Journal of Oceanography, Vol. 54, pp. 115 to 122. 1998
Comparison of Kuroshio Surface Velocities Derived from
Satellite Altimeter and Drifting Buoy Data
HIROSHI UCHIDA1, SHIRO IMAWAKI 2 and JIAN-HWA HU3
1Department
of Earth System Science and Technology, Interdisciplinary Graduate School of
Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816, Japan
2Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816, Japan
3Department of Oceanography, National Taiwan Ocean University, Keelung 202, Taiwan, R.O.C.
(Received 19 September 1997; in revised form 1 November 1997; accepted 1 November 1997)
Sea-surface geostrophic velocities for the Kuroshio region calculated from TOPEX/
POSEIDON altimetry data together with in situ oceanographic data are compared with
surface velocities derived from drifting buoy trajectories. The geostrophic velocities
agree well with the observed velocities, suggesting that the Kuroshio surface layer is
essentially in geostrophic balance, within measurement error. The comparison is improved
a little when the centrifugal acceleration is taken into account. The observed velocities are
divided into the temporal mean and fluctuation components, and the partitioning of
velocities between these two components is examined. For the Kuroshio region, most of
the fluctuation components of the velocities derived from drifting buoys are found to be
positive. This result suggests that Eulerian mean velocities for the Kuroshio region
estimated from drifting buoy data tend to be larger than actual means, due to the buoy’s
tendency to sample preferentially in the high-velocity Kuroshio.
(i.e., departures from some temporal mean) derived from
altimetry data with velocity anomalies obtained from repeated
shipboard acoustic Doppler current profiler (ADCP) measurements across the Kuroshio. In their comparison, the ship
track was oblique to subsatellite tracks and altimetry-derived
velocities had to be interpolated with reference to the ship
track position. Those previous works are described in detail
in the discussion section below. It is important to avoid
smoothing in time and space, especially for the Kuroshio
region, where fluctuations with short time scales and small
spatial scales are large. To our knowledge, no studies have
been carried out on a nearly instantaneous comparison
between altimetry-derived velocities and observed velocities without notable smoothing in space.
The altimetry satellite TOPEX/POSEIDON (hereafter
T/P) has been collecting SSH data since late September
1992 (Fu et al., 1994). A group entitled Affiliated Surveys
of the Kuroshio off Cape Ashizuri (ASUKA) carried out
oceanographic surveys along a subsatellite track of T/P
crossing the Kuroshio south of Shikoku, Japan (Fig. 1),
during 1993–1995 (Imawaki et al., 1997a, b). Horizontal
SSDT profiles estimated from in situ oceanographic data
along the ASUKA line were combined with fluctuation
SSDT profiles derived from the T/P data, in order to obtain
the temporal mean SSDT profile. The sum of the mean
SSDT profile so obtained with each of the fluctuation SSDT
profiles gave accurate absolute SSDT profiles along the
1. Introduction
Satellite altimetry has been recognized as one of the
most useful methods to observe variations of the sea-surface
topography and velocity fields globally, with high spatial
resolution at short time intervals. A microwave radar altimeter
on board a satellite measures the sea-surface height (hereafter SSH) which consists of large-amplitude undulations of
the geoid and small-amplitude undulations of the sea-surface
dynamic topography (SSDT). In practice, however, only the
temporal fluctuation component of the SSDT can be accurately determined because the present geoid model is not
accurate enough for the SSDT to be extracted from the SSH
(Imawaki, 1995). In order to determine the absolute SSDT
and geostrophic velocity fields, the temporal mean SSDT
lost in the analysis must be determined by some other
method.
Verification of the altimeter data has been done mostly
for the SSDT, but several studies have also been done to
verify the altimetry-derived geostrophic velocity field.
Willebrand et al. (1990), Ichikawa et al. (1995), and Yu et
al. (1995) compared two-dimensional velocity fields derived
from altimetry data with surface velocity fields derived from
drifting buoy data. In their comparison, altimetry-derived
velocity fields were considerably smoothed in time and
space with optimal interpolation to obtain gridded data, and
observed velocity fields were also smoothed. Ebuchi and
Hanawa (1995) compared cross-track velocity anomalies
115
Copyright  The Oceanographic Society of Japan.
Keywords:
⋅ TOPEX/
POSEIDON,
⋅ satellite altimeter,
⋅ drifting buoy,
⋅ geostrophic
velocity,
⋅ gradient-wind
velocity,
⋅ Kuroshio.
Fig. 1. Trajectories of surface drifting buoys (thin lines) in the
WOCE-TOGA SVP during September 1992 through November 1995 and their estimated velocities (arrows) on the ASUKA
line (thick line). The open circle at 29°N indicates the location
of Ocean Data Buoy No. B21004. The triangle at the northern
end of the ASUKA line shows the tide gauge location. See text
for label A near the northern end.
ASUKA line, which compared very well with the individual
in situ SSDT profiles obtained repeatedly (Uchida and
Imawaki, in preparation).
In the present paper we compare cross-track surface
geostrophic velocities, derived from the above-mentioned
absolute SSDT profiles, with surface velocities determined
from drifting buoy trajectories. Additionally, we take the
centrifugal acceleration into account in this comparison.
Observed velocities are divided into temporal mean and
fluctuation components, and the partitioning of velocities
between these two components is examined; the result
suggests that there is a sampling problem for drifting buoy
data from the Kuroshio region. The present paper aims to
verify the accuracy of the absolute SSDT derived from the
T/P altimeter data and to examine how geostrophy holds at
the sea surface in the Kuroshio region.
2. Data and Data Processing
The altimeter data used in the present study were taken
from the T/P Merged Geophysical Data Record (M-GDR),
which consists of scientific data from the National Aeronautics and Space Administration (NASA) altimeter system,
TOPEX, and from the Centre National d’Etudes Spatiales
116
H. Uchida et al.
(CNES) altimeter system, POSEIDON. We used data from
subsatellite pass No. 112, which is almost identical with the
ASUKA line (Fig. 1), with 10-day repeat cycles from
September 1992 to April 1996 (Cycles 1 to 132). The
sampling interval was 1 s, corresponding to 6.2 km along the
subsatellite track. We applied standard geophysical data
corrections (Benada, 1993) as follows. The SSH was corrected using electromagnetic bias, ionospheric, dry and wet
tropospheric, and inverse barometer corrections. The solid
earth and pole tides were removed. These correction data
were provided in M-GDR. The CSR3.0 tidal model (Eanes
and Bettadpur, 1995) was used to remove the ocean tides.
The JGM-3 gravity model (Tapley et al., 1996) was used to
determine the satellite orbit height. We corrected for an error
in the algorithm used in correction for TOPEX oscillator
drift, which was found in summer 1996. The relative bias
between TOPEX and POSEIDON altimeters was not taken
into account, because it is estimated to be fairly small (less
than 2 cm; Haines, personal communication, 1996).
We processed the data to obtain fluctuation SSDT,
using the collinear method (Cheney et al., 1983). The effect
of the cross-track and along-track geoid gradients was
removed by using the mean sea-surface data provided in MGDR. After this correction, the SSH data were collocated
onto a set of latitudes and longitudes during Cycle 48, which
was chosen as a reference. The temporal mean SSH over
three years (Cycles 6 to 116) was calculated at each reference point. The fluctuation SSDT was determined by subtracting the temporal mean SSH from the individual SSH for
each cycle. To remove small scale measurement errors, the
fluctuation SSDT was low-pass-filtered twice along the
track with a 3-point Hanning filter with a half power gain at
48 km wavelength.
The temporal mean SSDT profile along the track was
estimated by a similar method to that of Imawaki and Uchida
(1995). At location x and time t, the absolute SSDT ζ(x, t) is
written as follows;
ζ ( x, t ) = ζ ( x ) + ζ ′ ( x, t )
(1)
where ζ ( x ) is the temporal mean SSDT, and ζ′(x, t) the
fluctuation SSDT. The absolute profile ζ(x, t) was estimated
repeatedly from a combination of moored current meter data
and repeated hydrographic data along the ASUKA line,
referred to the tide gauge data (see Fig. 1 for location). The
fluctuation profile ζ′(x, t) was derived from the T/P altimeter
data together with the tide gauge data which were used to
improve the SSDT profiles near the coast (Uchida and
Imawaki, 1996). Using those profiles, the unknown temporal
mean SSDT profile ζ ( x ) was estimated from Eq. (1), using
the least-squares method. The sum of the resulting mean
SSDT profile and a fluctuation SSDT profile from the T/P
altimeter data gave a very accurate individual absolute
SSDT profile (Uchida and Imawaki, in preparation).
Cross-track surface geostrophic velocities are calculated from the along-track gradient of this absolute SSDT
profile, with a horizontal resolution of 12.4 km. The shorter
interval of finite difference gives sharper velocity structures,
but noisier velocity profiles. The chosen interval of 12.4 km
is a compromise with stable estimates. The geostrophic
velocities obtained every 10 days are interpolated to the time
when a drifting buoy crossed the ASUKA line.
Drifting buoy data have been collected by the World
Ocean Circulation Experiment-Tropical Oceans Global
Atmosphere (WOCE-TOGA) Surface Velocity Program
(SVP), using the ARGOS system to locate positions of
freely-drifting surface buoys. The data used in the present
study were quality-controlled and optimally interpolated to
uniform six-hour interval trajectories (Hansen and Poulain,
1996). All buoys were attached to drogues centered at 15-m
depth and transmitted signals continuously. The velocities
of drifting buoys are computed from the six-hourly position
data by finite difference, and then linearly interpolated onto
the ASUKA line. Figure 1 shows the twenty drifting buoy
trajectories (thin lines) which are used in this study. The
figure also shows the drifting buoy-derived surface velocities
(arrows) which are compared with the T/P altimetry-derived
geostrophic velocities on the ASUKA line; twenty-eight
cases are shown. Here one drifting buoy (No. 14967) has
been excluded from the present comparison (and Fig. 1)
because the velocity of that drifting buoy changed abruptly
near the ASUKA line and its spatial interpolation onto that
line is inappropriate.
The sea-surface wind data used in the present study
were obtained by Ocean Data Buoy No. B21004 off Shikoku,
which has been collecting marine meteorological and
oceanographic data (Fig. 1). We used the wind data at threehour intervals for three years (1993–1995). These data were
low-pass-filtered with a one-day running mean.
3. Results
In the present study, we compare the two surface
velocities, estimated from the T/P altimeter and drifting
buoy data, for the cross-track component (east-northeastward
flow).
Figure 2 shows the scatter plot of geostrophic velocities (Vg) derived from the absolute SSDT profiles (estimated
from T/P altimeter data) against surface velocities derived
from the drifting buoy trajectories. Closed circles show the
results for velocities associated with the Kuroshio, so judged
subjectively on the basis of altimetry-derived geostrophic
velocity profiles. The dotted circle shows the result for the
velocity labeled A near the northern end of the ASUKA line
in Fig. 1, which was observed in the Kuroshio region but
located considerably distant from the Kuroshio at that time.
Open circles show the results for velocities measured south
of the Kuroshio region (south of 31°N), including a fairly
Fig. 2. Scatter plot of geostrophic velocities derived from altimeter data against surface velocities derived from drifting buoy
data. Closed circles are for the Kuroshio, the dotted circle is
for the velocity labeled A in Fig. 1 (see text for details) and
open circles are for the region south of the Kuroshio. Twentyeight cases are shown. The correlation coefficient (C.C.) and
the slope of the regression line (thick solid line) are also
shown. Thin dashed lines represent one standard deviation
from the regression line. The rms difference between the two
quantities is 16 cm sec–1.
strong eastward flow near 25°N (Fig. 1). The agreement of
these cross-track velocities is excellent. The correlation
coefficient (0.92) is high, the slope (0.92) of the regression
line is close to unity, and the rms (root-mean-square) difference (16 cm sec–1) between the two quantities is fairly small.
This fact suggests that flows in the surface layer of the
Kuroshio region and adjacent area are essentially in
geostrophic balance.
The Kuroshio changes its location and strength temporally. The velocities used in the present comparison were
observed opportunistically at the time and location when
and where drifting buoys crossed the ASUKA line. Therefore, two interesting questions arise regarding this data
sampling. First, what is the partition between the temporal
mean and fluctuation components of the observed velocities?
If the fluctuation component is small, the altimeter data are
not important in the present comparison. Second, can averaged velocities derived from drifting buoys give true longterm Eulerian mean velocities? These questions can be
answered with the aid of the altimetry-derived geostrophic
velocities, instead of the drifting buoy-derived velocities,
because the former are originally formed as sums of mean
and fluctuation components as described in the previous
section, while the latter are not readily separable into mean
and fluctuation components.
The first question about the partition of the temporal
Kuroshio Velocities from Altimeter and Drifting Buoy
117
mean and fluctuation components is answered by their
scatter plot, shown in Fig. 3. For the Kuroshio (closed
circles), both components are important, although the mean
component is a little larger than the fluctuation component
in general. For the region south of the Kuroshio (open
circles), the fluctuation component is larger than the mean
component. Therefore the good comparison shown in Fig. 2
is not only due to accurate estimates of the mean SSDT
profile, but also due to those of the fluctuation SSDT
profiles derived from altimeter data. Note that for the case of
the velocity labeled A in Fig. 1, the mean and fluctuation
components have almost the same amplitudes, but opposite
signs.
The second question about averaged velocities from
drifting buoy data is more important. Figure 3 clearly shows
that most of the fluctuation components are positive for the
Kuroshio region; namely, most of individual total velocities
are larger than the mean components there. This is a reflection
of the fact that most drifting buoys tend to continue to follow
the Kuroshio very well, even if the Kuroshio fluctuates and
shifts its location laterally. In other words, drifting buoys are
only rarely expected to measure velocities outside of the
fluctuating Kuroshio. Therefore, the data from drifting
buoys are likely to be biased due to this sampling tendency
for the Kuroshio region, especially in the case where the
Kuroshio changes its axis temporally. Drifting buoy-derived
velocities are not likely to reflect the fact that the Eulerian
mean velocity field is weakened and broadened by lateral
shift of a strong current. There is only one exception in the
Fig. 3. Scatter plot of fluctuation components against mean
components of geostrophic velocities derived from T/P altimeter data, following the present data sampling scheme of
drifting buoys. Closed circles are for the Kuroshio, the dotted
circle is for the velocity labeled A in Fig. 1 and open circles are
for the region south of the Kuroshio. Twenty-eight cases are
shown.
118
H. Uchida et al.
present analysis, the velocity labeled A in Fig. 1 and shown
by the dotted circle in Fig. 3, which indicates a large
negative fluctuation component. This drifting buoy showed
a somewhat different trajectory from the others; it followed
a small meander of the Kuroshio southeast of Kyushu,
approached the ASUKA line, and then escaped from the
Kuroshio to enter the bay (Bay Tosa) south of Shikoku (see
Fig. 1).
As an example of biased Eulerian means, temporal
mean velocities estimated from the present drifting buoy
data are compared with the temporal mean geostrophic
velocities, which were estimated by combining the in situ
oceanographic observation data and T/P altimeter data (see
the previous section) and are considered as reference velocities. The results for the Kuroshio region are shown in
Fig. 4. Here the averages were taken for bins of 24.8 km
width along the ASUKA line. Data distribution in time (Fig.
4(a)) shows that more data were obtained in the early half of
this three-year period, but some data were also obtained in
the latter half; the data distribution is not homogeneous, but
Fig. 4. Eulerian mean velocities derived from drifting buoys in the
Kuroshio region. (a) is the data distribution in time (in Julian
day from the beginning of 1993) and space along the ASUKA
line. (b) is the horizontal distribution of the surface layer
velocity. Solid line is the reference three-year Eulerian mean
velocity. Open circles and the dotted circle are drifting buoyderived velocities. Closed circles are Eulerian means of drifting buoy-derived velocities within bins of 24.8 km width;
vertical bars show their estimated errors. Triangles are threeyear means estimated from combination of the drifting buoy
data and fluctuation velocity data from the altimeter.
it is acceptable, as shown below. All differences of the mean
velocities so obtained (closed circles in Fig. 4(b)) from the
mean geostrophic velocities (thick line) are positive and
remarkably large; they are as much as 30–40 cm sec–1.
These differences are not due to differences between
the drifting buoy velocities and altimetry-derived geostrophic velocities, but due to the data sampling tendency of the
drifting buoys mentioned above. This is confirmed by a
subsidiary calculation of similar Eulerian means of altimetry-derived velocities with the same data sampling scheme
as the drifting buoys, which gives almost the same values as
the above-mentioned means. The weak velocity labeled A in
Fig. 1 makes a large contribution to reducing the biased
Eulerian mean estimates from drifting buoy data in the most
coastal bin, centered at 32°35′ N; without this, the estimated
mean differs much more from the reference mean.
It might be suspected that those departures from the
reference mean could be due to the inhomogeneous distribution of drifting buoy data; such results could be obtained if
the Kuroshio were stronger in the early half of the three-year
period and weaker in the latter half. Indeed, the mean
velocity for the most coastal bin is a little larger in the early
half than the latter half, and therefore the departure mentioned above (37 cm sec–1) may be partly due to the bias of
the temporal sampling scheme. But the difference (36 cm
sec–1 ) between these two mean velocities during the
subperiods would introduce only a small departure (11 cm
sec–1) from the three-year reference mean, on average, and
the results are not seriously affected. No remarkable differences are detected for the other four bins and therefore most
departures are not due to bias of the temporal sampling
scheme.
an example of the estimation of the curvature of the flow.
The radius of curvature is estimated assuming a circle
through three positions of a drifting buoy which were
located immediately before crossing the ASUKA line, 12
hours before that, and 12 hours after that. To avoid large
error in the estimates, the drifting buoy positions were lowpass-filtered with a Hamming filter designed to have a half
power gain at 80 hour period. From the altimetry-derived
geostrophic velocity Vg and the radius R of curvature, we
compute the surface gradient-wind velocity Vgr normal to
the ASUKA line, using the relations Vg = Ṽg cosα and Vgr =
Ṽgr cosα, where α is the angle between the ASUKA line and
the local radius of the drifting buoy track. In this example,
the radius R is –320 km and the ratio Vg/Vgr is 0.95. Figure
5(b) shows the histogram of this ratio for the Kuroshio. The
ratio has a mode centered at 0.97. The radius R is estimated
to be –200 to –600 km for most cases.
Figure 6 shows a comparison of the surface gradientwind velocities estimated from the altimeter data with the
surface velocities derived from drifting buoy trajectories, as
a revision of Fig. 2. Agreement is a little improved in
comparison with the geostrophic velocity case. In particu-
4. Sources of Discrepancy
Agreement between the geostrophic velocities and the
observed velocities is excellent (Fig. 2), but the slope of the
regression line is slightly smaller than unity. As can be seen
from the drifting buoy trajectories in the Kuroshio (Fig. 1),
this may be due to the effect of centrifugal acceleration. The
curvature of the flow can be estimated from the drifting buoy
trajectories, and therefore gradient-wind velocities can be
estimated. The cross-stream momentum balance is written
as follows;
fṼgr +
Ṽgr2
R
= −g
∂ζ
= fṼg
∂n
(2)
where f is the Coriolis parameter, g the acceleration due to
gravity, ζ the SSDT, n the distance normal to the stream, R
the radius of curvature, and Ṽgr and Ṽg are the down-stream
components of the gradient-wind velocity and geostrophic
velocity, respectively. The radius R is positive (negative)
when the flow is cyclonic (anticyclonic). Figure 5(a) shows
Fig. 5. Ratio of Vg/Vgr for the Kuroshio. Panel (a) shows an
example of estimating a radius of curvature. Closed circles
indicate six-hourly positions of a drifting buoy. Solid line is
the ASUKA line. The center of curvature (open circle) is
estimated by using three drifting buoy positions. Selected
bottom topography contours (m) are also shown. (b) is the
histogram of the ratio Vg/Vgr . Twenty-one cases are shown.
Kuroshio Velocities from Altimeter and Drifting Buoy
119
Fig. 6. Same as Fig. 2, except for gradient-wind velocities. The
rms difference is 16 cm sec–1 .
lar, the slope (0.96) is much closer to unity. The correlation
coefficient (0.93) is slightly improved, although the rms
difference (16 cm sec–1) between the two quantities is almost the same as the previous comparison.
The sea-surface velocities estimated from the altimeter
data compare well with the surface velocities obtained by
drifting buoys. There are, however, some differences between
them. Possible sources of this discrepancy are discussed
below.
First we discuss errors in drifting buoy measurements.
Satellite ranging with the ARGOS system can locate positions globally within a 1-km radius (Niiler et al., 1995).
Therefore the rms error of velocities derived from the sixhour averaged drifting buoy trajectory is estimated to be less
than 7 cm sec–1. The drifting buoy has wind-produced slip
of as much as 0.1% of wind speed (Niiler et al., 1995). Ocean
Data Buoy B21004 (Fig. 1) south of Shikoku provides an
estimate of the three-year (1993–1995) mean surface wind
speed of 5.6 m sec–1. Therefore the wind-produced slip in
this region is estimated to be less than 1 cm sec–1 on average.
The overall error of the present drifting buoy-derived velocity
is estimated to be about 7 cm sec–1.
Second we discuss possible errors of the T/P altimetryderived geostrophic velocities. Measurement errors of SSH
with relatively large horizontal scales hardly affect
geostrophic velocities. The total SSH measurement error
with small horizontal scale is estimated to be 2.1 cm (including instrument noise of 1.7 cm, ionospheric correction
error of 0.5 cm and wet tropospheric correction error of 1.1
cm; Fu et al., 1994), with decorrelation distances of 20–50
km (Tapley et al., 1994). The rms error is reduced to 1.1 cm
by applying an along-track low-pass filter, if we assume that
the error is white noise. Therefore the rms error of the
120
H. Uchida et al.
altimetry-derived geostrophic velocities is estimated to be
17 cm sec–1 in finite difference over 12.4 km. This estimated
error may be an overestimate, however, because the rms
error of the comparison (Fig. 2) is not much improved, as
would be expected when a finite difference distance is
chosen to be considerably larger than 12.4 km; the larger
finite difference distance should give a smaller estimated
error if the altimeter noise is white. The assumption of white
noise for the altimeter measurement error may thus not hold.
In addition, the mean geostrophic velocity profile also
includes an error. Therefore the overall error of the altimetry-derived velocity is estimated to be about 17 cm sec–1.
Finally, the discrepancy may be partly due to the
difference of sampling scheme in time and space between
the T/P altimeter and drifting buoy data. The present altimeter
data are instantaneous data at 10-day interval with 12.4 km
resolution in space, while the drifting buoy data give, in
principle, nearly instantaneous velocities at a selected spot.
So the interpolated altimetry-derived velocities may not
have resolved fluctuations with short time scale and small
spatial scale, which the drifting buoy-derived velocities did
resolve. This might be the reason why the slope (0.96) of the
regression line is still slightly smaller than unity in the
comparison with gradient-wind velocities (Fig. 6), and why
the amplitudes of variation (56 cm sec–1 in standard deviation) of the altimetry-derived velocities is slightly smaller
than that (58 cm sec–1) of the drifting buoy-derived velocities. It may also be partly due to the smoothing of the
altimeter data using the Hanning filter (see Section 2).
These error estimates show that the discrepancy (16 cm
sec–1 in rms difference) found in the present comparison
(Figs. 2 and 6) is smaller than the overall measurement error,
including a rather large altimeter measurement error.
Therefore it is concluded that the T/P altimetry-derived
geostrophic velocities as well as the gradient-wind velocities agree with the observed velocities, within measurement
error. In fact, no departure from geostrophy is detected in the
surface layer of the Kuroshio region and the adjacent area.
One possible major source of departure from geostrophic flow is the wind-driven current. For the drifting buoy,
the wind-driven current at 15 m depth is statistically estimated
to be 0.5% of wind speed and 68°to the right of the wind
vector in the northern hemisphere (Niiler and Paduan, 1995).
If we use the mean wind speed at the Ocean Data Buoy, the
wind-driven current at 15 m depth is estimated to be about
3 cm sec–1 on average. There are other probable nongeostrophic currents, including inertial oscillations, tidal
currents and internal waves, which are not discussed here.
5. Discussion
In the previous section, the sea-surface geostrophic
velocities and gradient-wind velocities estimated from the
altimeter data compare well with the surface velocities
obtained by drifting buoys. Those results are compared with
previous studies as follows. In most previous studies for
verification of the altimetry-derived velocities, fluctuation
SSDT’s from altimeter data were combined with temporal
mean SSDT which is approximated with geopotential
anomalies determined from hydrographic observations, in
order to obtain surface velocity maps (Willebrand et al., 1990;
Ichikawa et al., 1995; Yu et al., 1995). Yu et al. (1995)
compared geostrophic velocities derived from T/P altimeter
data with surface velocities derived from carefully selected
drifting buoy data for the western tropical Pacific. The
comparison showed a surprisingly good agreement; for the
zonal (meridional) component of velocities, the correlation
coefficient was 0.92 (0.76) and the rms difference was 5 (5)
cm sec–1. Their velocity range (from –40 to 40 cm sec–1) was
a little smaller than the present study (from –50 to 150 cm
sec–1). In strong-current regions like the Kuroshio (Ichikawa
et al., 1995) and the Gulf Stream Extension (Willebrand et
al., 1990), however, comparison of surface velocities derived
from Geosat altimeter data with drifting buoy data showed
that altimetry-derived velocities were weaker than drifting
buoy-derived velocities; the slope of the regression line was
0.41 for the Kuroshio and 0.36 for the Gulf Stream Extension regions. These systematic differences are considered to
be the consequence of both the objective analysis procedure,
which essentially removed all variabilities of scales less
than O (100 km) from the altimetric map, and the error of the
mean SSDT field. The comparison was improved when the
drifting buoy data were smoothed at the same scale as the
altimetric maps for the Gulf Stream Extension region; the
correlation coefficient was 0.81 and the rms difference was
10 cm sec–1 for the zonal component of velocities, which
ranged from –40 to 50 cm sec–1 (Willebrand et al., 1990).
Geostrophic velocity anomalies derived from T/P altimeter data were compared with surface velocity anomalies
derived from shipboard ADCP data for the Kuroshio region
(Ebuchi and Hanawa, 1995). The result showed that altimetry-derived velocity anomalies were smaller than ADCPderived velocity anomalies; the slope of the regression line
was 0.51. This is considered to be a consequence of the fact
that the ship track was oblique to the subsatellite tracks and
therefore the altimetry-derived velocities had to be interpolated with respect to the ship track position.
The present study differs from those previous studies in
the following two points. First, the absolute SSDT profiles
are used after a careful calibration with the in situ oceanographic observation data, including moored current meter
data at mid-depth. Second, altimetry-derived geostrophic
velocities are compared with observed velocities for a strong
current with least smoothing.
The effect of the centrifugal force becomes larger as the
current becomes stronger. In the Gulf Stream meander, the
ratio of the geostrophic velocity to the gradient-wind velocity
(Vg/Vgr) is typically 1 ± 0.1 (Liu and Rossby, 1993). In the
present study, the ratio is typically 0.97. This relatively
stable value of less than unity is explained by the fact that the
Kuroshio is located north of the local stationary anticyclonic
warm eddy off Shikoku (Hasunuma and Yoshida, 1978), as
well as the fact that the geometry of the continental slope
favors the anticyclonic flow.
The problem of bias of Eulerian mean velocities derived
from drifting buoy trajectories is rather serious for the
Kuroshio region. Estimated means are 1.5–2 times as large
as the actual three-year mean velocities in the present
example (Fig. 4), although the number of the data used is not
sufficiently large to be sure of the statistical significance.
This effect has not been taken into account in previous
studies of velocity statistics based on drifting buoy data for
the Kuroshio (e.g., Hsueh et al., 1996; Maximenko et al.,
1997). Problems for estimating Eulerian mean velocities
from Lagrangian data to describe the general circulation
have been pointed out (Freeland et al., 1975; Davis, 1991;
Poulain et al., 1996). The situation could be improved if the
fluctuation component of velocity is known at the time when
the drifting buoy measures the Kuroshio. For example, T/P
altimeter data can give a time series of the fluctuation
component of the geostrophic velocity without any in situ
oceanographic observation data. The unknown mean velocity can be estimated in the same way as Eq. (1) for velocity
instead of SSDT. The mean velocities so estimated (after
averaging) are shown by triangles in Fig. 4(b). Generally,
the newly estimated mean velocities are much smaller than
the original mean velocities and closer to the reference
three-year mean velocities (thick line), except for the most
offshore bin, where no improvement is obtained for some
unknown reason. Therefore this method is useful for estimating Eulerian mean velocities which are less affected by
the sampling tendency of the drifting buoys.
6. Conclusion
Sea-surface geostrophic velocities for the Kuroshio
region calculated from T/P altimeter data combined with in
situ oceanographic data are compared with surface velocities derived from drifting buoy trajectories. The geostrophic
velocities agree well with the observed velocities; the correlation coefficient between them is 0.92, the rms difference
is 16 cm sec–1, and the slope of the regression line is 0.92.
This suggests that the Kuroshio surface layer is essentially
in geostrophic balance within measurement error. The comparison is improved a little when the centrifugal acceleration is taken into account and gradient-wind velocities are
compared rather than geostrophic velocities; in particular,
the slope (0.96) of the regression line becomes closer to
unity. The observed velocities are divided into the temporal
mean and fluctuation components, and the partitioning of
velocities between these two components is examined. Both
the temporal mean and fluctuation components are found to
be important, and therefore the good comparison is not only
due to the accurate estimates of the mean profile, but also
Kuroshio Velocities from Altimeter and Drifting Buoy
121
due to those of the fluctuation profiles by the altimeter. For
the Kuroshio region, most of the fluctuation components of
the drifting buoy-derived velocities are found to be positive.
This result suggests a problem of data sampling of drifting
buoys for the Kuroshio region; namely, Eulerian mean
velocities for the Kuroshio region estimated from drifting
buoy data tend to be larger than actual means, because of the
buoy’s tendency to sample preferentially in the high-velocity Kuroshio.
Acknowledgements
The T/P altimeter data, M-GDR, were provided by the
Physical Oceanography Distributed Active Archive Center
at the Jet Propulsion Laboratory. The authors wish to thank
P. Niiler for allowing them to use WOCE-TOGA drifter
data, which were quality-controlled and optimally interpolated at the National Oceanic and Atmospheric Administration, Atlantic Oceanographic and Meteorological Laboratory. The oceanographic observation data along the
ASUKA line were obtained by the ASUKA Group. The
surface wind data from Ocean Data Buoy No. B21004 were
provided by the Japan Meteorological Agency. We also
thank two anonymous referees and Mark Wimbush for
valuable comments, which improved the paper considerably. This research was financially supported in part by a
Grant-in-Aid for Scientific Research from the Ministry of
Education, Science, Sports and Culture, Japan.
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