Journal of Oceanography, Vol. 53, pp. 489 to 516. 1997
Global Surface Circulation and Its Kinetic Energy
Distribution Derived from Drifting Buoys
YOICHI ISHIKAWA, TOSHIYUKI AWAJI and KAZUNORI AKITOMO
Department of Geophysics, Kyoto University, Kyoto 606-01, Japan
(Received 25 March 1996; in revised form 28 June 1997; accepted 7 July 1997)
A dataset derived from 1864 drifting buoys archived at the MEDS (Marine Environmental
Data Service) in Canada and the JODC (Japan Oceanographic Data Center) are analyzed
to obtain the global surface circulation and its kinetic energy distribution on a 2° × 2° grid
system (1° × 1° grids in specific regions). The current distribution presents more realistic
features of the global surface circulation at meso- to large scales than previously obtained.
For example, jet-like structures within the western boundary current and the equatorial
current, which have never been resolved in the previous studies with coarser grids, are
successfully reproduced. Moreover, the conspicuous seasonal cycle of surface current,
such as drastic flow reversal, is captured in the Indian Ocean and the equatorial regions.
A large mean kinetic energy (>1000 cm2s–2) appears in the equatorial current, the western
boundary current and its extension, and in the Antarctic Circumpolar Current region. In
these regions, the eddy kinetic energy is comparable to or larger than the mean kinetic
energy, suggesting strong interactions between mean flow and eddies. When the energy
distribution is compared with that from eddy resolving general circulation models, both
synoptic views of the mean fields are found to be in fairly good agreement. In the eddy
field, however, the energy level in the models is much smaller (by a factor of 5) than the
buoy-derived energy level. This result is basically consistent with the previous studies
using altimeter data, but the energy level obtained from drifting buoy data is larger than
that from altimeter data. The difference here is due to the relatively long sampling
intervals of altimeter observations and disregard of the ageostrophic component in
calculating altimeter-derived velocities. These results show that the surface circulation
field derived from drifting buoys provides useful information which can be used to make
models more realistic.
and temporal repetition. However, one major problem is that
the geoid, which has geographical height variations much
greater than those due to the ocean currents, is not well
known on length scales of a few hundred kilometers (Qiu,
1994). This lack of the accurate geoid information has
limited most studies based on altimetric data to the timevarying components of the sea surface height (SSH) for
mesoscale phenomena. For many oceanographic applications, an accurate mean SSH with length scale of several
hundred kilometers is required. This is particularly true for
western boundary currents and their extensions, where spatial
changes of the mean SSH are comparable to those of the
time-varying ones. Thus it is necessary to assume a mean
SSH, for example, based on climatological hydrographic
data (Willebrand et al., 1990). However, the estimated mean
SSH field involves errors due to the uncertainty of specifying
the reference velocities and this may lead to significant
errors in the velocity field. Another error source is the
1. Introduction
Measurement of the velocity of ocean currents is one of
the most important tasks in physical oceanography. The
complex ocean-atmosphere interactions and their effect on
climate can never be fully understood until an accurate
estimation of the velocity field of the oceans is realized
(Nerem et al., 1990). For example, the heat flux at sea
surface is affected significantly by heat transport due to the
surface current (Hastenrath and Lamb, 1980; Hastenrath
and Greischar, 1993; Qiu and Kelly, 1993).
For observing surface current, the drifting buoy has
some advantages because it measures the in-situ absolute
velocity through tracking of the buoy movement by satellites.
With many buoy data that cover a vast geographical extent,
the time series of the realistic surface current field can be
obtained (Richardson, 1983).
Satellite altimetry offers another effective means of
obtaining the surface circulation because of its wide coverage
489
Copyright  The Oceanographic Society of Japan.
Keywords:
⋅ Drifting buoy data,
⋅ global surface
circulation,
⋅ kinetic energy
distribution,
⋅ annual mean
current,
⋅ seasonal variation,
⋅ interaction of the
mean and eddy
currents,
⋅ western boundary
currents,
⋅ equatorial current
systems,
⋅ altimeter data,
⋅ numerical model.
assumption of geostrophic balance, because contributions
from the ageostrophic components in the western boundary
current and the equatorial current can be substantial.
At present, therefore, and in the absence of more
synoptic means of surface current measurement, drifting
buoy data represent the best opportunity to measure mesoscale surface circulation fields. For the larger scale circulation, there remains one major problem. Since drifting
buoys cannot be deployed systematically, there is a bias in
buoy distribution. This has meant that most studies of ocean
circulation based on buoy data focus on specific regions,
such as the North Atlantic (Richardson, 1983; Krauss and
Käse, 1984) and the southern oceans (Patterson, 1985; Piola
et al., 1987). This restriction is serious for surface currents
in the regions accompanied by a significant horizontal
divergence of flow (Hoffman, 1985). Poor observations
compelled the rather coarse energy maps of surface current
in most of the previous studies.
Recently, however, drifting buoy data archived at the
MEDS (Marine Environmental Data Service) in Canada
have been steadily growing in volume thanks to the efforts
of the international drifter community (e.g., Niiler et al., 1987;
Molinari et al., 1990; Wooding et al., 1990; Lukas et al.,
1991). This historical dataset covers broader regions with
finer resolution than before, permitting us to describe the
global surface circulation and its kinetic energy distribution
in more detail. In doing so, we closely examine not only the
mean field of the global ocean circulation but its eddy field.
This is because the eddy kinetic energy is thought to be
larger than the energy of mean flow in regions such as the
western boundary current (Wyrtki et al., 1976), where interactions between mean flow and eddies have an important
influence on the nature of the velocity field (Holland et al.,
1983). Since existing general circulation models still do not
fully reproduce the observed features due to several flaws
such as the insufficient parametrization of mixing processes
(e.g., Mellor and Ezer, 1991), a detailed analysis of ocean
circulations using drifting buoy data can significantly contribute to improving the numerical modeling.
In Section 2 the data and methodology are described.
The energy and velocity maps of the annual mean field are
presented in Section 3 as well as its errors. The low and high
frequency components of the eddy field are examined in
Section 4. Comparison with coarser mapping of drifter data
and previous studies based on ship drift data, altimeter data,
and numerical models are discussed in Section 5, and major
results and conclusions are summarized in Section 6.
2. Data and Methodology
The drifting buoy records of the dataset used in this
study are provided mainly by the MEDS and partly by the
Japan Oceanographic Data Center (JODC). Originally, this
dataset consisted of 2409 buoys some of which had very
short lifetimes (less than 1 day) and also included several
490
Y. Ishikawa et al.
Fig. 1. The number of the drifting buoys for each month since Jan.
1978.
mooring buoys. Removal of these groups left a remaining
1864 drifting buoys available for our analysis with a mean
life time of about 10 months. Figure 1 shows the number of
buoys for each month since 1978; though interannual and
decadal changes in the number of buoys can be seen, most
were deployed after 1984. The annual mean number of the
buoys during this period is about 221 and its standard
deviation is about 65. Further, the ENSO (El Niño and
Southern Oscillation) event as a typical interannual variation occurs in both years with positive and negative peaks of
the buoy population. These facts allow us to perform a
climatological analysis for the mean and eddy fields of the
surface circulation with only minor influences from
interannual change in the number of buoys. Concerning the
decadal variation in the buoy population, Fig. 1 indicates
that this study can be considered to best treat the climatology
for the 10 year period from 1984. Figure 2 shows the
released positions of buoys considered here and clearly
demonstrates that our dataset covers the global ocean except
for the tropical Atlantic and Indian Oceans.
To derive the surface velocity field from the buoy
dataset, each buoy needs to be treated to have almost the
same drifting characteristics. According to Niiler et al. (1987)
and Geyer (1989), differences in buoy configuration such as
whether they are drouged or undrouged affects the drift
characteristics. However, there is no information about
buoy configurations in this dataset. Although there is the
possibility that systematic differences in drift characteristics
could be present, many of the buoys used in this study were
deployed after 1983 (associated with the WOCE program)
and can be considered to be of a similar configuration. So,
in this study, we neglect the influences of such differences
on estimating the climatological velocity field from drifting
buoys.
The time series of buoy positions are determined mainly
by the satellites at several times per day (the mean interval
of which is 3 hours). Previous estimates of positional errors
have a somewhat broad range. McNally and White (1985)
quoted 5 km error for drifters tracked by the Random Access
Measurement System (RAMS) whereas 1 km (McNally and
White, 1985; Piola et al., 1987) or 100–200 m (Richardson,
1983) have been assumed for the recent ARGOS system.
Although the error level of positioning is not well known for
the present dataset because of lack of detailed information,
we assume that it has almost the same accuracy as in
previous studies (Piola et al., 1987), i.e., error of approximately 1 km. This error corresponds to a velocity error of
about 10 cm s–1 (1 km per 3 hours). The time series of
positional data are processed with the following procedure
to compute velocities along the trajectory of each buoy.
After removing poor quality data flagged by the MEDS, all
of the trajectories are smoothed using a two-dimensional
cubic spline function to avoid augmenting computational
errors induced by the noise within the positional data
(Patterson, 1985) and hourly buoy positions are obtained
from these smoothed trajectories. Subsequently, high frequency fluctuations like inertial oscillations and tidal motions, which are out of scope in this study, are removed. The
resulting trajectories allow us to compute the hourly velocity
along each trajectory by a central differencing scheme.
From hourly velocities covering a 17 year period from
1977 to 1993, we have constructed the following climatological dataset of monthly mean velocities for each 2° × 2°
grid. As in Patterson (1985), the velocities of zonal and
meridional components u, v and kinetic energy E are averaged over each month in time and each grid in space as
follows:
u
j
Ej =
1
=
nj
1
nj
nj
∑ uij ,
i =1
v
j
 uij2 + vij2 
∑  2 ,

i =1 
nj
1
=
nj
nj
∑ vij ,
i =1
(1)
is greater than the unlikely value of 300 cm s–1 even in the
western boundary currents. Further, we remove velocity
data which depart from the monthly average in each grid by
a factor of twice the standard deviation to ensure a 95%
confidence level in the final data set.
Figure 3 shows the spatial distribution of the total
number of hourly velocity data in each grid throughout the
study period. Areas of no data appear in the northern part of
the North Pacific (e.g., the Okhotsk Sea), the western Indian
Ocean, around northern Australia and Antarctica, and in the
tropical Atlantic. It is worth noting, however, that in several
regions such as the North Atlantic, the equatorial and the
northwestern Pacific, and to the south of Africa, the number
of data is large enough to make a new dataset with a finer
spatial resolution. In such regions, the velocity and the
kinetic energy are averaged over a 1° × 1° grid for more
detailed analysis, as shown later.
Using this dataset, we can obtain the kinetic energy for
the annual mean field and the eddy field as follows. Generally,
any velocity can be divided into a temporal mean, u , and a
deviation from it, u′:
u = u + u′ ,
(3)
v = v + v′ .
When estimating the kinetic energy for each grid from
the buoy-derived velocity, we need to further divide the
temporal mean into the average over one grid, 〈u〉, and the
departure, ũ (e.g., Patterson, 1985):
u = u + ũ,
v = v + ṽ.
( 4)
v = v + ṽ + v′ .
( 5)
That is to say,
u = u + ũ + u′ ,
It should be noted that 〈 u 〉 and 〈 v 〉 defined above essentially
correspond to 〈 u 〉j and 〈 v 〉j in Eq. (1), respectively.
Based on this notation, the energy for the annual mean
and the eddy field can be expressed as follows:
· The total kinetic energy (TKE)
(2)
TKE =
where uij(vij) is the zonal (meridional) component of the i-th
velocity observation (hourly velocity) during the j-th month,
nj is the number of velocity observations on a certain grid in
the j-th month ( j = 1~12) for the observation period. We
average over a 2° × 2° grid to gain more detailed maps of the
current and kinetic energy distributions with greater statistical
reliance than obtained in previous studies (shown later).
However, extreme values of velocity still remain on some
grids, probably due to perturbations from collisions with
ships. Hence, the velocity data are removed if their magnitude
=
u2 + v2
2
u
2
+ v
2
2
+
ũ 2 + ṽ 2
2
+
u′ 2 + v′ 2
2
.
(6)
· The kinetic energy of the annual mean flow (MKE)
MKE =
u
2
+ v
2
2
.
Global Surface Circulation from Drifting Buoy Data
( 7)
491
492
Y. Ishikawa et al.
Fig. 2. The initial position of the drifting buoys.
Global Surface Circulation from Drifting Buoy Data
493
Fig. 3. The spatial distribution of the number of hourly velocity data. Heavy (light) shadings indicate regions where the number of buoy
data is greater than 1000 (200).
· Annual mean of the eddy kinetic energy (EKE)
EKE =
ũ 2 + ṽ 2
+
2
u′ 2 + v′ 2
.
2
( 8)
Thus the present definition of the MKE and EKE is
somewhat different from the conventional one. In our case,
the EKE includes not only the energy of time-dependent
eddies but the energy of standing eddies whose scale is
smaller than one grid length. Therefore, careful discussion
is required when comparing results with those from the
mooring measurements. However, MKE and EKE estimated
in general circulation models are essentially the same as
those in this study and comparisons will be made later. Note
that the kinetic energy for the annual mean and eddy fields
in the following sections can only be calculated using the
monthly dataset described above.
3. Mean Field
The annual mean field of the global surface circulation
is obtained by averaging the monthly velocity data as
u =
1
m
m
∑
j =1
v =
u j,
1
m
m
∑
j =1
(9)
v j,
where the notation is the same as described earlier and the
small letter m denotes the number of months with data
available on each grid per year as shown in Fig. 4.
The mean kinetic energy per unit mass (MKE) can be
calculated using Eq. (7). To check reliability of the estimated
MKE, it is instructive to introduce the standard error of the
MKE determined as
ERR MKE
 u 2
= 2
 m
 σ uj2 
v 2
∑  n / 240  + m 2

j =1  j
m
 σ vj2  
∑  n / 240  
 
j =1  j
m
1/ 2
,
(10 )
where the variances, σuj2 and σvj2 , about both components of
the monthly mean velocities are given by
n
σ uj2 =
n
σ vj2 =
(
j
),
(11)
(
j
).
(12 )
j
1
uij − u
∑
n j − 1 i =1
j
1
vij − v
∑
n j − 1 i =1
2
2
In the above, in order to secure the statistical independence
of observed velocities, the integral timescale of buoy data is
494
Y. Ishikawa et al.
taken to be 10 days (i.e., 240 hours) in accord with previous
studies (Richardson, 1983; Krauss and Käse, 1984; Patterson,
1985). It should be noted that this time scale is determined
from the analysis of the buoy trajectories under the assumption that a drifting buoy stays in one grid for this time
scale (10 days). When a drifting buoy moves from one grid
into the next grid within this time scale, the error of the MKE
derived here is overestimated (S/N ratio is underestimated),
especially in the regions of strong current.
Figures 5A and 5B show the spatial distributions of the
MKE with 2° × 2° grids and the signal to noise (S/N) ratio
(=MKE/ERRMKE), respectively. A look at Fig. 5B shows a
rather broad range of S/N ratio, in which values less than
unity appear in several regions where the statistical reliance
of the estimated MKE is low. Therefore, the following
discussion is limited to the regions in which the S/N ratio is
over unity.
It can be readily seen in Fig. 5A that the MKE is largest
in the so-called strong current regions such as western
boundary zones, the equatorial current, and the Antarctic
Circumpolar Current (ACC) region. In these cases the value
of MKE exceeds 1000 cm2s–2 (corresponding to the velocity
of about 45 cm s–1). Interestingly, in the ACC region, many
isolated areas of high MKE can be found, some of which
may be associated with bottom topography as suggested by
Wilkin and Morrow (1994). For example, the values of
MKE greater than 1000 cm2 s–2 of MKE appear around the
confluence region of the Agulhas Current and the ACC
(20°E, 40°S), between the Madagascar Plateau and the
Crozet Plateau (40°E, 40°S), east of the Kerguelen Plateau
(70°E, 45°S), east of the Macquarie Ridge (170°E, 55°S),
and around the Pacific-Antarctic Ridge (140°W, 55°S). In
the Drake Passage centered at (70°W, 60°S), the MKE
exceeds 500 cm2s–2. The EKE in all of these regions (described later) has almost the same magnitude as the MKE,
implying that the feature mentioned above can be attributed
to the presence of a significant topographic gap.
Areas of low MKE (less than 200 cm2s–2 corresponding
to a velocity of 20 cm s–1) extend over the interior region.
Though some regions of relatively large MKE are found in
the interior, these seem to be artifacts due to the scarcity of
data (see Fig. 3).
Velocity vectors of mean current in regions with an
MKE S/N ratio larger than 1 are shown in Fig. 6. This figure
represents well the general flow pattern in the surface
velocity field reported previously. For example, strong
currents exceeding 50 cm s–1 concentrate around the western boundary currents such as the Kuroshio and the Gulf
Stream and their extension regions, the tropical region, and
the ACC. Since the mean circulation is averaged not only in
time but in space with 2° × 2° grids, narrow jets like the
western boundary currents are somewhat blurred. Finer
resolution is required to investigate the detailed structure of
the jet-like currents. In the interior region, rather short
Global Surface Circulation from Drifting Buoy Data
495
Fig. 4. The spatial distribution of the number of months for which data exist. Heavy, middle, and light shadings indicate that the number
of months is greater than 10, 7, and 4, respectively.
496
Y. Ishikawa et al.
Global Surface Circulation from Drifting Buoy Data
497
Fig. 5. (A) The spatial distribution of the kinetic energy of mean flow (MKE) with 2° resolution (unit in cm2s–2). (B) S/N ratio of MKE.
The heavy (light) shadings indicate regions where the S/N ratio is greater than 1.5 (1).
498
Y. Ishikawa et al.
Fig. 6. The global velocity map for the annual mean current with 2° resolution. The velocity vectors are plotted in regions with a S/
N ratio of MKE larger than 1.
Fig. 7. The velocity map for the annual mean current in the region around the Kuroshio with 1° resolution. The velocity vectors are
plotted in regions with a S/N ratio of MKE larger than 1.
vectors with various directions show week flows.
Figures 7 to 10 show the velocity fields around the
Kuroshio, the Gulf Stream, the Agulhas current (the western
boundary current in the South Indian Ocean), and tropical
Pacific for the case of 1° × 1° grids (note that these vectors
also are mapped in the regions with an MKE S/N ratio larger
than 1). We can see in Fig. 7 that the Kuroshio is fed by the
northward branch of the North Equatorial Current (NEC)
after its bifurcation off the Philippine coast. To the south of
Japan (e.g., at 32°N, 140°E), two axes of the Kuroshio
current can be seen. This feature reflects the bimodality of
the Kuroshio path between the straight and the large meandering one. Separation of the Kuroshio path from the
Japan coast is located at 35°N and its extension current flows
until approximately 160°E. It then bifurcates into eastward
and northeastward branches around the Shatsky rise, as
previously reported (McNally et al., 1983; Qiu et al., 1991).
The Gulf Stream (Fig. 8) originates in the Gulf of Mexico,
flows northward along the coast of North America and
finally separates from the coast into the interior region at
37°N. Its extension reaches the North Atlantic ridge centered at 27°W. The Agulhas current (Fig. 9) retroflects off
the southern tip of Africa (around 40°S, 20°E), and a part
joins the ACC to cause the intense meandering jet with a
wavelength of a few hundred kilometers.
Data for the tropical Pacific (Fig. 10) successfully
capture the alternating bands of eastward and westward
flowing currents which are salient features of the circulation
in the tropical Pacific. In particular, the westward NEC
north of 10°N, the eastward North Equatorial Countercurrent (NECC) around 5°N, and the double core structure of
the westward South Equatorial Current (SEC) around the
equator and 5°S are seen. The double core structure of the
SEC was suggested by Philander et al. (1987) but previous
research was unable to define it clearly. The velocity field in
the western tropical Pacific is very complicated. Since it is
Global Surface Circulation from Drifting Buoy Data
499
Fig. 8. Same as Fig. 7 but in the region around the Gulf Steam.
Fig. 9. Same as Fig. 7 but in the region around the Agulhas Current.
500
Y. Ishikawa et al.
Fig. 10. Same as Fig. 7 but in the tropical Pacific.
Global Surface Circulation from Drifting Buoy Data
501
wellknown that significant seasonal variation is dominant in
this region associated with the Asian Monsoon, we examine
the seasonal variability of this surface circulation later.
Finally, we present a simple discussion concerning
another influence of temporal bias on the monthly data (i.e.,
the parameter m in Eq. (9)) used in estimating the annual
mean velocity field. Generally, the quality of the estimated
mean velocity becomes better with increase in the parameter
m. Thus the mean velocity for m larger than 7 in Fig. 4
(which means the presence of monthly velocity data for
more than 6 months) should represent a good estimation. In
contrast, the estimated mean velocity for other cases (mostly
in the South Atlantic and Indian Oceans) is expected to have
a significant temporal bias leading to less reliable results.
However, close examination of the presence of monthly data
reveals fairly wide seasonal coverage for m larger than 4,
implying that the estimated mean velocity even for this case
has relatively small seasonal bias and hence is not necessarily
meaningless. Most of the features of the annual mean field
described above are nevertheless for regions with parameter
m larger than 7 and with high S/N ratio. Hence the present
results derived from the buoy data are of high statistical
validity. Further drifter observations, especially within the
regions of sparse coverage shown in Fig. 4, are desirable in
order to improve the dataset.
1
LFEKE =
m
m
∑
j =1
(u j ′ ) + ( v j ′ )
2
2
2
,
(15)
where uj′ and vj′ are the zonal and meridional components,
respectively, of the departure of the mean velocity in the jth month from the annual mean:
uj ′ = u
j
− u ,
vj ′ = v
j
− v .
(16 )
Since the confidence interval for estimates of variances can
be considered to be based on the Chi-square distribution, so
the error of LFEKE is defined as follows:
4. Eddy Field
4.1 Eddy kinetic energy
The energy of fluctuations (regarded here as the eddy
kinetic energy EKE) is obtained according to Eq. (8) and can
be rewritten using the monthly data of the kinetic energy Ej
in Eq. (2) as
EKE =
1
m
m
∑ E j − MKE.
(13)
j =1
The error within EKE is estimated from the relation
(
ERR EKE = ERR 2LF + ERR 2HF
)
1/ 2
,
(14 )
where ERRLF and ERRHF are the estimated errors associated
with the low- and high-frequency components of the EKE as
described later. Note that in the case of EKE, the S/N ratio
is largest in the region where the greatest number of observations are available (Patterson, 1985).
The spatial distribution of EKE on a 2° × 2° grid and the
corresponding S/N ratios are shown in Fig. 11. The high
energy areas of EKE (e.g., in the ACC) show good correspondence with those of high MKE (Fig. 5) with the values
of the EKE being slightly greater than those of MKE,
suggesting strong interactions between eddies and mean
502
flow. The areas of low EKE (less than 200 cm2s–2 corresponding to velocity fluctuations of 20 cm s–1) extend over
the interior region, similar to those of the MKE. The S/N
ratio of EKE is over unity across a broad region. This means
that the number of the data is large enough to make an
accurate EKE map on a 2° × 2° grid (since error within EKE
is related to the number of the data).
To examine the eddy field in more detail, we partition
the eddy kinetic energy into high and low frequency parts,
using a monthly dataset as in Patterson (1985). The low
frequency part (LFEKE) is defined as an energy for the
fluctuations of the monthly mean velocities relative to the
annual mean:
Y. Ishikawa et al.
ERR LF =
ν ⋅ LFEKE  1
1 
− 2 ,

2
2
 χ1− α / 2 χ α / 2 
(17)
where χ = χ(ν) is the Chi-square function with ν the number
of degrees of freedom, and α is the confidence level chosen
to be 0.68 in order to keep consistency with the earlier error
estimates. In this case, each monthly mean velocity is
assumed to be statistically independent so that ν = m – 1.
The high frequency part (HFEKE) is defined as a
residual between the total eddy kinetic energy and the low
frequency part:
HFEKE = EKE – LFEKE.
(18)
Thus the HFEKE represents the fluctuation of the hourly
velocities from the monthly mean. The error of HFEKE is
estimated in a manner analogous to that for LFEKE, namely,
ERR HF =
ν ⋅ HFEKE  1
1 
− 2 ,

2
2
 χ1− α / 2 χ α / 2 
(19)
where the number of degrees of freedom is given by ν = (n/
240) – m – 1.
The spatial distribution of LFEKE (Fig. 12A) and the
corresponding S/N ratios (not shown) are very similar to
those for EKE. For example, large LFEKE appears in the
western boundary current region and the tropical Pacific.
This is especially so in the western tropical Pacific where the
surface current is greatly affected by the Asian Monsoon
(Philander, 1990). The presence of a zonal band with significant LFEKE between 20°S and 30°S in the Indian Ocean
and the western Pacific probably indicates the presence of
long Rossby waves.
The S/N ratio of HFEKE (not shown) is small except
within certain regions, such as in the western tropical Pacific,
the eastern Pacific, and in the north Atlantic, although the
number of degrees of freedom in Eq. (19) is somewhat small
and leads to an underestimation of the S/N ratio as is
mentioned in previous section. The low S/N ratio of HFEKE
means that the number of the observations is too small to
calculate the energy of the mesoscale eddies, so that we can
examine the HFEKE only in limited regions where the S/N
ratio is over 1. Although the distribution of the HFEKE (Fig.
12B) is basically similar to that of the LFEKE, close comparison shows that the areas of high HFEKE in the Gulf
Stream are not co-located with those of high LFEKE but are
somewhat downstream. This implies that the seasonal
variation is dominant in the Gulf Stream region up to the
point of separation from the coast, whereas mesoscale eddy
activity, possibly due to baroclinic instabilities, is dominant
in its extension region. In other western boundary currents,
this feature is unclear because of the small number of drifters
(low S/N ratio).
4.2 Seasonal variability
The seasonal current field is calculated from the monthly
dataset in the same manner as the annual mean current
except for the averaging over each season. For the purpose
of averaging, the winter period is defined from January to
March, spring is taken between April and June, summer
between July and September, and autumn between October
and December.
The global maps of the seasonal current for winter and
summer based on a 2° × 2° grid and for S/N ratio over unity
are shown in Fig. 13. The S/N ratio is calculated in the same
manner as for the MKE except for the averaging over each
3 month period. Since the number of velocity data in each
season is smaller than that for the annual mean map due to
the shorter average period, areas of no data extend more
widely (particularly in autumn), causing a lower statistical
reliability than that of the annual mean field.
A look at these figures shows the presence of conspicuous seasonal variabilities in several regions. In the
Indian Ocean, where currents are much affected by the
monsoonal wind, the NEC at about 5°N flows westward in
boreal winter but its direction reverses to the east in boreal
summer. On the equator, the eastward jet called the Yoshida
jet (Yoshida, 1959) appears only in spring and autumn (not
shown). Another prominent feature is the the seasonal
reversal of the Somali Current in the western part.
Seasonal variability can be also seen in the western
boundary current regions. In particular, the change in the
western boundary currents of the subpolar gyre such as the
Oyashio and the Labrador Current seems to be significant,
but this is less reliable because of relatively poor observations in the subpolar region. The western boundary currents
of the subtropical gyres do not show particularly distinct
seasonal variations. The most striking seasonal change in
the eastern boundary currents is the variation of the Benguela
Current in the Atlantic Ocean, showing more intense flow in
boreal winter than in boreal summer. This may be associated
with the seasonal change in eddy shedding from the Agulhas
retroflection region (Zlotnicki et al., 1989; Shum et al., 1990).
The tropical Pacific is also a region where significant
seasonal variabilities appear. To see the variabilities more
precisely, we made finer resolution velocity maps with 1° ×
1° grids as shown in Fig. 14. In the eastern region, the most
significant feature is the weakening of the NECC in boreal
spring, in response to the weakening of the trade wind. The
circulation in the western tropical Pacific shows a complex
structure. The most interesting feature is that the southward
branch of the NEC feeds the Indonesian throughflow in
boreal spring and summer whereas it joins the NECC and the
eastward New Guinea Coastal Current (NGCC) in boreal
autumn and winter. The NGCC flows westward to join the
NECC in boreal spring and summer. These features are
similar to the modeling results of Miyama et al. (1995).
Although interesting seasonal changes are expected to occur
in other tropical oceans as suggested by Philander (1990),
lack of the data prevents our investigation there.
5. Discussion
5.1 Comparison with coarse resolution maps
Our velocity and energy maps derived from the drifting
buoy data are processed with finer spatial resolution data
than have been previously available (e.g., 5° in Patterson
(1985) and 4° in Piola et al. (1987)). To illustrate this advantage, we have derived an MKE map in the North Pacific
on a 5° × 5° grid to compare with that from the 2° × 2° grid.
Figure 15A shows the MKE on a 5° × 5° grid for the
North Pacific. It is obvious that the Kuroshio becomes
unclear in this case. This is due to the fact that the narrow jets
such as the Kuroshio current and Gulf stream cannot be
resolved with such a coarser grid. We further examine the
dependence of its reliability on the grid size, using the S/N
ratios of MKE (Fig. 15B) and EKE (not shown). Since the
error of the mean field is determined by the variance of
velocities (Eq. (10)), the S/N ratio of the coarse grid MKE
decrease in the narrow jet regions. In fact, the S/N ratios in
the Kuroshio region for the 5° × 5° grid (Fig. 15B) are much
Global Surface Circulation from Drifting Buoy Data
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Fig. 11. Same as Fig. 5 but for the annual mean of the eddy kinetic energy (EKE).
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Global Surface Circulation from Drifting Buoy Data
507
Fig. 12. Spatial distributions of (A) the low frequency part of the EKE (LFEKE) and (B) the high frequency part of the EKE (HFEKE).
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509
Fig. 13. The seasonal mean global velocity maps for the surface current in (A) winter (Jan.–Mar.) and (B) summer (Jul.–Sep.). The
velocity vectors are plotted for regions with S/N ratio larger than 1.
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511
Fig. 14. The seasonal mean currents in the tropical Pacific with 1° resolution for (A) winter and (B) summer. The velocity vectors are
plotted for regions with S/N ratio larger than 1.
Fig. 15. (A) The spatial distribution of the kinetic energy of mean flow (MKE) in the North Pacific region with 5° resolution (unit in
cm2s–2 ). (B) S/N ratio of MKE shown in Fig. 15A.
smaller than those for the 2° × 2° grid (Fig. 5B). Thus the 5°
grids used in previous studies are inadequate to resolve the
reliable jet-like current structures. In the case of EKE, it is
easily understood from Eqs. (14), (17) and (18) that the S/N
ratio should increase with increasing grid size (the number
of the data in each grid). Actually, the S/N ratio of the EKE
with 5° × 5° grids is over 2 in a very broad region (not
shown). However, it should be noted that the EKE includes
both spatial (subgrid scale) variation of the surface current
(see Eq. (8)) and temporal variation.
5.2 Comparison with other data
There are several methods of surface current observation. Wyrtki et al. (1976) (henceforth WMH) obtained the
global distribution of kinetic energy from historical data of
ship drift (figures 3 and 4 of Wyrtki et al. (1976)). Although
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the MKE and EKE distributions of our results are consistent
with those of WMH, on quantitative comparison, the latter
shows smoother distributions because the grid size selected
by WMH is rather coarse (5°) and also the area covered by
the ship-drift data is broader than that of the drifting buoys
(Patterson, 1985). Despite smoother distributions, the western
boundary currents appear as maximum bands of MKE in
WMH. This is because ship traffic would routinely navigate
either to take advantage of the boundary current or to avoid
it. Thus, as Patterson (1985) suggested, high speed currents
such as the western boundary current tend to be emphasized
in the WMH map.
In general, the MKE and EKE values in WMH are
smaller than those from the drifting buoy data in high energy
regions. For example, the MKE level in the eastern tropical
Pacific is 500 cm2s–2 in the ship-drift map but 1000 cm2 s–2
Fig. 15. (continued).
in this study. The EKE value shows a similar tendency (e.g.,
1000 cm2s–2 with ship-drift data and 2000 cm2s–2 with the
buoy data). However, the MKE and EKE values from shipdrift data are greater than those from drifter data in the low
energy area (e.g., the EKE is 400 cm2s–2 with ship-drift data
and 200 cm2s–2 with drifter data). This is explained by
Richardson (1983) as follows. The energy distribution in
WMH can not resolve mesoscale eddies because ship-drift
data are averaged over a 1-day navigation period corresponding to about 400 km. Hence the energy from ship-drift
data tends to lower in the high energy region. In the low
energy region, inaccuracy in the determination of ship-drift
velocity creates an apparent EKE. This noise-induced apparent EKE makes the EKE of WMH higher by approximately 200 cm2 s–2. Patterson (1985) also noted that the EKE
map of WMH shows the energy distribution mainly for low
frequency fluctuations such as the seasonal variation.
Next, eddy kinetic energy obtained from the Geosat
altimeter data (e.g., Shum et al., 1990) is compared with the
EKE in this study. While there are some discrepancies
between the characteristics of these two data, the maps (not
shown) indicate a good agreement qualitatively except for
the tropical region (within about 10° of the equator) where
the geostrophic assumption cannot be applied to the altimetric
data. With quantitative comparison, the EKE obtained from
the altimeter is smaller than that from the buoy data. For
example, in high EKE areas (greater than 2000 cm2s–2) such
as the Gulf Stream and the Agulhas Current, the altimeter
data indicate an energy smaller than that for the buoy data.
This is due to the long interval of the altimetric measurement
(17 days in the case of Geosat) which causes a cut off in the
high frequency component. It may also be attributed to the
ageostrophic component, i.e., Ekman drift. In fact, Daniault
and Ménard (1985), who compared the EKE from buoy data
Global Surface Circulation from Drifting Buoy Data
513
with that from Seasat altimeter data measured every 3 days,
showed a similar result. They also examined the band-pass
filtered EKE from the buoy data, which corresponds to the
sampling interval of the Seasat altimetry, and found a better
agreement in both cases. Though this result seems to imply
that the ageostrophic component is not important, it should
be noted that the ageostrophic component contributes
mainly at the higher frequencies whose amplitudes were
much reduced by the band-pass filter used in their study.
5.3 Comparison with numerical models
Comparison of the mean and variable states of the
surface current from the drifting buoy data with those from
numerical models is an effective way of examining the
accuracy of model representations. This information can be
used to make models more realistic (e.g., Mellor and Ezer,
1991; Ishikawa et al., 1996). Here, we choose results from
the following numerical models for comparison; the global
model of Semtner and Chervin (1992) (henceforth SC model),
the Fine Resolution Antarctic Model (FRAM Group, 1991)
in the southern oceans, and the North Atlantic World Ocean
Experiment (WOCE) model (Böning et al., 1991). All of
these models are eddy resolving general circulation models
(EGCM) designed with the goal of reproducing realistic
ocean circulation and including mesoscale variability.
While model eddy kinetic energy has often been compared with that derived from a variety of observations, only
one comparison of the mean kinetic energy between models
and buoy observations (Piola et al.,1987) has been made by
Garraffo et al. (1992) in the southern oceans. In addition,
their map is too coarse to represent precisely the distribution
of mean kinetic energy. Therefore, the distributions of
kinetic energy on a 2° × 2° grid for the global ocean and on
a 1° × 1° grid for the specified regions in this study are
compared with the results of these numerical studies.
First, a synoptic view of the mean surface current is
compared with the SC model results. The major difference
between our result and the model output is that the modeled
separation point of the Gulf Stream and the Kuroshio current
is rather to the north. This is often seen in many of numerical
models and also occurs in the WOCE model. Other marked
differences from the SC model result from the use of
modified coastal lines in the model, e.g., the submerging of
the Indonesian islands, the connection of the Madagascar
Island to the Africa Continent, and the artificial boundary in
the northern part of the North Atlantic. These modifications
are expected to alter the circulation even in distant but
dynamically connected regions as well as within the modified
region itself. For example, the SEC in the Indian Ocean
tends to be reinforced. Except for these differences, the two
maps are fairly consistent as far as a qualitative and synoptic
comparison is concerned.
For more detailed and quantitative comparison, the
Gulf Stream region in the WOCE model (Treguier, 1992)
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Y. Ishikawa et al.
and the Kuroshio/Oyashio region and the South Atlantic in
the SC model (Garraffo et al., 1992) are selected. In the Gulf
Stream region, the WOCE model gives unrealistic eddies at
the separation point (not shown). The modeled mean kinetic
energy level is about half the value of our result except for
the unrealistic eddies, despite the fact that the model grid
size is smaller than in this study and is therefore expected to
lead to larger mean kinetic energy.
In the Kuroshio current region, the MKE of the SC
model (figure 11 of Garraffo et al. (1992)) is larger than that
in this study, being over 2000 cm2s–2 in the SC model and
about 1000 cm2s–2 in our results. The MKE in the southern
part of the Kuroshio extension in the model is of a similar
energy level to that in our study whereas the MKE in the
northern one is much lower. On the other hand, the EKE in
both northern and southern parts of the extension region in
the SC model is much lower, particularly in the upstream
region.
In the Agulhas Current region, both the SC model and
our result show a discontinuity of the energy maximum band
at its retroflection point. The energy level of this maximum
band is at almost the same level as in this study but in other
regions it is lower by a factor of ~2. In particular, the eastern
boundary current in the South Atlantic, the Benguela Current is not seen in the model result, the energy levels of
which is greater than 200 cm2s–2 (corresponding to 20
cm s–1) in our result. The reason for this can be interpreted
as follows. The buoys in this region come from the ACC
region. Some of these buoys flow directly into this current
and others are engulfed in the eddies associated with the
Agulhas retroflection and then join the Benguela Current.
This implies that the eddies in the Agulhas retroflection
region are related to the formation of the Benguela Current
and hence such a weak eddy activity in the model is the cause
for the poor reproduction of this current.
Comparison of the eddy kinetic energy derived from
the buoy data in this study with that of the SC model shows
that the eddy kinetic energy of the model is much less than
that from the buoy data. For example, the energy level
obtained from the buoy data in the Agulhas retroflection
region reaches 2000 cm2s–2 while that in the SC model is 500
cm2s–2. This result is consistent with those of Garraffo et al.
(1992) and Wilkin and Morrow (1994) who compared the
distributions of eddy kinetic energy from surface currents of
the SC model with that from altimetry in both the south
Atlantic and whole southern ocean, respectively. They
concluded that the peak energy from the model result is less
than that from the altimetry by a factor of 4. Wilkin and
Morrow (1994) further showed that in the region of low
eddy energy, model results indicate an energy level lower by
a factor of 10, similar to the results from the comparison
between the WOCE model and altimetry in the North
Atlantic (Spall, 1990; Stammer and Böning, 1992).
6. Summary
Our study has successfully obtained the global surface
current and its kinetic energy distribution using 2° × 2° grids
(1° × 1° grids in specified regions) based on archived drifting buoy data archived from the MEDS and the JODC. The
large number of data points permits us to make a finer scale
map than obtained in previous studies (e.g., Wyrtki et al.,
1976). Since the distribution of the mean and the eddy
kinetic energy is significantly affected by spatial resolution
(grid size), our finer scale maps provide a more realistic
description of the global surface circulation than before. For
example, the jet-like structures of the western boundary and
equatorial currents, which cannot be resolved with coarser
resolution in the previous studies, are well reproduced.
Features in the seasonal current field have also been
examined. The result revealed outstanding seasonal variabilities such as flow reversal in the Indian Ocean and the
tropical Pacific. The circulation in the western tropical
Pacific shows quite complex seasonal variabilities. The
seasonal variability of the western boundary currents of
subtropical gyres such as the Kuroshio and the Gulf Stream
is at a low level whereas the western boundary currents in
subpoler gyres such as the Oyashio and the Labrador Current show significant seasonal variability.
We divided the kinetic energy into two parts: the
energy of mean circulation (the mean kinetic energy) and
that of variable component (the eddy kinetic energy). These
maps reveal that the mean kinetic energy is greater than
1000 cm2s–2 in the western boundary currents and their
extensions, the equatorial current, and in the ACC region. In
these regions, the eddy kinetic energy is of comparable order
to the mean kinetic energy (more accurately, somewhat
larger than the mean energy), suggesting the presence of
strong interactions between the mean flow and the eddies.
The eddy field was obtained compared with that from
altimeter data (e.g., Shum et al., 1990). While there are some
discrepancies between the nature of these two data sources,
our comparison shows qualitatively good agreement except
within the tropical region where the error of the eddy field
estimated from the altimeter data is amplified due to the
breakdown of the geostrophic assumption. Generally, the
energy level of the altimeter data tends to be smaller than
that from the buoy data because of the long sampling
interval of altimetric observations and the disregard of the
ageostrophic velocity component.
The eddy kinetic energy was further divided into low
and high frequency parts (corresponding to seasonal and
intraseasonal variations, respectively). In the tropical Pacific, the low frequency component dominates, especially in
the western Pacific where significant seasonal change occurs
in relation to the Asian Monsoon. In the western boundary
current and its extension region, the low frequency component
is more visible on the upstream (i.e., near the coast). This is
primarily due to the seasonal migration of the separation
point. However, such features become unclear on the
downstream side. Instead, the high frequency component is
dominant on the downstream side, representing the generation
and growth of eddies associated with meanders of the zonal
jet.
The model results by Semtner and Chervin (1992), the
FRAM group (1991), and the WOCE community (Böning et
al., 1991) were compared with our result. The synoptic view
of the mean circulation of the models is in rather good
agreement with our drifting buoy data, while its energy level
is somewhat low. In the eddy field, model results are very
quiet, i.e., the energy level in the eddy field is much smaller
(by a factor of ~5). The difference of the energy level is
larger than that in previous studies using altimeter data.
Our study shows that drifting buoy data are quite a
useful means of understanding realistic features in the
global surface circulation. An effective means of further
investigation would be to combine drifting buoy data with
other methods such as the altimeter data and numerical
models. For this, however, many drifting buoys need to be
deployed, especially in the interior regions of gyres and in
the subpolar region, in order to gain a more realistic view of
ocean circulations.
Acknowledgements
We express our hearty thanks to the Marine Environmental Data Service in Canada and the Japan Oceanographic
Data Center for their offers of drifting buoy data. We also
thank the international drifter community for their courtesy
in providing the sources of the data available to us. These
valuable data were collected as part of many scientific
programs (e.g., NORPAX, WEPOCS, and WOCE). Our
thanks are extended to a co-editor and two anonymous
reviewers for their invaluable comments on the first version,
and to Dr. J. P. Matthews for his critical reading of our
manuscript. Numerical calculations were done on the
FACOM M1800 at the Data Processing Center of Kyoto
University.
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