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, zhou.h@whu.edu.cn

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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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