Submesoscale Eddies in the Taiwan Strait Observed by High-FrequencyRadars: Detection Algorithms and Eddy Properties
YEPING LAI, HAO ZHOU, JING YANG, YUMING ZENG, AND BIYANG WEN
School of Electronic Information, Wuhan University, Wuhan, China
(Manuscript received 16 August 2016, in final form 23 February 2017)
ABSTRACT
This study compared the efficiencies of two widely used automatic eddy detection algorithms—that is, the
winding-angle (WA) method and the vector geometry (VG) method—and investigated the submesoscale
eddy properties using surface current observations derived from high-frequency radars (HFRs) in the Taiwan
Strait. The results showed that the WA method using the streamline and the VG method based on the
streamfunction field have almost the same capacity for identifying eddies, but the former is more competent
than the latter in capturing the eddy size. The two algorithms simultaneously identified 1080 submesoscale
eddies, with the centers and boundaries determined only by the WA method, and they were further used to
investigate the eddy properties. In general, no significant difference was observed between the cyclonic and
anticyclonic eddies in terms of radius, life span, and kinematics, as well as the evolution during their life cycles.
The typical radius of the eddy in this region was 3–18 km. And a strong correlation was observed between the
life span and the radius. The spatial distribution of the eddies indicated that topography played a significant
role in the generation of the eddies. And the trajectories of the eddies suggested that all the eddies in this area
mostly tended to move southeastward. Statistically, three different stages of the eddy’s life span could be
identified by the significant growth and decay of the radius and the mean kinetic energy. This study shows the
great capability ofHFRs in oceanography research and applications, especially for observing the submesocale
dynamics.
1. Introduction
A lateral current structure with the velocity vectors
rotating clockwise or counterclockwise around a center
is referred to as an eddy or a vortex appearing in the
upper ocean frequently and ubiquitously. It is generally
more energetic than the surrounding currents. The di-
ameters of such eddies vary substantially from a few
hundred meters to hundreds or thousands of kilometers.
These eddies, characterized by anO(1) Rossby number,
are largely formed over the shelf and coastal slope de-
pendingmuch on the bottom topography and the coastal
orography (Zatsepin et al. 2011). Eddies are an impor-
tant component of dynamical oceanography, making a
significant contribution to the transportation of heat,
mass, momentum, and biogeochemical properties
(Mcwilliams 2008; Wang et al. 2012; Simons et al. 2015),
and they are an important cross-isobath transport
mechanism for nutrients, particles, and larvae (Bassin
et al. 2005). Moreover, eddies can have a profound in-
fluence on offshore advection, dispersion of river plumes
(Corredor et al. 2004), buoyant substances, and pollut-
ants (Chérubin and Richardson 2007). In addition, in-
creasing coastal activities, such as fisheries, pollution
monitoring, and offshore industry, also raise the need
for studying eddy properties as well as the interactions
between eddies and inshore circulation to produce re-
liable hydrodynamic forecasts of littoral water.
The study area is located in the southern Taiwan Strait
(Fig. 1), which has a quite uneven topography. The
water depth is less than 30m along Fujian coast, about
40–60m in the offshore, and greater than 1000m in the
southeastern area. The current pattern in this area is also
quite complicated. Hu et al. (2010) has summarized the
evolution of the investigation about the current circu-
lation in this area as well as its surroundings. There are
three flows coexisting in the Taiwan Strait: the extension
of the South China Sea warm current (SCSWCe) flowing
northeastward, the Zhemin Coastal Current (ZCC)Corresponding author e-mail: Hao Zhou, [email protected]
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coming from the northeast, and the Kuroshio intruding
from the Pacific (Fig. 1). Moreover, the SCSWCe and
the ZCC flow through the Taiwan Strait with the op-
posite current directions. Therefore, with complex to-
pography and intricate flow, the southern Taiwan Strait
is an area with strong eddy activities.
In the past decades, several eddies have been captured
by in situ observations in our study region and its sur-
roundings, including an anticyclonic eddy located at
218N, 117.58E with a scale of some 150km and a vertical
extension as deep as 1000m (Li et al. 1998), and three
long-lived anticyclonic eddies (Nan et al. 2011). Un-
doubtedly, in situ measurements havemade tremendous
contributions for oceanographers to understand the
formation mechanisms of eddies. However, statistical
characteristics of eddies are quite difficult to gain from
in situ instruments owing to the limited coverage. For-
tunately, in recent years high-precision satellite altime-
ters coming into use have essentially revolutionized our
capacity for observing ocean processes, which has made
striking progresses in our understanding and modeling
of ocean circulations. Satellite altimeter data for sea
surface height anomalies (SSHA) or sea level anomalies
(SLA) have been extensively applied to study the
statistical characteristics of surface eddies (Liu et al.
2012; Chelton et al. 2011; Chen et al. 2011; Chaigneau
et al. 2008; Wang et al. 2003). Properties like radius,
lifetime, vorticity, and spatial distribution have also
been discussed in these studies.
The satellite altimeters have made a great contribu-
tion toward oceanographers’ study of ocean processes.
However, some researchers argued that submesoscale
eddies with a radius smaller than 30km cannot be
identified and extracted from satellite altimetry but can
be captured by high-frequency radars (HFRs), which
can measure ocean surface current over a large hori-
zontal extent with a high spatial–temporal resolution.
Chavanne and Klein (2010) compared sea level anom-
alies obtained from satellite altimeter with those derived
from HFRs, and they suggested that satellite altimeter
cannot observe the submesoscale process due to the
signal contamination from high-frequency motions, in-
coherent internal tides, and cross-track currents mea-
surement noise. Pomales-Velázquez et al. (2015) studiedthe characteristics of mesoscale and submesoscale
eddies in southwestern Puerto Rico using satellite im-
agery (i.e., sea surface height anomalies, chlorophyll-a,
and floating algae index images) and surface currents
sensed by HFRs. They found that a submesoscale eddy
lasting for 3 days was not resolved by satellite altimetry
products but captured by HFRs. In this study, we used
two shore-based HFRs to investigate the characteristics
of the submesoscale eddies in the southern Taiwan Strait
(Fig. 1). Although the HFR technology has been used to
study the current characteristics in the southern Taiwan
Strait (Shen et al. 2014; Lai et al. 2017), this is the first
time for it to be used to study the submesoscale eddy
properties in this region. The results showed the great
capability of the HFR in oceanographic researches and
applications, especially for the observation of sub-
mesocale dynamics.
Besides the observation tool, competitive eddy de-
tection algorithm is also vital for eddy characteristics
analysis. Numerous schemes for automatic eddy de-
tection have been proposed, based on either physical or
geometric properties of the flow field (Jeong andHussain
1995; Portela 1997; Sadarjoen and Post 1999). Schemes
based on physical properties compare the values of a
specified physical parameter with a preset threshold, in-
cluding pressure and sea level anomalymagnitude (Jeong
and Hussain 1995; Fang and Morrow 2003; Chaigneau
and Pizarro 2005), vorticity (Mcwilliams 1990), and var-
ious quantities derived from the velocity gradient tensor
(Morrow et al. 2004; Isern-Fontanet et al. 2003). On the
other hand, techniques based on the geometric criteria
are also numerous: the winding-angle (WA) method
(Sadarjoen and Post 2000, 1999; Sadarjoen et al. 1998),
FIG. 1. Orientation map of the study area and its surroundings.
Summarized upper-layer current pattern in the Taiwan Strait
during the winter is shown schematically as arrows (the dataset
used in this study was collected in the winter; see section 2a).
SCSBK andKETe denote the South China Sea branch of Kuroshio
and the Kuroshio’s eastern Taiwan Strait’s extension, respectively
[redrawn according to Fig. 9a in Hu et al. (2010)]. Thin gray lines
are contour lines of the ocean depth [m; the bathymetry data were
taken from ETOPO1 (Amante and Eakins 2009)]. The two red
dots represent the locations of the two radar sites (XIAN and
SHLI). The area marked by the black rectangle is the region we
focus on in this study (23.158–24.358N, 117.408–118.908E).
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the vector geometry (VG) method (Nencioli et al. 2010),
the vector pattern matching (Heiberg et al. 2003), the
Clifford convolution (Ebling and Scheuermann 2003),
and the feature extraction (Guo 2004). A comparison
between the physical-parameter-based methods and the
geometry-based methods suggested some limitations
of the former, which failed to detect some obvious eddies
and tended toward regarding a nonvortical structure as an
eddy (Chaigneau et al. 2008; Sadarjoen and Post 2000).
Among all the geometry-basedmethods, theWAmethod
and the VGmethod are considered to be the primary and
the most widely used geometrical techniques for eddy
detection in oceanography. Unfortunately, there is no
literature providing a comparison of them. Thus, another
goal of this study is to compare these two geometrical
eddy detection methods.
For the above-mentioned goals, we first compared the
WA and VG methods. After establishing the suitability
of theWAmethod to extract eddies from a flow field, we
applied it to investigate eddy activities in the southern
Taiwan Strait using the current fields observed by two
shore-basedHFRs. The paper is organized as follows. In
section 2, we describe the HFR dataset, the two eddy
identification algorithms, the eddy attribute determina-
tion, and the tracking algorithms. Section 3 compares
the eddy detection results from both eddy detection
schemes. The mean eddy properties in the study region
are dealt with in section 4. And a summary of the results
is provided in section 5.
2. Data and method
a. HFR data
From 11 January to 31 March 2013, two HFRs named
Ocean State Measuring and Analyzing Radar, type S
(OSMAR-S), were deployed at SHLI (248090500N,
1178590000E) and XIAN (238440300N, 1178360100E) in
Fujian Province, China, to observe the surface current of
the southern Taiwan Strait, as shown in Fig. 1. The
OSMAR-S, a direction-finding HFR, is equipped with a
compact cross-loop–monopole antenna for receiving. A
linear frequency-modulated interrupted continuous
wave (FMICW)-type waveform is adopted with a center
frequency of 13MHz and a bandwidth of 60 kHz. The
range resolution is correspondingly 2.5 km. Table 1
provides the specific settings of the OSMAR-S. During
the observation period, the two radars were 60.5 km
apart. A raw radial current velocity map is obtained
every 6.5min, and three successive sparse radial maps
are combined to achieve a final radial map with an in-
terval of 20min. Then, the final radial current maps from
the two sites at the same time were synthesized to give
total vector current maps on a Cartesian grid. In this
study, 20-min total vector current maps were achieved
on a 32 3 34 longitude–latitude grid covering from
23.258 to 24.188N and from 117.638 to 118.628E with a
spacing of 0.038 in both dimensions.
A series of experiments have proved the accuracy and
reliability of the current and wave products extracted by
theOSMAR-S system (Wen et al. 2009; Zhou et al. 2014,
2015; Wei et al. 2016). Here, the temporal coverage rate
of the dataset, as shown in Fig. 2, was calculated at every
cell as the proportion of time instants when there is a
valid vector current measurement (invalid solutions
were mainly caused by interruptions, system calibra-
tions, and short-duration system malfunctions). It shows
that most cells, except for a very small number of cells at
the edge of the radars’ detection area, have a temporal
coverage rate greater than 0.8. An intercomparison of
TABLE 1. Major technical parameters for OSMAR-S current
measurements.
Parameter Setting
Transmit frequency (MHz) 13
Transmit bandwidth (kHz) 60
Maximum detection range (km) 120
Sweep period (s) 0.38
Nominal range resolution (km) 2.5
Nominal bearing resolution (8) 3
Radial current resolution (cm s21) 5.5
Time resolution (min) 20
No. of transmit antenna elements 1
No. of receive antenna elements 3
Average transmitter power (W) 100
Transmitted waveform FMICW pulses
Technique of azimuthal resolution Direction findingFIG. 2. Spatial distribution of the temporal coverage rate. The
two red dots represent the locations of the two radar sites (XIAN
and SHLI). The two small black triangles indicate the locations of
two buoys (A and B), which are equipped with ADCP for mea-
suring current velocity.
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this dataset with current vectors measured by two
moored acoustic Doppler current profilers (ADCPs)
was conducted. The locations of the radar sites and the
two ADCPs can be seen in Fig. 2, and the comparison
results are shown in Fig. 3. It can be seen that the u–y
components of the currents measured by the HFRs
coincide well with those by the ADCPs (Fig. 3). The
correlation coefficients reach up to 0.92 and the root-
mean-square errors (RMSEs) are smaller than 0.18ms21.
These correlation coefficients indicate a comparable per-
formance between OSMAR-S and the Coastal Ocean
Dynamics Applications Radar (CODAR; Liu et al. 2014),
but the RMSE values are slightly higher than the recent
CODAR’s comparison result (Liu et al. 2014), which is
mainly attributed to different external noise (Merz et al.
2015). Thus, these intercomparison results show the high
quality of the radar measurements, indicating that the
dataset is suitable for further applications. In particular,
this dataset has been used to study the regional tidal and
residual current characteristics (Lai et al. 2017).
According to the existing literature, only a very small
number of submesoscale eddies observed by HFRs can
survive longer than a day (Pomales-Velázquez et al.
2015; Kim 2010). This means that we should reserve the
high-frequency components of the currents measured by
the HFRs and take full advantage of the high temporal
resolution of the HFRs. Therefore, within the eddy
detection procedure, no time averaging or smoothing
was imposed on the 20-min interval vector current maps.
b. Eddy detection schemes
Among all the documented eddy detection schemes,
two methods are counted as the primary geometrical
techniques for eddy identification in oceanography,
which are independent of physical parameters and ex-
clusively based on the geometry properties of the flow
field: one is the WA method developed by Sadarjoen
and Post (2000) and the other one is the VG method
proposed by Nencioli et al. (2010).
1) VG METHOD
When the VG method was developed, it was con-
firmed that it can be applied to detect eddies for HFR-
derived velocity fields (Nencioli et al. 2010). The VG
method was purely based on the geometry features of
velocity vectors that depict the vector current field re-
lated to eddy patterns. For example, there is a minimum
velocity near the eddy center, and the tangential velocity
increases approximately linearly with distance from the
center before reaching a maximum value and then de-
caying (Nencioli et al. 2010, 2008).
There are only two steps for the VG method to de-
termine an eddy structure. The first step is to identify the
eddy center, which follows four constraints: 1) along the
FIG. 3. Time series of the current vectors’ u–y components—(a),(b) Au and y, respectively;
and (c),(d) Bu and y, respectively— measured by the HFRs (red) and the buoys (blue). Cor-
relation coefficient r and RMSE are shown at the top of every panel.
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east–west section, the north–south component of the
current velocity reverses in sign across the eddy center
and its magnitude increases away from the center;
2) along the north–south section, the east–west compo-
nent of the current velocity reverses in sign across the
eddy center and its magnitude increases away from the
center; 3) there is a local minimum of the velocity
magnitude at the eddy center; and 4) the direction of the
vector current around the eddy center changes with
the same trend and two neighboring vectors lie within
the same or two adjacent quadrants (which are defined
by the north–south and west–east axes). Two parame-
ters need to be specified to implement these constraints.
The first parameter, for the first, second, and fourth
constraints, is referred to as a, defining the positions
where the magnitudes of the north–south (east–west)
component along the east–west (north–south) axes are
checked, and also determining the curve around the
eddy center along which the change in direction of the
velocity vectors is inspected. The second parameter, for
the third constraint, is referred to as b, defining the di-
mension (in grid points) of the area used to search for
the local minimum of velocity. The sensitivity tests of
the detection algorithm for different values of these two
parameters can be found in Nencioli et al. (2010), which
reported a 5 3 and b 5 2, which can offer a relatively
higher success of detection rate (SDR) and a lower ex-
cess of detection rate (EDR). Furthermore, the values of
a5 3 and b 5 2 were also adopted by other researchers
to identify the eddy structures, such as Liu et al. (2012),
Pomales-Velázquez et al. (2015), and Lin et al. (2015).
Therefore, we also used these values in this study.
The second step is to compute the eddy boundary,
which is defined as the outermost closed contour line of
the streamfunction field around the center. The
streamfunction at a given position (i, j) is computed as
c(i, j)5
ð (i, j)
(0,0)
2y dx1 u dy,
where u and y are the Cartesian velocity components of
the vector currents observed by the HFRs. For more
implementation details, one can refer to Nencioli
et al. (2010).
2) WA METHOD
The WA method is motivated by the concrete defi-
nition of a vortex provided by Robinson (1991), which is
described as instantaneous streamlines exhibiting a
roughly circular or spiral pattern around a center. In
fact, this definition is consistent with the one assumed by
the VG method. The WA method tries to determine an
eddy structure by a point, which defines its center, and
looped streamlines, which correspond to the eddy edge.
The center of the looped streamlines is approximated to
the eddy center for this method (Sadarjoen and
Post 2000).
Thus, the process of detecting eddies with the WA
method for each flow field observed by the HFRs consists
of three main stages: computing streamlines, selecting
streamlines associated with eddies, and clustering the
distinct streamlines corresponding to the same eddy.
Considering the high spatial resolution of our dataset,
there were no more spatial interpolations and the
streamlines were computed on every 0.038 3 0.038 gridpoint. For each streamline, the step size used was 0.1
(corresponding approximately to 0.35km) and the maxi-
mum number of vertices was 10000. Thus, the maximum
length of a streamline was set at 3500km, which allows for
circling around the observation region boundary 10 times
and guarantees enough length for a streamline with an
outward expansion spiral pattern. After the streamlines
for a flow field have been computed, they were selected
according to the criterion of the winding angle being
greater than or equal to 2p. The winding angle is defined
as the cumulative change of the directions for the seg-
ments on each streamline [a schematic representation of
the winding angle can be found in Sadarjoen and Post
(2000) and Chaigneau et al. (2008)]. Then, the selected
streamlines were grouped and combined into a distinct
number of clusters. Streamlines belonging to the same
cluster were considered to be part of the same eddy. To
determine the eddy boundary, the ellipse fitting was done
on all streamlines within an eddy. And the fitting pro-
cedure is similar to the one used in Sadarjoen and Post
(2000), but some modifications were conducted (see the
appendix for more details).
c. Specific eddy attributes determination
The two eddy identification algorithms described
above were applied to the entire HFR dataset to detect
eddy structures. After an eddy was identified, several
eddy properties were computed. The eddy radius R was
calculated as the mean distance from the center to every
point on the boundary. The eddy area A corresponding
to the area delimited by the eddy boundary was ap-
proximated to a circular area with an equivalent radius
equal to R. In addition, the eddy kinetic energy (EKE)
was calculated by the classical relation
EKE51
2(u2 1 y2) ,
where u and y are the velocity components derived di-
rectly from the HFRs. The mean eddy kinetic energy
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(MEKE) was defined as the average kinetic energy
within an eddy area,
MEKE5EKE
A.
To investigate the principal eddy kinematic properties,
we also computed their vorticity and deformation rates.
First, in the local Cartesian coordinate system, the gra-
dients of the velocity components were
g115
›u
›x, g
125
›u
›y, g
215
›y
›x, and g
225
›y
›y.
By these gradients, we can denote the vorticity
z 5 g212 g
12,
the shearing deformation rate
ss5 g
211 g
12,
the stretching deformation rate
sn5 g
112 g
22,
the total deformation rate
s5ffiffiffiffiffiffiffiffiffiffiffiffiffiffis2s 1 s2n
q,
and the divergence
c5 g111 g
22.
d. Eddy-tracking algorithm
After eddies were identified during the entire period
of the observation, eddies were tracked by comparing
the eddy centers at successive time intervals, starting
from the first sampling time. An eddy track usually
lasts more than one observation interval (20min in this
study); hence, the number of eddy tracks is much
smaller than the amount of eddies. The eddy-tracking
algorithm employed in this study is adapted from that
introduced by Nencioli et al. (2010). The track of a
given eddy at time step t was updated by searching
eddy centers of the same type (cyclonic or anticy-
clonic) at time t 1 1. And a searching radius of 12 km
was chosen for HFRs that generally have a bearing
offset of about 108 (Liu et al. 2010; Paduan et al. 2006),
which corresponds to a 12-km spatial offset at a de-
tection range of 70 km (the detection range of the
HFRs used here is 60–80 km, which was determined by
the external noise). If any center was not discovered
within the searching area at t1 1, then a second search
was performed at t 1 2 with a searching radius being 1.5
times as large as the search radius at t 1 1. The current
eddywas supposed to vanish when therewas no update at
t 1 2. In addition, if an eddy was not connected to any
center identified in the previous two time steps, then it
was considered to be a new eddy.
3. Comparison between the VG and WA eddydetection methods
It is not a trivial task to make an objective assessment
of the eddy detection algorithms due to the absence of a
dataset in which the eddy distribution is definitely
known. Moreover, manual eddy detection, even by ex-
perts, shows a varying number of results (Chaigneau
et al. 2008) due to the challenges in identifying the rel-
atively small features. Therefore, we compared those
two detection methods by means of eddy detection re-
sults (eddy positions and radii) from the same dataset
rather than evaluating the SDR or EDR.
During the observation period, 1275 and 1350 eddies
were identified by the VGmethod and the WAmethod,
respectively, and the total number of eddies identified
by both methods was 1080 with 546 cyclones and 534
anticyclones. They were confirmed by the type, time
instant, and location. Figure 4 shows two eddies identi-
fied by the two algorithms. Unfortunately, the eddies
observed by the HFRs are unable to be verified by ob-
servations from other sensors due to the absence of a
measurement, whose temporal–spatial resolution is
comparable with the HFR dataset.
Figure 5 exhibits the separation distance of the eddy
centers determined by the VG method and the WA
method. The histogram has a peak located at 1 km, and a
steep decrease for a distance greater than 1km can be
seen clearly. The average separation distance between
the results from these two eddy detection methods was
2.6 km, which was less than the spatial resolution (the
spatial resolution is about 3km for the data used in this
study). Thus, the offset of eddy locations determined by
the two methods was insignificant. And this can also be
seen in Fig. 4, in which the centers determined by the
two methods are close. On the other hand, it is well
known that vorticity within an eddy varies from its
center to its boundary. Furthermore, the magnitude of
the vorticity is maximum at the center and reaches zero
at its boundary theoretically. Thus, we checked the
distance between the eddy center’s position and the
maximum magnitude of the vorticity within a minimum
rectangular region exactly covering both eddy bound-
aries determined by the VG and WA methods. The
distributions of the distance shown in Fig. 6a are close
to aGaussian distribution with a subtle slant on the large
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FIG. 4. Two examples of eddy detection. Current velocity field observed by theHFRs at (a) 0600UTC 12 Jan 2013
and (b) 0320 UTC 17 Jan 2013. (c),(d) Contour lines of the streamfunction (thin lines) and eddy boundary (thick
circle) derived from the VGmethod associated with the flow fields in (a),(b). (e),(f) Instantaneous streamlines (thin
lines) and eddy boundary (thick circle) derived from the WA method corresponding to the flow fields in (a),(b).
Stars in (c)–(f) indicate the eddy center computed by the relative algorithms.
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values for both the VG method and the WA method.
The agreement between the two eddy identification
methods also verifies that the eddy centers determined
by the two methods were very close. The average dis-
tances between the maximum magnitude of vorticity
and the eddy centers ascertained by the two schemes
were almost equal to 22 km, which is up to 7 times as
large as the spatial resolution. Evenmore amazingly, the
distance variation as a function of the eddy radius was
increasing, as shown in Fig. 6b. It indicated that a max-
imum of vorticity was located outside of the eddy
boundaries. Therefore, the adoption of vorticities as a
criterion for eddy centers is inadvisable. In summary, the
idea of estimating an eddy center by vorticity is unwise,
and the number of detected eddies and its center de-
termined by the two methods suggest that the VG and
WA methods have almost the same capacity for
identifying eddies.
The eddy boundary is another necessity for depicting
an eddy that combines the center defining the eddy
within a flow field. Thus, it is necessary to inspect the
boundary for the same eddy picked out by both the VG
method and the WA method. However, it is rather in-
convenient to compare the veritable boundaries. For-
tunately, the eddy size corresponding to its radius is a
quantitative property that can be a substitute for the
boundary and is easy to compare. The distribution of the
radius difference (radius derived from the WA method
minus that computed by theVGmethod) shown in Fig. 7
indicates that the radius difference varied on a large
scale with a ratio of 20% when it is larger than 5km and
32% when it is larger than 3.5 km. Given the relatively
small size of the eddy in this study (see the radius dis-
tribution in Fig. 10), such a radius difference was sig-
nificant. This distinction of the radius mainly stemmed
from the boundary definition in the VG method, which
calculates the largest closed curve of the streamfunction
field (Nencioli et al. 2010). However, there may be no
closed contour line of the streamfunction field around
the eddy center, which leads to the incapability of this
scheme to capture the eddy boundary. In the case of no
closed contour line of the streamfunction field (e.g.,
Fig. 4c), Nencioli et al. (2010) proposed the VG method
and adopted a2 1 (see section 2b for the definition of a)
as the eddy radius (the eddy boundary shown in Fig. 4c
was exactly calculated as a2 1); and no exiting literature
has so far proposed a new solution to this problem. Thus,
the physical radius of eddies varied with the value of a.
Moreover, the case of no closed contour line embracing
the eddy center was not scarce. The proportion of such
eddies identified by the VG method was 49% for a 5 3
FIG. 5. Histogram of distance between eddy centers identified by
the VG and WA methods.
FIG. 6. (a) Distance between the eddy centers and the local maximum magnitude of vorticity. (b) Variation of
distance as function of eddy radius for both the VG and WA methods.
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(only the 1080 eddies mentioned above have been taken
into account). And this proportion increased to 52% for
a5 4 [all the detected eddies (1185 eddies actually) have
been taken into account]. Figure 8 shows the histograms
of the eddy radius for a 5 3 and a 5 4. Figure 8a
suggests a radius distribution for a 5 3 centered around
6km and stood extremely out for both the cyclonic and
anticyclonic eddies. In contrast, the outstanding peak for
a 5 4 was at 9 km. They were exactly corresponding to
the production value of a2 1 and the spatial resolution.
Thus, the VGmethod is often incapable of capturing the
eddy size. In contrast, the WA method employs the
feature of the streamlines, which guarantees their pres-
ence and reflects the eddy size. Therefore, we adopted
the eddy attributes derived from the WA method for
studying the eddy statistics properties.
4. Mean eddy properties
a. Eddy frequency, radius, and life span
The submesoscale eddies covered a large proportion
of the observed region, and their frequency is shown in
Fig. 9. The interpretation for this is straightforward be-
cause it corresponds for every grid to the percentage of
time instants when the grid was located within eddies. It
indicates that the occurrence of eddies was more pref-
erential in the southern part (Fig. 9). Moreover, the
eddies most frequently appeared in the region where the
topography varies sharply with a distinct arc outline
(the 230- and 240-m isobaths reveal an obvious arc).
Therefore, the topography played an important role in
the formation of the eddies. Moreover, the results of the
eddy-frequency contour lines were also influenced by
the limited observation area. For example, the contour
lines in Fig. 9 with a value of zero are approximated to
the radars’ coverage area (Fig. 2) and the relative low
frequency in the southern part was also observed due to
those areas being close to the edge of theHFR coverage.
Thus, it is necessary to establish a radar network to ex-
pand the observation area and then obtain an accurate
eddy spatial distribution.
The distribution of the radius shown in Fig. 10a de-
viates from a Gaussian distribution with a slight skew
toward the larger size, and a peak at 6 km for both the
cyclonic and anticyclonic eddies. No distinct difference
was observed between the size of the cyclones and that
of the anticyclones. The mean radius values were 10.1
and 9.2 km for the cyclones and the anticyclones, re-
spectively. Moreover, the histograms also show that
eddies with a radius larger than 20km were quite in-
frequent. In addition, there were 290 and 271 trajecto-
ries for the cyclones and the anticyclones, respectively.
FIG. 7. Radius difference between the eddies determined by the
VG and WA methods.
FIG. 8. Histograms of the radius distribution of the VG method: (a) a 5 3 and (b) a 5 4.
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The histogram of their life spans is shown in Fig. 10b.
There were no significant differences between the life
span of the two eddy types. The mean life span was
about 0.7 h. An overwhelming majority of the eddies
survived for less than 1h, and only a few eddies lasted
more than 3h. To assess the relationship between the
life span and the radius, we took the maximum radius of
the eddies, composing a trajectory, as the trajectory ra-
dius. And the variation of the life span versus the tra-
jectory radius is shown in Fig. 11. On average, the eddy
life span increased from less than 0.5 h for a very weak
eddy with a near-zero radius to 2h for a strong eddy
with a radius larger than 20 km. This monotonic re-
lationship implies that an eddywith a larger scale usually
subsisted for a longer time.
b. Eddy kinematics
The cyclonic and anticyclonic eddies have similar
average vorticities with an order of 2.43 1025s21 in
absolute value, as listed in Table 2. And the probability
density function of the normalized vorticity (z/f ), shown
in Fig. 12a, also indicates that the vorticity of the cy-
clonic eddies seemed to be the same as that of the an-
ticyclonic eddies. The dominant Rossby number of the
eddies observed in this study was 0.3–0.4 (Fig. 12a).
Furthermore, the joint probability density for the radius
and the normalized vorticity presented an overview of
the submesoscale eddies, as shown in Fig. 12b. The
eddies had an effective radius about 3–18km and a
Rossby number about 0.1–1.
The statistics of the eddy kinematic parameters are
listed in Table 2. The vorticities for both the cyclonic and
FIG. 9. Contour lines for the eddy frequency of occurrence
during the observation (%, thick lines) and regional isobaths
(m, thin lines).
FIG. 10. Histogram of (a) radius distribution and (b) eddy life span distribution.
FIG. 11. Variation of eddy life span as a function of the radius;
heavy line is a linear fit with a correlation coefficient of 0.97 and
a root-mean-square difference of 0.1 h.
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anticyclonic eddies had an order of 2.4 3 1025 s21. In
contrast, other kinematic parameters, such as the
shearing, stretching deformations rates, and the di-
vergences, were smaller than the vorticities even to
several orders of magnitude for both types of the eddies
on average. In addition, a total deformation rate of
1026 s21 indicates that eddies tend to be deformed and
are not perfectly circular. Figure 13a shows the variation
of the total deformation rate versus the radius. The total
deformation decreased over all of the radius scope. It
suggests that the smaller eddies were less deformed and
more circular. To confirm this result and to better in-
vestigate the eddy shape, we checked the eccentricities
of the eddies. As expected, the mean ellipse eccentricity
decreased with the radius, as shown in Fig. 13b. Fur-
thermore, almost the same trend can be clearly seen
between the eccentricity and the total deformation rate.
These solid evidences adequately disclose that the
smaller eddies were more circular.
c. Eddy life cycle
Figure 14a shows the trajectories of the eddies with a
life span no less than 1.5h. The total number of such eddy
trajectories was 30 for the cyclonic eddies and 32 for the
anticyclones. The eddies mainly appeared at 23.58 610 0N, where the eddies arose most frequently (Fig. 9).
Moreover, the distribution of the trajectories’ direction is
also displayed in Fig. 14b. In this study, the direction for
each trajectory was defined as the azimuth of the ending
position to the starting position calculated clockwise from
north. The distribution shown in Fig. 14b suggests that the
eddies predominantly moved southeastward.
Besides the position, other parameters of each eddy also
varied during each eddy’s life span. In this study, we in-
vestigated the evolution of the radius and the MEKE. We
analyzed their average temporal values throughout the
eddies’ lifetime with the eddies surviving no less than 1.5h
(whose trajectories are shown in Fig. 14a). To compare the
eddies with different life spans, we normalized each eddy
ageby its life span. Similarly, the radius and theMEKEalso
have been normalized by theirmaximumvaluewithin each
eddy’s life span. The normalized temporal evolutions are
shown in Fig. 15. Both eddy types exhibited similar varia-
tion trend in terms of the radius and the kinetic energy
during the whole eddy life cycle. The eddy size and the
mean kinetic energy increased in the first 30% of an eddy
life cycle and then fluctuated in a small scope for next 40%
of the life cycle. In the last 30%of themean life cycle, these
parameters decreased to a value similar to the initial level.
5. Summary
This study compared the efficiencies of two widely used
automatic eddy detection methods and investigated the
TABLE 2. Mean statistics of the eddy kinematics.
Mean Std dev Min Max
Cyclonic eddies (1025 s21)
Vorticity 2.42 1.40 0.19 9.41
Divergence 20.05 0.70 23.85 2.06
Shearing deformation 20.09 0.66 22.81 4.31
Stretching deformation 0.52 0.66 24.06 3.81
Total deformation 0.86 0.64 0.01 4.61
Anticyclonic eddies (1025 s21)
Vorticity 22.33 1.10 26.98 20.17
Divergence 20.67 0.87 210.25 11.15
Shearing deformation 20.01 0.75 22.11 9.33
Stretching deformation 20.37 0.65 23.62 3.74
Total deformation 0.82 0.67 0.06 10.00
FIG. 12. (a) Probability density function of z/f. (b) Joint probability density of radius and normalized vorticity.
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submesoscale eddy properties using the 80-day-long HFR
measurements with a high spatial–temporal resolution.
Both of the eddy detection methods are exclusively based
on the geometry properties of flowfield and originate from
the same definition of an eddy. The total number of eddies
identified by the winding-angle method was almost equal
to that of the eddy recognized by the vector geometry al-
gorithm. Moreover, the eddy centers for the same eddies
picked out by the two different methods were also close.
This proved that the two automatic detection methods
have almost the same capacities in identifying eddies.
However, the distributions of the eddy sizes derived from
the two algorithms differed greatly on account of the in-
capability of the vector geometry algorithm to capture the
eddy boundary. This incapability, which will affect the
eddy properties analysis greatly, results from the absence
of a closed contour line of the streamfunction field around
eddy centers. Therefore, the study revealed that the
winding-angle method appeared to be more competent
than the vector geometry algorithm. We strongly recom-
mend the use of the winding-angle method for de-
termination of the eddy boundary.
Then, 1080 eddies, identified by both the winding-
angle method and the vector geometry method, were
FIG. 13. (a) Variation of the total deformation rate as a function of the radius. Solid line shows a third-order
polynomial fit with a correlation coefficient of 0.91 and a root-mean-square difference of 13.08 3 1025 s21.
(b) Variation of the eccentricity as a function of the radius. Solid line shows a third-order polynomial fit with
a correlation coefficient of 0.93 and a root-mean-square difference of 0.05.
FIG. 14. (a) Eddy trajectories: red (blue) lines are trajectories of the cyclonic eddies (anticyclones); solid circles
indicate the starting positions of an eddy track, and asterisks denote the ending positions. (b) Statistics of the
trajectory direction. Trajectory direction was defined as the bearing angle of the ending position (stars in Fig. 14a)
to the starting position (solid circles in Fig. 14a) calculated clockwise from north.
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selected to analyze the mean eddy properties in the
southern Taiwan Strait. In general, no significant dif-
ference was observed between the cyclonic and anticy-
clonic eddies in terms of the radius, life span, kinematics,
and evolution during their life cycle. The typical radius
of the eddy in this region was 3–18km with a Rossby
number of 0.1–1. However, the mean radius of all eddies
was about 10 km and their mean lifetime was roughly
0.7 h. Moreover, the eddies could survive longer if they
had a larger size. They were more frequently observed
within 23.58 6 100N. And the general occurrence fre-
quency exhibits a strong correlation with the topogra-
phy. The observed eddies were more circular with a
smaller size, since the eccentricity and the total de-
formation rate decrease with increasing radius. And
they lived through three phases during their life cycle
with remarkable radius and kinetic energy growth
and decay.
The results may be useful for selecting and developing
an efficient eddy detection algorithm and validating
high-resolution regional models, and they could even be
of interest to the biological community to investigate
links between ecosystems and eddy activities.Moreover,
it demonstrates the great capability of the high-frequency
radars in oceanographic research and applications, espe-
cially for observing submesocale dynamics, which can fill
the gap of the temporal–spatial resolution between the
in situ and satellite measurements.
Acknowledgments. The authors thank the personnel
of Wuhan Device Electronic Technology Co., Ltd.,
Wuhan, China, for carrying out the radar experiment,
and Dr. S Shang and his team at Xiamen University,
Xiamen, China, for providing the buoy data. This work
was supported by the National Natural Science Foun-
dation of China (NSFC) under Grant 61371198 and the
National Special Program for Key Scientific Instrument
and Equipment Development of China under Grant
2013YQ160793.
APPENDIX
Ellipse Fitting
As explained in section 2b, the winding-angle algorithm
attempts to recognize an eddy by selecting and clustering
closed streamlines. Let us consider clustered streamlines.
We denote the coordinates of all the points on these clus-
tered streamlines asM. Then, the cluster covariance C can
be easily obtained. Sadarjoen et al. (1998) and Sadarjoen
and Post (1999, 2000) provide the same approach to fit the
streamlines to an ellipse (i.e., regarding the eigenvalues r of
C as the ellipse axis lengths). This is inaccurate andneeds to
be revised. Let us consider a cluster with only one
streamline and this streamline is a perfect ellipse with a
semimajor axis of l1 and a semiminor axis of l2.Moreover,
for simplification, we assume the angle of the inclination to
be zero. Thus, the coordinates of all the points on the
streamline can be denoted as
�x5l
1sinu
y5 l2cosu
where u is evenly distributed in the 0 to 2p range. Thus,
the cluster covariance can be expressed as
C5D(x) 0
0 D(y)
� �,
FIG. 15. Evolution of the eddy characteristic parameters: (a) radius and (b) mean kinetic energy. Only the eddies
with a life span of no less than 1.5 h are included in this analysis. Solid lines calculated by a third-order polynomial fit
show profiles of a variation trend.
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where theD(�) denotes the variance. The eigenvalues ofthe cluster covariance can be expressed as
r5D(x)
D(y)
� �.
Distinctly, the elements of r are not the semimajor axis
and the semiminor axis. But the following relational
expression can be illuminated:
D(x)
D(y)
� �5
l21 0
0 l22
� �D(sinu)
D(cosu)
� �.
Since u is evenly distributed in the 0 to 2p range, then
D(sinu) 5 D(cosu) 5 1/2. Thus, we can derive the
relation as
ffiffiffiffiffi2r
p5
�l1
l2
�.
We thought this should be the correct relation between
the eigenvalues of the cluster covariance and the ellipse
axis lengths. And this relation has been adopted in
this study.
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