PUBLICATIONSJournal of Geophysical Research: Oceans
RESEARCH ARTICLE
10.1002/2013JC009262
Key Points:
 The density-driven current in
Jiaozhou Bay was simulated by adiagnostic model The results by nonsynchronous data
are quite different with synchronousdata The results by tidally averaged data
are consistent with synchronous data

Correspondence to:Z. Liu,zliu@ouc.edu.cn

Citation:
Cai, Z., Z. Liu, X. Guo, H. Gao, and Q.
Wang (2014), Inﬂuences of intratidal
variations in density ﬁeld on thesubtidal currents: Implication from asynchronized observation bymultiships and a diagnostic
calculation, J. Geophys. Res. Oceans,
119, 2017–2033, doi:10.1002/
2013JC009262.
Received 9 JULY 2013
Accepted 10 FEB 2014
Accepted article online 18 FEB 2014
Published online 18 MAR 2014

Influences of intratidal variations in density field on thesubtidal currents: Implication from a synchronized observation
by multiships and a diagnostic calculation
Zhongya Cai1, Zhe Liu1, Xinyu Guo2, Huiwang Gao1, and Qiang Wang3
1

Key Laboratory of Marine Environment and Ecology, Ministry of Education, Ocean University of China, Qingdao, China,
Center for Marine Environmental Studies, Ehime University, Matsuyama, Japan, 3North China Sea Marine Forecasting
Center of State Oceanic Administration, Qingdao, China

2

Abstract Using synchronous observational water temperature and salinity data collected simultaneously
by 21 ships in summer and a three-dimensional robust diagnostic model, we calculated the density-driven
current in Jiaozhou Bay (JZB), a semienclosed bay in the Yellow Sea. Special attention was paid to the inﬂuences of intratidal variations in temperature and salinity on the density-driven current. The density-driven
current in JZB has a maximum speed of 0.1 m s21 and is stronger than the tide-induced residual current
in some places. The density-driven current is characterized by the intrusion of high-density (low-density)
water in deep (shallow) areas. The results of the diagnostic model depend heavily on the observational
data. For example, the density-driven current calculated from nonsynchronous data obtained by one ship at
the same 21 stations is not consistent with that calculated from synchronous data because the nonsynchronous data correspond to different tidal phases at different stations. The intratidal variations of the density
ﬁeld result in a false spatial variation of density in the nonsynchronous data, which induces a false densitydriven current that is of the same order as that calculated from the synchronous data. In contrast, the tidally
averaged water temperature and salinity, which were used to remove intratidal variations from the synchronous data, diagnosed a density-driven current consistent with that from synchronous data. We, therefore,
conclude that it is not necessary to explicitly resolve the intratidal variations in density in the calculation ofdensity-driven current, but it is necessary to remove intratidal variations in the density ﬁeld before thecalculation.

1. Introduction
Density-driven current, an important component of coastal circulation, can be calculated by diagnostic
models [Sarkisyan and Ivanov, 1971; Holland and Hirschman, 1972]. It is commonly known that the accuracyof a diagnostic model depends on the quality of water temperature and salinity data used [Holland andHirschman, 1972]. In the open ocean, the hydrographic properties of water vary slowly; thus, steady ﬁelds ofwater temperature and salinity are usually used in diagnostic models [Sarkisyan and Ivanov, 1971; Hollandand Hirschman, 1972; Sarmiento and Bryan, 1982; Fujio and Imasato, 1991]. However, the strong tidal current
in coastal regions and consequent intratidal variations in water temperature and salinity suggest that it is
not reasonable to diagnose the density-driven current in a semienclosed bay using steady ﬁelds of watertemperature and salinity.
In principle, the intratidal variations in water temperature and salinity require the use of synchronous in situ
observation data with sufﬁcient temporal and spatial resolutions to diagnose a density-driven current. However, it is very difﬁcult to obtain the labor, equipment, and ﬁnancial resources required to engage dozens ofsurvey ships simultaneously to make synchronous observations. In practice, nonsynchronous data (e.g., datacollected at different stations at different times by one ship) or so-called climatological mean data (i.e., thestatistical means of data measured on several cruises over many years) are most widely used in diagnostic
models, and the impact of intratidal variations of temperature and salinity on density-driven currents has
seldom been reported [e.g., Fujio and Imasato, 1991; Yanagi and Takahashi, 1993; Guo and Yanagi, 1996;
Guo et al., 2004; Lee et al., 2004; Lee and Chao, 2003; Liu et al., 2010].
In the summer of 2009, we used 21 ships to carry out a synchronous observation at 21 stations in a semienclosed bay, Jiaozhou Bay (JZB), on the western coast of the Yellow Sea. Using the synchronously observed

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water temperature and salinity data from this ﬁeld campaign, we established athree-dimensional robust
diagnostic model to demonstrate how and to what
extent the intratidal variations in the water temperature and salinity affect thedensity-driven current.
JZB (35 580 N-–36 180 N,
120 040 E–120 230 E) is a semienclosed shallow water bodywith an area of 397 km2, anaverage depth of approximately 7 m, and a maximum
Figure 1. Bathymetry (m) of Jiaozhou Bay. The inset in the top-right corner shows the location
depth of 60 m at the bayof Jiaozhou Bay. The gridded region is the tidal ﬂat. ‘‘ST’’ followed by a number denotes the sammouth (Figure 1). JZB is conpling stations where observations were conducted in August 2009. Additional surface current
data were collected at stations denoted by black triangles. The winds and sea level werenected to the Yellow Sea byrecorded at Xiaomaidao and Dagang, respectively. The black line is the route of the virtuala narrow channel. Freshwaterobservation described in section 2.1. The black dashed line denotes the section across which
input into the bay comes prithe density-driven current is shown in Figure 8, and the dotted line at bay head denotes thelocation of the cross-sea bridge’s piers in JZB.
marily from the Dagu River(Figure 1) [Han et al., 2007].
The water movement in JZB is affected by strong tidal currents, of which the M2 tidal constituent is
the strongest [Ding, 1992]. Under the inﬂuence of semidiurnal tides, the water temperature and salinity
have been reported to vary intratidally [Liu et al., 2005]. However, the density-driven current in JZB
and the inﬂuences of intratidal variations in water temperature and salinity on this current have notbeen reported in previous studies [e.g., Shi et al., 2011; Wang et al., 2009; Liu et al., 2007, 2004; Chenet al., 1999].

2. Data and Methods
2.1. Field Observations and Data Processing
To reveal the spatial and intratidal variations of water temperature and salinity in JZB, a synchronous observation campaign was conducted in August 2009. The observation network comprised 21 anchor stations(Figure 1). At each anchor station, one boat with three to four persons and one set of conductivitytemperature-depth (CTD) (see Table 1 for the type of instrument) were used. In total, 21 ships and >80
crewmembers worked together. The observation began at approximately 13:00 on 17 August and lasted
over 25 h (i.e., one lunar day). However, it began to rain at 06:00 on 18 August. To exclude the effects of therain, we used only the in situ observational data of temperature and salinity in the ﬁrst M2 tidal period inthis study. In addition to the in situ data, the hourly winds measured at the Xiaomaidao weather station andsea level data from 1 August 2009 to 31 August 2009 recorded at Dagang tidal gauge were also used in thisstudy. The temperature, salinity, and wind data were used to drive the model, and the current and sea level
data were used to validate the model results.
Generally, vertical proﬁles of water temperature and salinity were obtained each hour at each station, except for at some shallow stations (Table 1). At these shallow stations, we measured watertemperature and salinity only in the surface layer (1.0–1.5 m). As we prepared the data for the diagnostic model, we assumed vertical homogeneity at these shallow stations. The interpolation of insitu data to the model grid was conducted linearly in the vertical direction at each station and trigonometrically in the horizontal direction. Linear interpolation was applied to obtain data at each time
step throughout the calculation. In addition to the hydrographic data taken at all 21 stations, thesurface current was also measured at eight stations (black triangles in Figure 1) by current meters(Table 1). These current data as well as the sea level data at Dagang tidal station (Figure 1) wereused to validate the model results.

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Table 1. Position and Mean Depth of the Observation Stations, Sampling Depth at Each Station, Instruments and Sampling Interval for Water Temperature (T) and Salinity (S), Observation Time at Each Station by the Virtual Ship Described in Section 2.1 and Corresponding Tidal Phase at the Virtual Ship’s Observation Time

StationLocation

Mean
Depth
(m)

ST1
ST2
ST3
ST4
ST5
ST6
ST7
ST8
ST9
ST10
ST11
ST12
ST13
ST14
ST15
ST16
ST17
ST18
ST19
ST20
ST21

120.325E, 36.179N
120.205E, 36.147N
120.226E, 36.158N
120.250E, 36.158N
120.289E, 36.155N
120.330E, 36.155N
120.187E, 36.133N
120.231E, 36.133N
120.276E, 36.132N
120.308E, 36.130N
120.177E, 36.104N
120.249E, 36.097N
120.292E, 36.100N
120.207E, 36.090N
120.233E, 36.067N
120.254E, 36.070N
120.301E, 36.082N
120.280E, 36.052N
120.244E, 36.037N
120.256E, 36.029N
120.283E, 36.035N

4.0
2.6
3.6
4.0
5.0
8.0
6.0
7.0
6.0
6.0
3.9
15.0
3.9
11.2
9.6
21.5
8.8
16.4
5.6
12.0
28.3

Sampling
Interval

Instrumenta
Sampling
Layer (m)1.0Proﬁle
1.0
1.0
1.0
Proﬁle1.0
Proﬁle
1.5
1.5
1.0
Proﬁle1.0
ProﬁleProﬁleProﬁleProﬁleProﬁle1.0
ProﬁleProﬁle

S

T

S

T

Time

Tide Phase

SYA2-2
Alec AAQ1183
SYA2-2
RBR XR-420-CTD
SYA2-2
RBR XR-420-CTD
SYA2-2
Alec AAQ1183
RBR XR-420-CTD
RBR XR-420-CTD
SYA2-2
RBR XR-620
Alec Compact-CT
Alec Compact-CT
Alec Compact-CT
RBR XR-620
Alec Compact-CT
Alec Compact CTD
SYA2-2
Alec Compact-CT
RBR XR-620

RBR TDR-2050

1h
1h
1h
1 min
1h
1h
1h
1h
1 min
1 min
1h
1h
1 min
1h
1h
1h
1h
1h
1h
1h
1h

1 min

17 Aug 18:34:02
17 Aug 22:10:19
17 Aug 21:43:13
17 Aug 21:16:07
17 Aug 19:07:25
17 Aug 18:05:20
17 Aug 22:37:36
17 Aug 20:45:25
17 Aug 19:36:47
17 Aug 17:34:20
17 Aug 23:08:22
17 Aug 20:11:28
17 Aug 17:02:33
17 Aug 23:38:35
18 Aug 00:09:47
17 Aug 16:01:04
17 Aug 16:35:34
17 Aug 15:27:02
18 Aug 00:41:08
18 Aug 01:07:16
17 Aug 15:00:00

Max ebb-low tide
Low tide-max ﬂood
Low tide-max ﬂood
Low tide (21:00)
Max ebb-low tide
Max ebb-low tide
Low tide-max ﬂood
Low tide (21:00)
Max ebb-low tide
Max ebb-low tide
Low tide-max ﬂood
Max ebb-low tide
Max ebb (17:00)
Max ﬂood (00:00)
Max ﬂood (00:00)
High tide-max ebb
Max ebb (17:00)
High tide-max ebb
Max ﬂood-high tide
Max ﬂood-high tideHigh tide (14:00)

RBR TDR-2050
RBR TDR-2050
RBR TDR-2050

RBR TDR-2050
Alec Compact-TD
Alec Compact-TD
Alec Compact-TD
Alec Compact-TD
Alec Compact-TD
Alec Compact-TD

1 min
1 min
1 min

1 min

1 min

a
SYA2-2 is a salinity meter made by Tianjin Marine Environmental Monitoring Central Station. TDR-2050 is a temperature and depth logger produced by RBR Ltd. AAQ1183 is amodernized compact and light-weight multiparameter water quality meter produced by Alec Electronics Co., Ltd. RBR XR-420-CTD and XR-620 are conductivity, temperature, anddepth loggers produced by RBR Ltd. Compact-TD, Compact-CT, and Compact-CTD are small, highly accurate two-channel recorders for temperature-depth, conductivity-temperature,and conductivity-temperature-depth, respectively, produced by Alec Electronics Co., Ltd.

To determine the difference between synchronous data and nonsynchronous data, we designed a virtual
observation to obtain nonsynchronous data from the hourly measured synchronous data. To simulate typical nonsynchronous observations, we assumed that only one ship with a speed of 10 nautical miles perhour visited all the stations and spent 20 min sampling at each station. With these assumptions, the virtual
observation started at 15:00 on 17 August at station ST21 and ﬁnished approximately 10 h later at station
ST20. The ship’s route is shown in Figure 1. The data for the virtual survey were derived from the data fromthe synchronous observation at the arrival time of the virtual ship at each station. If the arrival time of thevirtual ship did not coincide exactly with the real sampling time at that station, a linear interpolation in time
was applied to the two neighboring data points to calculate the data for the virtual observation. The tidally
averaged ﬁelds of water temperature and salinity were obtained by temporally averaging the hourly synchronous data. The nonsynchronous data and the tidally averaged data were spatially interpolated to all
the grid points and ﬁxed throughout the calculation.
2.2. Robust Diagnostic Model
Sarmiento and Bryan [1982] proposed the concept of robust diagnostic model, which has since been widelyused by many studies to calculate density-related currents [Fujio and Imasato, 1991; Yanagi and Takahashi, 1993;
Guo and Yanagi, 1996; Guo et al., 2004; Lee et al., 2004; Lee and Chao, 2003; Wright et al., 2006; Liu et al., 2010].
Based on the Princeton Ocean Model [Blumberg and Mellor, 1987; Mellor, 2004], we established a robust
diagnostic model following the method of Sarmiento and Bryan [1982]. The original Princeton Ocean Model
was modiﬁed by adding a damping term to the right-hand side of the conservation equations for watertemperature and salinity:






@C @uC @vC 1 @xC @@C@@C
1 @ Av @C
1
1
1
5
AH
1
AH
1
1cðC  2CÞ;@t@x@y D @r@x@x@y@y
D @r D @r(1)

where C represents the water temperature or salinity; t is the time; x, y, and r are the three spatial coordinates; u, v, and x are the components of the velocity in the three respective spatial coordinates; AH and Av
are the horizontal and vertical diffusivity coefﬁcients, respectively; C* is the datum observed at each grid
point interpolated from the in situ observational data; and c is a nonnegative constant controlling the role

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of the observed data C*. The last term in equation (1) prevents the calculated value C from deviating greatly
from the observed value C*.
The model domain (Figure 1) includes a tidal ﬂat region, which was treated by a wetting and drying scheme[Oey, 2005]. There are 159 3 185 grid points with a resolution of 200 m in the horizontal direction and 15
evenly arranged vertical levels. The time step is 1.5 s for the external mode and 12 s for the internal mode. In
addition to prescribing the observational data for C* in equation (1), we also speciﬁed the M2 and S2 tidal forcings at the open boundary and wind stresses at the sea surface. The amplitudes and phases of the M2 and S2
tidal constituents at the open boundary were obtained from the marine atlas of the Bohai Sea, Yellow Sea,and East China Sea [Chen et al., 1992]. The radiation condition was used for the normal component of thevelocity and no-ﬂux condition was used for salinity and temperature along the open boundary. The windstress (s) was calculated from the wind data collected at the Xiaomaidao weather station (Figure 1) as follows:2
s5qa CD U10;(2)where qa 5 1.3 kg m23 is the density of air, U10 is the wind speed (m s21) at 10 m and CD is the drag coefﬁcient, which has a value of 1.64 3 1023, according to the equation given by Stewart [2008]. The current andsea level were initialized to zero and the calculation time was 70 days.
Synchronous data were used in Case 1 (Table 2), which includes the inﬂuence of intratidal variations inwater temperature and salinity on the density-driven current. Nonsynchronous data collected by the virtual
ship were used in Case 2 (Table 2), which calculates a false density-driven current caused by false spatial
variations in the density ﬁeld arising from temporal (intratidal) variations in water temperature and salinity.
Tidally averaged data were used in Case 3 (Table 2), which clariﬁes the strength of the inﬂuences of intratidal variations in water temperature and salinity on the density-driven current.
The hourly model results of these three cases on the last 25 h were saved for further analysis after theyreached equilibrium. The density-driven current in these cases was obtained by subtracting the overall current from an accompanying calculation of current in which the tide and surface winds were considered but
a constant density was used. This subtraction method was applied to the model results saved on the last 25
h in the three cases. The difference in the hourly current ﬁeld given by the subtraction method on the last
25 h was averaged to obtain the tidally averaged density-driven current.
In the robust diagnostic model, an important issue is the determination of the damping coefﬁcient c. If c iszero, the modeled temperature and salinity are independent of the observation data and the model is afully prognostic model. As c becomes larger, C* plays a more important role. As c tends toward inﬁnity, themodel becomes a purely diagnostic model (C 5 C*).
To examine the relative importance of the damping term to the horizontal advection term in equation (1),Sarmiento and Bryan [1982] introduced a scale velocity V* and a scale length L* so that the ratio of thedamping term to the horizontal advection term is cL*/V*. The authors calculated the circulation in the Atlantic using a depth-dependent c that decreased from 1/50 day21 at the surface to 1/250 day21 at the bottom.
Because the scale length L* is much smaller in JZB than in the Atlantic, a larger c is needed to make thedamping term balance the advection term. In addition, because the data in this study were measured synchronously, a large c is preferred because high-quality data help to diagnose a reliable ﬂow ﬁeld.
Because the density-driven current is primarily driven by the baroclinic pressure gradient, we need to know
how the horizontal gradient of density in the model changes with the damping coefﬁcient c. A variable M,
representing the magnitude of the horizontal gradient in the density ﬁeld, is deﬁned as

Table 2. Conditions Used in the Numerical Experiments to Investigate the Mechanisms Governing the Density-Driven Current
Case
1
2
3
4
5

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Type of Data

Vertical Turbulent
Viscosity Coefficient

Usage

Hourly synchronous data
Nonsynchronous data
Tidally averaged data
Hourly synchronous data
Hourly synchronous data

Calculated in the modelCalculated in the modelCalculated in the model
From Case 2
From Case 3

Background ﬂow ﬁeld
Effects of nonsynchronous data on density-driven current
Effects of tidally averaged data on density-driven current
Effects of vertical turbulent viscosity in Case 2 on density-driven current
Effects of vertical turbulent viscosity in Case 3 on density-driven current

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Figure 2. Absolute difference in the averaged horizontal gradient of the modeled water density (Mmodel) and the observed water density(Mobs) versus the damping coefﬁcient c. See equation (1) for the deﬁnition of c and equation (3) for the deﬁnition of M.

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
s
 
ﬃ
@q @q @r 2
@q @q @r 2
M5
1
1
1
;
@x @r @x@y @r @y(3)

where q is the density. Figure 2 shows the spatial mean of the difference in M between observation andsimulation in JZB as a function of c21. As c decreases, the difference between the objectively interpolated
water temperature and salinity and those calculated by equation (1) increase and the density distribution is
gradually controlled more by the advection term in equation (1). The difference between the modeled andobserved density gradient becomes relatively stable when c is lower than 0.25 h21 (Figure 2), indicatingthat the density distribution is approximately stable after being adjusted by equation (1). Hence, c was set
to a slightly higher value (0.25 h21) to retain the information of the synchronous observation data as muchas possible in this study.

3. Results
3.1. Model Validation
The model was calibrated with the sea level at Dagang tidal station and the sea surface current measured
at eight stations (Figure 1). The error in the M2 amplitude and the phase of sea level between observationand simulation are 0.02 m and 0.54 , respectively. Because the velocity data were measured only over a 25
h period, the ellipse parameters of the semidiurnal tide were used to validate the calculation of velocity. At
ST12 and ST16, the results differ a little largely from the observation (Table 3). A reasonable explanation on
this conﬂict is the resolution of the model (i.e., 200 m) that is apparently insufﬁcient to resolve the steep
topography around two stations (Figure 1). But at most stations the simulated and observed harmonic constants of tidal currents show reasonable agreement (Table 3). The mean difference of the semimajor axis
between the simulated and observed velocities is 0.11 m s21. The mean difference of ellipse inclination andphase is both <15 .
Because this study focuses on the density-driven current, it is also necessary to validate the subtidal currents in the model output. The overall subtidal current, which was calculated by averaging the observed
current velocity over the 25 h period, has three components: the tide-induced residual current, the densitydriven current, and the wind-driven current. It is difﬁcult to separate these three components of the observation. Therefore, to validate the model result, tidal, and wind forcing as well as the temperature and salinity ﬁelds were all included in the model calculation. The modeled subtidal current in Case 1 was thenobtained by averaging the model results over the 25 h period.
According to Table 4, the magnitude of the subtidal current is usually one order of magnitude smaller thanthat of tidal current in JZB. Consequently, it is more difﬁcult to accurately simulate the subtidal current than
the tidal current. Besides, the existence of the cross-sea bridge (Figure 1) can affect the subtidal current byaltering local topography. The diameter of the bridge piers is 1.8 m and the distance between ST7 and its
nearest pier is <200 m. Owing to the horizontal resolution of 200 m, it is difﬁcult for the model to take into
account the inﬂuence of cross-sea bridge on the currents and consequently we observed a slightly large
error between simulated current and observation data at ST7. However, the modeled subtidal currents are
generally consistent with the observed currents at most stations. The differences in direction and magnitude

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Table 3. Observed and Modeled Tidal Ellipse Parameters for Surface Semidiurnal Tides at the Stations in Figure 1
Observation

Station
ST5
ST7
ST8
ST10
ST12
ST13
ST16
ST21
Mean
RMS

Absolute Value of Difference Between
Observation and Simulation

Simulation

Semimajor
Axis (m s21)

Semiminor
Axis (m s21)

Inclination
( )

Phase
( )

Semimajor
Axis (m s21)

Semiminor
Axis (m s21)

Inclination
( )

Phase
( )

Semimajor
Axis (m s21)

Semiminor
Axis (m s21)

Inclination
( )

Phase
( )

0.36
0.30
0.31
0.30
0.24
0.29
1.09
0.8

0.08
0
0.04
0.02
0.01
0.05
0.01
0.03

43.93
110.51
97.06
54.14
128.91
59.74
97.24
154.58

59.35
45.13
65.2
30.07
15.49
24.5
65.39
54.9

0.28
0.33
0.31
0.33
0.36
0.37
0.64
0.88

0.03
0.01
0.04
0.03
0
0.07
0.05
0.06

59.13
126.81101.25
62.92
98.77
65.51
100.74
153.2

46.32
45.59
51.72
47.06
56.38
34.17
62.84
38.85

0.08
0.03
0.00
0.03
0.12
0.08
0.45
0.08
0.11
0.14

0.05
0.01
0
0.01
0.01
0.02
0.04
0.03
0.02
0.02

15.2
16.3
4.19
8.78
30.14
5.77
3.5
1.38
10.66
9.55

13.03
0.46
13.48
16.99
40.89
9.67
2.55
16.05
14.14
12.37

of the modeled and observed subtidal currents are approximately 35 and 30%, respectively. We, therefore,
conclude that the diagnostic model can capture the general features of the residual current in JZB.
3.2. Modeled Temperature and Salinity Fields
Figure 3 shows the horizontal distributions of the calculated temperature, salinity, and density during theM2 tidal cycle. The hydrographic features in JZB are inﬂuenced by the freshwater input from rivers and the
intrusion of Yellow Sea water from the bay mouth. The former is characterized by low salinity and low density, whereas the latter has high salinity and high density. In addition, the combination of surface heating,tidal mixing, and bathymetry results in high temperatures in shallow regions (e.g., at the bay head) and low
temperatures in deep regions (e.g., at the bay mouth). Fronts of salinity and density are found in the offshore area near the Dagu River mouth. The position of the fronts changes within a tidal cycle. During theﬂood tide, the fronts move to the river mouth as the low-temperature, high-salinity Yellow Sea water enters
the bay. During the ebb tide, the fronts move to the bay mouth as the Yellow Sea water exits (Figure 3).
The spatial variations in water temperature, salinity, and density over the entire bay are 2.5 C, 1.50, and
2.0 kg m23, respectively, as observed in their tidally averaged ﬁelds (Figure 4, top). The temporal variation isdemonstrated by the difference between the maximum and minimum values of temperature, salinity, anddensity in a tidal cycle (Figure 4, bottom). The range of the temporal variations in water temperature, salinity, and density is 1.5 C, 1.50, and 1.5 kg m23, respectively, near the river mouths; these ranges decrease
toward the bay mouth.
3.3. The Density-Driven Current Calculated With Synchronous Data
In the surface layer (Figure 5a), the density-driven current is southward around the bay mouth, ﬂowing fromthe shallow area to the deep area. The current is westward in the northern area of the bay and southwestward in the western area of the bay (Figure 5a). The maximum speed of the surface density-driven current
is >0.1 m s21 near the bay mouth. In the bottom layer (Figure 5b), the density-driven current is generally
weak and in a different direction than that in the surface layer. At the bay mouth, the bottom
Table 4. The Comparison of Residual Currents From Observation and From the Diagnostic Model in the Surface Layera
Observation

Simulation

StationMagnitude (cm s21)

Direction ( )Magnitude (cm s21)

Direction ( )Relative Differenceof Magnitude (%)

Absolute Differenceof Direction ( )

ST5
ST7
ST8
ST10
ST12
ST13
ST16
ST21

2.1
1.6
5.2
4.1
5.2
3.0
25.1
23.3

265.8
49.7
205.9
265.0
260.1
151.0
52.4
237.1

1.7
0.8
5.0
3.4
6.3
3.7
14.3
18.6

291.6
285.3
209.4
2141.0
278.6
173.8
32.9
206.5

17.3
51.8
3.2
15.7
20.8
25.1
43.2
20.2

25.8
135.0
23.5
76.0
18.5
222.8
19.5
30.6

a

The angles 0 , 90 , 180 , and 270 indicate that the direction of ﬂow is north, east, south, and west, respectively.

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Figure 3. (left) Sea surface temperature ( C), (middle) sea surface salinity, and (right) sea surface density (rt) obtained by synchronous
observation at different tidal phases (low tide, maximum ﬂood, high tide, and maximum ebb).

density-driven current is northward, ﬂowing into the bay through the deep western channel (see Figure 1
for bathymetry).
The vertical distribution of the density-driven current normal to a section across the bay mouth is presented
in Figure 6. The current is southward in the upper layer but northward in the lower layer. The interface ofthe two opposite currents is at a depth of 20 m. It is clear that the Yellow Sea water enters JZB in the bottom layer while the bay water leaves JZB in the surface layer.
The water movement in JZB is dominated by tidal motion and M2 tide is the dominant tidal constituent
that accounts for 80% of kinetic energy [Ding, 1992]. The magnitude of tidal currents is higher than that of

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Figure 4. (a) Tidally averaged sea surface temperature ( C), (c) sea surface salinity, and (e) sea surface density (rt) and (b) difference between the maximum and minimum values of sea
surface temperature ( C), (d) sea surface salinity, and (f) sea surface density (rt) over a tidal cycle.

subtidal currents by one order. Owing to the nonlinear effects in the tidal currents, tide-induced residual
current inevitably accompanies the tidal currents throughout the year. Following many previous studies[e.g., Shi et al., 2011; Chen et al., 2011; Lv et al., 2010; Lou et al., 2009; Liu et al., 2004], tidal motion is considered to provide a background for the physical variables such as water temperature, salinity, and densitydriven currents in this study. The tide-induced residual current in the surface layer is strong around the bay
mouth, where its magnitude is larger than 0.1 m s21 (Figure 7a). It is weaker in the central part and bay
head. Generally, the tide-induced residual current is weaker in the bottom layer (Figure 7c) than in the surface layer (Figure 7a). The spatial pattern of the tide-induced residual current found in this study (Figures 7aand 7c) is consistent with that reported in previous studies [e.g., Lou et al., 2009; Shi et al., 2011].
The magnitude ratio a of the density-driven current to the tide-induced residual current was calculated asfollows:
a5j~
V d j=j~
V t j;(4)

where ~
V d is the density-driven current and ~V t is the tide-induced residual current. The ratio in the surface(bottom) layer was calculated for areas where the magnitude of ~V t is greater than 0.01 m s21 (0.005 m s21).
The ratio is greater than 0.5 in most areas of both the surface and bottom layers (Figures 7b and 7d), indicating that the density-driven current is an important component in the summer circulation in JZB.
3.4. The Density-Driven Current Calculated With Nonsynchronous Data
As described in section 2.1, nonsynchronous data were obtained by ‘‘implementing’’ a virtual observation.
The density ﬁeld from nonsynchronous data generally has the same spatial distribution as the averaged
synchronous density ﬁeld. We can identify the low-density area in the northwestern area of JZB in both thesurface and bottom layers (Figures 8a and 8c). However, the difference between the nonsynchronous data
and averaged synchronous data (Figures 8b and 8d) is also clear. For example, the water density in westernpart of JZB is lower in the nonsynchronous data than in the tidally averaged synchronous data (e.g., the difference of about 2.0 kg m23 off Dagu River mouth), while the density in eastern part of JZB is higher in
the nonsynchronous data than in the tidally averaged synchronous data (e.g., the difference of about 0.3

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Figure 5. Horizontal distribution of the tidally averaged density-driven current (m s21) in the (a) surface layer (the topmost sigma layer)and (b) bottom layer (the lowest sigma layer). The color shows the magnitude of the velocity. This deﬁnition of the surface and bottom
layers is also used in the following ﬁgures.

kg m23 in the northeast of JZB) (Figures 8b and 8d). Consequently, the horizontal spatial gradient in density
is greater in the nonsynchronous data than in the tidally averaged synchronous data.
In Case 2, the density-driven current calculated using the nonsynchronous data (Figures 9a and 9c) is stronger than that calculated using the synchronous data (Figure 5). For example, the density-driven current in
the surface layer is intensiﬁed offshore of the Dagu River mouth, where the density gradient is greater in
the nonsynchronous data than in the synchronous data (Figure 8). The direction of the density-driven current also changes. For example, the surface density-driven current north of the bay mouth becomes eastward (Figure 9a). In the bottom layer, a strong northward inﬂow is found offshore of the Dagu River mouth
and an apparent westward current is found north of the bay mouth (Figure 9c). These features are signiﬁcantly different from those found using the synchronous data (Figure 5).
The vector difference (b1) and relative difference (b2) between the density-driven current calculated with
the nonsynchronous and synchronous data in the surface (Figure 9b) and bottom (Figure 9d) layers were
calculated as follows:b1 5~
V s 2~
V ns
b2 5jj~V s j2j~
V ns jj=j~
V s j;(5)

where ~
V s is the velocity calculated with the synchronous data (Case 1) and ~V ns is that calculated with thenonsynchronous data (Case 2). In areas where the density-driven current calculated with the synchronous

Figure 6. Vertical distribution of the tidally averaged density-driven current (m s21) over a cross section at the bay mouth. Positive current
is deﬁned to ﬂow northward.

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Journal of Geophysical Research: Oceans

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Figure 7. The tide-induced residual current in the (a) surface layer and (c) bottom layer, with color showing the magnitude of velocity; the ratio of magnitudes between the tidally averaged density-driven current and the tide-induced residual current in the (b) surface layer and (d) bottom layer.

data is sufﬁciently weak (<0.01 m s21 in the surface layer and 0.005 m s21 in the bottom layer), the relative
difference was not calculated. According to Figures 9b and 9d, the vector difference between the two
density-driven currents reaches 0.1 m s21 at the bay mouth, and b2 is close to or larger than 1.0 in someplaces (e.g., offshore of the Dagu River mouth and near the bay mouth) (Figures 9b and 9d). Therefore, thefalse current calculated with the nonsynchronous data is of the same order of magnitude as the densitydriven current calculated with the synchronous data.
3.5. The Density-Driven Current Calculated With Tidally Averaged Synchronous Data
To examine the inﬂuence of climatological mean data on the calculation of the density-driven current, Case
3 was designed. In Case 3, the tidally averaged water temperature and salinity data are used for C* in equation (1). The intratidal variations in the density ﬁeld are not included in this calculation.
The density-driven current calculated with the tidally averaged synchronous data (Figures 10a and 10c) does
not signiﬁcantly differ from that calculated with the original hourly synchronous data (Figures 5a and 5b). The
magnitude ratio b2 (Figures 10b and 10d) is <0.5 in most areas of JZB. Generally, the magnitude of densitydriven current calculated from tidally averaged data is slightly larger (5%) than that by synchronous data.

4. Impact of Data Type on the Diagnostic Model
The results in section 3 indicate that the nonsynchronous data fail to accurately reproduce the density-driven current, whereas the tidally averaged data are capable of showing the basic pattern of the density-driven current. To

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Figure 8. The density ﬁeld (rt) in the (a) surface layer and (c) bottom layer and the density difference between the nonsynchronous data and the tidally averaged synchronous data inthe (b) surface layer and (d) bottom layer. The nonsynchronous data were obtained by the virtual observation described in section 2.1.

understand the causes of these results, the horizontal pressure gradient and vertical turbulent viscosity (VTV) are
analyzed here. These two variables are major factors inﬂuencing the modeled density-driven current.
4.1. Horizontal Pressure GradientTo analyze the inﬂuence of the nonsynchronous data on the calculated baroclinic horizontal pressure gradient, we separated the driving force of the density-driven current into two components: a steady part andan oscillatory part. The steady part is deﬁned as the tidal average of the pressure gradient, and the oscillatory part represents its intratidal variation.
The pressure gradient force at depth z0 in the horizontal direction x can be decomposed into two terms:
ð g

ð
@ g
@q
@g
gqdz5gdz1qz5g
;
@x z0
@x
z0 @x

(6)

where q is the water density, g is the gravity acceleration (9.8 m s22), and g is the sea level. The density
observed by the synchronous observations and the water level in the model can be assumed to be the sumof its tidally averaged value and intratidal part:
(

0

q5
q 1q

0

;

(7)

g5
g 1g

 is tidally averaged density, g is the tidally averaged sea level, and q0 and g0 are their intratidal variawhere q
00
tions, respectively. For simplicity, we assume that q 5acos ðxt2ua Þ and g 5bcos ðxt2ub Þ, where a and b

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Figure 9. (a and c) The density-driven current calculated with the nonsynchronous data and (b and d) the difference in the density-driven
current between Case 1 and Case 2, as deﬁned by equation (5). Arrows show the vector difference and color shows the relative difference.
(left) The results in the surface layer and (right) the results in the bottom layer.

ÐT 0
are amplitudes, ua and ub are phases, and x is frequency. These functions satisfy the conditions 0 q dt50
ÐT 0
and 0 g dt50, where T is the tidal period.
Drho 1DA, where rho , A, and L are the characteristic values of the tidally averThe characteristic value of @qL@x isaged density, the intratidal variation of density, and the horizontal scale, respectively, and D represents thespatial variation of a variable. The ﬁrst term (the vertical integration of the horizontal density gradient) on
the right side of equation (6) has a characteristic value of gHðDrhoL 1DAÞ, where H is the characteristic value ofthe water depth. In Case 3, the density-driven current was calculated using the tidally averaged density
data. The term gHDA
L is zero when averaged over a tidal cycle.

During the nonsynchronous observation cruise (i.e., the virtual cruise), data at different stations were inevitably measured in different tidal phases. Hence, the intratidal variation in the density ﬁeld results in an errorgHðDrho 1DAÞof gHA. The amplitude of the intratidal variation of density is considerable when compared
L inLwith the horizontal mean density difference D rho. For instance, the virtual observation measures Station 17
at about high tide but Station 7 at about low tide (Table 1) and estimates a surface layer density difference
between Station 17 and Station 7 of 3.4 kg m23. However, the tidally averaged observation data show asurface layer density difference of only 1.7 kg m23 between the two stations. Hence, nonsynchronous
observation can introduce signiﬁcant errors in the density gradient. Although we conducted only one virtual cruise, such errors cannot be avoided for any nonsynchronous cruise in JZB because cruises usually lastfor 9–15 h, which is close to the M2 tidal period in JZB, according to observations.
The modeled ﬂow ﬁeld driven by the tidally averaged temperature and salinity data in Case 3 was consistent with the tidally averaged ﬂow ﬁeld driven by the hourly synchronous data in Case 1. This consistency

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Figure 10. (a and c) The density-driven current calculated with tidally averaged data and (b and d) the difference in the density-driven current between Case 1 and Case 3 as deﬁned by equation (5). Arrows show the vector difference and color shows the relative difference.
(left) The results in the surface layer and (right) the results in the bottom layer.

implies that the impact of the intratidal variation in temperature and salinity ﬁelds on density-driven current
is rather limited. The tidally averaged baroclinic horizontal pressure gradient can be obtained from equations (6) and (7):


ð  ð
ð  ð
ð
1 T @ gg T @ g
@ g
gqdz dt5
qdz1
qdz dtT 0 @x z0
T 0 @x z0@x gð T ð g
ðg
g
@q
@
g
@q
@g
@
g
5
dz1qz5g1
dz1 qz5g 2qz5g
dt
T 0
@x
@x
@x
g @x
z0 @x
ð ð
ð
ð g
@
q
@
g g T g @q
g T 0 @g0
q
dt:
dz1g
q z5g
1
dzdt1
5g
@x T 0 g @x
T 0 z5g @x
z0 @x

(8)

Clearly, the characteristic values of the parts of baroclinic horizontal gradient explained by the tidally averaged density (the ﬁrst two terms on the right-hand side of the ﬁnal equation) are gHDrho =L and0grho DC=L, and the parts explained by the intratidal variation of density (the last two terms) are gC Drho =L0
and gADC =L. Here C and C0 are the characteristic values of the tidally averaged and intratidal variation of0
sea level, respectively. The ratios of the last two terms to the ﬁrst term are Drho C =Drho H and0
ADC =Drho H, respectively. In the calculations, C0 (1.5 m) and DC0 (0.1 m) are smaller than H (10 m), D
rho and D rho are approximately the same size (<3 kg m23) and A (1 kg m23) is smaller. Therefore, theintratidal variation of density cannot induce a signiﬁcant difference in the average horizontal pressure
gradient.

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Figure 11. (a–c) The vertical structure of the modeled density (rt) and (d–f) the vertical turbulent viscosity (m2 s211023) in (a and d) Case
1 (synchronous data), (b and e) Case 2 (nonsynchronous data), and (c and f) Case 3 (tidally averaged data) in section AB off the Dagu Rivermouth (shown in Figure 11a). The density and vertical turbulent viscosity are averaged over a tidal cycle for simplicity.

4.2. Vertical Turbulent Viscosity
The interaction between the horizontal density gradient and the vertical current shear leads to a forcing
mechanism known as ‘‘tidal straining’’ [Simpson et al., 1990], which tends to produce periodic stratiﬁcation.
As described in section 3.4, the horizontal density gradient, especially off the Dagu River mouth, increases
in the nonsynchronous data, which would lead to vertical stratiﬁcation through tidal straining. Furthermore,
the vertical stratiﬁcation would affect the VTV [Simpson, 1997; Simpson et al., 2005], and density-driven current would vary with the change in VTV. In this section, the modeled density and VTV in Cases 1 (synchronous data), 2 (nonsynchronous data), and 3 (tidally averaged data) in the section off the Dagu River mouth(shown in Figure 11a) are examined. These two variables are averaged over a tide cycle for simplicity. In

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Figure 12. The difference in the density-driven current (a and c) between Case 1 and Case 4 and (b and d) between Case 1 and Case 5 asdeﬁned by equation (5). Arrows show the vector difference and color shows the relative difference. (left) The results in the surface layerand (right) the results in the bottom layer.

Cases 1 and 3, the density is almost homogenous in the vertical direction (Figures 11a and 11c), whereas
stratiﬁcation appears with the larger horizontal density gradient in Case 2 (Figure 11b). The VTV in Cases 1
and 3 has the same pattern, but the VTV in Case 2, especially in the lower layers, is quite different from thatin Case 1.
It should be pointed out that vertical current shear would be different if different data types are used, which
would affect the VTV in the model. However, more emphasis should be given to the inﬂuence of different
VTV on the calculation of density-driven current than to the mechanism of the change in the VTV. Toward
this end, two additional experiments, Cases 4 and 5, were conducted. In Case 4, the synchronous data andthe VTV coefﬁcient from Case 2 were used, whereas Case 5 used the synchronous data and the VTV coefﬁcient from Case 3 (Table 2). The differences between these two cases and Case 1 were calculated according
to equation (5). The primary difference between Case 1 and Case 4 is located around the Dagu River mouth,
where the horizontal density gradient is large and the relative difference in density-driven current is greaterthan 1.0 (Figures 12a and 12c). Therefore, changes in both the horizontal density gradient and the verticalturbulent viscosity due to use of the nonsynchronous data inﬂuence the density-driven current. In contrast,
the differences between Cases 1 and 5 are relatively small (Figures 12b and 12d), indicating that changes inthe vertical turbulent viscosity that were introduced by the use of tidally averaged data have limited inﬂuence on the density-driven current.
From the above discussion on the impact of the data used in the model, some suggestions can be made forusing observational data in the diagnostic model. First, calculations of the density-driven current using nonsynchronous data observed in a tidal-current-dominated area will be inaccurate. In JZB, if the observation

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time is similar to or longer than a tidal period, it is impossible to obtain the basic pattern of density-driven
current from a diagnostic model using nonsynchronous data. Second, the climatological mean dataobtained by averaging observational data taken repeatedly at the same places are potentially useful in diagnostic models to obtain the density-driven current pattern. In JZB, the direction of density-driven current
calculated from tidally averaged data is consistent with that from synchronous data, although the magnitude is slightly larger by about 5%. In practice, it is therefore necessary to examine whether the data averaging method may effectively eliminate intratidal variations in the density ﬁeld.

5. Conclusions
Using a robust diagnostic model, the density-driven current was calculated using synchronous observational data in JZB. The density-driven current is characterized by a gravitational circulation, i.e., intrusion ofhigh-density water in deep areas and outﬂow of low-density water in shallow areas. The current calculated
in the diagnostic model depends strongly on the type of observational data used in the model. In areas
such as JZB, where the intratidal variation in the density ﬁeld is signiﬁcant and comparable to the spatial
variation in the density ﬁeld, nonsynchronous data will inevitably induce considerable errors in the calculated density-driven current. In a nonsynchronous survey, the data taken at different stations will generally
not be measured in the same tide phases; these intratidal variations will introduce errors in the density gradient and vertical turbulent viscosity. However, using the tidally averaged density ﬁeld obtained by averaging the synchronous data did not induce signiﬁcant errors into the calculated density-driven current. The
ﬁndings in this study will help to design more suitable observation plans in tide-dominated water bodies
like JZB.

Acknowledgments
The study was ﬁnancially supported by
the Special Fund for Public Welfare
Industry (Oceanography) (grant
200805011). The authors would like tothank all the crews involved in thesurvey and Guangliang Liu, Jing Xu,
Jiuzhi Yan, and Jian Zhao for theirassistance in data processing. We arealso grateful to the High Performance
Center of Ocean University of China for
their technical support for our
programs running on the computing
cluster.

CAI ET AL.

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