Ocean Dynamics (2021) 71:157–173
https://doi.org/10.1007/s10236-020-01438-5

Seasonal variations in the water residence time in the Bohai Sea
using 3D hydrodynamic model study and the adjoint method
Chongxin Luo 1 & Lei Lin 2 & Jie Shi 1 & Zhe Liu 1,34& Zhongya Cai & Xinyu Guo

1,5& Huiwang Gao

1

Received: 27 August 2020 / Accepted: 26 December 2020 / Published online: 5 January 2021
# Springer-Verlag GmbH, DE part of Springer Nature 2021

Abstract
The Bohai Sea is a large, semi-enclosed bay of China with a transport timescale of more than 1 year. Residence time (RT) is an
important indicator used to determine the water exchange rate of coastal oceans, and it has a significant influence on coastal
ecosystems and the environment. In this study, the RT and its seasonal variability within the Bohai Sea were investigated using a
3-D hydrodynamic model and the adjoint method of the RT. The model results show that the annual mean RT in the Bohai Sea is
3.43 years, and the RT increases from the Bohai Strait to the northwestern coast. The seasonal variability of the RT averaged overthe entire Bohai Sea is not obvious; however, the regional RT has a significant seasonal variation, which could be more than
290% on average. When the monsoon winds were removed from the model, the sensitivity experiment showed an annual mean
RT increase of ~ 90% with negligible seasonal variations in most areas of the Bohai Sea. The wind-induced residual current
controls the seasonal variation in ocean circulation and induces the seasonal variability in RT; thus, monsoon winds play adominant role in the seasonal variations of the water exchange rate in the Bohai Sea. Sensitivity experiments also suggest thattides can slow the water exchange rate, whereas the baroclinic processes and river runoff can accelerate the water exchange rate in
the region near the Yellow River estuary. This study highlights the critical role of monsoon winds in affecting seasonalvariabilities in the coastal transport timescale and exchange rate.
Keywords Residence time . Seasonal variation . Monsoon winds . Adjoint method . Bohai Sea

1 Introduction
The transport of water and its exchange rate in coastal areas
are important factors affecting the spatial and temporal distribution of marine organisms, nutrients, and pollutants (Bolin

Responsible Editor: Guoping Gao* Zhe Liu
zliu@ouc.edu.cn
1

Key Laboratory of Marine Environment and Ecology (Ministry of
Education), Ocean University of China, 238 Songling Road,
Qingdao 266100, China

2

College of Ocean Science and Engineering, Shandong University of
Science and Technology, Qingdao 266590, China

3

Present address: Department of Earth Sciences, National Natural
Science Foundation of China, Beijing, China

4

State Key Laboratory of Internet of Things for Smart City andDepartment of Civil and Environmental Engineering, University of
Macau, Macau, China

5Center for Marine Environmental Studies, Ehime University, 2-5
Bunkyo-Cho, Matsuyama 790-8577, Japanand Rodhe 1973; Takeoka 1984; Delhez et al. 2014). They
also have important impacts on marine primary productivity,
and the carbon and nitrogen cycles (Santos et al. 2009; Liuet al. 2019). As the self-purification of coastal oceans mainly
depends on the exchange of water with the open ocean, thecoastal water exchange rate has drawn wide attention fromoceanographers (Liu et al. 2004; Wan et al. 2013; Du et al.
2018; Lin and Liu 2019a; Liu et al. 2019).
Residence time (RT) is an important indicator for quantifying the transport timescale and water exchange rate, which
is defined as the time that a water parcel needs to leave thecontrol region. The RT of seawater within a region considers
the complete movement of a water parcel and it can reflectspatiotemporal differences in the water exchange within theregion (Bolin and Rodhe 1973; Zimmerman 1976; Takeoka
1984). With the development of the constituent-oriented age
and residence time theory (CART: Deleersnijder et al. 2001;
Delhez and Deleersnijder 2002; Delhez et al. 2004, www.
climate.be/CART), RT is widely used as an indicator in
research on coastal hydrodynamics and the associatedenvironment, such as the transport of pollutants andnutrients into the open ocean (Liu et al. 2004; Shen andHaas 2004; Gong et al. 2008).

158

Owing to the complexity and variability of hydrodynamics
in the coastal ocean, RT often shows strong spatiotemporalvariations with respect to multiple dynamic factors (Gourgue
et al. 2007; Li et al. 2009; Cheng et al. 2019; Lin and Liu
2019a). Du and Shen (2016) found significant interannual
and seasonal variations in RT within the Chesapeake Bay,
which was mainly related to river runoff, and Sun et al.
(2014) found that there were large differences in the RT within
an estuary between dry and wet seasons. River runoff is one of
the most important factors influencing coastal RT, especiallyin estuarine areas, whereas tidal effects play a more importantrole in the water exchange within shelf seas (because the effectof river runoff is weaker) (Yuan et al. 2007; Lin et al. 2015;
Lin et al. 2020). Wind is also an important factor affecting thecoastal RT. For example, Safak et al. (2015) found that winddecreased the RT of water in the Virginia Coast Reserve, andthe effect of wind on the RT was more significant in relatively
confined bays. In addition, Zhang et al. (2019) found that local
wind reduced the RT in Daya Bay by intensifying the upwelling (downwelling) circulation, and it had substantial effects on
the spatial distribution of RT therein.
The Bohai Sea, including the Liaodong Bay (LDB), Bohai
Bay (BHB), Laizhou Bay (LZB), Central Basin (CB), andBohai Strait (BS), is a semi-enclosed bay with an area of
77,000 km2, and an average depth of 18 m. The BS is the only
channel of exchange between the Bohai Sea and the external

Ocean Dynamics (2021) 71:157–173

waters (Fig. 1) (Wang et al. 2008; Liu et al. 2012). Water
flows into the Bohai Sea through the north and out throughthe south of the BS at a transport rate of 0.14 Sv in winter and
0.2 Sv in summer (Duan et al. 2020; Wu et al. 2019). The
Bohai Sea is affected by a typical monsoon climate, and thehydrodynamic environment of the sea is complex with significant seasonal variation. The statistical results from monthly
averaged European Remote Sensing Satellites (ERS-1/2)
wind stress measurements (http://www.ifremer.fr/cersat)
showed that the prevailing wind direction is NW in theautumn and winter, and S-SE during the remaining seasons(Wang et al. 2008). In addition, many seasonal rivers flow into
the Bohai Sea, with a total annual average river runoff of > 5.
0 × 1010 m3, of which the Yellow River contributes > 50% of
the total volume (Bulletin of Chinese River sediment 2015;
Ding et al. 2020). The seasonal variability of the circulation
within the Bohai Sea is well documented (Duan et al. 2020;
Guo et al. 2018; Wang et al. 2008; Wei et al. 2001; Wu et al.
2019; Zhou et al. 2017). In the autumn and winter, the residual
current is towards the south and southeast in the central CB,
counterclockwise in the southern part of the BHB and LZB,
and clockwise in the LDB (Guo et al. 2018; Wang et al. 2008).
In the spring and summer, the residual currents in the threebays are counterclockwise, the water in the central CB moves
north, and there are small residual vortexes in the Bohai Sea(Wang et al. 2008; Wei et al. 2001; Zhou et al. 2017). The

Fig. 1 Water depth (m) and subdomains within the Bohai Sea. OB1 and OB2 are the boundaries of the control region and the computational region of the
RT model, respectively

Ocean Dynamics (2021) 71:157–173

residual current in the BS in winter is similar to that in summer, except the residual vortex in the central BS (Guo et al.
2018; Wei et al. 2001;).
Rapid economic development has occurred in China, andan increasing number of land-based pollutants are being
discharged into the Bohai Sea, which have caused tremendous
pressure on the marine environment (Li et al. 2015a; Zhuang
and Gao 2015; Zhao et al. 2018). The Bohai Sea has a relatively long transport timescale. For example, Wang et al.
(2010a) estimated a freshwater residence time of 2.6 years in
the 1960s, and a weak upward trend was found in the 1990s.
In addition, Liu et al. (2012) calculated a mean age of 3.0 years
for Yellow River water within the entire Bohai Sea.
Previous studies have shown that there are significant seasonal variations in the RT within coastal regions when thetransport timescales are relatively short (days to months). In
these systems, the water particles can be affected by the dynamic forcing only one time or less when transported outward.
However, in systems where the transport timescales are much
longer than the seasonal timescale, as seen with the Bohai Sea,
the water particles can be affected by cyclical forcing (such as
monsoon winds or seasonal river discharge) twice or moretimes when transported outward. Thus, the RT’s response toseasonal variations in the hydrodynamics within the Bohai
Sea may be different from that in the coastal regions andrequires further investigation.
To understand how the RT in the Bohai Sea responds tosignificant seasonal variations in the hydrodynamics (such as
the wind-driven circulation and runoff), this study calculated
spatiotemporal variations in the RT of the Bohai Sea using athree-dimensional hydrodynamic model and the adjoint method. The effects of different dynamic factors on the RT werethen quantitatively analyzed using numerical experiments tounderstand the physical mechanisms that prompt RT variations. The remainder of this paper is organized as follows:
Section 2 details the configurations of the hydrodynamic model and the residence time model; spatiotemporal variations in
the RT of the Bohai Sea are shown in Section 3; the effects ofcontrolling dynamic factors, including wind, tide, river runoff,and baroclinic processes, and the role of monsoon winds on
seasonal variations in the RT are discussed in Section 4; and,Section 5 provides a brief conclusion.

159
Table 1

Numerical experiment schemes

Case

Wind

Tide

Baroclinic process

River runoff

0
1
2
3
4

Yes
No
Yes
Yes
Yes

Yes
Yes
No
Yes
Yes

Yes
Yes
Yes
No
Yes

Yes
Yes
Yes
Yes
No

the model is 1/18°, and there are 21 sigma layers in the verticaldirection. The time step of the model was 9 s and 360 s in theexternal and internal modes, respectively. Climatologicalmonthly mean forcings, including monthly averaged wind, heat
flux, rainfall, evaporation, and river runoff, are used (Guo et al.
2003), and tides are prescribed at the open boundaries of themodel (Matsumoto et al. 2000). This model has been well validated and previously applied in hydrodynamic studies of theBohai Sea. As shown by Wang et al. (2008), the model accurately reproduced the four major tidal constituents, and themodeled cotidal chart successfully recreated the observed
patterns. Moreover, the modeled seasonal patterns of water

2 Methodology
2.1 Hydrodynamic model
The hydrodynamic model used in this study was established by
Guo et al. (2003) and is based on the Princeton Ocean Model(POM) (Mellor 2002). The domain of the model covers theeastern shelf seas of China, including the Bohai Sea, Yellow
Sea, and East China Sea (Fig. 1). The horizontal resolution ofFig. 2 a Seasonal variations in spatially and vertically averaged RT for
the Bohai Sea and sub-bays. The results were treated with a moving
average of 15 days to filter out tidal variations. b Annual mean RT
within the Bohai Sea

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Ocean Dynamics (2021) 71:157–173

Fig. 3 Mean RT within the Bohai
Sea for the four seasons: a Winter,b spring, c summer, and d autumn

temperature and salinity were also consistent with the observed
findings. Additionally, Liu et al. (2012) and Li et al. (2017)used this model to estimate the water age of the Yellow Riverin the Bohai Sea, and analyzed how this was influenced by awater regulation event. Each of these studies indicated that thismodel could adequately reproduce the hydrodynamic characteristics of the Bohai Sea. Following a 3-year spin-up, the predicted variables of the fourth year were output to drive the RTmodel of the Bohai Sea.

2.2 Residence time model
Based on the concept of RT (Bolin and Rodhe 1973; Takeoka
1984), the adjoint method developed by Delhez et al. (2004)
Table 2Sea

Seasonal mean RT (units: years) in subdomains of the Bohai

Subdomains

Annual mean

WinterSpringSummerAutumn

LDB
BHB
LZB
CB
BS

5.28
4.12
0.72
3.51
0.05

5.53
4.50
1.02
3.51
0.03

5.54
4.43
0.82
3.37
0.06

4.97
4.00
0.51
3.57
0.09

5.08
3.55
0.54
3.60
0.03

was used to analyze spatiotemporal variations within the RTof the Bohai Sea. The adjoint equation of RT derived by
Delhez et al. (2004) is as follows,∂θþ δω ðXÞ þ V  ∇θ þ ∇  ½K  ∇θ ¼ 0∂t

ð1Þ

where ω denotes the control region, which includes the entire
Bohai Sea bounded by OB1 (the blue dotted line in Fig. 1) inthis study, θ denotes the RT, δω ðXÞ ¼ f 1 ∀X∈ω 0 ∀X∉ωis the characteristic function of the control region ω, X denotes
the position vector, V is the instantaneous current, and K is the
diffusion coefficient.
The RT diagnosis model established by Lin and Liu et al.
(2019a) based on Eq. (1) was used in this study. The RTmodel is part of the Marine Environment Research andForecasting (MERF) ocean model (MERF-2.1, Liu et al.
2016; Lin and Liu 2019a, b). The model uses the total variation diminishing advection scheme with alternating limiters(TVDal) and the splitting method to improve accuracy andeliminate numerical dispersion (Lin and Liu 2019b). ThisRT model has been successfully applied in RT studies in
Jiaozhou Bay, Zhuyi Bay, and the eastern shelf seas ofChina (Cheng et al. 2019; Lin and Liu 2019a; Lin et al. 2020).
The RT model uses the same grids as those of the aforementioned hydrodynamic model of the Bohai Sea.

Ocean Dynamics (2021) 71:157–173

161

Fig. 4 a SV distribution in the
Bohai Sea; b and c are the months
in which the maximum andminimum RT occurred within
1 year, respectively

Hydrodynamic field data (including the water level, threedimensional flow velocity, and diffusion coefficient) fromthe hydrodynamic model were used to drive the RT model.
It is of note that when using the adjoint method to calculate
RT, hydrodynamic field files are input in reverse time
(Delhez et al. 2004). In this study, a homogeneous
Dirichlet boundary condition (θ=0) was used as the open
boundary condition for Eq. (1) at OB1 and the river boundary (Fig. 1). Using this value, the time taken for a waterparcel to leave the control region for the first time was determined (Delhez et al. 2004; Delhez 2006; Delhez andDeleersnijder 2006). To improve computational efficiency,
OB2 (Fig. 1) was set as the computational boundary of the
RT model (i.e., the grids outside of OB2 were not considered during the calculation). The model reached a steadystate after 30 years of spin-up, and the results of the 31styear were used to conduct the analyses.

2.3 Quantification of the seasonal variation of the RT
An index SV, which denotes the fraction between the range
and average of the monthly mean RT in any position, wasused to quantify the magnitude of the seasonal variations in
the RT within the Bohai Sea, and was calculated as follows:SVðXÞ ¼maxðMRT ðXÞÞ−minðMRT ðXÞÞmeanðMRT ðXÞÞ
 100%

ð2Þ

where MRT denotes the monthly mean RT, and X denotes the
position vector. The SV distribution was used to quantify
spatial variations in the magnitude of the seasonal variationin the RT. By comparing the SVs obtained in different experiments, the effects of different dynamic factors on the seasonalvariation in the RT in the Bohai Sea were evaluated.

2.4 Calculation of Lagrangian residual current
The Lagrangian residual current (LRC) is defined as the net
displacement of the labeled water parcel over one or a few
tidal cycles divided by the corresponding time interval(Zimmerman 1979). In this study, it is used to explain thespatiotemporal distribution of RT in the Bohai Sea, and theequation for the LRC (Zimmerman 1979; Feng et al. 2008) is
as follows,uL ðX; τ; t 0 Þ ¼ huðX0 þ ξðt; τ ÞÞ; t; τ i ¼

ξnr
nT

ð3Þ

where uL is the LRC; X denotes the position vector; t0 is theinitial time at which the water parcel is tracked; X0 is the initial162

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Based on Eq. (3), we used the particle tracking method toderive the net displacement of particles after 15 days (the least
common multiple of the periods of the M2 and S2 tidal constituents, approximately), and we then calculated the LRC by
dividing the displacement by 15 days. Particles were released
at the center of each of the model’s grids in the Bohai Sea
every hour throughout the year, and the seasonal mean valueof the LRC was used to represent the long-term transport
velocity field in winter, spring, summer, and autumn.

2.5 Numerical experiment schemes
Numerical sensitivity experiments were designed to assess theimpact of the monsoon winds and other dynamic factors (including tides, the baroclinic process, and river runoff) on the
RT in the Bohai Sea. The configurations of the numericalexperiments are shown in Table 1. Case 0 was the control
run that considered all dynamic factors (wind, tide, baroclinic
processes, and river runoff) in the model. In Case 1, the windspeed in the hydrodynamic model was set to 0 m/s, and RT
was calculated using the new dynamic field to assess the impact of monsoon winds on the RT. In Case 2, tidal forcing wasremoved from the open boundary in the hydrodynamic model,
and the RT was calculated using the no-tide hydrodynamic
field. In Case 3, the seawater temperature and salinity were
set to constant values (temperature of 10 °C, salinity of
35 psu). Lastly, in Case 4, all of the river runoff inputs to
the Bohai Sea (including the Yellow River, Haihe River, andLiaohe River) were removed from the hydrodynamic model.

3 Results

Fig. 5 a Annual mean RT in Case 1; b spatial distribution of annual mean
diffRT(1) (annual mean RT in Case 0 minus that in Case 1), and c SV
distribution in Case 1

position vector; u(X0 + ξ(t; τ)) and ξ(t; τ) are the instantaneous velocity and the displacement of the water parcel, respectively, where ξ = X − X0 and u¼ ∂ξ
∂t . ξnr is the net displacement of the water parcel over n tidal cycles; and T is
the tidal period.

The model results showed that the annual mean of the spatially and vertically averaged RT within the entire Bohai Sea is
3.43 years. The longest and shortest were 3.57 years and3.33 years in winter and autumn, respectively, which suggeststhat the seasonal variation in the RT averaged over the entire
Bohai Sea is not obvious (~ 7%). The annual mean RT wasclose to the estimated value based on the observation data. For
example, Wang et al. (2010a) used a box model based on the
freshwater fraction method to estimate an RT of 2.6 years in
the Bohai Sea. Liu et al. (2017) estimated that the RT within
the Bohai Sea was 1.7 ± 0.8 years by a 226Ra/228Ra mass balance model. It is of note, however, that box models usually
overestimate the exchange rate of the system and thus underestimate RT (Yang et al. 2012). Therefore, the hydrodynamic
and RT models were believed to be reliable for use in thisstudy.
The results showed evident regional and temporal variations in RT within the Bohai Sea (Figs. 2 and 3). There wasan increase in the annual mean RT from the BS to the northwest coast, with higher values of RT in the center andOcean Dynamics (2021) 71:157–173

163

Fig. 6 Mean RT within the Bohai
Sea for the four seasons: a Winter,b spring, c summer, and d autumn
for Case 1

northwest of the Bohai Sea (Fig. 2b). The annual means of thespatially and vertically averaged RT were 0.05, 0.72, 3.51,
4.12, and 5.28 years in the BS, LZB, CB, BHB, and LDB,
respectively (Table 2). Although the seasonal variation of thespatially mean RT was not obvious, there were significant
differences in the spatial pattern of RT within the Bohai Sea
during the four seasons (Figs. 2a and 3). The value of RT wasmuch higher in winter and autumn in the center of CB (~6 years). The longest RT (> 7 years) appeared in the northwestern part of the LDB in winter and the bay mouth of LDB
in autumn (Fig. 3a, d). The shortest RT appeared in summer in
LZB (< 1 year) (Fig. 3c), and in autumn in the southern part of
BHB (~ 2 years) (Fig. 3d).

Table 3

Mean SV (units: %) within the Bohai Sea for different cases

Subdomains

Case 0Case 1Case 2

Case 3

Case 4

Bohai Sea
LDB
BHB
LZB
CB
BS

292.8643.90
50.14
162.86143.53
1937.73

87.36
15.40
13.45
22.68
33.45
647.95123.3755.12
103.72165.8195.07
397.80359.61
64.00
30.12
100.91
170.552489.88232.37
39.94
21.68
76.29
131.081472.93

The SV results showed an increase in the seasonal variationfrom northwest to southeast in the Bohai Sea (Fig. 4a). It wasless than 100% in the western Bohai Sea (including the whole
LDB, BHB, and the western CB), and more than 300% in theeastern part of CB; even reaching 1000% in the BS. The
annual mean of spatially and vertically averaged SV was approximately 300% over the entire Bohai Sea, which suggests a
significant seasonal variation in RT within the Bohai Sea.
From the results above, the seasons and months in which
the spatially and vertically averaged RT were highest andlowest differed across the various subregions (Fig. 4b, c, andTable 2). In the coastal regions, the highest value appeared in
winter or spring (Table 2): it occurred in January or February
in BHB, LZB, the center of LDB, and the western part of CB(Fig. 4b), and in April in the east of LDB, the southern part of
LZB and CB. The lowest value appeared in summer or autumn (Table 2); for example, the RT was lowest in Septemberin the western part of LDB, BHB, and LZB, in October, orNovember in the eastern part of those regions (Fig. 4c).
Whereas in the center of CB, the value was the lowest in
spring (April, May, or June), and the highest in autumn (Fig.
4b, c). In the BS, the maximum RT in the northern (southern)occurred in August (April), with the minimum appearing in
December (Fig. 4b, c). These results provided evidence ofstrong regional differences in RT variations throughout the164

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Fig. 7 Annual mean RT in the
Bohai Sea in (a) Case E1, (b)Case E2. Spatial distribution of(c) diffSV(E1) and (d) diffSV(E2)

Bohai Sea, implying that environmental management policies
could be tailored to local conditions.

4 Discussion
4.1 Influence of dynamic factors on the RT of theBohai Sea
Winds, tides, river runoff, and baroclinic processes affect thehydrodynamics and transport timescales of coastal oceans(Yuan et al. 2007; Wang et al. 2008; Wang et al. 2010b; Caiet al. 2014; Sun et al. 2014; Li et al. 2015b; Du and Shen 2016;
Lin et al. 2020; Ju et al. 2020). To understand their influenceson the RT of the Bohai Sea, we conducted four sensitivity
experiments and then discussed the influences of the different
dynamic factors.
4.1.1 Wind
Compared to the control run, the spatial pattern of the annual
mean RT in Case 1 also shows an increase from the BS to thenorthwest coast, but the value is much higher (Fig. 5a). The
annual mean RT in the northwest and LDB increases to morethan 10 years and 20 years, respectively, and is approximately

200% of that in Case 0. The annual mean of the spatially andvertically averaged RT within the Bohai Sea increases byapproximately 90% after removing the wind from the hydrodynamic model. There are increases of 230.34% in BS,
109.40% in BHB, and 101.85% in LDB (Fig. 5a). In thispaper, two indexes diffRT(i) and diffSV(i) were used to reflect
the differences in RT and SV between cases i and Case 0,
which was calculated as follows,diff RT ðiÞ ¼ RT Case 0 −RT Case i ði ¼ 1; 2; 3; 4; E1; E2; …E7Þð4Þ
diff SV ðiÞ ¼ SV Case 0 −SV Case i ði ¼ 1; 2; 3; 4; E1; E2; …E7Þ
ð5ÞThe spatial distribution of annual mean diffRT(1) (Fig. 5b)shows that monsoon winds decrease the RT in most regions of
the Bohai Sea.
The spatial patterns of the seasonal RT across the four
seasons are very similar to each other in Case 1 (Fig. 6), whichsuggests that there is a significant decrease in SV throughout
the entire Bohai Sea in Case 1. In most areas of the Bohai Sea,
the SV is less than 20% (as shown in Fig. 5c), although it ismore than 100% in regions near the BS, and approximately
50% in the east of the CB (this value was approximately 200%
in Case 0). The average SV in the Bohai Sea of Case 1 wasOcean Dynamics (2021) 71:157–173

165

Fig. 8 Annual mean RT in the Bohai Sea in (a) Case 2, (b) Case 3, and (c) Case 4. Spatial distribution of annual mean (d) diffRT(2), (e) diffRT(3), and (f)diffRT(4)87.36%, which is much less than that in Case 0 (only approximately 30% of that in Case 0) (Table 3). The SVs in each
subregion also decrease significantly in Case 1 and are only
15–35% of those in Case 0 (Table 3). These results imply thatmonsoon winds can reduce the RT and facilitate water exchange in the Bohai Sea, and monsoon winds play an important role in the seasonal variation of RT in the Bohai Sea.
Previous studies have shown that both local and remotewinds could affect the water exchange processes in the coastal

Fig. 9 SV distribution in (a) Case 2, (b) Case 3, and (c) Case 4

regions (Jordi et al. 2011; Mitarai et al. 2009; Shen and Gong
2009; Wang and Elliott 1978). Thus, two additional experiments (Cases E1 and E2) were designed to quantify the relative importance of local (i.e., from within the Bohai Sea) andremote (i.e., from the Yellow Sea and East China Sea (ECS))
winds in controlling the RT of the Bohai Sea. In Case E1, thelocal winds from within the Bohai Sea were removed from thehydrodynamic model; in E2, the winds from the Yellow Sea
and ECS were removed. The RT in these two cases was then166

calculated using the adjusted hydrodynamic data. The results
show that the RT value within the Bohai Sea increased significantly in Case E1, especially in the LDB and north of the CB(Fig. 7a). The diffSV(E1) shows an obvious increase in the
LZB and eastern CB (Fig. 7c); however, the RT and SV observed in Case E2 are similar to those in Case 0 (Fig. 7b, d).
Therefore, the effects of local winds on the RT in the Bohai
Sea are shown to be much stronger than those of the remotewinds, with local winds playing a more dominant role in theseasonal variation of the RT as well.

Ocean Dynamics (2021) 71:157–173

The SV pattern in Case 3 is similar to that of the control run(Fig. 9b), even though there is a local difference near theestuary. It should be noted that the baroclinic effect is more
important for ocean circulation in summer than in the otherseasons, and the effect of the baroclinic processes on the RT in
spring and summer is also slightly stronger than that in the

4.1.2 Tide
The value of RT decreased significantly in most areas of theBohai Sea when tides were excluded from the hydrodynamic
model in Case 2 (Fig. 8a). The annual mean of the spatially andvertically averaged RT for the entire Bohai Sea was reduced to1.21 years, a decrease of 64.75% compared to Case 0. Tides can
reduce the coastal circulation in shelf seas by intensifying bottom friction and thus increase shelf water RT (Lin et al. 2020).
The spatial pattern of annual mean diffRT(2) (Fig. 8d), which
can reflect the effect of tides on the RT, is similar to the RT
spatial patterning seen in Case 0. Thus, we can conclude thattides could be the primary factor determining the spatial distribution of the annual mean RT in the Bohai Sea.
Although the mean SV decreased to 123.37% in Case 2(about 40% of that in Case 0), there are significant regional
differences in the Bohai Sea. The SV is more than 50% in theentire Bohai Sea and approximately 300% in the BS whentides are removed from the hydrodynamic model in Case 2(Fig. 9a). Compared to the control run, the SV in Case 2
increased by approximately 100% in the BHB but decreased
by 80% in the BS (Table 3). However, the SV in Case 2 issimilar to that of Case 0 in the other regions. These results
suggest a significant regional difference in the effect of tides
on the seasonal variations of RT in the Bohai Sea.
4.1.3 Baroclinic processes
The baroclinic processes can affect the hydrodynamic fieldin coastal waters, particularly near estuaries, and thus has an
impact on the water exchange (Wang et al. 2010b; Cai et al.
2014; Du et al. 2018). When the baroclinic processes were
removed, the mean RT within the entire Bohai Sea was
3.70 years. The RT pattern in Case 3 differs from Case 0,
especially in regions near the Yellow River estuary and thecentral CB (Fig. 8b), which indicates that the baroclinic
processes have a significant effect on the RT in these regions. The spatial pattern of annual mean diffRT(3) showsthat the impact of the baroclinic process varies between
regions: the RT increases (decreases) in the north (south)of the Bohai Sea (Fig. 8e).

Fig. 10 a Annual mean RT in Case E3; b Spatial distribution of annual
mean diffRT(E3), and c the SV distribution in Case E3

Ocean Dynamics (2021) 71:157–173

autumn and winter. However, when compared to the windeffect, the baroclinic effect on the SV of the RT in the Bohai
Sea is relatively weak. Therefore, baroclinity is likely not themain factor controlling the SV of RT within the Bohai Sea.
4.1.4 River runoff
Freshwater discharge intensifies the flushing of estuaries andcoastal waters, thereby enhancing water exchange (Wanget al. 2010b; Du and Shen 2016). The effect of river runoff
on the hydrodynamics and RT consists of the baroclinic andbarotropic components. The baroclinic component is mainly
induced by the effect of river runoff on salinity levels. To
distinguish the effect of river runoff and the baroclinic processes on the RT in the Bohai Sea, an additional case (CaseE3) was added in which the salinity was held constantthroughout the entire Bohai Sea to exclude the baroclinic effects induced by the river plume.
When river runoff was removed from the hydrodynamic
model (Case 4), the mean RT of the entire Bohai Sea is
4.91 years. The pattern of RT in Case 4 is similar to that inCase 3; however, the RT is much longer, particularly in regions near the Yellow River estuary (Fig. 8c). The spatial
distribution of annual mean diffRT(4) shows that river runoff
decreases the RT by ~ 5 years in the south of the Bohai Sea,
Fig. 11 Spatial distribution of (a)diffSV(E4), (b) diffSV(E5), (c)diffSV(E6), and (d) diffSV(E7)167especially in the LZB (Fig. 8f). The diffRT(E3) likely reflects
the effect of the baroclinic processes of river runoff on the RT.
As shown in Fig. 10b, the baroclinic process of river runoff
significantly decreases the RT by more than 3 years in theestuarine regions of the BHB, LDB, and LZB. Both Case E3(Fig. 10) and Case 4 (Fig. 8c, f, Fig. 9c) suggest that thebaroclinic processes resulting from river runoff plays a dominant role in the effect of river runoff on the RT in the Bohai
Sea.
In addition, Case 4 shows an obvious decrease in the SV of
the RT near estuaries, especially near the Yellow River (Fig.
9c), and it decreases by approximately 50% in LZB and BHB,
respectively. However, the SVs of the other subregions arevery similar to those in Case 0. These results indicate thatthe effect of river runoff on SV also has regional variations,especially near the Yellow River.

4.2 Impact of monsoon winds on RT seasonalvariability
The above results indicate that the winds are the main controlling factor determining the seasonal variation in RT within the
Bohai Sea. The RT reflects the long-term transport timescale,and its value and spatiotemporal distribution depend on thehydrodynamic field within the control region (Liu et al. 2004;

168

Ocean Dynamics (2021) 71:157–173

Du and Shen 2016). Water transport is controlled by the advection and diffusion processes from Eq. (1). Therefore, weused an index, the Péclet number, to quantify the relative
importance of each process in controlling RT within the
Bohai Sea. The Péclet number (Pe) is defined as the ratio ofhorizontal advection to diffusion (Guyon et al. 2001; Jenkins
2003; Patankar 1980), and the equation is as follows,
Pe ¼

vLchar horizontal advection transport¼
horizontal diffusion transportDð6Þ

where v is the residual velocity, Lchar is the characteristic
length of the research domain, and D is the horizontal diffusion rate. In the Bohai Sea, v is ~10−2 m/s, Lchar is ~ 105 m, andD is ~ 102 m2/s from the hydrodynamic model. Thus, Pe in the
Bohai Sea is ~ 10, which means that the effect of horizontal
advection on the RT is approximately one order of magnitude
greater than that of the diffusion. An added experiment excluding horizontal diffusion from the model further confirms
its negligible effect on the RT. Furthermore, four additional
experiments were included to quantify the effect of the change
in vertical diffusion induced by the winds, tides, baroclinic
processes, and river runoff, (Cases E4–E7, respectively).
The experiments were calculated using the same variables as
Case 0 save for the vertical diffusion values from Cases 1–4,
Fig. 12 Lagrange residual
currents (white arrows) in (a)winter, (b) spring, (c) summer,and (d) autumn. The colors show
the patterns of the LRC speed(cm/s)

respectively. The RT and SV within the Bohai Sea were calculated using the adjusted hydrodynamic data from each case.
DiffSV(E4) − (E7) are shown in Fig. 11, and they are relatively
smaller than diffSV(1) − (4). Which suggests that the effect of
the change in the vertical diffusion induced by the dynamic
factors is much weaker than that of the change in the advection. As mentioned in Section 4.1, the wind is the main factor
controlling the SV in RT within the Bohai Sea. Thus, we canconclude that the effect of winds on the RT is mainly related tothe effect of winds on the currents. In addition, long-termtransport in a tidally dominated system is highly related to
the residual current, and many studies have suggested that
the LRC is related to long-term transport in a macro-tidal
system (Feng et al. 1986, 2008; Jiang and Feng 2011, 2014).
Thus, we further analyzed seasonal variations in the LRC andthe effect of winds on the LRC in the Bohai Sea.
Significant seasonal variations in the LRC (Fig. 12) were
found within the Bohai Sea, and this result is consistent withthose of previous studies (Wei et al. 2001, 2004; Wang et al.
2010b; Zhou et al. 2017; Guo et al. 2018). As shown in
Fig. 12a, the speed of the LRC is much lower in the center
than in the coastal regions of the Bohai Sea in winter. Water inthe eastern/southwestern areas flows to the southwestern/southeastern area of the Bohai Sea, and only water near theOcean Dynamics (2021) 71:157–173

BS is transported out of the Bohai Sea. In spring and summer,
there is an evident decrease in the speed of the LRC, which islower in the BHB and on the west coast but higher in the LZB
and the center of the Bohai Sea (Fig. 12b, c). In the southern
Bohai Sea, the LRC flows to the northeast but moves south in
the western LDB. In addition, water in the LZB and near the
BS can be transported out of the Bohai Sea. In autumn, the
LRC in the Bohai Sea is similar to that in winter, except forregions in the center of the CB, where there is a residual
current vortex (Fig. 12d), and water in the BHB and LZB
can be transported out of the Bohai Sea.
These seasonal variations in the LRC induce significant
differences in the transport pathways of water parcels released
in different seasons, which results in seasonal variations in the
RT within the Bohai Sea. However, compared with the spatial
distribution of RT, there is spatial consistency between thelower/higher speed of the LRC and higher/lower RT values(for example, in the top and central areas of the LDB and thecentral/western areas of the CB) (Fig. 3). As shown by the169

trajectory of typical particle tracking in Fig. 13, particles released in the central CB are transported to the west in theautumn, remain in the LZB for more than 1 year in winter,and move out of the Bohai Sea through the southern BS insummer. Thus, the RT in the CB is longer in autumn andwinter. In the BHB, the particles released in the autumn are
more easily transported to the LZB and out of the Bohai Sea,
while they spend more time in the BHB and LZB in the otherseasons. Hence, the RT of the BHB is relatively short in autumn. Particles released in the LDB remain there for moretime in the spring and elsewhere in the Bohai Sea in winter,
while they are more likely to be transported out of the Bohai
Sea in the summer and autumn. Therefore, the longer RT of
the LDB occurs in the winter and spring. In conclusion, the
LRC appears to be the main factor controlling the RT and its
SV within the Bohai Sea.
Seasonal variations in the LRC are mainly induced by themonsoon winds, as demonstrated by the results of Case 1: thepatterns and directions of the LRC in the Bohai Sea are very

Fig. 13 Particles trajectories released in CB, BHB, and LDB in four seasons (the color of lines show the trajectories of different particles released at thesame point)

170

similar in all four seasons (Fig. 14). Therefore, water parcels
released in the same location in different seasons have similarfates, and this explains the disappearance of seasonal RT variations when winds have been removed. The LRC is also
weakened considerably when monsoon winds have been removed from the hydrodynamic model. The average velocityof the LRC in the four seasons in Case 1 was ~ 4.9 × 10−3 m/s,
which is approximately half the value of the control run. It isthus difficult for the water masses in most of the interior regions of the Bohai Sea to be transported to the strait and out of
the Bohai Sea when the monsoon winds have been removed,
which means that RT has higher values in Case 1 (Fig. 5).
The wind-induced residual current (Fig. 15e–h), which was
calculated using the LRC in Case 0 minus that in Case 1, issimilar to the LRC in the Bohai Sea during the four seasons.
This suggests that the wind-induced residual current plays adominant role in the LRC. Therefore, significant variations in
the LRC should be related to the wind-induced residual current and thus to the seasonal shift in the wind direction. In thecenter of the Bohai Sea, the wind-induced residual current ismainly affected by the wind because of the smooth topography (Huang et al. 1999; Deng and Zhao 2020). The directionof water transport is related to the wind direction, water depth,
qﬃﬃﬃﬃﬃﬃ
and Ekman layer thickness (π 2Av
j f j , where Av is the verticalFig. 14 Lagrange residual
currents (white arrows) in (a)winter, (b) spring, (c) summer,and (d) autumn for Case 1. The
colors show the patterns of the
LRC speed (cm/s)

Ocean Dynamics (2021) 71:157–173

viscosity and f is the Coriolis parameter) (Monismith 1986;
Huang et al. 1999; Pfeiffer-Herbert et al. 2015; Deng andZhao 2020). According to Ekman theory, if the water is deep
enough, wind-driven transport is oriented perpendicular to thewind (Ekman 1905), whereas if the water is shallow and lessthan half the Ekman layer thickness, the wind-driven transport
direction is basically consistent with that of the wind direction(e.g., Estrade et al. 2008). In winter and autumn, due to strong
winds and surface cooling, the water is well mixed in thevertical direction, and the Av is of the order of 10−2 m2/s andf approximately 10−4 rad/s from the hydrodynamic model.
The Ekman layer thickness is thus more than 40 m and muchlarger than the mean water depth (~ 18 m) of the Bohai Sea.
Therefore, the wind-induced residual current flows to thesouthwest along the wind direction, especially in the centerof the Bohai Sea (Fig. 15e, h). However, under the effect of
the north wind and modulation of the shoreline, the windinduced residual current flows to the east in the nearshore
regions. In spring and summer, stratification is strengthened,
and the vertical viscosity is weakened (Av ~ 10−3 m2/s), andthe Ekman layer thickness decreases to approximately 15 m,
which is shallower than the mean water depth. Therefore, thewind-induced residual current is oriented perpendicular to thewind and flows to the northeast within the Bohai Sea

Ocean Dynamics (2021) 71:157–173

171

Fig. 15 Wind field used in the hydrodynamic model in (a) winter, (b)spring, (c) summer, and (d) autumn. The colors show the patterns of thewind speed (m/s). The wind-induced residual current (LRC in Case 0

minus that in Case 1) in (e) winter, (f) spring, (g) summer, and (h) autumn. The colors show the patterns of the wind-induced residual current
speed (cm/s)(Fig. 15f, g). By driving the shift of the wind-induced residual
current, the monsoon winds cause seasonal variations in the
LRC within the Bohai Sea and thus induce significant seasonal RT variability.

Bohai Sea. Sensitivity experiments show that the effects oftides, baroclinic processes, and river runoff on seasonal variations in RT within the Bohai Sea are much weaker than thoseof the wind. The tidal effect on the seasonal variation in RT ismainly located in the BS and BHB, while the effects of river
runoff and baroclinic processes are mainly located in the central CB and near the Yellow River estuary.

5 Conclusions
This study used a 3-D hydrodynamic model with the adjoint
method of RT to investigate the RT of water in the Bohai Sea
and its seasonal variations. The model results show that theannual mean spatially averaged RT in the entire Bohai Sea is
3.43 years. The mean seasonal variation in RT was more than
290%. However, it shows an increasing pattern from thenorthwestern to southeastern area of the Bohai Sea. In addition, there is evident spatial variation in the maximum andminimum values of RT with respect to the seasons andmonths. Sensitivity experiments suggest that the monsoon
wind is the dominant factor affecting the seasonal variationin the RT within the Bohai Sea. The annual mean RT increased by approximately 90% and the SV decreased significantly over the entire Bohai Sea if the winds were removed
from the hydrodynamic model, suggesting that wind could
enhance the water exchange and play an important role inthe seasonal variation in the RT. Wind could enhance theresidual currents in the Bohai Sea and thus accelerate thewater exchange rate of the Bohai Sea. The residual currents
vary seasonally because of the seasonal shift of the monsoon
wind, which induces the seasonal variability of RT in the

Acknowledgments The authors are grateful to Dr. Haiyan Wang of the
National Marine Environmental Forecasting Center, China, for her valuable suggestions.

References
Bolin B, Rodhe H (1973) A note on the concepts of age distribution andtransit time in natural reservoirs. Tellus 25(1):58–62
Bulletin of Chinese river sediment (2015) The Ministry of Water
Resources of the People’s Republic of China. China Water Power
Press, Beijing, Chinese (in Chinese)
Cai Z, Liu Z, Guo X, Gao H, Wang Q (2014) Influences of intratidal
variations in density field on the subtidal currents: implication froma synchronized observation by multiships and a diagnostic calculation. J Geophys Res Oceans 119(3):2017–2033
Cheng Y, Mu Z, Wang H, Zhao F, Li Y, Lin L (2019) Water residence
time in a typical tributary bay of the three Gorges Reservoir. Water(Switzerland) 11(8):1585
Deleersnijder E, Campin JM, Delhez EJM (2001) The concept of age inmarine modelling I. theory and preliminary model results. J Mar
Syst 28(3–4):229–267
Delhez EJM (2006) Transient residence and exposure times. Ocean Sci
2(1):1–9

172
Delhez ÉJM, Deleersnijder É (2002) The concept of age in marine modelling: II. Concentration distribution function in the English Channel
and the North Sea. J Mar Syst 31:279–297
Delhez ÉJM, Deleersnijder É (2006) The boundary layer of the residence
time field. Ocean Dyn 56(2):139–150
Delhez ÉJM, Heemink AW, Deleersnijder É (2004) Residence time in asemi-enclosed domain from the solution of an adjoint problem.
Estuar Coast Shelf Sci 61(4):691–702
Delhez ÉJM, de Brye B, de Brauwere A, Deleersnijder É (2014)
Residence time vs influence time. J Mar Syst 132:185–195
Deng Z, Zhao Y (2020) Impact of tidal mixing on water mass properties
and circulation in the Bohai Sea: a typhoon case. J Mar Syst
206(January):103338
Ding X, Guo X, Zhang C, Yao X, Liu S, Shi J et al (2020) Water conservancy project on the Yellow River modifies the seasonal variation of chlorophyll-a in the Bohai Sea. Chemosphere 126846
Du J, Shen J (2016) Water residence time in Chesapeake Bay for 1980–
2012. J Mar Syst 164:101–111
Du J, Park K, Shen J, Dzwonkowski B, Yu X, Yoon BI (2018) Role of
Baroclinic processes on flushing characteristics in a highly stratified
estuarine system, Mobile Bay, Alabama. J Geophys Res Oceans
123(7):4518–4537
Duan H, Wang C, Liu Z, Wang H, Wu X, Xu J (2020) Summer wind
gusts modulate transport through a narrow strait, Bohai, China.
Estuar Coast Shelf Sci 233(September 2019):106526
Ekman VW (1905) On the influence of the Earth’s rotation on oceancurrents. Ark Mat Astr Fys 2(11):1–52
Estrade P, Marchesiello P, De Verdière, Colin A, Roy C (2008) Crossshelf structure of coastal upwelling: a two-dimensional extension of
Ekman’s theory and a mechanism for inner shelf upwelling shut
down. J Mar Res 66(5):589–616
Feng S, Cheng RT, Xi P (1986) On tide-induced Lagrangian residual
current and residual transport: a. Lagrangian residual current.
Water Resour Res 22(12):1623–1634
Feng S, Ju L, Jiang W (2008) A Lagrangian mean theory on coastal sea
circulation with inter-tidal transports I. Fundamentals. Acta Oceanol
Sin 27(6):1–16
Gong W, Shen J, Jia J (2008) The impact of human activities on the
flushing properties of a semi-enclosed lagoon: Xiaohai, Hainan,
China. Mar Environ Res 65(1):62–76
Gourgue O, Deleersnijder E, White L (2007) Toward a generic method
for studying water renewal, with application to the epilimnion of
Lake Tanganyika. Estuar Coast Shelf Sci 74(4):628–640
Guo X, Hukuda H, Miyazawa Y, Yamagata T (2003) A triply nested
ocean model for simulating the Kuroshio—roles of horizontal resolution on JEBAR. J Phys Oceanogr 33(1):146–169
Guo W, Wu G, Xu T, Li X, Ren X, Hao Y (2018) Numerical modelling of
temporal and spatial patterns of petroleum hydrocarbons concentration in the Bohai Sea. Mar Pollut Bull 127:251–263
Guyon E, Hulin J-P, Petit L, Mitescu C, Jankowski D (2001) Physicalhydrodynamics. Appl Mech Rev 55(5):B96–B97
Huang D, Su J, Backhaus JO (1999) Modelling the seasonal thermal
stratification and baroclinic circulation in the Bohai Sea. Cont
Shelf Res 19(11):1485–1505
Jenkins WJ (2003) Tracers of ocean mixing. In: Holland HD, K. K. B.
T.T. on G. Turekian (eds) Treatise on Geochemistry, pp 223–246
Jiang W, Feng S (2011) Analytical solution for the tidally induced
Lagrangian residual current in a narrow bay. Ocean Dyn 61(4):543–558
Jiang W, Feng S (2014) 3D analytical solution to the tidally induced
Lagrangian residual current equations in a narrow bay. Ocean Dyn
64(8):1073–1091
Jordi A, Basterretxea G, Wang DP (2011) Local versus remote windeffects on the coastal circulation of a microtidal bay in the
Mediterranean Sea. J Mar Syst 88(2):312–322

Ocean Dynamics (2021) 71:157–173
Ju X, Ma C, Yao Z, Bao X (2020) Case analysis of water exchange
between the Bohai and Yellow Seas in response to high winds inwinter. J Oceanol Limnol 38(1):30–41
Li X, Yuan D, & Sun J (2009) Simulation of water exchange in Bohaibay. Advances in Water Resources and Hydraulic Engineering Proceedings of 16th IAHR-APD Congress and 3rd symposium of
IAHR-ISHS, 1341–1346
Li J, Dong H, Zhang D, Han B, Zhu C, Liu S, Liu X, Ma Q, Li X (2015a)
Sources and ecological risk assessment of PAHs in surface sediments from Bohai Sea and northern part of the Yellow Sea, China.
Mar Pollut Bull 96(1–2):485–490
Li Y, Wolanski E, Zhang H (2015b) What processes control the net
currents through shallow straits? A review with application to the
Bohai Strait, China. Estuar Coast Shelf Sci 158:1–11
Li Z, Wang H, Guo X, Liu Z, Gao H, Zhang G (2017) Influence of awater regulation event on the age of Yellow River water in the
Bohai. J Ocean Univ China 16(5):727–737
Lin L, Liu Z (2019a) Partial residence times: determining residence timecomposition in different subregions. Ocean Dyn 69(9):1023–1036
Lin L, Liu Z (2019b) TVDal: total variation diminishing scheme withalternating limiters to balance numerical compression and diffusion.
Ocean Model 134:42–50
Lin L, Liu Z, Xie L, Gao H, Cai Z, Chen Z, Zhao J (2015) Dynamics
governing the response of tidal current along the mouth of Jiaozhou
Bay to land reclamation. J Geophys Res Oceans 120(4):2958–2972
Lin L, Liu D, Guo X, Luo C, Cheng Y (2020) Tidal effect on water export
rate in the eastern shelf seas of China. J Geophys Res Oceans 125(5)Liu Z, Wei H, Liu G, Zhang J (2004) Simulation of water exchange in
Jiaozhou Bay by average residence time approach. Estuar Coast
Shelf Sci 61(1):25–35
Liu Z, Wang H, Guo X, Wang Q, Gao H (2012) The age of Yellow River
water in the Bohai Sea. J Geophys Res Oceans 117(11):1–19
Liu Z, Lin L, Xie L, Gao H (2016) Partially implicit finite difference
scheme for calculating dynamic pressure in a terrain-following coordinate non-hydrostatic ocean model. Ocean Model 106:44–57
Liu J, Du J, Yi L (2017) Ra tracer-based study of submarine groundwater
discharge and associated nutrient fluxes into the Bohai Sea, China: ahighly human-affected marginal sea. J Geophys Res Oceans
122(11):8646–8660
Liu X, Dunne JP, Stock CA, Harrison MJ, Adcroft A, Resplandy L(2019) Simulating water residence time in the coastal ocean: a global
perspective. Geophys Res Lett 46(23):13910–13919
Matsumoto K, Takanezawa T, Ooe M (2000) Ocean tide models developed by assimilating TOPEX/POSEIDON altimeter data into hydrodynamical model: a global model and a regional model around
Japan. J Oceanogr 56(5):567–581
Mellor GL (2002) Users guide for a three-dimensional, primitive equation, numerical ocean model. Ocean Model 8544(June):0710
Mitarai S, Siegel DA, Watson JR, Dong C, McWilliams JC (2009)
Quantifying connectivity in the coastal ocean with application to
the Southern California Bight. J Geophys Res Oceans 114(10):1–21
Monismith S (1986) An experimental study of the upwelling response of
stratified reservoirs to surface shear stress. J Fluid Mech 171:407–
439
Patankar Suhas V (1980) Numerical heat transfer and fluid flow. New
York: McGraw-Hill. p. 102. ISBN 0-89116-522-3
Pfeiffer-Herbert AS, Kincaid CR, Bergondo DL, Pockalny RA (2015)
Dynamics of wind-driven estuarine-shelf exchange in the
Narragansett Bay estuary. Cont Shelf Res 105:42–59
Safak I, Wiberg PL, Richardson DL, Kurum MO (2015) Controls on
residence time and exchange in a system of shallow coastal bays.
Cont Shelf Res 97:7–20
Santos IR, Burnett WC, Chanton J, Dimova N, Peterson RN (2009) Landor ocean?: assessing the driving forces of submarine groundwater
discharge at a coastal site in the gulf of Mexico. J Geophys Res
Oceans 114(4):1–11

Ocean Dynamics (2021) 71:157–173
Shen J, Gong W (2009) Influence of model domain size, wind directions
and Ekman transport on storm surge development inside the
Chesapeake Bay: a case study of extratropical cyclone Ernesto,
2006. J Mar Syst 75(1–2):198–215
Shen J, Haas L (2004) Calculating age and residence time in the tidal
York River using three-dimensional model experiments. Estuar
Coast Shelf Sci 61(3):449–461
Sun J, Lin B, Li K, Jiang G (2014) A modelling study of residence timeand exposure time in the Pearl River Estuary, China. J Hydro
Environ Res 8(3):281–291
Takeoka H (1984) Fundamental concepts of exchange and transport timescales in a coastal sea. Cont Shelf Res 3(3):311–326
Wan Y, Qiu C, Doering P, Ashton M, Sun D, Coley T (2013) Modelingresidence time with a three-dimensional hydrodynamic model: linkage with chlorophyll a in a subtropical estuary. Ecol Model 268:93–
102
Wang D-P, Elliott AJ (1978) Non-tidal variability in the Chesapeake Bay
and Potomac River: evidence for non-local forcing. J Phys
Oceanogr 8(2):225–232
Wang Q, Guo X, Takeoka H (2008) Seasonal variations of the Yellow
River plume in the Bohai Sea: a model study. J Geophys Res Oceans
113(8):1–14
Wang H, Gao Z, Zou T, Liu G, Liu Z (2010a) Freshwater residence timein the Bohai Sea. Chin J Ecol 29(3):498–503 (in Chinese withEnglish abstract)
Wang J, Shen Y, Guo Y (2010b) Seasonal circulation and influence
factors of the Bohai Sea: a numerical study based on Lagrangianparticle tracking method. Ocean Dyn 60(6):1581–1596
Wei H, Wu J-p, Pohlmann T (2001) A simulation on the seasonal variation of the circulation and transport in the Bohai Sea. J Oceanogr
Huanghai Bohai Seas 19(02):1–9

173
Wei H, Hainbucher D, Pohlmann T, Feng S, Suendermann J (2004)
Tidal-induced Lagrangian and Eulerian mean circulation in the
Bohai Sea. J Mar Syst 44(3–4):141–151
Wu X, Wu H, Wang H, Bi N, Duan H, Wang C, Bian C, Xu J (2019)
Novel, repeated surveys reveal new insights on sediment flux
through a Narrow Strait, Bohai, China. J Geophys Res Oceans
124(10):6927–6941
Yang S, Lee D, Ho T (2012) The isotopic composition of cadmium in thewater column of the South China Sea. Geochim Cosmochim Acta
98:66–77
Yuan D, Lin B, Falconer RA (2007) A modelling study of residence timein a macro-tidal estuary. Estuar Coast Shelf Sci 71(3–4):401–411
Zhang H, Cheng W, Chen Y, Shi Z, Gong W, Liu S (2019) Importance oflarge-scale coastal circulation on bay-shelf exchange and residence
time in a subtropical embayment, the northern South China Sea.
Ocean Coast Manag 168:72–89
Zhao J, Ran W, Teng J, Liu Y, Liu H, Yin X et al (2018) Microplastic
pollution in sediments from the Bohai Sea and the Yellow Sea,
China. Sci Total Environ 640–641:637–645
Zhou F, Huang D, Xue H, Xuan J, Yan T, Ni X, Zeng D, Li J (2017)
Circulations associated with cold pools in the Bohai Sea on the
Chinese continental shelf. Cont Shelf Res 137:25–38
Zhuang W, Gao X (2015) Distributions, sources and ecological risk assessment of arsenic and mercury in the surface sediments of thesouthwestern coastal Laizhou Bay, Bohai Sea. Mar Pollut Bull
99(1–2):320–327
Zimmerman JTF (1976) Mixing and flushing of tidal embayments in thewestern Dutch Wadden Sea part I: distribution of salinity and calculation of mixing time scales. Neth J Sea Res 10(2):149–191
Zimmerman JTF (1979) On the Euler-Lagrange transformation and thestokes’ drift in the presence of oscillatory and residual currents.
Deep Sea Research Part . Oceanogr Res Papers, 26(5), 505–520