Temporal and spatial variation of the conversion factor fromthe motion-induced voltage to the transport
K. Rikiishi, H. Matsuda, M. Michigami,rikiishi@, hidekazu@, michigam@cc.hirosaki-u.ac.jp
Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
Y. Hashimoto
hashimot@riam.kyushu-u.ac.jp
Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan
１． Introduction
Motion of the seawater in thegeomagnetic field induces the voltage as
predicted by the theory of electro-magneticinduction. The motion- induced voltage increases
with velocity or volume transport, and then it ispossible to monitor time variation of an ocean
current by measuring the cross-stream voltage
using a submarine cable. Western part of theNorth Pacific is one of the best regions in theworld to apply such a method, because there aremany islands that are connected by telephone
cables with each other. As of July 2000, 12 cables
are being used to monitor temporal variation ofthe ocean currents around Japanese Islands.
Theoretical basis for this method wasestablished by, for example, Longuet-Higgins etal. (1954). When the current is vertically andhorizontally uniform, the theory is rather
straightforward and the voltage is directly relatedwith the velocity or volume transport. If thecurrent is horizontally uniform but varies withdepth, then the voltage is related with the verticalmean velocity. Horizontal structure of the current,
both in the cross- and down- stream directions,modifies the voltage, but its effects are believed tobe generally small provided that the cable covers
a relatively short distance. The voltage is also
affected by the resistivity of the seawater and theseabed. Accordingly, the voltage may vary withincreasing temperature or salinity of the seawater,
and its magnitude depends on the electric
structure of the seabed or earth’s crust.
However, precise information on the seabed
conductivity and the horizontal and verticalstructures of the current is not generally available
a priori. It is therefore difficult to predict themagnitude of motion-induced voltage. Under

these circumstances, it is reasonable to compare
observations of the voltage with those of thetransport so that we may determine an empirical
relation or calibration factor between them.
In this paper, we first determine anempirical voltage – transport relation for theTsugaru Strait, for which direct observations of
the transport are available. Then we proceed tothe cases of the Izu Islands region and the Tokara
Strait for which the direct observation of transport
is not available. In these cases, we compare tidal
signals of the voltage with the tidal currents
obtained from a numerical tidal model.
Discussion will be given of why the calibration
factor thus determined differs considerably fromregion to region and why it varies with time.
2. Voltage calibration factor for the Tsugaru
StraitTsugaru Strait separates Hokkaido fromHonshu (Japanese Main Island) and connects theSea of Japan with the Pacific. In the Tsugaru
Strait, both the amplitude of tidal current and theocean current (sub-tidal current) are greater than 1
m/s in the western ends of the strait. The
motion-induced voltage across the Tsugaru Strait
was measured during the period February 1994 –July 2000, with several times of breaks. The
voltage was measured at intervals of about one
second,and10-minute
averages
wereautomatically transmitted once a day to theremote laboratory by using telephone. We also
monitored time variation of the geomagnetism sothat we may estimate the effect of geomagnetic
disturbances on the voltage.
According to the theory of geostrophic flow,
the sea surface is expected to incline along thecross-stream direction. Then the daily meanvalues of voltage have been compared with thoseof the sea level differences between Tappi(Honshu) and Yoshioka (Hokkaido). A linear
relation between them, with the voltage of 100 mv
being corresponding to the sea level difference of
20 cm, was obtained, though some exceptions
were seen which were ascribed to abnormal sea
levels due to occasional storm surges. It was has
also been that the voltage is considerably
contaminated by geomagnetic disturbances.
However, if we are concerned with the sub-tidal
current with time scales larger than a couple ofdays, we can smooth out the geomagnetic effects
by simply applying the moving averagetechnique.
Then, we made direct observations of thevolume transport by repeating the cross section at
the western end of the Tsugaru Strait by using
Acoustic Doppler Current Profiler (ADCP). It
required 60 – 70 minutes for us to complete asection, and time variation of the transportreflected that of the tidal current. Some of thetransport observations were effected by thegeomagnetic disturbances, and we applied astatistical method to reduce the geomagneticeffects. From comparison of the transports withthe voltages, we found a linear relation between
them, with the voltage of 1 v being corresponding
to the volume transport of 12 x 106m3/s.
3. Voltage calibration factor for the Izu
Islands region and the Tokara Strait
Direct observations of the transport areavailable only for the sea of shallow water,
because the acoustic method is applicable to thedepth shallower than 400 m. Also, it is notpractical to cover a wide cross-section with anumber of mooring stations. For the Izu Islands
region and the Tokara Strait, therefore, it isdifficult to make direct observation of thetransport.
For these regions, it is suggested to use thetidal part of the voltage measurements. In general,
the tidal current is vertically uniform while thevelocity of ocean current (sub-tidal current)
decreases considerably with depth. The tidal
current is also rather uniform in the cross-stream
direction while the ocean current is more or lessconcentrated. If we integrate the tidal current withrespect to the depth and width, the tidal current
transport becomes very large. For this reason,
amplitude of the tidal signal of the voltage turns
out to be very large. It is therefore possible toobtain a reasonable calibration factor bycomparing the tidal signal of the voltage with theintegrated tidal current that is available from anumerical tidal model.
In the Izu Islands region, we setup anobservation station at Miyake Island to monitor
the voltage between Oshima and Miyake Islandand between Miyake and Hachijo Islands. Ingeneral, the voltage between Miyake and Hachijo
Islands becomes very large when the Kuroshio
flows between the two islands, and becomes verysmall when the Kuroshio flows south of Hachijo
Island. Fig. 1 shows tidal signals of the voltage(Miyake - Hachijo Islands) for the year 1999,
which are obtained by subtracting 25-hourrunning averages from the original hourly values.
It shows clear alternations of the neap and springtides at intervals of two weeks. The total
amplitude of the tidal signals is roughly as large
as 0.6 v at the spring tide, which is comparablewith the range of the low-frequency variation of
the voltage (about 0.8 v).
Recently, on the other hand, Matsumoto etal. (2000) have developed very fine tidal models
in which tide gauge data and satellite altimeterdata are assimilated into a full hydrodynamicalmodel. Their high-resolution (5‘x5’) model forthe region around Japan (NAO.99Jb model) has
demonstrated a very high performance in terms ofrms misfit. Accordingly, we have reproduced
harmonic constants (amplitude and phase) of thetidal current for eight major constituents (M2, S2,N2, K2, K1, O1, P1, Q1) from their model inorder to calculate the barotropic tidal current. The
eastward component of the tidal currents areintegrated from the surface to the bottom along
the meridian 139 54’ E ( 33 00’ – 34 12’ N) toobtain the tidal current transport. Obviously, thetidal transport changes its direction with time andno net transport is expected after all.
If we compare the tidal current transportwith the tidal signals of the voltage (Fig. 1), thenwe can see that both coincide very well in termsof tidal phase such as ebb and flood, and neap andspring tides (figure not presented). This suggeststhat we can indeed obtain the calibration factor bycomparing the two envelopes. We have thus foundthat the voltage of 1 v corresponds to the volumetransport of 60 x 106m3/s. Note that this value isabout 5 times as large as the calibration factor forthe Tsugaru Strait.
The same method has been applied to theTokara Strait, through which the Kuroshio flows
from the East China Sea to the Pacific. The tidal
current transport has been obtained by integratingthe eastward component of the barotropic tidal
current vertically and horizontally along themeridian 130 18’ E (28 24’ – 30 18’ N). We havecompared the envelope of the voltage tidal signals(Yaku - Amami Islands) with that of the tidaltransport, and have found that the voltage of 1 v
corresponds to the tidal transport of about 25 x
106m3/s. Note that this value is about two times
as large as the calibration factor for the Tsugaru
Strait.
4.

Discussion
Now that the calibration factor has been
determined, the voltage observations may give us
information on the variation of the transport of theKuroshio. However, the cable from Miyake toHachijo Islands does not necessarily cover theentire stream of the Kuroshio. In other words, theKuroshio sometimes flows north of the Hachijo
Island and sometimes south. Thus, variation of thevoltage represents north-south migration of theKuroshio axis rather than the variation of theKuroshio transport. Accordingly, the maximum
value of the voltage corresponds to the case inwhich the Kuroshio flows between the Miyake
and Hachijo Islands, and the minimum to the casein which the Kuroshio flows south of the Hachijo
Island. Therefore, the value of the maximum
minus minimum voltage may represents the actual
volume transport of the Kuroshio. Since thedifference is about 0.8 v, we may conclude thatthe mean transport of the Kuroshio is about 48 x
106m3/s. This value is very consistent with former
estimations from the hydrographic observations
by assuming the motionless layer of 1,000m.
For the Tokara Strait, on the other hand, thecable from Yaku to Amami-Oshima Islands covers
the entire stream of the Kuroshio. The variation ofthe voltage, therefore, may represent the variationof the Kuroshio transport. In other words, we canonly estimate the range of variation of thetransport, not the value of transport itself. It has
been found that the range of variation of theKuroshio transport is about 5 x 106m3/s in theTokara Strait.
One of the most important findings of thisstudy is the fact that the voltage calibration factor
differs considerably from region to region. Thecalibration factor has been shown to be 12 x
106m3/s/v for the Tsugaru Strait, 60 x 106m3/s/v
for the Izu Islands region, and 25 x 106m3/s/v forthe Tokara Strait. Note that the calibration factor
for the Tsushima Strait is about 12 x 106m3/s( Lyu and Kim, 2001). It is rather surprising that

we have this large difference of the calibration
factor, and we present some explanation below.
According to the theory of Longuet-Higgins
et al. (1954), the voltage calibration factor k may
be given by k = Ho (1+ Hs Cs/Ho Co)/Fz when
the current is uniform in the horizontal space.
Here, Fz represents the vertical component of thegeomagnetism (almost constant value), Ho thewater depth, Hs the penetration depth of the
motion-induced electric current under the seabed,
Co the resistivity of the sea water, and Cs theresistivity of the seabed. Since the tidal current
is generally uniform in the horizontal space, theabove theory may apply to our cases. Unknown
factors in the above formulation are Hs and Cs.
We first assume that 1 >> ( HsCs/HoCo),then the calibration factor reduces to simply k =(Ho/Fz). This follows that calibration factor onlydepends on the water depth. However, thisexpression fails to explain the actual differenceof the calibration factor among the four regions.
We next consider another extreme case of 1 <<( HsCs/HoCo). In this case, k = (HsCs) / (FzCo).
Since Hs and Cs may be constant values, thecalibration factor may be inversely proportional
to the resistivity of the seawater, which becomesthe minimum in summer and the maximum inwinter. In fact, the calibration factors for thethree regions show a clear seasonal fluctuation
with the maximum in summer and the minimumin winter, as suggested in Fig. 1. We may
therefore conclude that the latter condition (1 <<HsCs/HoCo) is the actual case.
We
next
assume,byfollowing
Longuet-Higgins et al. (1954), that Hs is nearly
equal to the width of the strait, and substitutetypical values for the water depth and width of thestrait. We may then expect that the value for Cs ofthe Izu Islands region is almost as large as that ofthe Tsugaru Strait, and Cs for the Tokara Strait 5times and Cs for the Tsushima Strait 10 times.
Here ,Cs for the Tsugaru Strait must be less than afew ohm-cm owing to the constraint of 1 <<( HsCs/HoCo).
Finally, it is noted that the calibration factor
k for Oshima – Miyake Islands (where volcanicand seismic activities are observed) shows agradual increase in these three years. We do notknow whether this implies that the resistivity ofthe seawater is decreasing or that the resistivity ofthe seabed is increasing there.

Acknowledgments: Dr. K. Matsumoto ofNational Astronomical Observatory, Mizusawa,
Japan, kindly reproduced the amplitudes andphases of the 8 major tidal current constituentsfrom their tidal model for the Izu Islands region
and the Tokara Strait.

References
Longuet-Higgins, M., M. Stern, and H. Stommel,
1954: Pap. Phys. Ocean. Meteor.,13, 1-37.
Matsumoto, K., T. Takanezawa, and M. Ooe,
2000: J. Oceanography, 56, 567-581.
Lyu, S.-J., and K. Kim, 2001: Extended Abstract,
OHP/ION Joint Sympojium, 236 – 240.

Tidal Signal of Voltage ( Miyake - Hachijo Islands) 1999

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voltage (mv)200-200-400-600-800
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Fig. 1 Time series of high-pass filtered voltage between Miyake and Hachijo Islands for the year 1999.