PUBLICATIONSJournal of Geophysical Research: Oceans
RESEARCH ARTICLE
10.1002/2017JC012715
Key Points:
 Coastal acoustic tomography data
were assimilated into a triangularmesh ocean model for the ﬁrst time Velocities obtained from assimilationagreed with ADCP data better thanthose from inversion or simulation
 Assimilation with a triangular meshﬁts complex coastlines well andenables reasonable circulation
calculations

Correspondence to:
X.-H. Zhu,
xhzhu@sio.org.cn
Citation:
Zhu, Z.-N., X.-H. Zhu, X. Guo, X. Fan,and C. Zhang (2017), Assimilation ofcoastal acoustic tomography datausing an unstructured triangular grid
ocean model for water with complex
coastlines and islands, J. Geophys. Res.
Oceans, 122, 7013–7030, doi:10.1002/
2017JC012715.
Received 4 FEB 2017
Accepted 5 AUG 2017
Accepted article online 11 AUG 2017
Published online 1 SEP 2017

Assimilation of coastal acoustic tomography data using an
unstructured triangular grid ocean model for water withcomplex coastlines and islands
Ze-Nan Zhu1,2, Xiao-Hua Zhu1,2, Xinyu Guo3

, Xiaopeng Fan1, and Chuanzheng Zhang1

1State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic
Administration, Hangzhou, China, 2Ocean College, Zhejiang University, Zhoushan, China, 3Center for Marine
Environmental Study, Ehime University, Matsuyama, Japan

Abstract For the ﬁrst time, we present the application of an unstructured triangular grid to the
Finite-Volume Community Ocean Model using the ensemble Kalman ﬁlter scheme, to assimilate coastal
acoustic tomography (CAT) data. The ﬁne horizontal and vertical current ﬁeld structures around the island
inside the observation region were both reproduced well. The assimilated depth-averaged velocities had
better agreement with the independent acoustic Doppler current proﬁler (ADCP) data than the velocities
obtained by inversion and simulation. The root-mean-square difference (RMSD) between depth-averaged
current velocities obtained by data assimilation and those obtained by ADCPs was 0.07 m s21, which wasless than the corresponding difference obtained by inversion and simulation (0.12 and 0.17 m s21,
respectively). The assimilated vertical layer velocities also exhibited better agreement with ADCP than thevelocities obtained by simulation. RMSDs between assimilated and ADCP data in vertical layers ranged from0.02 to 0.14 m s21, while RMSDs between simulation and ADCP data ranged from 0.08 to 0.27 m s21. These
results indicate that assimilation had the highest accuracy. Sensitivity experiments involving the eliminationof sound transmission lines showed that missing data had less impact on assimilation than on inversion.
Sensitivity experiments involving the elimination of CAT stations showed that the assimilation with four
CAT stations was the relatively economical and reasonable procedure in this experiment. These results
indicate that, compared with inversion and simulation, data assimilation of CAT data with an unstructured
triangular grid is more effective in reconstructing the current ﬁeld.

1. Introduction
Ocean models can provide simultaneous current ﬁelds over a large coastal sea area, which can overcome
the limitations of conventional measurement techniques such as moored or shipboard ADCP measurements. However, the results are constrained by the boundary and initial conditions, and they need to be
veriﬁed by observational data.
Coastal acoustic tomography (CAT), which, like an ocean model, can map a rapidly changing and complicated current ﬁeld, is superior to conventional measurement techniques inasmuch as it requires the deployment of only a few instruments on the periphery of the observation region [Yamaoka et al., 2002]. CAT has
been used successfully to monitor the current ﬁeld of coastal seas in recent years [Zhu et al., 2013; X.-H. Zhu
et al., 2015; Zhang et al., 2015; Zhu et al., 2016].

C 2017. American Geophysical Union.
V

All Rights Reserved.

ZHU ET AL.

However, the inverse method, which is the most common technique used to reconstruct the current ﬁeld
from CAT data, is still in need of improved accuracy. Because it solely aims to solve the equations relating
the current ﬁeld to travel time differences at present, further improvements are needed to take into accountboundary conditions [Park and Kaneko, 2001]. Furthermore, the solution is sensitive to the number of equations (i.e., sufﬁciency of the CAT sound transmission lines) in the inverse problem [Wunsch, 1996]. However,both complex coastlines and missing data are common in coastal observation experiments. Assimilating
CAT data into an ocean model is a better scheme for reconstructing the current ﬁeld observed by CAT. Parkand Kaneko [2000] achieved the ﬁrst assimilation of CAT data into a barotropic ocean model by using theensemble Kalman ﬁlter (EnKF) scheme. Near boundaries, the current ﬁelds obtained by assimilation are
more reasonable than those obtained by inversion. Lin et al. [2005] also assimilated CAT data into a 2-D

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barotropic ocean model using the EnKF scheme. They smoothed the Kalman gain through a time stepwhen considering strong currents in their observations. They further conﬁrmed that the 5 min interval
assimilation had the highest accuracy in reconstructing the current ﬁeld in their study.
Previous studies of CAT data assimilation [Park and Kaneko, 2000; Lin et al., 2005] have used the Princeton
Ocean Model (POM) with structured grids [Blumberg and Mellor, 1987]. Although boundary conditions aretaken into consideration, the structured grid cannot perform well in regions of complex coastlines, especially where there are islands in the middle of the observation region [Chen et al., 2003]. The unstructured
triangular grid has proven that it can ﬁt complex coastal geometries more precisely and provide more reasonable model results near boundary regions [Chen et al., 2003, 2007].
Furthermore, the previous studies of CAT data assimilation [Park and Kaneko, 2000; Lin et al., 2005] used a 2D ocean model, which considered the depth-averaged velocities. Because the multipath signals cannot be
distinguished by CAT, the data observed by CAT were considered to be depth-averaged data. However, inmany experiments, the ray patterns were not distributed at full depth, such as in the Zhoushan and Qiongzhou strait experiments, in which rays were mainly distributed in the upper 15 m and upper 40 m, respectively [Zhu et al., 2013; X.-H. Zhu et al., 2015]. Thus, the scheme, which assimilated CAT data into a 2-D ocean
model, was not suitable for all situations. Meanwhile, the 2-D model cannot satisfy our purpose of studying
vertical variations in coastal regions. Assimilation with a 3-D ocean model to show the variations in verticallayers was also necessary.
In this study, for the ﬁrst time, we successfully assimilate the travel time difference data obtained by CAT
into an unstructured triangular grid 3-D ocean model using the EnKF scheme. After evaluating the effects ofdata assimilation by comparing the results of assimilation, simulation, and the inverse method with theindependent moored acoustic Doppler current proﬁler (ADCP) data, we conﬁrm that data assimilation witha triangular mesh can be more effective in reconstructing the current ﬁeld in regions with complex
coastlines.

2. Model and Assimilation Scheme With a Triangular Grid
The ocean model used in this study is the Finite-Volume Community Ocean Model (FVCOM) [Chen et al.,2003]. The vertical and horizontal coordinates are r and spherical coordinates, respectively. The numberof r vertical layers was set to be 11. The spatial resolution of the triangular mesh is about 3 km near
the open boundary and decreases to about 250 m in the main observation region (Figure 1b). The triangular mesh ﬁts the complex coastlines well, especially near Yangjiao Island in the observation region(Figure 1c).
The EnKF scheme [Evensen, 1994, 2003, 2009; Chen et al., 2009] accompanied Monte Carlo method is used
to assimilate the CAT data into the ocean model. The state vectors at time t update the following equation:
wa 5wf 1K y2Hwf :(1)
Here w are the model state vectors (i.e., the east and north velocity components and sea level in this study);
the superscripts a and f denote the assimilated and forecast state vector in the assimilation step, respectively; K is the Kalman gain [Evensen, 2003]; y denotes the observational data (i.e., the averaged velocity
along the sound transmission lines) [Park and Kaneko, 2001]; and H is the matrix representing the linear relationship between the observational data and the model state vectors.
In order to establish a relationship between CAT data and model states, the relationship between thesound transmission lines and the triangular mesh is described in Figure 2. The original CAT data are travel
time differences (Ds) between two acoustic CAT stations. At ﬁrst, we transfer Ds to average velocity in the2direction along the transmission lines (VCAT ) between the two stations using the equation VCAT 52 C02LDs[Zheng et al., 1997], where C0 is the reference sound speed [Munk et al., 1995] and L is the station-tostation distance. Meanwhile, the average velocity along the transmission line in the ocean model (Vmodel ÞP
can be calculated by Vmodel 5 ni51 lLi ðui cos h1vi sin hÞ, where u and v are the eastward and northward
ocean model velocity components, respectively; n is the number of triangular grids that are crossed by
the sound transmission line; the subscript i indicates the ith triangular grid in the sound transmission line

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and the corresponding distance is li; and h is the direction of the sound transmission line, rotating anticlockwise from due east.
In theory, VCAT equals Vmodel , so the relationship between CAT data and model states can be written as2

C0 2 Ds Xn li
ðui cos h1vi sin hÞ:
5
i51 L
2L

(2)

Thus, the relationship between CAT measurements and state vectors of the simulation can be written as0
1 0
C0 2 Ds1
2

B
L1 C
C B
B
C B
B
B C 2 Ds C B
0
j C B
B
C BB2
B
Lj C5B
C B
B
C B
B
⯗
C B
B
C B
B
@ C0 2 Dsm A @

2
Lm
0

l11
cos h1
L1

l11
sin h1
L1



l1n 1
cos h1L1

l1n 1
sin h1
L1

lj1
cos hjLj

lj1
sin hj
Lj



ljn j
cos hjLjljn jsin hjLj⯗
lm1
cos hmLm

lm1
sin hmLm⯗l mn ml mn mcos hmsin hm
Lm
Lm

u1

1

C
1B
B v1 CC   CB
C
B
C
B
⯗
CB
C
CB
C
CB
C
u
Ni C
C
CB
C;
CB
vNi C
CB
C
B
CB
C
CB
AB ⯗ CCC B
B uN C
A
@

(3)

vN

where N is the element number in the model mesh; the subscript m denotes the sound transmission line
number and; j denotes the jth sound transmission line. Thus, the ﬁrst matrix in the right hand of equation(3) is H. Here we just show some coefﬁcients that are crossed by the transmission lines for example. Someelements of the observational matrix H can be zero. The velocity u and v are simpliﬁed as depth-averagedin equations (2) and (3). Thus, the observational matrix H contains operation of depth averaging of velocity.
In this study, the 3 day (6–9 September 2009) CAT data [Z.-N. Zhu et al., 2015] obtained from seven stations located in Sanmen Bay, adjacent to the East China Sea (Figures 1a and 1b), is assimilated into the
FVCOM. The interval of assimilation is 3 min, which is same as the sampling interval of CAT observation.
The successful acquisition number of sound transmission lines was 21 (m 5 21). Data from three independent moored ADCP (RDI, 1200 kHz, Workhorse) instruments were used for comparison with model
results (Figure 1c). The unstratiﬁed model was forced by the tidal level of M2 tide along the open boundary (red line in Figure 1b) with the mean amplitudes and phases of 2.09 m and 14.88, respectively. The
external and internal time steps of simulation in this study are 1.0 and 6.0 s, respectively. The model isspun up for 5 days to make the sea level and current ﬁeld stable. Then, the model states at 18:00, 6 September 2009 (China Standard Time, CST) are considered the initial ﬁelds of assimilation. The CAT data
were considered as full-depth-averaged data in all 21 sound transmission lines [Z.-N. Zhu et al., 2015].
The number of ensemble members for EnKF was set to 20 by following the studies of Chen et al. [2009]
and Xue et al. [2011]. The random perturbed of 20 members, which were conformed to normal distribution with zero mean and standard deviations of 0.2 m and 1.58 (i.e., 10% of the mean amplitudes andphases along the open boundary), were added to the open boundary [Park and Kaneko, 2001; Lin et al.,2005]. The measurement errors, which range from 0.02 to 0.06 m s21, were determined by the CAT
measurements [Zhu et al., 2012]. The measurement errors are assumed to be temporally uncorrelated inspite that the temporally interpolated CAT data are used for assimilation. Then perturbations which wereadded to the observations were constructed by forming the product of measurement errors of CAT sections and random numbers drawn from a normal distribution with zero mean and unity standard deviation [Chen et al., 2009].

3. Data Collection
Tidal sea level validation between simulated and predicted values in tidal tables for the Jiantiao tide gauge
station performed well (Figure 3a), with root-mean-square differences (RMSD) of 0.27 and 0.31 m for thesimulation and assimilation, which are both less than 10% of the observed tidal amplitude (Figure 3a). Considering that the tide gauge station was located at the marginal region of the model grid where the topography data were not of sufﬁcient accuracy, the relative error of about 10% was still acceptable for theZHU ET AL.

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29.3
36oN

33oN

30 (m)

Ch
ina

Se
a

29.1

20

Ea

st

30oN

27oN

28.9
10

24oN

(a)
118oE 120oE 122oE 124oE 126oE 128oE 130oE

28.7

0

(b)
121.5

121.7

121.9

122.1

1 km

C1

C7

C2
Yangjiao Island

C6

A1
A3
C3
A2

C5
(c)

C4

Figure 1. (a) Location of Sanmen Bay and (b) the triangular mesh and bathymetry of the ocean model. The thick red line denotes theopen boundary. The black star denotes a tidal gauge station named Jiantiao. (c) Bathymetry of the CAT measurement region. Black dots
and red stars are the CAT and moored ADCP stations, respectively. Black (and blue) lines denote the CAT sound transmission lines.

simulation. Furthermore, the RMSD between assimilation is only slightly larger than those in the simulation,
indicating that the relationship among variables was not broken during data assimilation. The tidal level variation also showed typical semidiurnal tide characteristics.
The three independent moored ADCPs in the observation region (Figure 1c) were synchronized with the CAT
observation (Figure 3b). The ADCPs in A1 were downward sampled every 10 s with a bin number and bin lengthof 30 and 0.5 m, respectively, at nighttime during the duration of the observation. The moored ADCPs in A2
were upward sampled every 10 min with a bin number and bin length of 15 and 1 m, respectively. The moored
ADCPs in A3 were upward sampled every 1 min with a bin number and bin length of 11 and 1 m, respectively.
The successful rate of 21 reciprocal sound transmissions ranged from 20.3% (C5–C7) to 85.4% (C2–C3), witha mean rate of 58.8% (Figure 3b). The noises in coastal seas and instrument failure were the main factors in
CAT data dropout. In order to make the inversion more accurate and the sensitivity experiments moreZHU ET AL.

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effective, interpolated data obtained with a harmonic analysis method that employed harmonic
constants of eight tidal constituents (i.e., K1, M2,
M3, M4, 2MK5, M6, 3MK7, and M8) [Z.-N. Zhu et al.,2015] were used for both inversion and assimilation in this study. The harmonic analysis of travel
time differences of raw CAT data shows themean ratios of M2, K1, M3, M4, 2MK5, M6, 3MK7,
and M8 are 1.00:0.07:0.07:0.11:0.04:0.11:0.04:0.03.
These indicated that M2 are predominant andthe other tidal constituents (i.e., K1, M3, M4,
2MK5, M6, 3MK7, and M8) are smaller. Thus, only
semidiurnal (M2) tidal constituent were added toopen boundary in FVCOM.

i

l

L

C3

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θ

4. Mapping Circulation by
Assimilation

Both the average depth and depth-dependent
components of the current ﬁelds for the assimilation were mapped. Except for Yangjiao Island,
Figure 2. An example of the sound transmission line between C3 andthe coastlines are mainly outside the observation
C4 crossing the triangular mesh (gray grids).
region (Figure 1c). Hence, circulation near Yangjiao Island was, in particular, plotted to evaluate
the performance of the triangular mesh in ﬁtting the coastlines. The circulation with high spatial resolution,
which we discuss in this section, was due to the ocean model itself rather than the assimilation scheme, but
the assimilation was still needed to improve the accuracy of the current ﬁeld.

C4

4.1. Horizontal Circulation
The tidal currents in the observation region were essentially rectilinear (Figure 4). Maximum southeastward
and northwestward currents (1.03 and 1.09 m s21, respectively) during ebb and ﬂood tide appeared at
02:12 and 20:27, respectively, on 8 September 2009 (CST) (Figures 4a and 4b). The vectors obtained byinversion (hereinafter Vinv) and assimilation (hereinafter Vass) were plotted every 1 km (i.e., spatial resolutionof the inversion) and every 1.2 km (about every eight horizontal grids), respectively (Figures 4a and 4b). Vass
(black) was oriented along the coastlines near Yangjiao Island and clearly increased in the leeward side of
the island (Figures 4c and 4d). These results indicate that the island had a strong impact on the current ﬁeld.
However, due to the limited spatial resolution of the inversion, the ﬁne structure of the current ﬁeld near
Yangjiao Island could not be described well by Vinv (red in Figures 4c and 4d).
The assimilation and inversion M2 tidal currents were mainly directed northwest-southeast, but the assimilation M2 tidal current ellipses were oriented along the coastline around the island (Figure 4e). RMSDs
between them for semimajor and semiminor axis lengths were 0.18 and 0.06 m s21, respectively. The residual currents of assimilation were relatively large and toward the island in the southeast and northwest directions with maximum speeds of 0.20 and 0.35 m s21 for eastward and northward velocity components.
These components then turned southwestward and northeastward near the island. There were also clockwise and anticlockwise structures northwest and north of the island, respectively (Figure 4f). These current
distributions around Yangjiao Island are similar to the tidally induced residual ﬂows around the island generated by the M2 tidal wave in the ideal experiment of Pingree and Maddock [1980]. However, the residual
currents obtained by inversion could not describe such a detailed structure and are all directed northwestward (red arrows in Figure 4f). The RMSDs of residual currents between assimilation and inversion for eastward and northward velocity components were 0.06 and 0.08 m s21, respectively.
4.2. Vertical Structures of Tidal Currents
The variations of Vass in vertical layers near Yangjiao Island at the corresponding time of Figure 4 were also
described in Figure 5. Here we should note that the number of vertical layers in ocean models was 11, andZHU ET AL.

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3
1.5
0
−1.5
−3

A1
A2
A3
C1−C2
C1−C3
C1−C4
C1−C5
C1−C6
C1−C7
C2−C3
C2−C4
C2−C5
C2−C6
C2−C7
C3−C4
C3−C5
C3−C6
C3−C7
C4−C5
C4−C6
C4−C7
C5−C6
C5−C7
C6−C7
09/07

09/08

09/09

Time (month/day)Figure 3. Synchronized CAT and ADCP measurements. (a) Tidal sea levels obtained by model simulation (blue line), assimilation (blackline), and tidal table data at the tide gauge station of Jiantiao (red dots). (b) Time periods of successful acquisition of reciprocal soundtransmission (blue cross) between each station pair and the moored ADCP (black bar).

we choose surface, middle, and bottom layers as the representative layers to be plotted in Figure 5. However, the inversion cannot obtain the vertical structure with only one arrival peak data.
Vass was almost the same direction in different layers but decreased from the surface to bottom in both theebb (Figure 5a) and ﬂood (Figure 5b) tide. During the ebb tide, the spatial mean of Vass near Yangjiao Island
for the eastward and northward components were 0.76 and 20.83 m s21, respectively, for the surface layer,
becoming 0.31 and 20.31 m s21, respectively, in the bottom layer. During ﬂood tide, those values became
20.78 and 0.78 m s21, respectively, in the surface layer, and 20.30 and 0.31 m s21, respectively, in the bottom layer.
The tidal currents clearly changed direction within the range of about 0.5 km from the Yangjiao Island. The
orientations were along the coastlines near Yangjiao Island (Figures 5a and 5b) in all vertical layers. Meanwhile, Vass became very small downstream of the tidal currents because of the impact of Yangjiao Island(Figure 5).
The distributions of M2 tidal current ellipses (Figure 5c) had similar patterns as the depth-averaged results(Figure 4e) near Yangjiao Island. The horizontal mean velocity magnitudes of M2 were 1.17 m s21 in the surface layer, 1.06 m s21 in the middle layer, and 0.47 m s21 in the bottom layer. The residual current also had
similar patterns in the different vertical layers. The horizontal mean velocities for the eastward component
were 20.08 m s21 in the surface layer, 20.06 m s21 in the middle layer, and 20.02 m s21 in the bottom
layer; those values for the northward component were 0.04 m s21 in the surface layer, 0.03 m s21 in the
middle layer, and 0.01 m s21 in the bottom layer. The residual current structures in all three layers (Figure

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Inversion

EnKF

1 m s−1(b)

1 m s−1

1 m s−1

(c)

(d)

0

m s−1

2

(e)

ADCP

1 m s−1(a)1

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10 cm s−1(f)Figure 4. Vector plots of depth-averaged currents obtained by inversion (red), ADCP (blue), and assimilation (black) during maximum (a)ebb tide at 02:12 and (b) ﬂood tide at 20:27 on 8 September 2009 (China Standard Time, CST). (c, d) Details of the current distributions
near Yangjiao Island at the corresponding times of Figures 4a and 4b, respectively. (e) M2 tidal current ellipses. (f) Residual current distribution for the observational period. Gray rectangles in Figures 4a and 4b indicate the location of Figures 4c–4f.

5d) are similar to depth-averaged results (Figure 4f) and show the similar patterns with Pingree and Maddock[1980].
The ﬁne vertical circulation near the Yangjiao Island was reproduced well by Vass. However, it is impossiblefor inversion to reconstruct the vertical circulation structure. It also cannot be achieved by CAT assimilation
with the 2-D ocean model. The 2-D mapping cannot describe the complex circulation in coastal seas well.
Thus, our scheme of CAT assimilation with a triangular mesh can not only ﬁt the complex coastlines well
but also describe variation in vertical layers.

5. Assimilation Performance
To evaluate the assimilation performance, the results of inversion, simulation, and assimilation were compared with independent ADCP data. Considering the inversion was 2-D, the results of simulation,ZHU ET AL.

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Figure 5. Vector plots of currents obtained by assimilation during maximum (a) ebb tide at 02:12, (b) ﬂood tide at 20:27 on 8 September
2009 (China Standard Time, CST), (c) M2 tidal current ellipses, and (d) residual currents in surface (black), middle (blue), and bottom (red)layers. The green vectors indicated the ADCP velocities in Figures 5a and 5b. Note that the scale of vectors was different in Figure 5d.

assimilation, and ADCP data were averaged in depth. Furthermore, the performance of simulation andassimilation in vertical layers was also considered.
5.1. Depth-Averaged Comparisons
Although the tidal level validation performed well, simulated velocities (hereinafter Vsim) were larger than
the independent ADCP velocities (VADCP), and agreement of Vsim with VADCP was worse compared to theagreement of Vinv and Vass with VADCP (Figure 6). The RMSDs of the eastward and northward velocity components between Vsim and VADCP were 0.20 and 0.16 m s21 for A1, 0.21 and 0.13 m s21 for A2, and 0.11 and0.18 m s21 for A3, respectively (Figure 7). The mean RMSD for the eastward and northward velocity components between Vsim and VADCP was 0.17 m s21. Compared with inversion and assimilation, these results indicate that the ocean model forced only by the tidal level along the open boundary was not accurate enoughto simulate the current structures in the observation region. More accurate topography data and more reasonable bottom roughness coefﬁcients are probably needed to improve the simulation of tidal currents inthe further studies.
Agreement of Vinv with VADCP was better than the agreement of Vsim with VADCP. The RMSDs of eastward andnorthward velocity components between them were 0.12 and 0.15 m s21 for A1, 0.10 and 0.12 m s21 for
A2, and 0.14 and 0.09 m s21 for A3 (Figure 7), respectively, with a mean RMSD of 0.12 m s21. Relative errors
for Vinv (mean ratio of RMSDs to maximum ADCP speeds for eastward and northward velocity components)
were 19.8%, 16.9%, and 17.4% for A1, A2, and A3, respectively. Vinv magnitudes were clearly larger thanthose of VADCP at A1 (Figure 6a), indicating that Yangjiao Island has a strong inﬂuence on the adjacent current ﬁeld. The inversion cannot reconstruct the current ﬁeld well near coastlines, because it ignores

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Inversion

Simulation

Assimilation

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ADCP

1

0.5

0

−0.5

(a)

Velocity(m s−1)

−1
1

0.5

0

−0.5

(b)
−1
1

0.5

0

−0.5

(c)
−1

00:00
09/07

12:00

00:00
09/08

12:00

00:00
09/09

12:00

Time
Figure 6. Vector plots of velocity obtained by inversion (red), simulation (gray), ADCP (blue), and assimilation (black) at stations (a) A1,(b) A2, and (c) A3. The vectors are plotted every 30 min (i.e., every 10 vectors).

boundary conditions [Park and Kaneko, 2001]. The current directions at A3 also exhibit poor agreement (Figure 6c), indicating that the accuracy of inversion was greatly impacted when the number of sound transmission lines decreased rapidly near the periphery of the observation region (Figure 1c). Vinv at A2 had thesmallest relative error (16.9%), indicating Vinv performed better in the middle of the observation region.
These results show that the boundary conditions as well as the sufﬁciency of sound transmission lines had
signiﬁcant effects on the inversion.
Comparing all three ADCP stations, the vectors of Vass and VADCP matched best in both magnitude anddirection (Figure 6). The RMSDs of eastward and northward velocity components between them were small:
0.10 and 0.09 m s21 for A1, 0.10 and 0.04 m s21 for A2, and 0.07 and 0.04 m s21 for A3 (Figure 7), respectively. The mean RMSD of the eastward and northward velocity components between Vass and VADCP was
0.07 m s21. Relative errors for Vass were 6.5%, 7.4%, and 9.2% at A1, A2, and A3, respectively, much smaller
than those for Vinv. These results indicate that data assimilation had the highest accuracy in reconstructing
the current ﬁeld. The accuracy improves when the boundary conditions are taken into consideration. Furthermore, data assimilation performed well in the area (A3) where the sound transmission lines weresparse.

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Inversion

Assimilation

1.2

rms_inv=0.12
rms_ass=0.10
0.8 rms_sim=0.20

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Simulation

rms_inv=0.15
rms_ass=0.09
rms_sim=0.16

0.4
0
−0.4
−0.8
−1.2

(a)

(b)

−1

Model Velocity (m s )1.2

rms_inv=0.10
rms_ass=0.10
0.8 rms_sim=0.21

rms_inv=0.12
rms_ass=0.04
rms_sim=0.13

0.4
0
−0.4
−0.8
−1.2

(c)

(d)

1.2

rms_inv=0.14
rms_ass=0.07
0.8 rms_sim=0.11

rms_inv=0.09
rms_ass=0.04
rms_sim=0.18

0.4
0
−0.4
−0.8
(e)
−1.2
−1.2 −0.8 −0.4

(f)
0

0.4

0.8

1.2 −1.2 −0.8 −0.4

−1

UADCP (m s )

0

0.4

0.8

1.2

−1

VADCP (m s )Figure 7. Scatter plots of (left) eastward and (right) northward velocity components with respect to ADCP at stations (top) A1, (middle) A2,and (bottom) A3. The RMSDs between the ADCP and the inversion, assimilation, and simulation are shown in the top left of each ﬁgure(in m s21).

In order to show the advantages of assimilation in the vicinity of complex coastlines and islands, the differences between Vsim and Vass are plotted in Figure 8. The RMSDs were larger in the southeastern part in Figure 8a, but larger in the northwestern part in Figure 8b. These results were mainly due to the fact that Vass
directed generally in a north-south direction in the northwestern part (Figure 4a) and in an east-west direction in the southeastern part (Figure 4b). Consequently, the modiﬁcations of assimilation contributed moreto the eastward velocity component in the northwestern part but contributed more to the northward velocity component in the southeastern part. In addition, the RMSDs of both eastward and northward velocity
components are relatively large near islands and complex coastlines, indicating that the results of simulation are modiﬁed by assimilation in the vicinity of the complex coastlines and islands. Observational datanear the coastlines or islands was unavailable, except for station A1 (near Yangjiao Island) and the results
near this station show that assimilation works well in adjusting the current ﬁeld closer to ADCP data. Thus,
this study scheme had a good performance adjacent to the complex coastlines and islands.

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(a)

U
0

0.05

0.1

10.1002/2017JC012715

(b)

V
0.15

0.2

0.25

Figure 8. Distributions of RMSDs between simulation and assimilation during the experiment period (in unit m s21). Velocity components
are showed in right bottom of each panel.

5.2. Comparisons in Vertical Layers
The distribution of VADCP, Vsim, and Vass in vertical layers at stations A1, A2, and A3 were compared (Figures
9A and 9B). However, the inversion could not describe the vertical variation. Thus, Vinv were not taken into
consideration in this section.
In A1, the magnitudes of Vsim and Vass were similar for both eastward and northward components whencompared with VADCP. However, the minimum northward velocity of Vass was closer to VADCP than Vsim. Comparing the RMSDs in the vertical layers, Vass for both eastward and northward components exhibited better
agreement with VADCP than with Vsim in all vertical layers (Figure 10).
In A2, Vsim was larger than VADCP for the eastward component during ebb tide (Figures 9A(d) and 9A(e)) andwas smaller than VADCP for the northward component during ﬂood tide (Figures 9B(d) and 9B(e)). The magnitudes of Vass were closer to VADCP than Vsim. The vertical structure of velocities became more similar to
VADCP after assimilation (Figures 9A(d)–9A(f) and 9B(d)–9B(f)). The RMSDs between Vass and VADCP for both
eastward and northward components (black lines in Figure 10) were smaller by about 0.1 m s21 at theupper depth when compared with those of Vsim.
In A3, the vertical structure of Vass was more similar with VADCP than that of Vsim (Figures 9A(g)–9A(i) and
9B(g)–9B(i)). The magnitudes of Vass were also closer to VADCP than Vsim. The RMSDs between Vass and VADCP
for the northward component in A3 (black lines in Figure 10b) were smaller by about 0.1 m s21 in all verticallayers when compared with those of Vsim. However, the RMSDs of the eastward component were smaller by
only about 0.05 m s21. These indicated that Vsim for the eastward components had already performed relatively well, while Vsim for the northward components had been obviously improved by the CAT data in theassimilation processes, making the results closer to VADCP.
The ray patterns were heterogeneously distributed in the vertical layers [Z.-N. Zhu et al., 2015], while theratios of the CAT data in the vertical layers were set to be the same as in the assimilation processes. These
led to the variations of RMSDs values in the vertical layers, especially in deeper layers. Thus, accurate ray
simulations were necessary when the 3-D CAT assimilation was carried out. Comparing Vass and Vsim with
VADCP in the three ADCP stations, Vass had better agreement with VADCP than Vsim, exhibited by both thevelocity structure and the RMSDs with VADCP. Thus, our scheme of CAT assimilation had a high accuracy invertical structure for current ﬁeld reconstruction. However, the vertical structure of the current ﬁeld could
not be obtained by inversion or previous 2-D CAT assimilation. Here we should note that the CAT data with
only one arrival peak are depth averaged and barotropic, and the vertical proﬁles were attributed to theocean model (i.e., the ﬁrst term in the right hand of equation (1)) rather than in assimilation (i.e., the second

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A0
5
10
1.2

Depth (m)

15
0

(a)

(b)

(c)

1
5
0.8

10
(d)

(e)

(f)

0.6

0
5

0.4

10

0.2
(g)

09/07

(h)

09/08

09/09

(i)

09/07

09/08

09/09

09/07

09/08

09/09
0

B0

−0.2

5
10

Depth (m)

15
0

−0.4
(a)

(b)

(c)

−0.6

5
−0.8
10
(d)

(e)

−1

(f)

0
−1.2

5
10
(g)

09/07

(h)

09/08

09/09

(i)

09/07

09/08

09/09

09/07

09/08

09/09

Time (month/day)Figure 9. Time series of the (A) eastward and (B) northward velocity component for (left) ADCP, (middle) simulation, and (right) assimilation at station (a–c) A1, (d–f) A2, and (g–i) A3.
The black line in each panel indicated the sea surface variation.

term in the right hand of equation (1)). However, multiarrival rays of CAT data are needed to reconstruct thebaroclinic structures, but it is difﬁcult for CAT to obtain such data in coastal regions.
5.3. Comparisons of Along Section Velocities
The averaged velocities along the 21 sound transmission lines are compared in Figure 11. The simulation
results demonstrate worse agreement with the CAT data (obtained by equation (2)) than assimilation
results. These results also indicate that the ocean model was not accurate enough to simulate the current
structures in the observation region. After assimilation, the velocities become very close to the CAT data inmany sections, such as C1–C4 (Figure 11c) and C3–C7 (Figure 11o). The RMSDs between assimilation and
CAT data ranged from 0.05 to 0.24 m s21. The differences were relatively large in section C1–C2 (Figure11a), C1–C6 (Figure 11e), and C1–C7 (Figure 11f). These could be explained as the simulation results of thesethree sections exhibited worse agreement with observations than other sections, and the RMSDs between
assimilation and observations are relatively larger than other sections (0.22, 0.19, and 0.24 m s21); the values

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1
2
3
4
5
6

Depth (m)

7
8
9
10
11
12
13
14
15

(a)
0

(b)
0.05

0.1

0.15

0.2

0.25

0.3

0

−1

RMSD_U (m s )

0.05

0.1

0.15

0.2

0.25

0.3

−1

RMSD_V (m s )Figure 10. Root-mean-square differences (RMSD) between simulation and ADCP (dash lines) and assimilation and ADCP (thick lines), for
A1 (red), A2 (blue), and A3 (black) in vertical layers.

of forecast ensemble spread in these three sections are about 0.1 m s21 (green lines in Figure 11), indicatingthat the forecast ensemble spread are not large enough to make the assimilation modify to the true values.
Meanwhile the prescribed measurement errors at these three sections were also relatively large (0.05, 0.03,
and 0.05 m s21), indicating that some components of the Kalman gain matrix K in equation (1) are verysmall, which made the observational data inefﬁcient in the EnKF scheme. The assimilation performance
results along these three sections were also mainly due to the relatively large differences between observation and simulation. Consequently, the assimilation cannot modify the results to make them very close toobservation. Overall, the assimilation scheme used in this study was sufﬁcient to make the results closer tothe CAT observation.

6. Sensitivity Experiments
First, three sensitivity experiments were carried out to evaluate the effects of sound transmission lines on
Vinv and Vass. The current ﬁelds obtained by inversion and assimilation with 21 sound transmission lines
were deﬁned as the standard experiments (E0). Experiment 1 (E1) eliminated three sound transmission lines
near A1 (Figures 12a and 12d), Experiment 2 (E2) eliminated three sound transmission lines near A2 (Figures
12e and 12h), and Experiment 3 (E3) eliminated three sound transmission lines near A3 (Figures 12h and12k), for both inversion and assimilation.
In E1, Vinv magnitudes were more sensitive to the missing sound transmission lines for both the eastward
and northward velocity components (Figures 12a and 12b). The maximum difference of inversion values
between E1 and E0 was 0.12 m s21. Compared with VADCP, the RMSDs became 0.15 and 0.17 m s21 for A1(Figures 13a and 13b), while the other two stations (Figures 13a and 13b) changed less compared with E0(Figures 7c–7f). The Vass differences between E1 and E0 were mainly less than 0.02 m s21 in the entire

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Journal of Geophysical Research: Oceans
1.2 C1−C2
0.8
0.4
0
−0.4
−0.8
−1.2 (a)Velocity (m/s)

1.2 C1−C3
0.8
0.4
0
−0.4
−0.8
−1.2 (b)1.2 C1−C4
0.8
0.4
0
−0.4
−0.8
−1.2 (c)1.2 C1−C5
0.8
0.4
0
−0.4
−0.8
−1.2 (d)1.2 C1−C6
0.8
0.4
0
−0.4
−0.8
−1.2 (e)1.2 C1−C7
0.8
0.4
0
−0.4
−0.8
−1.2 (f)
1.2 C2−C3
0.8
0.4
0
−0.4
−0.8
−1.2 (g)
09/07

C2−C4

10.1002/2017JC012715

0.2

C3−C7

0.1
0
−0.1

error=0.05

rms=0.22(h)error=0.02

rms=0.08

C2−C5

(o)

error=0.02

rms=0.13

C4−C5

−0.2
0.2
0.1
0
−0.1

error=0.03

rms=0.18(i)error=0.02

rms=0.08

C2−C6

(p)

error=0.03

rms=0.08

C4−C6

−0.2
0.2
0.1
0
−0.1

error=0.02

rms=0.08(j)error=0.02

rms=0.10

C2−C7

(q)

error=0.02

rms=0.08

C4−C7

−0.2
0.2
0.1
0
−0.1

error=0.02

rms=0.11(k)error=0.03

rms=0.16

C3−C4

(r)

error=0.02

rms=0.09

C5−C6

−0.2
0.2
0.1
0
−0.1

error=0.03

rms=0.19(l)error=0.03

rms=0.06

C3−C5

(s)

error=0.03

rms=0.13

C5−C7

−0.2
0.2
0.1
0
−0.1

error=0.05

rms=0.24(m)error=0.02

rms=0.06

C3−C6

(t)

error=0.02

rms=0.07

C6−C7

−0.2
0.2
0.1
0
−0.1

error=0.05

rms=0.15

09/08

09/09

(n)
09/07

error=0.02

rms=0.07

09/08

09/09

(u)
09/07

error=0.05

rms=0.05

09/08

09/09

−0.2

Time (month/day)Figure 11. Depth-averaged velocities along the sound transmission lines obtained by CAT data (red), simulation (blue), assimilation (black) and forecast ensemble spread (green). The
measurement errors (the RMSDs between assimilation and CAT data) are presented in the (right) lower middle of each panel (units are m s21). Note that the green lines are in different
axes.

region with a maximum value of 0.03 m s21 (Figures 12c and 12d). Compared with VADCP, the RMSDs(Figures 13a and 13b) were almost equal to those for E0 (Figure 7).
In E2, the Vinv magnitudes were more sensitive in the southeast part of the region, where the three missing
sound transmission lines intersected (Figures 12e and 12f). The maximum difference of inversion values
between E2 and E0 was 0.14 m s21. Compared with VADCP, the RMSDs became 0.15 and 0.12 m s21 for A2,
and 0.10 and 0.12 m s21 for A1 (Figures 13c and 13d), respectively, while A3 (Figures 13c and 13d) changed
less compared with E0 (Figures 7a and 7b). The Vass difference between E2 and E0 was still primarily less than
0.02 m s21 in the entire region with a maximum value of 0.03 m s21 (Figures 12g and 12h). Compared with
VADCP, the RMSDs (Figures 13c and 13d) were almost equal to those for E0 (Figure 7).
The missing transmission lines distributed at the center of observation region in both E1 and E2. Comparedwith ADCP, the RMSDs were relatively large near the regions where the missing sound transmission lines

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10.1002/2017JC012715

Figure 12. Distribution of velocity differences between experiments with missing and whole sound transmission lines. The black (red) lines indicate the retained (missing) sound transmission lines. The blue contour line indicates 0.10 m s21. The sensitivity experiment designations, schemes, and velocity components are indicated in the top right, top left, and bottom
right of each ﬁgure, respectively.

intersected. The sensitivity of inversion was mainly caused by the missing equations (i.e., missing soundtransmission lines observed by CAT) in the inverse problem [Wunsch, 1996]. The coefﬁcients which represent the relationship between velocities and the travel time differences obtained by inversion along thesound transmission lines were also impacted by the missing data [Park and Kaneko, 2001]. Thus, the inversion was more sensitive to the missing data than the assimilation, especially in the region where there werefewer sound transmission lines.
Because of the missing sound transmission lines on the periphery of the observational region in E3, the Vinv
differences were almost all larger than 0.10 m s21 in the southwest part of the region, with a maximum
value of 0.31 m s21 (Figures 12i and 12j). The RMSDs became 0.41 and 0.32 m s21 for A3 (Figures 13e and13f), which is about 50% of the VADCP maximum. Near A3, Vinv values were in very poor agreement with
VADCP. However, Vass performed surprisingly well in E3 (Figures 12k and 12l). Differences in the entire region
were primarily less than 0.01 m s21, and became slightly larger (0.02 m s21) near the missing sound transmission lines. Compared with VADCP, the RMSDs in E3 (Figures 13e and 13f) were also almost equal to thosein E0 (Figure 7). The assimilation scheme only makes the simulation close to observations, and the ocean
model itself still can keep the current ﬁeld reasonable even if observations are missing in the assimilation.
In other words, the stability of assimilation was mainly due to the ﬁrst-guess ﬁeld (i.e., the ﬁrst term in theright hand of equation (1)), while the assimilation processes can improve the accuracy.

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A2

A3

RMSD_A1= 0.17 / 0.08
RMSD_A2= 0.12 / 0.05
RMSD_A3= 0.09 / 0.06

A1

A2

A3

0.8

0

0

−0.8

−0.8

U (m s−1)(b)

RMSD_A1= 0.10 / 0.10
RMSD_A2= 0.15 / 0.09
RMSD_A3= 0.13 / 0.06

A1

A2

A3

RMSD_A1= 0.12 / 0.08
RMSD_A2= 0.12 / 0.05
RMSD_A3= 0.08 / 0.05

A1

A2

A3

0.8

0

0

−0.8

−0.8
(c)

(d)

RMSD_A1= 0.11 / 0.11
RMSD_A2= 0.10 / 0.10

A1

A2

0.8 RMSD_A3= 0.41 / 0.06
U (m s−1)

V (m s−1)

(a)

0.8

V (m s−1)

A1

A3

RMSD_A1= 0.17 / 0.08
RMSD_A2= 0.13 / 0.05
RMSD_A3= 0.32 / 0.06

A1

A2

A3

0.8

0

0

−0.8

V (m s−1)

U (m s−1)

0.8

RMSD_A1= 0.15 / 0.10
RMSD_A2= 0.10 / 0.09
RMSD_A3= 0.11 / 0.06

10.1002/2017JC012715

−0.8
(e)

−1.2 −0.8 −0.4

(f)0

0.4 0.8 1.2 1.6
UADCP (m s−1)2

2.4 2.8 3.2 3.6 −1.2 −0.8 −0.4

0

0.4 0.8 1.2 1.6

2

2.4 2.8 3.2 3.6

VADCP (m s−1)

Figure 13. Scatterplots for assimilation (black) and inversion (red) with ADCP measurements for the (left) eastward and (right) northward velocity components, (a, b) E1, (c, d) E2, and(e, f) E3. The RMSDs between assimilation (inversion) and ADCP data are presented in the top left of each ﬁgure (units are m s21). For visual clarity, 1.2 (2.4) m s21 has been added to all
ADCP values for A2 (A3) in each ﬁgurer.

Second, we carried out ﬁve more sensitivity experiments the elimination of CAT stations to optimize theschedule of deploying the CAT stations in this observation. The RMSDs between experiment cases and Case
0 of inversion increased from 0.184 to 0.485 m s21 with the decrease of CAT stations (Table 1). The inversion
RMSDs increased when the number of stations decreased (Table 1), indicating that the inversion was sensitive to the number of stations. The more stations that were deployed, the more accuracy current ﬁeld would
be reconstructed by inversion. The resolution and accuracy of inversion would be improved by deploying
more stations [Park and Kaneko, 2001], but it was not the most economical and reasonable schedule to only
increase the number of stations in CAT observations. The ﬁve experiments of assimilation showed that the
RMSDs between sensitivity experiments and Case 0 ranged from 0.028 to 0.118 m s21, which were clearlyless than those values from inversion (Table 1). The RMSDs of assimilation varied little with the decrease in
the number of stations compared with inversion. Even when there was only one ray to assimilate (Case 5),
the results were still close to Case 0 (RMSD 5 0.118 m s21). These results indicate that assimilation allowed
the researchers to deploy fewer stations as well as obtain a higher accuracy current ﬁeld.
Then, the velocities obtained by inversion and assimilation of Cases 1–5 at the three ADCP stations werecompared with ADCP measurements. The RMSDs with ADCPs were larger for the inversion than for theassimilation in all ﬁve cases (Figure 14), indicating that assimilation had a higher accuracy than inversion
with a decrease in the number of CAT stations. Furthermore, the accuracy of assimilation was more stable

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Journal of Geophysical Research: Oceans
Table 1. Comparison With Standard Experiments of Inversion and
Assimilation for Eliminating the Station Number

Case 0Case 1Case 2
Case 3
Case 4
Case 5

RMSDs With
Case 0 (m s21)

Retained
Stations

Ray Number

Inversion

Assimilation

C1–C7
C2–C7
C1, C3–C6
C1, C3, C4, C6
C3, C4, C7
C4, C7

21
15
10
6
3
1

0.184
0.214
0.264
0.319
0.485

0.028
0.059
0.056
0.072
0.118

10.1002/2017JC012715

than inversion when the number of stations
decreased from six to two in A1, A2, and A3. The
RMSDs between sensitivity cases of inversion
and ADCP data in A3 were obviously larger thanA1 and A2 with a maximum value of 0.526 m
s21 in Case 4 (Figure 14), while the RMSDs
between sensitivity cases of assimilation and
ADCP data in A3 were about 0.1 m s21 in all ﬁve
cases (Figure 14). This also meant that theassimilation was more stable than inversion in
the peripheral regions of the CAT observation.

In this observation, the performance of Case 2
and Case 3 by assimilation (i.e., the number of stations was ﬁve and four, respectively) was almost the same,
which was slightly worse than Case 1 (Table 1). Compared with ADCP data, the mean RMSDs of Case 2 andCase 3 was also very close to values of 0.11 and 0.12 m s21, respectively. The mean RMSDs compared with
ADCP data were about 0.10 m s21 for Case 1 to Case 3, but larger than 0.15 m s21 for Case 4 and Case 5.
Thus, the schedule with four stations (i.e., Case 3) was the most economical and reasonable deployment byusing assimilation in Sanmen Bay observation.
All the sensitivity experiments indicate that the inversion was not only strongly affected by the loss of soundtransmission lines but also sensitive to the distribution of the remaining sound transmission lines. The assimilation would obtain a more accurate current ﬁeld against the loss of sound transmission lines; the effects of losing a few sound transmission lines or stations were negligible. Missing values are ineluctable in CAT
observations, especially in coastal seas with heavy ship trafﬁc and high environmental noise levels [X.-H. Zhu
et al., 2015]. Thus, data assimilation provides a more accurate and adequate method for reconstructing the current ﬁeld using CAT data.

7. Summary

RMSD (m s−1)

In this study, we present the assimilation of CAT data with the EnKF scheme using a triangular mesh in Sanmen Bay, adjacent to the East China Sea. We determined the measurement operator H that relates ocean
model velocities to CAT observations
Case 1Case 2
Case 3
Case 4
Case 5used in the EnKF scheme, by calculat0.6
ing the location and direction of soundtransmission lines in triangular meshes.
This is the ﬁrst application of triangular0.5mesh for CAT assimilation, which issuitable to regions with complex
coastlines.
0.4

Figure 14. The root-mean-square differences (RMSD) for inversion (triangular)
and assimilation (circle) of Cases 1–5 with ADCP in A1 (red), A2 (black), and A3(blue).

The triangular meshes, with a spatial
resolution of about 250 m in the observation region, ﬁt the complex coastlines well. The ﬁne structure of thecurrent ﬁelds near Yangjiao Island in
the observation region was described
well using assimilation, although this
could not be achieved by inversion or
by a structured grid ocean model withrough coastlines [Chen et al., 2003,
2006]. Furthermore, the distribution ofcurrent ﬁelds in vertical layers was also
described well, which cannot be
achieved by inversion or a 2-D ocean
model of CAT assimilation.

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0.3

0.2

0.1

0
6

5

4

3

2

Station number

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Journal of Geophysical Research: Oceans

10.1002/2017JC012715

Accuracy of the assimilated current velocities was higher than that obtained by either inversion or simulation. In depth-averaged comparisons, the RMSDs of the eastward and northward components as comparedto ADCP data were 0.09 and 0.06 m s21 for assimilation, 0.12 and 0.12 m s21 for inversion, and 0.17 and0.16 m s21 for simulation, respectively. In vertical layers, the RMSDs of the eastward and northward components as compared to ADCP data ranged from 0.02 to 0.14 m s21 for assimilation, while ranged from 0.08 to
0.27 m s21 for simulation.
Furthermore, the result of assimilation was less affected than that of inversion when three sound transmission lines were removed. The sensitivity experiment indicated that the observation with four CAT stations in
Sanmen Bay was the relatively economical and reasonable situation by using assimilation. Although only
one set was carried out in sensitivity experiment, the region surrounded by these four stations covered
main observational region of this experiment.
From our study, the performance of CAT data assimilation was superior to that of tomographic inversion ormodel simulation. The application of triangular meshes in complex coastlines regions when assimilating the
CAT data into an ocean model also provides the ﬁne structures of tidal currents and residual currents. In
addition, considering the complex variation of current ﬁelds in coastal regions, the 3-D results with assimilation are more beneﬁcial for researchers in understanding the structure of current ﬁelds in detail. Thus, data
assimilation with a 3-D triangular mesh ocean model in the coastal regions appears to be more effective inreconstructing the current ﬁeld using CAT data.

Acknowledgments
This study was supported by the
National Natural Science Foundationof China (41776107, 41606113,
41476020, 41621064, 41576001,
41576031, and 41606012); the National
Key Research and Development
Program of China (2016YFC1400104);
the Scientiﬁc Research Fund of SIO
under grants JT1604 and JG1621; theNational Programme on Global
Change and Air-Sea Interaction (GASIIPOVAI-01–02); the Zhejiang Provincial
Natural Science Foundation of China(LQ17D060003); the Project of StateKey Laboratory of Satellite Ocean
Environment Dynamics, Second
Institute of Oceanography(SOEDZZ1701); the grants from thegovernment to national university
corporations for Joint Usage/ResearchCenter, MEXT, Japan. Numericalmodeling was supported by the High
Performance Computing andCommunications at the Stat Key
Laboratory of Satellite Ocean
Environment Dynamics. We also thankShen Zheqi for the help of data
assimilation. The data used in thispaper are available on request (contact
Zhu X.-H. at xhzhu@sio.org.cn). The
observational data (ADCP and CATdata) are also available fordownloading at https://www.dropbox.
com/s/lmm57awgdt2zyvb/data_of_
CAT_assimilation.zip?dl50.

ZHU ET AL.

References
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