#2012 The Acoustical Society of Japan

Acoust. Sci. & Tech. 33, 1 (2012)

PAPER

Tidal current measurement in the Kurushima Straitby the reciprocal sound transmission method
Yudi Adityawarman1 , Arata Kaneko1; , Naokazu Taniguchi1 ,Hidemi Mutsuda1 , Katsuaki Komai1 , Xinyu Guo2 and Noriaki Gohda3
1Graduate School of Engineering, Hiroshima University,
1–4–1 Kagamiyama, Higashi-Hiroshima, 739–8527 Japan
2
Center for Marine Environmental Studies, Ehime University,
2–5 Bunkyo-cho, Matsuyama, 790–8577 Japan
3
Aqua Environmental Monitoring Limited Liability Partnership,
12–2 Aobadai, Mihara, 723–0047 Japan( Received 13 May 2011, Accepted for publication 18 September 2011 )Abstract: The tidal current in the Kurushima Strait of the Seto Inland Sea, Japan was successfullymeasured during July–August 2009 (36 days) among the three acoustic stations (KR4, KR5 and KR6),
located on both sides of the strait. The travel time diﬀerences for the two sound transmission lines
KR4–KR5 and KR4–KR6 are converted into the range-averaged currents along the transmission lines.
The hourly mean of the range-averaged currents varied in the range from 31:1 to 53.8 cm/s for the
KR4–KR5 and in the range from 45:4 to 48.7 cm/s for the KR4–KR6 with the error bars of 5.0 cm/s
and 6.6 cm/s, respectively. The hourly mean along-line currents are further transformed into thegeophysical coordinates with the variation range from 99:1 to 91.6 cm/s and the mean current of
6:6 cm/s for the eastward component VE , and that of (54:2–31.5) cm/s and the mean current of
7:6 cm/s for the northward component VN . The cross-line volume transport varied in the range of(17:928 to +17.569)  104 m3 /s, resulting in the mean westward transport of 0:727  104 m3 /s.
This mean transport reaches a signiﬁcant level over the error bar of 0:474  104 m3 /s.
Keywords: Tidal current, Volume transport, Reciprocal sound transmission method, Kurushima
Strait, Seto Inland Sea
PACS number: 43.30.Pc

1.

[doi:10.1250/ast.33.45]

INTRODUCTION

The Kurushima Strait is a narrow passage of widthabout 1 km, located at the central part of the Seto Inland
Sea and separates the Aki-nada and Hiuchi-nada (Fig. 1).
The strait is the most important shipping route not only in
the inner Japan, but also between Korea and China, andJapan, and then always crowded by traﬃc ships. Furthermore the strong, complicated tidal currents occur especiallyaround the central parts of the strait, surrounded with small
islands. These environmental conditions have frequently
caused the traﬃc accident such as ship wrecks andcollisions.
The tidal current measurement in the strait has been
limited due to heavy shipping. Especially the current
measurement from ﬁxed-position type sensors such ase-mail: akaneko@hiroshima-u.ac.jp

bottom-mounted and subsurface-moored currentmeters is
prohibited in the ship traﬃc route at the central part of thestrait by the Japan Coast Guard (JCG). The half-monthmeasurement by the surface drifters was performed in 1956
by the JCG. The predicted values of surface current are
now opened to the public because they provide important
information which makes the operation of traﬃc ships safe
(http://www1.kaiho.mlit.go.jp/KAN6/2 kaisyo/tidal-current/
tidalc forecast.html).
However, the near surface current is not good enoughto assess environmental issues like the volume exchange ofwater (volume transport) between the neighboring seas
(Aki-nada and Hiuchi-nada). For the environmental protection and management, the volume transport of water ispreferable to be measured in addition to the surface current.
The ﬁrst ﬁxed point observation of tidal currents in the
Kurushima Strait was carried out during the half month,using the four moored JCG buoys, deployed during the45

Acoust. Sci. & Tech. 33, 1 (2012)
Plastic
Container

AkinadaGPS Antenna

Hiuchinada
Battery

10m
5m

Tomography
System

60m 60m

40m

40m

6.3km
Cable
Rope

BreakwaterRay

Acoustic
stationWeightAcoustic
Transducer (f=4kHz)

KR4

20m

OshimaKR4
Kurushima
60m
40m
StraitKR620m
KR5Imabari

Fig. 1 Location map of the experimental site and thesurrounding region with the bathymetric chart. KR4,KR5 and KR6 are the acoustic stations. The solid lines
connecting the stations show the travelling soundtransmission lines. The tide gauge station is shownwith the star mark. The whole region of the Seto Inland
Sea is shown in a shrinkage scale at upper right of theﬁgure.

dredge work for the extension of ship route [1]. The time
variation of tidal currents was roughly understood by
this experiment although less accuracy is caused by theapplication of rotor-type velocimeters in the strong tidal
current and no data across the strait were acquired. The
advanced current measurement in the Kurushima Strait was
carried out by the shipboard ADCP in 1993. However, theobservational lines did not cross the central part of the straitfrom a safety viewpoint and the repeat ADCP surveys
continued only for several hours [2,3]. The tidal current in
the Kurushima Strait was simulated by the 3D coastal sea
circulation model with a sea level forcing at the open
boundaries. However, the results were not validated by the
direct observation of current although the vortex generation
behind the islands was reasonably simulated [4]. The halfmonth current measurement was performed by two bottommounted upward-looking ADCPs, located in the speciﬁed
positions displaced from the traﬃc route [5]. The data at
the central part were supplemented by the 10-hour repeat
operation of the shipboard ADCP. However, the results did
not reach a level to estimate the volume transport throughthe strait. The data sampling in the vertical cross section
across the strait is insuﬃcient both horizontally andvertically to estimate the volume transport. It is, thus,
concluded that the volume transport through the Kurushima
Strait has never been measured with satisfactory accuracy.
The coastal acoustic tomography system (CATS),
which has been developed by Hiroshima University as anapplication of deep-sea acoustic tomography [6], and well

Breakwater

Acoustic
station20m

46

Surface

KR5
BottomFig. 2 Schematic diagram of the tomography system forthe reciprocal sound transmission experiment, placedon the breakwater of the ﬁsheries ports (KR4 and KR6)
and trade port (KR5).

operated in the coastal seas around Japan [7], is applicableto the Kurushima Strait as well, located on the eastern sideof Aki-nada [12]. The current measurement can be done
without disturbing the shipping from the sound transmission and reception stations (acoustic stations), locatedon both sides of the strait.
The CATS is here applied to measure the tidal current
in the Kurushima Strait and to estimate the volumetransport through the strait. This is the ﬁrst applicationof CATS to transport variations in straits with heavy
shipping.

2.

EXPERIMENT

A reciprocal sound transmission experiment was
carried out among three acoustic stations (KR4, KR5 andKR6) during July–August 2009 (36 days) to measure thetidal current in the Kurushima Strait of the Seto Inland Sea(Fig. 1). The horizontal distance is 6.32 km for the station
pair KR4–KR5 and 4.13 km for the station pair KR4–KR6.
The reciprocal sound transmission data were obtained
between both the station pairs. The sound transmission forthe station pair KR5–KR6 was prohibited by the protruded
artiﬁcial shoreline. The ﬂoor depth for the mean sea level is
13 m at KR4 and increased rapidly to 57 m at 1.5 km awayfrom KR4. The ﬂoor depth is gradually decreased from
44 m at 2.5 km to 10 m at KR5. For KR4–KR6 the ﬂoor
depth forms a more simple proﬁle such that it is increased
to about 60 m at the middle from about 10 m at the edge. A
coastal acoustic tomography system (CATS) was placed on
the breakwater which protects the ﬁsheries ports (KR4and KR6) and the trade port (KR5). The 4 kHz acoustic
transducer was suspended down by a rope in water 5 m
below the surface in front of the oﬀshore side of the
breakwater and connected to the CATS via a cable (Fig. 2).
The CATSs were operated by the 12 V rechargeable battery
and sound was transmitted with 24 V power, using two
12 V batteries in a serial connection.

Y. ADITYAWARMAN et al.: TIDAL CURRENT MEASUREMENT IN THE KURUSHIMA STRAIT

The transducer (ITC 2002A) is of the broad-band typewith central frequency 4 kHz and band width 1.5 kHz. The
transducer works not only for sound transmission, but also
for sound reception. The source level of the broad-band
transducer is 192 dB re 1 mPa at 1 m and the average power
consumption is 480 W during the sound transmission.
In this experiment, the transmitted signal was phasemodulated by the 10th order M sequence to increase thesignal-to-noise
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ratio (SNR) of received signals by
20 log 210  1 ¼ 30 dB. This gain of SNR is attained by
the cross-correlation of received signals with the M
sequence, used in the transmission. The 3 cycles per digit(Q-value) was selected to transmit the phase-modulated
sound from the broad-band transducer. The transmission of
4 kHz sound in the 3 cycles per digit requires the frequency
band-width 4 kHz/3 = 1.3 kHz which the present transducer satisﬁes. Notice that the smaller Q-values are
selectable for the transducer of the wider frequency range.
The time resolution for multi-path arrivals tr , deﬁned as
one-digit width of M sequence, is given 0.75 ms. One
period (0.76725 s) of 4 kHz sound, phase-modulated by
the M sequence, was released every 4 minutes at thesynchronized timing from KR4, KR5 and KR6. The
4-min interval data were smoothed through an hourly
moving average to increase thesignal-to-noise ratio (SNR)
pﬃﬃﬃﬃﬃ
of received signals by 20 log 16 ¼ 12 dB.
The received signals are sampled with a verticalresolution bit of 10 at the frequency of 8 kHz and crosscorrelated with the M sequence. The travel times are
determined at a maximum peak point in each of thecorrelation waveforms, obtained every 4 minutes. The
range-average velocity Vm and sound speed Cm between
two acoustic stations may be estimated from the travel time
diﬀerence t and mean travel time tm , respectively, in thefollowing formulation [13]:
L
;
ð1Þ
t1 ¼
Cm þ Vm
L
t2 ¼
;
ð2Þ
Cm  Vm
where L denotes the station-to-station distance, and the t1
and t2 denote the travel times from station T1 to T2 andfrom station T2 to T1, respectively. By solving the coupled
Eqs. (1) and (2), we obtain
L
t;
ð3Þ
Vm ¼
2t1 t2
L
Cm ¼
tm ;
ð4Þ
t1 t2
where t ¼ t2  t1 and tm ¼ ðt1 þ t2 Þ=2.
The CTD casts were performed at a 0.5 km interval on
July 15 along the sound transmission line KR4–KR5. The
results were used as data not only to know the proﬁles of

KR4

KR5

Fig. 3 Result of the range-independent ray simulation
for the launch angles at an increment of 0.2 between
2:0 and +2.0 , performed by using the CTD data at
the maximum depth (1 km from KR4) on July 15. The
vertical proﬁles of sound speed (C) are shown at left of
the ﬁgure.

(a)

(b)

Fig. 4 (a) Acoustic travel times and (b) ray lengths for
all the rays, plotted against the launch angles.

temperature, salinity and sound speed, but also to executethe range-independent ray tracing simulation of travellingsound. The temperature and salinity are well homogenized
due to the strong tidal current that always occurs in thestrait. As a result, the sound speed is monotonicallyincreased with the pressure, forming a constant gradient.
The result of ray simulation serves to know the depth range
at which rays travel in a vertical section, and is shown in
Fig. 3. Sound travels, spanning almost all the verticalsections except the trough, placed at 1.0–1.5 km from KR4
and the near-bottom region at 3.5–5.0 km from it.
The acoustic travel times and ray lengths for the rays
with launch angles at an increment of 0.2 between 2:0
and +2.0 are plotted against the launch angles at thesource in Figs. 4(a) and 4(b), respectively. The travel time
data are separated into two groups, bounded at 0:5 oflaunch angle and centered at 4.13081 s to 4.13112 s while
the ray length draws a rough parabolic curve. However
the variation range of travel time diﬀerence of 0.30 ms
is smaller than tr ¼ 0:75 ms (one-digit length of the M
sequence), the time resolution for multi-path arrivals. The

47

Acoust. Sci. & Tech. 33, 1 (2012)

time resolution of tr ¼ 0:75 ms for multi-path arrivals
determines the resolution of velocity measurement. As aresult, the multi-path arrivals cannot be resolved in thereceived signals, so all the arrival rays cooperate toconstruct a broad arrival peak. This property provides a big
advantage in estimating the vertical-section average current
from the travel time for the biggest, broad arrival peak. The
ray lengths distribute in the range from 6,320.3 m to
6,322.2 m.
We shall here refer the resolution of velocity measurement, related to the time resolution of tr ¼ 0:75 ms for
multi-path arrivals. By substituting tr into t in Eq. (3), thevelocity resolution is determined 13.9 cm/s. The velocity
resolution reduces to 5.6 cm/s when tr is replaced by thesimulated variation range of travel time diﬀerence(0.30 ms).

3.

RESULTS AND DISCUSSION

The correlation waveforms of acoustic signals travelingfrom KR5 to KR4 during 9:00 of July 7 to 9:00 of July 8
are shown in Fig. 5 with the stack diagrams as a typicalcase together with those from KR4 to KR5. In this ﬁgure,the transmission time on the vertical axis is elapsed
upward. Furthermore the stack diagrams for 5:00–6:00 of
July 8 are shown in a magniﬁed scale at right of the ﬁgures.
There is a big peak in each of the correlation waveforms toshow the arrival of travelling sound. The travel times are
determined at top of the peak. Only the peak points withthe signal-to-noise ratios SNR > 7 are used as signiﬁcantarrival signals in estimate of range-averaged current. The
frequent occurrence of data lacking are visible in the stackdiagrams. The hull of crowded traﬃc ships and theirassociated bubble-included wakes which frequently passthe Kurushima Strait make a barrier to the travelling soundand cause the data lacking.
The range-averaged current is calculated for periods
when the reciprocal data are successfully acquired andpermit the estimation of travel time diﬀerence. The rangeaveraged currents V5 and V6 for the station pairs KR4–KR5 and KR4–KR6 are shown with the time plot in
Figs. 6(a) and 6(b). Both the 4-min interval original data
and the hourly mean data are shown in the ﬁgures. The
hourly mean current varies in the range from 31:1 to
53.8 cm/s for the KR4–KR5 and from 45:4 to 48.7 cm/s
for the KR4–KR6. The mean for two fortnightly periods(27.32 days) is 7.7 cm/s for the KR4–KR5 and 10.2 cm/s
for the KR4–KR6. The semi-diurnal and fortnightly
variations of tides are more clearly seen for the KR4–KR5 data than for the KR4–KR6 data. For KR4–KR5 thetidal variation is diminished due to the large period of data
lacking during July 27–31. The root mean squares diﬀerence (RMSD) between the original data and hourly meandata is 5.0 cm/s for KR4–KR5 and 6.6 cm/s for KR4–KR6.

48

KR5

KR4

(a)
KR4

KR5

(b)
Fig. 5 Stack diagrams of the correlation waveforms,
obtained at KR4 (upper panel) and KR5 (lower panel)for the station pair KR4–KR5 during 9:00 of July
7–9:00 of July 8. The diagrams for 5:00–6:00 of July 8
are shown in a magniﬁed scale at right of the ﬁgures.
The biggest peaks are located with the red dot on eachcorrelation waveform. The correlation functions arelabeled with r.

The RMSD may be regarded as an upper limit of errors forhourly current measurement because the errors are included in the short-term variability [14]. The upper limit oferror is here called the error bar. The error bar is estimated
5.0 cm/s for KR4–KR5 and 6.6 cm/s for KR4–KR6. It ishere worth noting that the error bars (5.0 cm/s and 6.6cm/s) are nearly equal to the resolution of velocity
measurement (5.6 cm/s), implying that almost all errors
are produced by the velocity resolution.
The along-line currents (V5 , V6 ) for (KR4–KR5, KR4–
KR6) are converted into the east and north components ofcurrent (VE , VN ) by the following formulae (Fig. 7):
V5 cos 6  V6 cos 5;sin 5 cos 6  cos 5 sin 6
V5 sin 6 þ V6 sin 5;
VN ¼
sin 5 cos 6  cos 5 sin 6
VE ¼

ð5Þ
ð6Þ

where 5 and 6 denote the angles of the transmission lines
KR4–KR5 and KR4–KR6 measured clockwise from thenorth, and are put as 5 ¼ 180:2 and 6 ¼ 219:6 ,respectively. Notice that the velocity data for the twotransmission lines located at diﬀerent places are necessary
to evaluate the vector components of current (VE , VN ), andEqs. (5) and (6) can be obtained under the assumption that
(VE , VN ) does not change between the two transmission
lines KR4–KR5 and KR4–KR6. As another explanation,(VE , VN ) may be considered as currents at the middle of
KR4–KR5 and KR4–KR6.

Y. ADITYAWARMAN et al.: TIDAL CURRENT MEASUREMENT IN THE KURUSHIMA STRAITRMSD=5.0 cm/s

VN
0

(a)
RMSD=6.6 cm/s

θ5

θ6

VE

Fig. 7 Sketch of the coordinate transformation fromthe along-line components (V5 , V6 ) into the east-northcomponents (VE , VN ). The origin of the coordinate
frame (VE , VN ) is placed at the center of KR4–KR5 and
KR4–KR6, and that of the shifted coordinate frame(VE 0 , VN 0 ) is placed at KR4 parallel to (VE , VN ) tomeasure the direction of transmission line.

Vn (mean)= -7.6 cm/s

Ve (mean)= -6.6cm/s(b)Fig. 6 Time plots of the range-averaged currents (V5and V6 ) obtained along the transmission lines (a) KR4–KR5 and (b) KR4–KR6. The 4-min interval original
data and hourly mean data are shown in the red andblue solid lines, respectively. The dashed line indicatesthe mean for two fortnightly periods (27.32 days). The
RMSD between both the data are presented at upper
right of both the ﬁgures.

The (VE , VN ) currents for the hourly mean data areshown in Fig. 8 with the time plots. The VE and VN for thehourly mean current vary in the range from 99:1 to
91.6 cm/s and from 54:2 to 31.5 cm/s, respectively. The
average of the hourly mean data for two fortnightly periods(27.32 days) is (6:6, 7:6) cm/s for the (east, north)component and thus the resultant current is directedsouthwestward.
The volume transport through the strait is calculated
from a product of the range-averaged current and verticalcross section area. The transport is calculated for both thetransmission lines KR4–KR5 and KR4–KR6. The rangeaveraged current (Vp ) in the directions perpendicular to

Fig. 8 Time plots of the hourly mean eastward current
VE (middle panel) and northward current VN (lower
panel) for the entire observational period. The 27.32
hours mean currents are shown with the horizontal,
dashed lines, and their values are put at upper right ofeach ﬁgure. The sea level data at the tide gauge station
IMABARI of the JCG are presented at upper panel ofthe ﬁgure.

KR4–KR5 and KR4–KR6 is calculated from (VE , VN ),obeying the following formulae:
Vp ¼ VE cos t  VN sin t ;

ð7Þ

where t ¼ 5  180 (5 ¼ 180:2 ) for KR4–KR5 andt ¼ 6  180 (6 ¼ 219:6 ) for KR4–KR6. By putting thevertical cross section area into A, the volume transport (Q)across KR4–KR5 and KR4–KR6 may be expressed by
Q ¼ Vm  A;

ð8Þ

where A ¼ 214;164 m2 for KR4–KR5 and A ¼ 161;325 m2
for KR4–KR6.

49

Acoust. Sci. & Tech. 33, 1 (2012)
Hourly mean

Q (mean)= - 0.727 x 104 m3/s

Fig. 9 Time plots of the hourly mean cross-line volumetransport for the entire observational period. The 27.32
hours mean transport for the hourly data is shown withthe horizontal, dashed lines, and its value is put atlower right of the ﬁgure.

The volume transport through the strait may be
estimated as the average of transports across KR4–KR5
and KR4–KR6, and is shown in Fig. 9 with the time plots
for the hourly mean data. The hourly mean data vary in therange of (17:928 to +17.569)  104 m3 /s, resulting in
the mean westward transport of 0:727  104 m3 /s.
The westward mean transport may be associated withthe counter-clockwise tidal vortex, generated on the southeastern side of the Oshima island during the eastward tidal
current phase [3,4]. This vortex is released southwestward
along the southern coast of the Oshima with the growth of
westward tidal current, forming the westward residualtransport. The eastward mean current in Aki-nada seems
to be erased by the stronger local eﬀect due to vortex
generation in the Kurushima Strait. The connectivity ofmean current from the former to latter requires further
study.

4.

SUMMARY

The tidal current in the Kurushima Strait is announced
at a real time from the JCG to the traﬃc ships for preventing
ship accidents. However, the opened data are predicted on
the basis of near surface tidal current data acquired at thecentral part of the strait, making the most priority for theannouncement to traﬃc ships. The whole vertical crosssection average of tidal current through the strait is diﬃcult
to be estimated from the data, acquired at the near surface
layer of the central part. Therefore the along-strait volumetransport has never been correctly estimated which play a
critical role in water exchange and environmental dependency between Aki-nada and Hiuchi-nada.

50

The reciprocal sound transmission experiment was
carried out for the two pairs of acoustic stations (KR4–KR5
and KR4–KR6), located on the both sides of the Kurushima
Strait. The range-averaged currents are estimated along thetwo transmission lines KR4–KR5 and KR4–KR6, using thetravel time diﬀerence data. The average current is close to
the current averaged over the vertical cross section because
the acoustic rays traveling between the acoustic stations
span almost all parts of the vertical section. The average
current for two fortnightly periods (27.32 days) is 7.7 cm/s
for the KR4–KR5 and 10.2 cm/s for the KR4–KR6. The
error bars are 5.0 cm/s and 6.6 cm/s smaller than thecorresponding average currents.
The two along-line currents are transformed into theeast and north components of current (VE , VN ). The
variation range from 99:1 to 91.6 cm/s for VE isconsiderably larger than that from 54:2 to 31.5 cm/s for
VN . VE stronger than VN is caused by that the strait isbounded by the 4th biggest Japanese main island (Shikoku)
and Oshima island on the southern and northern sides,
respectively. The 27.32-day mean current (6:6, 7:6)
cm/s (10.1 cm/s in magnitude) for the (east, north)component is directed southwestward with a signiﬁcantlevel over the error bar (5.8 cm/s on average).
The volume transport through the strait is estimated bytaking a product of the hourly mean cross-line current andvertical cross section area. The volume transport makesa variation range of (17:928 to +17.569)  104 m3 /s,
resulting in the mean westward volume transport of
0:727  104 m3 /s. This westward mean transport reaches
a signiﬁcant level over the error bar because the error barsof current (5.0 cm/s and 6.6 cm/s for KR4–KR5 and KR4–
KR6, respectively) cooperate to produce the error bar oftransport (0:474  104 m3 /s).
The reciprocal sound transmission method provides aninnovational technique to measure the tidal current variations in straits with crowded shipping like the Kurushima
Strait. The volume transport through the strait is successfully estimated over the error level, but more accurate
result may be obtained by increasing the station-to-station
distance.

ACKNOWLEDGEMENTS
We thank Mr. Hiromitsu Ichiki for his contribution in
observation and data analysis. Dr. Yoshio Takasugi isgreatly acknowledged for the kindest support in the
instrumentation. This study is supported by a grant fromthe Japan Society for the Promotion of Science.
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