotsk. Thanks are extended to all the participants in the cruise for their collaboration. We would like to thank Kenneth H. Brink and David C. Chapman for the numerical code of the CTWs. Profiling float data were obtained under the cooperation with Stephen C. Riser. This work was sponsored by the Core Research for Evolutional Science and Technology of the Japan Science and Technology Corporation. J.O. was supported by 21st Century Center of Excellence Program funded by the MEXT. All figures were produced with the GFD-DENNOU Library. References Brink, K.H., 1990. On the damping of free coastal-trapped waves. Journal of Physical Oceanography 20, 1219–1225. Brink, K.H., Allen, J.S., 1978. On the effect of bottom friction on barotropic motion over the continental shelf. Journal of Physical Oceanography 8, 919–922. Brink, K.H., Chapman, D.C., 1987. Programs for computing properties of coastal-trapped waves and wind-driven motions over the continental shelf and slope, second ed. Technical Report WHOI-87-24, Woods Hole Oceanographic Institution, 119pp. Cartwright, D.E., 1969. Extraordinary tidal currents near St Kilda. Nature 223, 928–932. Cartwright, D.E., Huthnance, J.M., Spencer, R., Vassie, J.M., 1980. On the St Kilda shelf tidal regime. Deep-Sea Research 27A, 61–70. Crawford, W.R., Thomson, R.E., 1982. Continental shelf waves of diurnal period along Vancouver Island. Journal of Geophysical Research 87, 9516–9522. Crawford, W.R., Thomson, R.E., 1984. Diurnal-period continental shelf waves along Vancouver Island: a comparison of observations with theoretical models. Journal of Physical Oceanography 14, 1629–1646. Foreman, M.G.G., 1977. Manual for tidal heights analysis and prediction. Pacific Marine Science Report 77-10, Institute of Ocean Sciences, Patricia Bay, Sidney, BC, 97pp. Foreman, M.G.G., 1978. Manual for tidal currents analysis and prediction. Pacific Marine Science Report 78-6, Institute of Ocean Sciences, Patricia Bay, Sidney, BC, 57pp. Freeland, H.J., 1988. Diurnal coastal-trapped waves on the east Australian continental shelf. Journal of Physical Oceanography 18, 690–694. Fukamachi, Y., Mizuta, G., Ohshima, K.I., Talley, L.D., Riser, S.C., Wakatsuchi, M., 2004. Transport and modification processes of dense shelf water revealed by long-term moorings off Sakhalin in the Sea of Okhotsk. Journal of Geophysical Research 109, C09S10. Katsumata, K., Ohshima, K.I., Kono, T., Itoh, M., Yasuda, I., Volkov, Y.N., Wakatsuchi, M., 2004. Water exchange and tidal currents

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