Ocean Modelling 180 (2022) 102137

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Ocean Modelling
journal homepage: www.elsevier.com/locate/ocemod

Seasonal variability of water residence time in the Subei Coastal Water,
Yellow Sea: The joint role of tide and wind
Lei Lin a,b ,∗, Dongyan Liu b , Qingjun Fu a , Xinyu Guo c , Guangliang Liu d , Hao Liu a , Shengli Wang aa College of Ocean Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, Chinab

State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai 200062, China
Center for Marine Environmental Study, Ehime University, Matsuyama 790-8577, Japand
Shandong Provincial Key Laboratory of Computer Networks, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250101, Chinac

ARTICLEINFOABSTRACT

Keywords:
Subei coastal water
Residence time
Transport timescales
Adjoint method
Residual current

Assessing the coastal water export rate is important for better solving the coastal environmental problems anddeveloping environmental management strategies. To investigate the water export rate and its spatiotemporalvariation in the Subei coastal water (SCW), a subregion of the Yellow Sea, this study applied water residence
time (RT) as an indicator and studied the roles of tides, wind, and river discharge on the water export rate using
numerical modeling and the RT adjoint method. RT had an annual and spatial mean of ∼80 days but presented
highly spatial and seasonal heterogeneity. Spatially, high RT (∼100–300 days) occurred in the nearshore region,and its location varied in seasons. Temporally, RT was the shortest in the spring (∼55 days), longest in thesummer (∼91 days), and median (∼81 days) in autumn and winter. Furthermore, the seasonal RT mismatched
the strength of residual transport velocity (RTV) at the current season but instead relied on the combined
effects of RTVs in the current and next seasons. Additional sensitivity experiments revealed that tides greatly
increased the RT, the Changjiang River runoff slightly decreased the RT, while monsoon wind dominated the
RT seasonal variation. As highlighted by an idealized analytical framework, increasing the magnitude ratio of
the wind- and tidal-induced RTVs could amplify the RT seasonal variability. Ecologically, the shortest RT in
spring might promote the rapid expansion of macroalgal blooms originating from the SCW into offshore waters,
thereby contributing to green tide occurrence in the Yellow Sea. Therefore, the seasonality of RT should beconsidered in coastal management and scientific planning.

1. Introduction

significance to quantify the coastal water export rate and its variability
for better understanding the coastal environmental problems and themarine ecosystem challenges. Meanwhile, understanding the water
export rate is important for improving environmental management
strategies in coastal areas (Grifoll et al., 2013).
Ocean dynamics determine the transport process and export rateof seawater (Wolanski, 2007). However, the actual dynamic in a realistic ocean is very complicated, making it difficult to quantify thewater transport or export rate directly from flow field. Therefore, itis necessary to introduce auxiliary variables that reflect the water
export rate in a target region (Deleersnijder et al., 2001; Lucas andDeleersnijder, 2020). Water residence time (RT) is a parameter serving
for this purpose. RT is defined as the time taken by a particle to leave
a water body or defined region of interest (Bolin and Rodhe, 1973;
Takeoka, 1984; Lucas and Deleersnijder, 2020), which is a suitabletimescale for quantifying the water export rate (e.g., Lin et al., 2020).
According to the definition, a longer RT means a slower water export.
The magnitude of RT can provide reference for the exchange rate

Coastal water connects the land and ocean. Due to the high productivity and species diversity, coastal water provides various beneficial
services for humans (Costanza et al., 1997), and is one of the mostimportant areas of oceans from human perspective. It also serves asfilters removing pollutants and other land-derived materials before they
entering the ocean (Ferreira et al., 2017). However, densely landbased human activities have led to severe environmental degradationin the coastal zone. In present, major coastal environmental problems
and marine ecosystem challenges are worldwide, such as coastal eutrophication, coastal hypoxia, heavy metals, and emerging pollutants
due to coastal exploitations (Lu et al., 2018). The water export rateof coastal water determines the rate of water and material transport
from land to ocean, which is very important for understanding marine
environmental problems and biogeochemical processes (e.g., Sun et al.,2020; Lucas and Deleersnijder, 2020; Qin and Shen, 2021). For example, a fast water export rate facilitates self-purification and alleviates
coastal pollution and eutrophication (Jickells, 1998). Thus, it is of great∗ Corresponding author at: College of Ocean Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China.

E-mail address: llin@sdust.edu.cn (L. Lin).
https://doi.org/10.1016/j.ocemod.2022.102137
Received 26 October 2021; Received in revised form 27 June 2022; Accepted 18 October 2022
Available online 26 October 2022
1463-5003/© 2022 Elsevier Ltd. All rights reserved.

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Ocean Modelling 180 (2022) 102137

Fig. 1. (a) Map of the Subei coastal water (SCW) and the hydrodynamic model domain. Dashed gray lines are isobaths (m). The black dashed box denotes the model domain for
the water residence time (RT) computation. (b) The bathymetry of the SCW and the observation points. Dashed gray lines are isobaths (m). The red circles and triangles denotethe observation site of cruise for the Yellow Sea and the Subei Coast, respectively. The red line (OBC1) denotes the open boundary of the control region for the RT calculation,and the area inside the blue line (OBC2) denotes the computation domain of the RT model. (c) and (d) show the climatological monthly mean wind over the Subei Coast and theChangjiang river runoff, respectively.

of nutrients in the seawater and the growth rate of phytoplankton,
which are important for knowing the formation mechanism of water
eutrophication and algal blooms (e.g., Lucas et al., 2009; Lillebø et al.,2005). Thus, RT of oceans has been widely investigated, especially insemi-enclosed regions, such as bays and estuaries, (e.g., Du and Shen,
2016; Gong et al., 2008; Meyers et al., 2017; Ranjbar and Zaker, 2017;
Sun et al., 2014; Yuan et al., 2007; Luo et al., 2021). However, there
are few studies on the RT in open coastal areas.
The Subei coastal water (SCW), with a mean depth of approximately
15 m, lies in the southwestern Yellow Sea (Fig. 1). The flat coastline of
SCW makes it relatively open water. However, it exhibits several environmental problems, including eutrophication and poor water quality(Ministry of Natural Resources of the People’s Republic of China, 2018;
Wang et al., 2021). The SCW is the cradle of the well-known greentide, which is a large-scale macroalgal bloom that occurs from spring
to summer in the Yellow Sea (Liu et al., 2013). Studying the RT of the
SCW would be helpful for further understanding these environmental
and ecological problems.
Tides, wind, and Changjiang River runoff are the major dynamic factors that influence hydrodynamics and water transport in the SCW (Wuet al., 2014; Wu et al. 2019; Yuan et al., 2017; Xuan et al., 2016). Tidal
rectification causes a tidal residual current, which affects the mean flowin the SCW (Xuan et al., 2016). Meanwhile, the strong tidal current in

the SCW increases the tidal-mean bottom resistance that modulates thewind-driven current (Wu et al., 2018). According to drifter trajectories,
Yuan et al. (2017) found that the Subei coastal current flows northward
under the southerly monsoon winds in summer. Conversely, under thenortherly wind forces in winter, the currents flow southward (Yuanet al., 2008; Yuan and Hsueh, 2010). The Changjiang River is one of
the largest rivers in the world, and its maximum discharge can reachmore than 50,000 m3 /s in the summer, which induces a wide range ofriver plumes (Wu et al., 2011). The expansion of the Changjiang River
plume is an important freshwater source for the SCW and can affect
SCW hydrodynamics (Wu et al., 2014; Zhu and Wu, 2018). Previous
studies showed that the SCW hydrodynamics is intricate and exhibits asignificant seasonal variability, which raises questions whether there
are also significant seasonal variations in the water export rate in
the SCW and what roles of different dynamic factors on the seasonalvariations. This study aims to investigate the seasonal variability of thewater export rate using RT as an indicator and to understand the rolesof the three dynamic factors (i.e., wind, tides, and Changjiang River
discharge) on the water export rate in the SCW.
The remainder of this study is organized as follows. Section 2
introduces the models employed for the hydrodynamic simulation andthe adjoint method for RT in the SCW. Section 3 discusses the RT in
the SCW and the effects of dynamic factors. Section 4 analyzes the2

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Ocean Modelling 180 (2022) 102137

residual transport velocity in the SCW in order to understand seasonal
RT variations and discusses the implications of the RT results. A brief
conclusion is given in Section 5.
2. Models and methods
2.1. Hydrodynamic model
2.1.1. Model description
The hydrodynamic model set up by Guo et al. (2003) and Wanget al. (2008) was used to simulate the flow field for SCW. This model
was based on the Princeton Ocean Model (Blumberg and Mellor, 1987).
As shown in Fig. 1a, the model domain covered the Bohai Sea, Yellow Sea, and East China Sea, and is discretized by orthogonal gridswith a horizontal resolution of 1/18◦ and 20 vertical layers. The
model used the monthly mean climatological forcing of the sea surface
winds, heat fluxes, river discharges, and boundary currents. For model
validation, we employed realistic daily forcing from the European
Center for Medium-Range Weather Forecasts for fairly evaluating themodel performance. Additionally, RT computed from hydrodynamic
results driven by monthly mean forcing presented a consistent seasonalvariation with that driven from daily forcing (see Figure S1 in the
Supplementary Materials). Meanwhile, applying monthly mean forcing further saved computational coasts in a series of runs. Therefore,hydrodynamic model results driven by monthly mean forcing wereused in the RT model. The tidal elevations of four predominant tidal
constituents (M2 , S2 , K1 , and O1 ) were added at the open boundary
to produce tidal motion in the model. The modeled values of thewater depth, currents, and diffusion coefficients were output at 30 min
interval to drive the adjoint model of the RT in SCW (introduced in
Section 2.2). The model was verified in previous studies and has beenused to study the interannual variation in the Yellow Sea cold watermass (Zhu et al., 2018) and the water export rate of the eastern shelfseas of China (Lin et al., 2020). To ensure the reliability of the model,
we further check the co-tidal charts and compare the modeled watertemperature and salinity with the in-situ observation.

Fig. 2. Co-tidal charts for the four tidal constituents (M2, S2, K1, and O1). The dashedand solid isolines denote the amplitude (cm) and phase (◦ ) of the tidal constituents,
respectively.

with the observed data. The correlation coefficients of water temperature between the model and observations in both the Yellow Sea andSubei Coast cruises were higher than 0.9. All the root-mean-squareerrors for the simulated water temperature were less than 1.94 ◦ C.
Meanwhile, the simulated salinity matched the observed data better (R> 0.8) in the summer when the Changjiang River discharge was larger.
In the spring and autumn, the salinity correlation between the model
results and observations was relatively low (R > 0.47). The relatively
large bias of the modeled salinity mainly occurred in the adjacent areaof the Changjiang River plume front and at the nearshore water (Figure
S2 in the Supplementary Materials), which is likely because of the highvariability of the river plume and the exclusion of some small rivers
along the Subei Coast in the model. However, the model captured thebasic pattern of the Changjiang River plume and its seasonal variability(Figure S3 in the Supplementary Materials), and all the root-meansquare errors for the simulated salinity were less than 1.29 (Fig. 3).
In addition, the model skill score (SS), which is defined as one minus
the mean square error divided by the observed variance, was further
calculated to evaluate the model performance. The SS for the watertemperature and salinity are 0.93 and 0.22 for the Yellow Sea cruises
and are 0.68 and 0.47 for the Subei Coast cruises, respectively. Usually,
SS > 0.2 suggests a good model performance (Allen et al., 2007).
Therefore, the model favorably reproduced the general hydrographic
characteristics of the SCW.

2.1.2. Model validation
The SCW is characterized by strong tides, in which semi-diurnal
tides are predominant. The modeled co-tidal charts of the four major
tidal constituents (i.e. M2, S2, K1, and O1) were derived from aharmonic analysis (Fig. 2). The tidal amplitude of M2 is larger than 1 m
along the Subei coast, which is much larger than that of the other threetidal constituents. The maximum tidal range in the SCW was more than
5 m. There is an amphidromic point for each tidal constituent at theoffshore water of the SCW, and the location of the amphidromic points
is in good agreement with the Ocean Atlas of the Yellow Sea (Chen,
1992). The simulated tidal charts are also highly consistent with theobservation-based charts (Fang et al., 2004) and those from different
models (e.g., Figure 3 in Xuan et al., 2016 and Figure 13 in Wu et al.,2014).
The simulated water temperature and salinity are compared withthe observed values during the Yellow Sea and Subei Coast cruises(Fig. 1b). The water temperature and salinity data in the western
Yellow Sea were collected during four cruises conducted in May 2014
(spring), November 2014 (autumn), August 2015 (summer), and January 2016 (winter), respectively. A conductivity–temperature–depth
instrument (CTD, SeaBird 911 plus) was used to measure seawatertemperature, salinity, and water depth with a sampling frequency of
24 Hz. The data were averaged per meter and only the data at thesurface, middle, and bottom layers were accessed and used in thevalidation in this study. The Subei Coast cruise was conducted in April
2018 when only the water temperature and salinity at the sea surface
were measured with a multiparameter water quality analyzer (YSI) due
to the strong mixing there (Wei et al., 2020; Wu et al., 2011). As shownin Fig. 3, the simulated water temperature and salinity were consistent2.2. Residence time model
There are three common methods for diagnosing RT including
the particle-tracking method, remnant function approach and adjoint
method. The particle-tracking method determines RT by recording theamounts of time particles spent in the domain of interest (e.g., Gong
et al., 2008). While, the remnant function approach (Takeoka, 1984)
diagnoses RT by integrating the concentration time series of a tracer
released at a certain time and location (e.g., de Brauwere et al.,2011). However, both the particle-tracking and the remnant function3

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Ocean Modelling 180 (2022) 102137

Fig. 3. Comparison of water temperature (left panels) and salinity (right panels) for the model results with four Yellow Sea cruises (a-h) and the Subei Coast cruise (i-j). The
correlation coefficient (R) and root-mean-square error (RMSE) values are indicated.

methods cannot easily derive continuous spatiotemporal variations ofRT, because in this case particles or tracers need to be released at eachmodel time step and grid cells of the domain of interest, and a huge
computational cost is required to run the model (Delhez et al., 2004;
Du and Shen, 2016; Lin and Liu, 2019a). In order to address this issue,

Delhez et al. (2004) proposed an adjoint method to compute the RT
in the framework of the constituent-oriented age and residence time
theory (CART) (Deleersnijder et al., 2001; Delhez and Deleersnijder,2002; Delhez et al., 2004). The adjoint method can derive spatiotemporal variations of RT with a single backward model run, which is4

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Table 1
Boundary conditions for the RT, ET, and PRT equations from the adjoint method.
For

Boundary conditions

Expressions

RT and PRTOpen boundary of 𝜔RT, ET, and PRT

Closed boundary of 𝜔

𝜃 =(0 )𝐧⃖⃗ ⋅ ∇𝜃 = 0

RT, ET, and PRT
PRT

Boundaries of the computational domain
Boundaries between subregions within 𝜔

𝜃=0/same grids and layers as the hydrodynamic model. The total variation
diminishing (TVD) scheme with a Superbee and MUSCL alternating flux
limiter (TVDal) was used to discretize the advection term, which has
a smaller numerical error than conventional TVD schemes, especiallyfor long-term integration (Lin and Liu, 2019b). This model has beensuccessfully applied in studies of the RT in the Jiaozhou Bay (Lin andLiu, 2019a), the Bohai Sea (Luo et al., 2021), the eastern shelf seasof China (Lin et al., 2020), and the tributary bay of the Three Gorges
Reservoir (Cheng et al., 2019).
As shown in Fig. 1b, the 30-m isobath was set as the open boundary(a part of OBC1) of the control region of RT, because the 30-m isobath
locates on the edge of the inner shelf slope which can be regarded as theboundary between the inner shelf and the middle shelf in the Yellow
Sea. To enclose the control region, we added two more open boundaries
at the north (35◦ N) and south (31.8◦ N) of the SCW, respectively (redlines in Fig. 1b). To calculate the PRTs, the control region was divided
into three subregions based on the water depth (H): H ≤ 10 m, 10 m
< H < 20 m, and 20 m ≤ H ≤ 30 m. The PRTs for these subregions
were labeled PRT1, PRT2, and PRT3, respectively. As aforementioned,
the homogeneous Dirichlet boundary conditions were prescribed at the
open boundary OBC1 (red lines in Fig. 1b) to calculate the RT and PRTs,
whereas no boundary condition was prescribed at boundary OBC1
to calculate the ET. In addition, the boundary of the computational
domain (i.e., OBC2, the blue lines in Fig. 1b) was set to zero for the
RT, PRTs, and ET (Delhez, 2013), which assumes that the water parcel
never returns to the SCW once it leaves OBC2. The initial field of
the model was set to zero (Delhez, 2006). It is worth noting that theinitial condition for the backward integration of the adjoint equation
actually prescribed final values of the RT, ET, or PRT. The final valuesof the RT, ET, or PRT fields are unknown. Therefore, a spin-up period isnecessary, which must be at least twice as long as the maximum valueof the timescales according to Delhez (2006). We integrated the models
for three years, and the integration times were longer than twice thelongest timescales (around one years) in the control region. After threeyears of model calculations, the RT, ET, and PRTs in the SCW showed astable seasonal variation, and the results in the fourth year were saved
for further analysis.

Note, 𝐧⃖⃗ is the outgoing unit vector normal to the boundary.

appropriate to diagnose the continuous seasonal variability of RT in
this study.
Following Takeoka (1984), the RT 𝜃 (𝐱, 𝑡) of a water parcel atlocation x and release time t can be expressed by integrating the tracer
concentration in the control region in a forward model as follows:∞𝜃 (𝐱 , 𝑡) =∫𝑡𝑟(𝑡′ )d𝑡′ ,

(1)

′

)
is the remnant function, 𝑚0 is the mass of the tracer
where 𝑟(𝑡′ ) = 𝑚(𝑡𝑚0
initially released at location x and time t, and 𝑚(𝑡′ ) is the tracer mass
remaining in the control region (𝜔) at time 𝑡′ . According to the adjoint
method of Delhez et al. (2004), the 𝜃 (𝐱, 𝑡) can be computed using theadjoint equation expressed as,[]𝜕𝜃+ 𝛿𝜔 (𝐱) + 𝐯 ⋅ ∇𝜃 + ∇ ⋅ 𝐊 ⋅ ∇𝜃 = 0,(2)
𝜕𝑡where 𝐯 is the three-dimensional velocity field, 𝐊 is the diffusion tensor,
and 𝛿𝜔 (𝐱){ is the characteristic function of the control region 𝜔 and1 ∀𝐱 ∈ 𝜔𝛿𝜔 (𝐱) =. The open boundary is assigned a homogeneous
0 ∀𝐱 ∉ 𝜔
Dirichlet boundary condition, i.e., 𝜃 = 0, which reflects the timerequired to exit the control region for the first time (Delhez et al., 2004;
Delhez, 2006; Delhez and Deleersnijder, 2006). In addition to the RT,
the partial residence time (PRT) and the exposure time (ET) were also
calculated for better understanding the residence time composition indifferent subregions of the control region and the influence of re-entry
processes on the transport timescale, respectively. The PRT is definedas the amount of time that a water parcel spends in different subregionsin the control region until its leaving from the control region (Lin andLiu, 2019a), which can be also computed using the adjoint method.
According to Lin and Liu (2019a), the adjoint equation for the PRT isexpressed as𝜕𝜃 𝜔𝑖

2.3. Residual transport velocity
In coastal waters with strong tides, the residual transport velocity(RTV) or residual current is a vital factor for determining subtidal andlong-term transport (e.g., de Kok et al., 1970; Nihoul and Ronday, 1975;
Prandle and Player, 1993; Salomon and Breton, 1993; Li and O’Donnell,
1997; Wu et al., 2014; Lin et al., 2015; Du et al., 2018). Thus, the RTV
in the SCW was calculated and analyzed to understand the RT variation.
The RTV was calculated as follows:⟨ 𝜂⟩⎧⎪𝑈 = ∫−𝐻 𝑢𝑑𝑧⎪ 𝑅(4)⟨ 𝜂𝐻 ⟩ ,⎨∫−𝐻 𝑣𝑑𝑧
⎪
𝑉
=
⎪ 𝑅
𝐻
⎩

[
]
+ 𝛿𝜔𝑖 (𝐱) + 𝐯 ⋅ ∇𝜃 𝜔𝑖 + ∇ ⋅ 𝐊 ⋅ ∇𝜃 𝜔𝑖 = 0,(3)
𝜕𝑡where 𝛿𝜔𝑖 (𝐱) is the characteristic function for subregion 𝜔𝑖 and 𝛿𝜔𝑖 (𝐱) ={1 ∀𝐱 ∈ 𝜔𝑖. The PRT equations used the same open boundary
0 ∀𝐱 ∉ 𝜔𝑖
condition with the RT equation and no boundary conditions need at theboundaries between the subregions (Lin and Liu, 2019a). ET is definedas the total time that the water parcel spent in the control region witha consideration of all subsequent re-entry processes (Delhez, 2006).
The ET can be computed using the same adjoint equation as the RT
except that no boundary conditions need to be prescribed on the
open boundaries of control region 𝜔. The boundary conditions for thecomputations of the RT, PRT, and ET are summarized in Table 1. In
addition, to quantify the influence of the re-entry process on the water−𝑅𝑇,renewal timescale, we calculated the return coefficient: 𝑟 = 𝐸𝑇𝐸𝑇
which measures the portion of the exposure time fraction attributed
to the re-entry water (de Brauwere et al., 2011; de Brye et al., 2013).
More details regarding the RT, ET, and PRT models are provided in
Delhez et al. (2004) and Lin and Liu (2019a).
Based on the adjoint equations (2) and (3), the RT model establishedby Lin and Liu (2019a) was used to diagnose RT variation in the
SCW, which belongs to a submodule of the model Marine Environment
Research and Forecasting model (Liu et al., 2016; Tang et al., 2021).
The equations are solved using the finite-difference method with thewhere UR and VR are the east–west and south–north components of
the RTV, respectively, 𝜂 and H denote the water elevation and meanwater depth, respectively, and ⟨⟩ denotes the time average over one
or several tidal periods. As this study focused on seasonal variation in
subtidal transport, the average time was set to 90 days to obtain themean RTVs in each season.
2.4. Sensitivity experiments
To assess the impact of three dynamic factors (i.e., tides, wind, andChangjiang River runoff), we conducted three sensitivity experiments.
For the three experiments, the tides, wind, and Changjiang River runoff
were removed from the hydrodynamic model, respectively. Then, thehydrodynamic fields output from the experiments are used to drive5L. Lin, D. Liu, Q. Fu et al.

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Fig. 4. The seasonal mean of the vertically averaged water residence time (RT) in the Subei coastal water (SCW). Following He et al. (2013) and Xia et al. (2021), the four
seasons in this study are defined as: spring (April, May, and June), summer (July, August, and September), autumn (October, November, and December), and winter (January,
February, and March), since the seasons in the ocean usually lag behind the land by about one month.

the RT model, in order to obtain the RT for the cases of no tides, nowind, and no Changjiang River runoff (hereafter, termed as ‘‘NoTide
Case’’, ‘‘NoWind Case’’, and ‘‘NoRiver Case’’, respectively). Finally, theRT from three sensitive experiments were compared with that from thecontrol run, which included all the dynamic factors, to investigate theimpact of each dynamic factor on the RT. To better understand theeffect mechanism of the tides on the RT, an extra experiment with
only the tidal mixing considered in the no-tide model was conducted(hereafter, termed as ‘‘TM case’’). In the experiment, the tides were
removed, but the tidal mixing was retained in the dynamic model.
Specially, we ran a no-tide model and replaced the turbulent mixing
coefficients of the model by those saved from the control run during
the model run.

strong mixing in the SCW, the RT was vertical homogeneous (Fig. 5).
Thus, only the vertical averaged results were analyzed below.
The daily mean of the spatially averaged RT in the SCW showedapparent seasonal variation that the highest RT in summer was around
two times of the lowest value in spring (Fig. 6). The monthly mean
RT in January was approximately 87 days, decreased to 50 days fromFebruary to early May, increased to approximately 100 days from
June to early September and decreased to approximately 80 days in
December. Consequently, its annual mean was approximately 80 days,
while its seasonal mean was lowest in spring (approximately 55 days),highest in summer (approximately 91 days), and almost the same inautumn and winter (approximately 81 days).
3.1.2. Influence of re-entry process
As shown in Fig. 6, the annual mean ET averaged for the SCW wasapproximately 150 days, which was approximately double of the RT,
suggesting that the water export rate could greatly decrease when there-entry process is considered. However, the ET was also highest insummer (approximately 180 days) and lowest in spring (approximately
110 days), showing a similar seasonal variation with the RT, whichsuggests that the re-entry process decreased the water export rate but
has little effect on its seasonal variation.
As shown in Fig. 7, the return coefficient was larger in the offshore
water than in the coastal water, suggesting that the impact of the reentry process on the water export rate was more significant in theoffshore water than in the coastal water. Further, the return coefficient showed a similar seasonal variation with the RT and an inverse
correlation with the RT spatial distribution, meaning that the return

3. Results
3.1. Water residence time in the SCW
3.1.1. Seasonal variation
As shown in Fig. 4, the RT in the SCW showed a significant spatial–
temporal variation. Spatially, RT was higher in the coastal region thanin the offshore region. The RT in the nearshore water in some seasons
was more than 300 days, implying that the pollutants released there at
the season could stay in the SCW for more than 10 months. In winterand summer, relatively high RTs occurred in the middle of the SCW;
in spring, the nearshore RT was more than 300 days south of 33◦ N but
lower than 100 days north of 33◦ N; in autumn, the pattern reversedwith a lower value in the south but a high value in the north. Due to the6

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Ocean Modelling 180 (2022) 102137

Fig. 5. The distribution of the seasonal mean of water residence time (RT) along the 34◦ 𝑁 transect in the SCW.

summer was approximately twice that in the spring, indicating that thewater transport rate reduced by half from the spring to summer.
3.2. Effects of different dynamic factors on the RT
Using sensitivity experiments, the effects of tides, wind, andChangjiang River discharge on the RT were investigated. The dailymean RT for the three sensitivity experiments and control run wereshown in Fig. 9. The annual mean RT for NoTide was approximately
31 days, which was much lower than that of the control run (80 days),while that of the NoWind and NoRiver cases were 88 days and 91 days,
respectively, which were close to that of the control run. These results
suggested that tides had the most significant impact on RT. When tides
were removed from the model, the mean RT in the SCW decreased by> 60%, as compared to the control run, indicating that the presence oftides greatly slowed the export rate of coastal waters, which has beenreported in the study on the eastern shelf seas of China by Lin et al.
(2020). Tides can modulate shelf currents by affecting water mixing
and bottom friction. However, the RT in the experiment with only
considering tidal mixing (the TM case) was very close to NoTide caseand still much smaller than that of the control run (Fig. 9), suggestingthat the tidal mixing had a little impact on the RT. This is mainly
due to the weak stratification in the SCW, which results in less impactof tidal mixing on residual currents (see e Figures S4 and S5 in the
Supplementary Materials). As discussed in Wu et al. (2018) and Lin
et al. (2020), tides could greatly weaken the wind-driven currents in
the SCW by increasing the bottom resistance, which can explain thehigher RT in the control run. In addition, tides could also change theseasonal variability of the RT. For instance, the minimum daily mean
RT for the NoTide case occurred in December rather than in the spring.
The annual mean RTs for the NoWind and NoRiver cases wereslightly higher than that of the control run (80 days), suggesting thatthe wind and Changjiang River runoff facilitated water export in the
SCW. However, the effects of the wind and river runoff on the seasonal
RT were different. When the Changjiang River was removed from themodel, the RT in spring increased, whereas when the wind was removed, the RT decreased in summer but increased in the other seasons.
In addition, the seasonal variability for both the NoWind and NoRivercases decreased, as compared to the control run. These results suggested
that wind and river runoff mainly influence seasonal variation of theRT, which was a reasonable result because they both exhibited anapparent seasonal variation (Figs. 1c and 1d).

Fig. 6. The daily mean water residence time (RT) and exposure time (ET) in the Subei
coastal water (SCW). The vertical dotted lines are the split lines for seasons.

coefficient was relatively low in the long RT region and high in the
short RT region.
3.1.3. Partial residence time
The PRTs that decomposed the RT into three subregions were shownin Fig. 8a. The water in the SCW had the longest retention in thesubregion of 10 m < H < 20 m, accounting for more than half of theRT. The long retention in this subregion was associated with its large
area. The PRTs showed a similar seasonal variation as the RT, with theshortest value in spring and the longest value in summer, suggestingthat the effect of the different subregions of the SCW on the seasonalvariation in RT was consistent.
The PRTs normalized by the volume of subregion (NPRT) wereshown in Fig. 8b. NPRTs can be used to compare the water transport
rates in different subregions (Lin and Liu, 2019). Because higher NPRTs
indicated lower water transport rates, the water transport was relatively
slow in the nearshore water (H < 10 m) and fast in the offshore water(20 m < H < 30 m). For the subregion of H < 10 m, the NPRT in the7

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Ocean Modelling 180 (2022) 102137

Fig. 7. Distribution of the return coefficient during the four seasons. The black dashed lines denote a contour of 0.5 for the return coefficient.

Fig. 8. (a) The daily mean partial residence times (PRTs) for the three subregions in the Subei coastal water (SCW). (b) The PRTs normalized by the volume of the corresponding
subregion. The vertical dotted lines in (a) and (b) are the split lines for seasons. (c) The three subregions 𝜔1 − 𝜔3 for PRT1–PRT3. The red dashed lines denote the boundaries
between different subregions.

4. Discussion

to Geyer and Signell (1992), in a residual current dominated system,
the estimating residence time could reduce to an estimation of theadvective time scale of the system, i.e., L/U, where the L and U denotethe magnitude of the spatial scale and residual velocity of the study
zone, respectively. In this study, the L of the SCW is ∼300 km andthe mean residual current is ∼0.05 m/s (Figure). Thus, L/U is ∼70days and is very close to the modeled mean RT value (∼80 days),suggesting that the SCW is closer to a system that the residual current
dominates. Other processes, e.g., tidal pumping or tidal dispersion,
could also play a role in water transport, particularly near topography.
In the SCW, the terrain is relatively flat within the region of water
depth < 30 m (the control region of this study). Therefore, the residual
current should be the dominant factor controlling the water transport
in the SCW. Herein, the RTVs in the SCW for the four seasons were
calculated based on the flow field outputs of the model. The RTV shows
significant seasonal variation (Fig. 10), which is consistent with the

The RT in the SCW shows significant seasonal variation, reaching a
low value in the spring and a peak value in the summer. To understandthe seasonal variation in the RT and its dynamic mechanism, we analyzed the seasonal variation in the RTV and water particle trajectories
in the SCW using the particle-tracking method. Moreover, we discuss
the implications of the RT results for the coastal environment andecology.
4.1. Seasonal variation in the RTV in the SCW
In coastal waters, the RTV has been recognized as a vital factor for
determining long-term transport (e.g., de Kok et al., 1970; Nihoul andRonday, 1975; Prandle and Player, 1993; Salomon and Breton, 1993;
Li and O’Donnell, 1997; Wu et al., 2014; Lin et al., 2015). According8

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Ocean Modelling 180 (2022) 102137

reversed to the south before they reach the boundary of the control
region. Thus, the particles released in the summer experienced much
longer excursions in the SCW, which explains why the RT in thesummer is much longer than that in the spring.
The seasonal variation in the RTV determined the different trajectories for the particles released in spring and summer, respectively.
The persistent northward motion of the particles released in the springis attributed to the constant direction (northward) of the RTV in thespring and summer. However, for the particles released in summer,
their trajectory eventually reversed to the south because of the reverse
RTVs in autumn and winter. Meanwhile, The RTV veer near 34◦ N insummer could play an important role on the reverse of the particles’
trajectories, because it blocked further northward transport in the endof summer and allows returning transport in the coming Autumn. In
addition, the RTV in the autumn is much lower than that in the summer
and spring (Fig. 10), which delays the export of the water released in
the summer.
4.3. Generation mechanism of RTV seasonal variability in the SCW

Fig. 9. Daily mean water residence time (RT) in the Subei coastal water (SCW) for
different cases. The vertical dotted lines are the split lines for seasons.

According to the particle tracking experiments, the seasonal variation in the RTV directly results in different fates for water in different
seasons, thereby inducing seasonal variation in the RT. Tides, wind, andChangjiang River runoff are three major dynamic factors influencing
the RTV in the SCW (Wu et al., 2011, 2018; Xuan et al., 2016; Yuan
et al., 2008). Therefore, in this subsection, we analyze the RTV components induced by these factors and its seasonal variation to determine
the generation mechanism of RTV seasonal variability in the SCW.
Based on the RTV sensitivity experiment results, we derived thethree components of the RTV. Because the difference in the RTV
between the NoWind case and the control run was induced by theabsence of the wind, the RTV induced by the wind (RTV-Wind) canbe approximately obtained by subtracting the RTV in the NoWind casefrom that in the control run. In a similar way, the RTV induced by the
Changjiang River runoff (RTV-River) can be approximately obtainedby subtracting the RTV of the NoRiver case from that of the control
run. Finally, the tidal-induced RTV (RTV-Tide) can be derived from anadditional numerical experiment with no wind and no river runoff. It
should be noted that the RTV induced tides, wind, and river could not
be separated completely from each other by the sensitivity experiments
due to their nonlinear interaction. Here, we assumed that the effectof the nonlinear interaction between the three factors on the residual
velocity is weak than that of single factors.
As shown in Fig. 12, the RTV-Tide remained the same for eachseason (Fig. 12e–h), flowing northward along the coast until approximately 34◦ N. Owing to the relatively strong tides in the nearshore
water, the RTV-Tide is stronger in nearshore area than in offshore
area. The RTV-Tide is mainly attributed to the Stokes drift resulting
from tidal stress (Xuan et al., 2016; Wu et al., 2018). Conversely, themagnitude and direction of the RTV-Wind showed significant seasonalvariation. The RTV-Wind exhibited strong southward flows in autumn
and winter, and relatively weak northward flows in spring and summer(Fig. 12i-l). Under the influence of the East Asian monsoon, the windover the SCW is strong and northerly in autumn and winter, becomes
weak and southerly in spring and summer (Su and Yuan, 2005). The
wind speed determines the strength of the RTV-Wind, and the changesof wind direction induces the opposite RTV-Wind over the SCW in
winter and summer (Yuan et al., 2008, 2017). For each season, the
RTV-River in the SCW were northward, and their magnitudes weremuch weaker than those of the RTV-Tide and RTV-Wind (Fig. 12m–p).
The RTV-River is proportion to the discharge of the Changjiang Riverand therefore is weaker in winter than in other three seasons. Basedon the three components of the RTV, we inferred that the consistent
direction of the RTV-Tide, RTV-Wind, and RTV-River in spring andsummer induced a strong northward transport. Meanwhile, when the
RTV-Wind opposed to the RTV-Tide and RTV-River in the autumn andmodel results in previous studies (e.g., Xuan et al., 2016; Wu et al.,2018). In winter, the nearshore RTV is northward along the Subei coast(from the Changjiang Estuary to approximately 34◦ N) because of thenearshore strong tides (Wu et al., 2018). Meanwhile, under northerly
wind, the RTV, at approximately 34◦ N, veers southeastward in theoffshore SCW and induces cross-shelf transport (Yuan et al., 2008; Yuan
and Hsueh, 2010). In spring and summer, the RTV was stronger thanthat in the winter, and its direction in most areas was northward, which
could be related to southerly winds (Yuan et al., 2017). Finally, the
RTV in the autumn was weaker, exhibiting a pattern similar to that inwinter.
The seasonal variability of the RTV can, to some extent, explain
the seasonal variation in the RT of the SCW. For instance, the waterflows northward in the spring and summer, and thus the spring RT islower in the north than in the south. Conversely, in the autumn andwinter, water flows southward in the offshore SCW, inducing a lower
RT in the south than in the north. However, the RTV also suggested thestrong (weak) RTV does not necessarily corresponds to a short (long)
RT. For example, the RTV fields in spring and summer are similar but
the RT field are different in two seasons (Fig. 4). Because the RT in ourstudy area is as long as several months, the transport of water parcels
released in summer is influenced not only by the summer RTV but also
by the autumn and even winter RTVs. This reflects the advantage of
the RT in quantifying the water export rate, which can summarize thecomplete and complex dynamics of a system in a single variable thatquantitatively indicates the rate of water export.
4.2. RT discrepancy between spring and summer
The RTV results show that water transport in the SCW is fast in
both spring and summer. However, the RT in the SCW in the summer
is the longest and is approximately two times that in the spring. To
understand the significant difference between the RTs in the spring andsummer, we released several natural particles, whose movement arecompletely controlled by water flow and have no self-sedimentation or
floating, in the central SCW along the latitude of 33.5◦ N and tracked
their trajectories for one year. The particles were released at 0 clock in
the first day of May and August, i.e., in the middle day of Spring andsummer, respectively. The particles initially located at the middle layer.
As shown in Fig. 11, when released in spring, the particles continued
moving northward, crossing the 30-m isobath and the transect at 35◦ N.
Consequently, they left the control region in a relatively short time.
Conversely, the particles released in summer had different trajectories.
Although they first moved northward for ∼90 days, these particles
9

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Ocean Modelling 180 (2022) 102137

Fig. 10. The mean residual transport velocity in the Subei coastal water (SCW) for all four seasons. The black dashed lines denote the boundaries of the control region.

Fig. 11. The trajectories of particles released in the (a) spring and (b) summer. The black dashed lines denote the boundaries of the control region. The black circles, triangles,
and squares denote the locations of particles on the 0, 90, and 180 days after their release, respectively.

winter, there was relatively weak transport. This causes an interesting
phenomenon that the RTV in the SCW is strong in spring and summer
when the wind is relatively weak, but weak in autumn and winterdespite of the presence of relatively strong winds.
Wind is an important factor influencing the water transport andexchange rates, and wind direction has an important effect on thespatiotemporal variation in the water transport timescales (e.g., Liuet al., 2012; Du and Shen, 2016; Luo et al., 2021). This study highlights
the importance of the directional consistency of the wind-driven flow
and tidal-induced residual current on the coastal RTV and long-termtransport. If the wind-driven flow follows the direction of tidal-induced
residual current, the wind will greatly facilitate water exchange. In
contrast, when the two current is against with each other, the wind,
to some extent, weakens the mean flow.
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Ocean Modelling 180 (2022) 102137

Fig. 12. The (a–d) residual transport velocity (RTV) in the Subei coastal water (SCW) for each season, and their components induced by the (e –h) tides, (i –l) wind, and (m –p)river runoff. The red arrows denote the overall direction of the flow.

4.4. Relationship between the RT and RTVs

Substituting expression (5) into Eq. (6) and solving the definite integral,
one can derive the following expression:

To further understand the seasonal variability of the RT in the
SCW, the quantitative relationship between the RT and the RTV is
derived. As shown in Fig. 12, the magnitude of the RTV-River in the
SCW is relatively small compared to the RTV-Tide and RTV-Wind. To
facilitate the derivation of analytical solutions, we assumed that thewater transport in idealized coastal water is only dominated by RTVTide and RTV-Wind and the roles of other dynamics processes on thewater transport are negligible. The RTV-Tide has no seasonal variationand thus its magnitude is a constant 𝑉𝑡 . The RTV-Wind has a seasonalvariation and can be expressed as −𝑉𝑤 ⋅ cos (2𝜋𝑡∕𝑇 ), where 𝑉𝑤 denotethe maximum magnitude of the RTV-Wind and T is one year (365 dayshere), and t denotes the day in a year. Here, the direction of RTV-Tide
is defined as positive, and in this study the RTV-Wind is opposite to
the RTV-Tide in winter and the same in summer. Thus, the expressionof the RTV-Wind has a minus sign in front of it. The total RTV which
determines the water transport should be the sum of the RTV-Tide and
RTV-Wind and thus is expressed as:]𝑇 𝑉𝑤 [sin (2𝜋 (𝑅𝑇 + 𝑡) ∕𝑇 ) − sin (2𝜋𝑡∕𝑇 ) = 𝐿.
(7)
2𝜋
The expression (7) can be transformed to the following expression:

𝑉 (𝑡) = 𝑉𝑡 − 𝑉𝑤 ⋅ cos (2𝜋𝑡∕𝑇 ) .

𝑉𝑡 𝑅𝑇 −

𝑅𝑇 =

∫𝑡

( )
𝑉 𝑡′ 𝑑𝑡′ = 𝐿.

(8)

The expression (8) gives us the analytic relationship between the RT
and the RTVs in the idealized case. According to model results, themagnitude of the 𝑉𝑡 and 𝑉𝑤 is ∼0.05 and ∼0.04 m/s in the SCW. The
spatial scale along the shore of the SCW is ∼300 km. Then, using thesevalues, we can solve the RT in the expression (8) using the graphic
method. As shown in Fig. 13a, the analytic solution of RT is close to thenumerical model result, though the peak of the analytic RT is later thanthat of the numerical model result. The lag of the peak could be related
to the missing of the RTV-River and the effect of tide–wind interaction
on the RTV in the analytic derivation. This simple expression can beconsidered to have reproduced the major mode of the RT seasonalvariability.
The analytic solution of the RT suggests that the magnitude of𝑉
the RT variability should be related to the 𝑉𝑤 , i.e., the ratio of the𝑡magnitude of the RTV-wind and the RTV-tide. As shown in Fig. 13b(13c), when the 𝑉𝑤 increases (decreases), the seasonal variability of the
RT will increase (decrease). In addition, when the RTV-wind is much

(5)

Assuming the V is homogeneous in the coastal water and the spatial
scale of the coastal water is L, the RT at the day t should satisfy thefollowing equation:
𝑡+𝑅𝑇

𝑇 𝑉𝑤
𝐿
sin (𝜋𝑅𝑇 ∕𝑇 ) cos (𝜋 (𝑅𝑇 + 2𝑡) ∕𝑇 ) + .
𝜋 𝑉𝑡
𝑉𝑡

(6)
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Ocean Modelling 180 (2022) 102137

seasonal variation in the RTV in the SCW, and the RT magnitude in
the current season was determined by the RTVs in both the current
and next seasons. The tides greatly increased the RT in the coastal
water, while the wind was the dominant factor for seasonal variationin the RT and the Changjiang River runoff slightly decreased theRT. The analytic relationship between the RT and RTV suggests thatthe magnitude ratio of the RTV-Wind and RTV-Tide determined themagnitude of the RT seasonal variability in a system dominated bywind and tides. The RT results could be helpful for understanding thecoastal ecological and environmental problems, implying that coastalmanagement and scientific planning should be conducted depending on
the season, which will be discussed in depth in our subsequent research.
CRediT authorship contribution statement
Lei Lin: Conceptualization, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing, Funding acquisition. Dongyan Liu: Writing – review & editing, Funding
acquisition. Qingjun Fu: Validation, Visualization. Xinyu Guo: Writing– review & editing. Guangliang Liu: Methodology, Software. Hao Liu:
Software. Shengli Wang: Software.

Fig. 13. The seasonal variation in RT derived from Expression (8) for 𝑉𝑤 = 0.04, 0.1,
and 0.01 m/s, respectively.

smaller than the RTV-tide, the high RT will be delayed until winter(Fig. 13c), which can explain the pattern of the RT for the NoWind case(Fig. 9). The above analysis can be helpful for evaluating the seasonalvariability of RT in other coastal water dominated by the tides and windwithout complicated numerical simulation.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared toinfluence the work reported in this paper.

4.5. Implications for coastal ecology and environment
Acknowledgments
Since 2008, the world’s largest trans-regional macroalgal bloom(also known as green tide) has occurred annually in the Yellow Sea.
The green tide covers more than 80,000 km2 , seriously affecting theenvironment and ecology of the Yellow Sea (Keesing et al., 2011; Liuet al., 2013). The green tide is caused by the floating green algae
originating from the Jiangsu coast in April and May (Liu et al., 2013).
This floating green algae is then transported northward in the western
Yellow Sea and reaches the Shandong coast in August. This study showsthat the annual mean RT in the SCW is approximately three months, but
the RT is the shortest in April and May, which is approximately one
and half months, indicating that the water export rate in the SCW ismuch faster in spring. Because of the rapid water export rate of coastal
water in April and May, the floating green algae can leave the SCW
sooner and enter the offshore water and form the algal blooms over thewestern Yellow Sea. Thus, the short RT in April and May could be an
important factor responsible for the rapid expansion of the macroalgal
blooms in the Yellow Sea, which suggests that the hydrodynamic could
be a critical condition for the occurrence of the ecological problem.
In addition, the RT results suggest that the water export rate in
the SCW has significant spatiotemporal variation, which is very helpful for coastal environmental management. Based on the RT results,
environmental managers can develop strategies to mitigate coastal
pollution. For instance, high-RT periods indicate slow water export
rates, suggesting that pollutant discharge should be strictly controlled
and even reduced at these periods to alleviate the marine environmental pressure. The optimization method of environmental management
strategies based on RT results will be discussed in future studies.

The authors thank Prof. Eric Deleersnijder and three anonymous
reviewers for their insightful and constructive comments, which significantly improved this manuscript. This study was supported by the
National Natural Science Foundation of China (Grant Nos. 41706011,
42030402, and 41876127), the National Key Research and Development Program of China (2020YFA0607900), and the Open Research
Fund of State Key Laboratory of Estuarine and Coastal Research (Grant
number SKLEC-KF202105). Xinyu Guo was supported by Grants-in-Aid
for Scientific Research (MEXT KAKENHI grant numbers: 20H04319).
The water temperature and salinity data acquisition in the Yellow
Sea were supported by the National Natural Science Foundation ofChina (NSFC) Open Research Cruise (Cruise No. NORC2014-01 andNORC2015-01), funded by the Shiptime Sharing Project of NSFC. The
cruises were conducted onboard R/V ‘‘DONGFANGHONG 2’’ by Ocean
University of China.
Appendix A. List of abbreviations

Abbreviations

Full name

RT
ET
PRT
SCW
RTV
TVDal

Residence time
Exposure time
Partial residence time
Subei Coastal Water
Residual transport velocity
Total variation diminishing scheme withan alternating flux limiter
Constituent-oriented Age and Residence
time Theory

5. Conclusions
CART
Using numerical modeling and the adjoint method of RT, this study
investigated the spatiotemporal distribution of RT in the SCW and its
control mechanism. RT had an annual mean of ∼80 days and showeda significant seasonal variability. The spatially averaged RT was thelowest in spring (approximately 55 days) and the highest in summer(approximately 91 days). The seasonality of the RT was related to the

Appendix B. Supplementary data
Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.ocemod.2022.102137.
12

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Ocean Modelling 180 (2022) 102137

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