RESEARCH ARTICLE
10.1029/2019JC015863
Key Points:• The tidal effect on the water export
rate in the eastern shelf seas ofChina (ESSC) is assessed from atimescale perspective• Average water residence time in the
ESSC is 2.12 years and reduces to0.64 year if tides are excluded in thehydrodynamic model• There is a high spatial variability ofthe tidal effect on the water export
rate, which is associated with thewater depth

Correspondence to:
L. Lin and D. Liu,
llin@sklec.ecnu.edu.cn;
dyliu@sklec.ecnu.edu.cn

Citation:
Lin, L., Liu, D., Guo, X., Luo, C., &Cheng, Y. (2020). Tidal effect on water
export rate in the eastern shelf seas ofChina. Journal of Geophysical Research:
Oceans, 125, e2019JC015863. https://doi.org/10.1029/2019JC015863
Received 9 NOV 2019
Accepted 28 MAR 2020
Accepted article online 04 APR 2020

Tidal Effect on Water Export Rate in the Eastern Shelf Seasof China
Lei Lin1, Dongyan Liu1, Xinyu Guo2

, Chongxin Luo3, and Yao Cheng4

1

State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai, China, 2Center for
Marine Environmental Study, Ehime University, Matsuyama, Japan, 3Key Laboratory of Marine Environment andEcology, Ministry of Education, Ocean University of China, Qingdao, China, 4School of Water Conservancy andHydroelectric Power, Hebei University of Engineering, Handan, China

Abstract Water export rate of shelf seas is a pivotal factor impacting the global carbon cycle. Tides haveimportant impacts on shelf hydrodynamics but are excluded in many climate models. To assess the effect oftides on export rates of shelf water, this study used a regional hydrodynamic model and a water residence
time (WRT) adjoint model and examined model runs with and without tides for the eastern shelf seas ofChina. The results show that the average WRTs in the Bohai, Yellow, and East China seas were 11.60, 4.95,
and 0.39 years, respectively. When tides were excluded, the WRTs decreased by >70% in the Bohai andYellow seas and by ~10% in the East China Sea, indicating a signiﬁcant acceleration in the shelf water export
due to the absence of tides. The tidal effect has spatial variability associated with the water depth. Sensitivity
experiments suggest that the tidal effect on the mean WRT was stronger than the effect of other dynamicalfactors (winds, rivers, and boundary currents). In the model with tides, tides weakened the wind‐driven
coastal current by intensifying the bottom resistance and thus slowed water export in the inner and middle
portions of the shelf, compared to the model without tides. Parameterization of the tidal bottom friction in
the model without tides could signiﬁcantly improve the WRT result. This study highlights the crucial role oftides on the long‐term transport of shelf seas and the signiﬁcance of parameterizing the effect of tidal friction
in climate models.

Plain Language Summary The export of water with a high carbon content to the deep oceansfrom shelf seas is a pivotal process impacting the global carbon cycle. Tides play an important role in thehydrodynamics of shelf seas and thus inﬂuence the water export. Hence, a quantitative assessment of thetidal effect on the water export rate is essential, in order to understand the role of tides in the global carbon
cycle. Using water residence time (WRT) as an indicator and numerical modeling, this study ﬁnds that themodel without tides decreased the WRT of the eastern shelf seas of China (ESSC) to ~1/3 compared to themodel with tides, indicating a signiﬁcant effect of tides on the water export from shelf seas. Meanwhile, thetidal effect on the water export in the ESSC was much stronger in the inner and middle shelves comparedwith that in the outer shelf. The ﬁndings of this study highlight the crucial impact of tides on the waterexchange between shelf seas and deep oceans, which implies that small timescale and space‐scale processes
should be simulated or effectively parameterized in climate models in order to accurately predict the oceanand climate change.

1. Introduction©2020. American Geophysical Union.
All Rights Reserved.

LIN ET AL.

Due to the high primary productivity, shelf seas (especially in temperate zones) usually act as net carbon
sinks (Cai et al., 2006; Thomas, 2004). Shelf seas exporting water with a high carbon content to the deep
oceans is a pivotal process that impacts the global carbon cycle (Bauer et al., 2013; Cai et al., 2006; Holtet al., 2009; Laruelle et al., 2018; Regnier et al., 2013; Thomas, 2004; Walsh, 1991). An accurate simulationof water export rates from shelf seas is therefore critical for the accurate representations and projectionsof the global carbon cycle and climate change. However, hydrodynamic processes in shelf seas cannot
usually be well represented in climate models due to their small spatial scale compared to the global ocean(Graham et al., 2018; Holt et al., 2017). In particular, as one of the major motions in shelf seawater, tides areeither excluded or parameterized in many climate models given their signiﬁcantly shorter timescales in comparison to those of climate, in addition to numerical stability problems (Holt et al., 2017; Lee et al., 2006;
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Luneva et al., 2015; Müller et al., 2010; Simmons et al., 2004; Voldoire et al., 2013). Therefore, it is signiﬁcantand necessary to quantitatively evaluate the tidal effect on the water export rate of shelf seas.
Tides can modulate shelf currents through affecting water mixing and bottom friction (e.g., Moon et al., 2009;
Palma et al., 2004; Wang et al., 2013; Wu et al., 2018). Tides can also inﬂuence the water transport by inducing residual currents, which is especially important for the nearshore water (e.g., Cai et al., 2014;
Delhez, 1996; Feng et al., 2008; Lin et al., 2015; Wu et al., 2018). In these ways, tides could have a signiﬁcant
inﬂuence on the shelf hydrodynamics and thus on the water export rate. For instance, in the Ross Sea, tides
enhanced the cross‐shelf exchange and the Antarctic bottom water export (Wang et al., 2010; Whitworth &Orsi, 2006), which suggests that tides could accelerate the shelf water export. However, numerical experiments conducted for the Southwestern Atlantic Shelf suggested that tides could weaken the shelf currents(Palma et al., 2004), which suggests that tides could inhibit the shelf water export. The opposite effects suggest that the tidal effect on the shelf water export rate should be of high spatial heterogeneity.
Water transport at the shelf break or at key transects is often used to quantify the shelf water export rate (e.g.,
Graham et al., 2018; Wang et al., 2013; Zhou et al., 2015), which is essential for understanding local waterexchanges. However, water transport cannot depict well the spatial variability of the water export rate overan entire shelf. For instance, the water export rate in an inner shelf is related not only to the cross‐shelf transport at the shelf break but also to the hydrodynamics in the inner and middle shelves. Therefore, the spatial
variability of the tidal effect on the water export rate on a shelf cannot be accurately assessed using only thecross‐sectional transport. In this study, we used the water residence time (WRT) to represent the water
export rate on the shelf. WRT is deﬁned as the time a water parcel needs to leave the region of interest forthe ﬁrst time (Bolin & Rodhe, 1973; Delhez et al., 2004; Takeoka, 1984). WRT provides a timescale approachfor summarizing the complex dynamics of a system and can reﬂect the spatial variability of the water export
rate over shelf seas and quantify the retention timescale of coastal water that constrains the coast‐ocean
exchange (e.g., Liu et al., 2019).
The eastern shelf seas of China (ESSC), which include the Bohai Sea (BS), the Yellow Sea (YS), and the East
China Sea (ECS), are one of the widest continental shelves in the world (Figure 1a). The ESSC cover an areaof more than 122 × 104 km2, with an average water depth of ~240 m (Su & Yuan, 2005). Strong tides occur inthe ESSC, and semidiurnal tidal constituents (M2 and S2) are predominant (e.g., Guo & Yanagi, 1998). This
study uses a regional hydrodynamic model and timescale diagnosis to examine the tidal effect on the WRT in
the ESSC, with the overall aim of better understanding the tidal effect on the water export rate over the ESSC
and its spatiotemporal variability. Hence, we anticipate that our ﬁndings will provide a reference material
for climate and Earth system modeling.
This paper is organized as follows. The hydrodynamic and WRT diagnosis models and the numerical experiment schemes are introduced in section 2. Section 3 shows the results of the WRT of the ESSC and the tidal
effect on the WRT. In section 4, the effect of the reentry process is evaluated, and the mechanism of the tidal
effect on the WRT and its implications for climate modeling are discussed. At last, a brief conclusion is given
in section 5.

2. Methods
2.1. Study Area
The ESSC connect rivers from eastern China (including the Changjiang River, the third longest river in theworld) and the western Korea Peninsula with the western Paciﬁc Ocean (Figure 1a). The ESSC represent avital carbon storage area and export ~15.25–36.70 × 109 kg of organic carbon per year to the Paciﬁc (Jiaoet al., 2018). The circulation system in the ESSC is basically composed of the Kuroshio along the shelf break,the Taiwan warm current, the Yellow Sea warm current (YSWC) (in winter), and coastal currents that areforced by the Asian monsoon winds (Figure 1b). The seasonal variability in water transport across the shelf
break and its dynamic mechanism in the ESSC have been previously studied using ocean models or in situ
observations (e.g., Ding et al., 2016; Guo et al., 2006; Zhou et al., 2015). Findings from these studies are very
helpful for understanding the local water export rate along the shelf break, while this study aims to provide
an understanding of the water export rate of the entire ESSC from a timescale perspective.

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Figure 1. (a) Topography and the model domain of the eastern shelf seas of China (ESSC). The red lines denote the prescribed open boundary of the control
region for the calculation of WRT. (b) Primary circulation pattern for the ESSC in winter. TWWC: Taiwan warm current; TWC: Tsushima warm current;
YSWC: Yellow Sea warm current. The gray dotted lines are the isobaths (m).

2.2. Hydrodynamic Model
A hydrodynamic model of the ESSC was initially developed by Guo et al. (2003) based on the Princeton
Ocean Model (Blumberg & Mellor, 1987; Mellor, 1998) and a triple‐nesting method. Wang et al. (2008) added
tidal forcing (including M2, S2, K1, and O1 tidal constituents) into the ﬁnest grid model and used a smaller
model domain (117.5–131.5°E and 24.0–41.0°N) covering the ESSC (Figure 1a), which is also used in thisstudy. The model domain is discretized by a grid space of 1/18 degree (~5–6 km) in the horizontal directionand 21 sigma levels in the vertical direction. The time steps for the external and internal modes in the modelare 9 and 360 s, respectively.
To focus on the results of climatological state, the model is driven by climatological mean monthly forcings,
including winds, heat ﬂux, precipitation and evaporation rates, and river runoff (Guo et al., 2003; Wanget al., 2008). A more detailed description and validation of the hydrodynamic model are provided in Guo
et al. (2003, 2006), Wang et al. (2008), and Zhu et al. (2018). This model has been applied by Liu et al. (2012)
to study the water age of the Yellow River in the BS, by Zhu et al. (2018) to study the interannual variation in
the YS cold water mass, by Zhao and Guo (2011) to study cross‐shelf transport of nutrients in ECS, and by
Zhang et al. (2019) to study the role of nutrients with different origins in the primary production in the
ECS. These studies demonstrated that the model presented a good representation of the hydrodynamic characteristics of ESSC. Following a 3‐year spin‐up, the model outputted data of the sea level, three velocity components, and the horizontal and vertical diffusivity coefﬁcients with a time interval of 0.5 hr over 1 year todrive the WRT diagnostic model (section 2.3).

2.3. Diagnosis of WRT
Since WRT is the time that a water parcel needs to leave the region of interest for the ﬁrst time, it follows thata longer WRT means a slower water export. In this study, the 200‐m isobath along the shelf break, which isusually regarded as the open boundary of the cross‐shelf exchange in the ESSC (e.g., Ding et al., 2016; Guoet al., 2006; Zhou et al., 2015), was set as the boundary of the region of interest for WRT (red line labeled SH

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Journal of Geophysical Research: Oceansin Figure 1a). To close the region of interest, we added two “gates” at the
Taiwan Strait (TS) and to the east of Cheju Island (CE) (Figure 1a).

Table 1
Boundary Conditions for the WRT Equation and Model
Boundary conditions
Open boundary of ω

Expressions
θ¼0
 
!
n  ∇θ ¼ 0

Closed boundary of ω
Boundaries of the computational domain

10.1029/2019JC015863

θ¼0

Note. !
n is the outgoing unit vector normal to the boundary.

The adjoint method proposed by Delhez et al. (2004) was used to determine the spatiotemporal distribution of WRT in the ESSC. By solving
the adjoint problem of the tracer transport, Delhez et al. (2004) derived
the spatiotemporal variation in WRT using equation 1:∂θ þ δ ðxÞ þ v∇θ þ ∇K∇θ ¼ 0δ ðxÞ ¼
ω
ω
∂t



1 ∀x ∈ ω0∀x ∉ ω

;(1)

where θ denotes WRT, v is the velocity ﬁeld, K is the diffusivity tensor, and δω(x) is the characteristic function of the control region ω. To solve WRT, equation 1 should be integrated backward in time (Delhez
et al., 2004). The initial ﬁeld is set to 0 for θ (Delhez, 2006). As listed in Table 1, a homogenous Dirichletboundary condition, θ ¼ 0, is prescribed at the open boundaries of the control region (Delhez et al., 2004).
 
The impermeability boundary condition, !
n  ∇θ ¼ 0, is used at the mouth of the estuaries, because in
the hydrodynamic model, the river discharges are treated as downward water ﬂux at sea surface over theriver grids, that is, by the corresponding increase in precipitation at these grids (Wang et al., 2008). In thehydrodynamic model, this type of boundary condition for river runoff may underestimate the momentum
at the estuarine regions. However, wind‐driven currents are the dominance on the shelf, and the underestimation of the momentum will not signiﬁcantly affect the water transport in the ESSC. In addition, theexperiment results show that the impact of the river boundary condition on the WRT in ESSC is unlikely
to be very signiﬁcant (see section 3.2). Therefore, this issue is believed to be a minor one for this study.
The WRT diagnostic model established by Lin and Liu (2019a) and Liu et al. (2016) based on equation 1 isused in this study. The WRT model is solved using the ﬁnite‐difference method with the same domain, grids,
and layers as the ESSC hydrodynamic model. The second‐order centered difference is applied to solve thediffusion terms. A second‐order total variation diminishing scheme with alternating Superbee and
MUSCL ﬂux limiters (TVDal, Lin & Liu, 2019b) is used to solve the advection terms. Using the climatologicalvelocity and diffusion coefﬁcients from the hydrodynamic model, we ran the WRT diagnostic model for
30 years to complete the spin‐up when a stable interannual variation of WRT in the ESSC was obtained
and the effect of the initial condition on the WRT disappeared (Delhez & Deleersnijder, 2006; Du &Shen, 2016). The WRT value of the 30th year was used for the analysis.
2.4. Sensitivity Experiments
To examine the tidal effect on the WRT in the ESSC, we conducted a numerical sensitivity experiment, inwhich the tides were excluded from the hydrodynamic model. Following a 3‐year spin‐up of the hydrodynamic model without tides, the WRT in the ESSC was diagnosed with the same procedures described in
section 2.3 (hereafter termed “NoTide case”). In addition, to compare the importance of tides with otherdynamic factors, that is, local winds, river runoff, and boundary currents (BCs), we carried out another three
sensitivity experiments. Two of these were similar to NoTide case but where winds and river runoff were
excluded instead, respectively (hereafter termed “NoWind case” and “NoRiver case,” respectively). The third
sensitivity experiment reduced the ﬂow velocity at the southern and eastern open boundaries to half of their
original values (hereafter termed “HalfBC case”). WRTs of different cases were compared with the control
run (with the complete set of forcings) to quantify the effect of each dynamic factor on the water export ratein the ESSC.

3. Results
3.1. WRT in the ESSC
The WRTs in the ESSC that were obtained from the control run are shown in Figure 2a. The annual mean
WRT in the ESSC was 2.12 years. The annual mean WRTs of the BS, YS, and ECS were 11.60, 4.95 (7.01 and4.56 for the north and south YS, respectively), and 0.39 years, respectively. The model results agreed with theestimated WRT based on the isotopic observations from previous studies (e.g., Chen, 1997; Kim et al., 2005;
Nozaki et al., 1991; Tsunogai et al., 1997). For instance, using Ra‐226 and Ra‐228 isotopes and their
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Figure 2. The annual mean of vertically averaged WRT in the ESSC for (a) the control run and (b) the NoTide case,(c) The daily mean WRTs over the ESSC for the ﬁve cases.

mass‐balance models, Kim et al. (2005) and Nozaki et al. (1991) derived an average WRT of 4.9 and 5–6 years
for water in the south YS, respectively, both of which are very close to our WRT of 4.56 years. Based on themean inventory of excess alkalinity, Tsunogai et al. (1997) and Chen (1997) estimated a WRT of 0.8 ± 0.3 and1.3 ± 0.4 years for the ESC continental shelf water, respectively, which are much shorter than the WRT in
the south YS. In addition, the WRT in the BS is ~4 years longer than that in the north YS, thus indicatingthat the water in the BS requires around 4 years to leave the BS, which is consistent with the mean water
age of the Yellow River water at the BS strait (~3.4 years) derived from another modeling study (Liuet al., 2012). Therefore, the WRT diagnostic model applied in this study is considered to be reliable.
Spatially, the WRTs increased from the outer shelf to the inner shelf (Figure 2a). The WRT of the 100‐m
isobath was <1 year, increasing to <3 years in the ECS, 3–10 years in the YS, and up to ~15 years in the
BS. The WRTs at the estuaries can approximately indicate the average time required for the river water toleave the ESSC. The modeled annual mean WRTs at the estuaries of the three major rivers along thecoast of the ESSC (i.e., the Changjiang, Yellow, and Yalvjiang rivers) were 2.70, 11.01, and9.25 years, respectively.
Compared to the annual mean, the seasonal variation in the spatial mean WRT was relatively small(Figure 2c). Average WRTs in the ESSC were shortest during March (~2.06 years) and longest during
September (~2.17 years). A relatively signiﬁcant seasonal variation in the WRT occurred at the Jiangsu
Coast and the Korea West Coast (Figure 3), which could be related to the seasonal variation in the
coastal currents dominated by the monsoon winds. In addition, WRTs showed a fortnightly variation
with an averaged magnitude of ~0.03 year, which corresponded to the spring‐neap tidal variation(Figure 2c). The WRTs in the ESSC were vertically homogenous during the winter and autumn due tovigorous vertical mixing. During the spring and summer, WRTs showed a slight vertical change due tostratiﬁcation (Figure 4).
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Figure 3. Vertically averaged WRT in the ESSC in summer, autumn, winter, and spring.

3.2. Tidal Effect on the WRT in the ESSC
Compared to the control run, the WRT reduced greatly when tides were excluded from the hydrodynamic
model (Figure 2b). The annual mean WRTs in the ESSC for the NoTide case were shorter than 4 years
throughout the ESSC (Figure 2b). The average WRT in the ESSC was <0.71 year over a year, with an annual
mean of 0.64 year, which was only ~1/3 of that obtained in the control run (2.12 years). This reduction in the
WRT indicates that the water export rate in the ESSC increased by more than three times on average whentides were excluded. For the NoTide case, the annual mean WRTs in the BS, YS, and ECS were 3.27, 1.02
(1.24 and 0.98 for the north and south YS, respectively), and 0.35 years, respectively. These represent
decreases of 72%, 79%, and 10%, respectively, compared to the control run. For the estuaries of the
Changjiang, Yellow, and Yalvjiang rivers, the WRTs for the NoTide case were 0.54, 3.05, and 1.16 years,
respectively. These represent reductions of 80%, 72%, and 87%, respectively, compared to the control run.
As expected, the fortnightly variation in the WRTs was not found in the NoTide case, while the weak seasonal variation remained (Figure 2c).
The relative difference between the annual mean WRTs of the control run and the NoTide case was calculated to understand the spatial variability of the tidal effect on the shelf water export rate. As shown in
Figure 5a, a signiﬁcant decrease in the WRTs occurred on the inner and middle shelves (water depth
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Figure 4. WRT along the transect of 124°E in summer, autumn, winter, and spring.

generally <80 m). The WRT change was relatively small on the outer shelf except that the WRT increased at
the central ECS (see the dashed circle in Figure 5a). As shown in Figure 5b, tides increased WRT at water
depth roughly <80 m, and the tidal effect on the WRT became stronger as the water depth got shallower.
The tidal effect became opposite in the relatively deep water (the water depth >80 m), but it was weaker
than the tidal effect on the shallow water (also see Figure 5a). The good correlation between the relative
difference and the water depth indicates that the tidal effect on the water export rate in ESSC is highly
related to the water depth.
The sensitivity experiments also show that the average WRTs in the ESSC for the NoWind, HalfBC, andNoRiver cases were 2.22, 2.00, and 2.40 years, respectively (Figures 2c and 6). These values were close to
the WRTs obtained from the control run. When compared to the control run, the relative changes in thesethree cases were <15%, which is far less than that in the NoTide case (~70%). These results indicate that tides
have a dominant impact on the WRT in the ESSC.
Although the spatially averaged WRTs in the ESSC obtained in the NoWind case were close to that obtainedin the control run, their spatial distributions of WRTs were signiﬁcantly different (Figure 6). Without winds,
the WRTs increased in the BS and north YS but decreased in the south YS, thus indicating that local winds
affected the spatial pattern of WRTs in the ESSC. To focus on the tidal effect on WRT, this study will not discuss the impact of winds on the WRT.

4. Discussion
4.1. The Impact of the Reentry Process on the Results
The concept and diagnosis method of the WRT was used to quantify the water export rate in ESSC according
to the Constituent‐oriented Age and Residence time Theory (Deleersnijder et al., 2001; Delhez &Deleersnijder, 2002; Delhez et al., 2004). The WRT results show that there is a signiﬁcant difference in thewater export rate between the ocean models with and without tides. WRT is deﬁned as the time that a waterparcel needs to leave the region of interest for the ﬁrst time. The use of WRT means that the boundary prescribed in this study represented a strict one to separate the shelf sea and the deep ocean and the effect of thereentry process is ignored (Delhez et al., 2004). This can be interpreted as that once a water parcel crosses the
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Figure 5. (a) The relative difference in the annual mean WRT between the control run and NoTide case. Negative(positive) values denote the WRT decreased (increased) percent of the NoTide case compared to the control run. The
gray dotted lines are the isobaths. (b) The relative difference in the annual mean WRT varying with the water depth withan interval of 5 m. The red squares denote the mean values, and the blue error bars denote their standard deviations. The
red dotted line is the linear regression for the mean values, and the regression equation is labeled at the top left corner.

boundary, its property will change from shelf water to oceanic water due to mixing and highly altered biogeochemical processes.
In some cases, the water parcel could reenter the control region due to the effect of return ﬂows at the open
boundary of the shelf sea. To assess the effect of the reentry process on the results, we calculated the water
exposure time (WET) and then the return coefﬁcient r introduced by de Brauwere et al. (2011), which
deﬁned as
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Figure 6. The annual mean of vertically averaged WRTs in the ESSC for three sensitivity experiments: (a) NoWind case; (b) HalfBC case (i.e., half ﬂow velocity at
the southern and eastern open boundaries); and (c) NoRiver case.

r ¼ ðWET − WRTÞ=WET:(2)

WET measures the total time spent in the ESSC as the water parcel leaves and reenters the region of interest(de Brye et al., 2012; Delhez, 2013). The equation of the WET is the same as that of the WRT except that noboundary conditions need to be prescribed on the open boundaries of the control region (de Brye et al., 2012;
Delhez, 2013). The return coefﬁcient r is comprised between 0 and 1. The larger the value of r, the stronger
the effect of the reentry process on the water transport timescale.
Figure 7a shows that the WET in ESSC had a very similar spatial pattern with the WRT. The annual mean
WET in the ESSC was 2.38 years and slightly higher than WRT (2.12 years), indicating that the reentry process could prolong the time that seawater spent on the shelf for 0.26 year on average. The return coefﬁcient
was basically less than 0.2 on the inner and middle shelves, with a relatively large value (r > 0.5) at the outer
shelf. The result suggests that the effect of the reentry process is more signiﬁcant on the outer shelf, especially near the open boundary (Figure 7b). For the NoTide case, the WET with an annual mean of 0.66 year
was very close to the WRT (Figure 7c). The mean return coefﬁcient for the NoTide case was 0.03, which wasmuch less than that of the control run (0.11), indicating that the tidal current could be the dominant
dynamics driving the water mass to return to the shelf. Moreover, the WET of the control run was 3.6 times
as long as that of the NoTide case, indicating that the tidal effect on the water export rate will be more signiﬁcant if considering the reentry process.
4.2. The Role of Tidal Mixing and Intensiﬁed Bottom Friction in the WRT
In order to examine the effect of tidally induced mixing and tidally intensiﬁed bottom friction on the WRT in
the ESSC, two extra numerical experiments were conducted. In one experiment, tides were excluded, but thevertical eddy viscosity and diffusivity coefﬁcients from the control run were used (hereafter termed “TMcase”). In the other experiment, linear bottom friction with parameterization of the tidal effect on the bottom
stress used by Lee et al. (2000) and Moon et al. (2009) was applied (hereafter termed “BF case”). In the control run, the bottom friction stress, !
τ b , in momentum equations of seawater motion that was used in thehydrodynamic model was derived from the quadratic law as deﬁned by equation 3:
 
!!
!
τ b ¼ ρCd  V V ;(3)!
where ρ is the water density, Cd is the friction coefﬁcient, and V is the instantaneous velocity. In BF case,instead of the quadratic bottom friction, a linear‐type bottom friction stress was applied to parameterize
the enhanced bottom friction due to tidal stress, as deﬁned by equation 4:
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Figure 7. The annual mean of (a) vertically averaged water exposure time (WET) and (b) the return coefﬁcient in the
ESSC for the control run. (c) The daily mean WRTs and WETs over the ESSC for the control run (‐CR) and the
NoTide case (‐NT).

!
!
τ b ¼ ρCd k V ;(4)where k is the coefﬁcient of the linear bottom friction. According to Lee et al. (2000) and Moon et al. (2009),
the coefﬁcient k can be calculated using equation 5:
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
k ¼ 1:23 U T 2 þ V T 2 ;(5)where UT and VT are the amplitude components of the depth‐averaged M2 tidal currents, which are derived
from the velocity ﬁeld of the control run.
The extra experiment results showed that WRTs in the TM case were very close to that obtained in the
NoTide case (Figures 8a, 8c, and 8d), thus indicating that the impact of tidal mixing on the shelf water export
rate was limited. The annual mean WRT in the BF case increased signiﬁcantly compared to the WRT
obtained for the NoTide case, and it was ~0.47 year lower than that obtained in the control run(Figures 8b and 8c). However, there is still a remarkable difference in the spatial distribution of WRT
between the BF case and the control run (Figure 8e), which may be related to the absence of the residual
tidal current and the interaction between tidal currents and shelf currents in the BF case. These results suggest that the tidally intensiﬁed bottom friction has a more important effect on the water export rate than the
tidal mixing in the ESSC. The parameterization of the tidal effect on the bottom friction in hydrodynamic
models can reduce the bias of the mean water export rate for the model without tides, but it can still induce
considerable biases in some areas on the shelf.
4.3. Impact of Tides on the Shelf Circulation in the ESSC
The sensitivity experiments showed that tides signiﬁcantly affect the WRTs over the ESSC. The water exportin shelf seas is determined by advection and turbulence mixing. The results of the TM case suggest that theeffect of the altered mixing on WRT is limited. Therefore, the effect of the tides on the shelf current should be
the main cause of the signiﬁcant differences in the WRTs between the control run and the NoTide case.
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Figure 8. The annual mean of vertically averaged WRTs in the ESSC for the (a) TM case and (b) BF case. (c) The daily
data of the averaged WRT in the ESSC in the TM and BF cases along with those in the control run and the NoTide case.
(d) The relative difference in the annual mean WRT between the control run and TM case. (e) The relative difference inthe annual mean WRT between the control run and BF case.

Here, we analyze the impact of the tides on cross‐shelf transport and shelf currents in the ESSC in order tounderstand the tidal effect on the water export rate in the ESSC.
As shown in Figure 9, the water transport across a zonal transect in the YS during the control run and the
NoTide case were remarkably different. When compared to the control run, the outﬂow across the 36°N
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Figure 9. Monthly transport (per unit width) across the zonal transect of 36°N in the Yellow Sea (YS) for (a) the control
run and (b) the NoTide case. (c) Daily mean transport over a year across three transects (TS, SH, and CE in Figure 1a) of
the open boundary of the ESSC for the control run (‐CR) and NoTide case (‐NT). Positive and negative values for thetransport denote inﬂow and outﬂow, respectively.

transect in the NoTide case increased by ~2.5 times over the year (Figures 9a and 9b), which explains thesigniﬁcant reduction in the WRT in the YS and BS. The increase in the outﬂow was more pronounced
during the winter half‐year (from October to March), which accounted for ~73% of the volume transport
for the entire year in the NoTide case. However, the impact of tides on water transport at the shelfboundary of the ESSC was limited. Figure 9c shows that the transports across the three transects of theopen boundary for the NoTide case were very close to those obtained during the control run. The annual
mean outﬂow/inﬂow for the NoTide case was ~3.2 Sv (1 Sv = 106 m3/s), which was only ~5% higher thanthat for the control run (~3.05 Sv). This explains the relatively small change in the WRTs in the ECS in
the NoTide case.
The remarkable difference in the transport across the transect in the YS between the control run and NoTide
case relates to the effect of tidal modulation on the circulation system of the YS. As shown in Figure 10, thecirculation intensities in the YS and BS decreased markedly in the presence of tides, especially during winter.
For the control run, the magnitude of the mean velocities in the YS and BS during the winter was basically<0.05 m/s, which agrees with the results of ﬁeld observations and previous modeling studies (e.g., Lin &LIN ET AL.

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Figure 10. Monthly mean velocity (vertically averaged, m/s) in February (a and b) and August (c and d) in the ESSC for
the control run and the NoTide case, respectively.

Yang, 2011; Lin et al., 2011; Ma et al., 2006). By contrast, the coastal currents in the YS, BS, and the YSWC for
the NoTide case reached 0.1–0.2 m/s, which was much stronger than of those in the control run (Figures 10aand 10b). The stronger coastal currents and the YSWC were also reproduced by models without tides in
Huang et al. (2005) and Moon et al. (2009). For the ECS, the Zhemin coastal current was also intensiﬁedin the NoTide case, whereas the tidal effect on the Kuroshio and other currents in the ECS was not assigniﬁcant as the effect on the currents in the YS and BS.
The signiﬁcant enhancement of the coastal currents and the YSWC in the NoTide case facilitated the waterexchange of the BS and YS and accelerated the water export from the YS and BS into the ECS, where waterexchange was faster. Therefore, the WRTs in the ESSC were greatly reduced in the NoTide case, although thewater transport at the open boundary of the ESSC did not increase signiﬁcantly. The results indicate that thewater export rate in the inner and middle shelves was strongly related to the local hydrodynamics and thatwater transport across the shelf boundary is more representative of the local water exchange rather than the
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Figure 11. Monthly mean sea level and geostrophic ﬂows (arrows) in February in the Bohai Sea (BS) and the Yellow Sea(YS) for (a) the control run and (b) the NoTide case. Geostrophic ﬂows were diagnosed using the barotropic geostrophic
balance (e.g., Cushman‐Roisin & Beckers, 2011).

water exchange rate over the entire shelf sea. When tides were excluded in the model, the simulated YSWC
was signiﬁcantly enhanced, which could bring more ECS water into the YS. Therefore, in the NoTide case,some water in the ECS could be staying longer in the shelf rather than be directly transported
through the open boundaries. This could explain the WRT increase at the central ECS in the NoTide case
(Figure 5a).
The difference in the magnitude of coastal currents in ESSC between the control run and the NoTide case ismainly related to the tidal effect on the bottom friction, which is supported by the results of the BF experiment in section 4.2. When tides are included in the model, the tidal mean bottom resistance could increase
by approximately one order of magnitude in coastal waters due to the nonlinear tidal effect on bottom friction stress (e.g., Parker, 1991; Wu & Wu, 2018). The intensiﬁed bottom resistance caused by tides could counteract wind stress, which dramatically weakens the wind‐driven coastal currents (e.g., Moon et al., 2009;
Palma et al., 2004; Wu & Wu, 2018). The reduction of coastal currents in the BS and YS induced a relatively
small sea‐level gradient for the YS that led to a relatively weak barotropic geostrophic current in the central
YS (Figure 11). Thus, the YSWC was weaker in the control run than in the NoTide case. The reduction of the
shelf currents by tides induced a slower water exchange in the shelf in the control run and thus increased the
WRTs in the YS and BS. On the other hand, tides have been reported to decelerate and even reverse thewind‐induced coastal currents via a tidal residual current (Lie & Cho, 2016; Moon et al., 2009; Wu &Wu, 2018), which could be important for the YS current during the summer (Moon et al., 2009). For the
ECS, due to the relatively deep water depth (average ~80 m), the inﬂuence of the change in the bottom friction on the shelf current was weaker than that of in the YS and BS, and thus, the tidal effect on the water
export rate was relatively small.
4.4. Implications for Climate Modeling
The results of this study showed the spatial variability of the tidal effect on the water export rate on the
shelf. The variability of tidal effects could be associated with the water depth of the shelf seas. For relatively shallow shelves such as the inner and middle shelves in ESSC and Southwestern Atlantic Shelf(water depth mostly <100 m), bottom stress usually plays a major role in the momentum balance(Palma et al., 2004). Tides enhance bottom friction resistance and therefore reduce the velocity of shelfcurrents and slow the shelf water export. However, for relatively deep shelves, the tidal effect on the
shelf water export even can be opposite. For instance, in the studies conducted in the Ross Sea(~500‐ to 700‐m average water depth), Whitworth and Orsi (2006) and Wang et al. (2013) found thattides facilitated the shelf water outﬂow to some extent. The geostrophic balance and the baroclinic current are commonly dominant in the deep water. The inﬂuence of tides on the water density structure
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becomes vital for the tidal modulation of shelf currents. Spatial variations in tidal mixing and tidal
advection could intensify the horizontal density gradients and thus increase the baroclinic current,
which could be favorable for water transport, for example, in the Ross Sea (Wang et al., 2010, 2013).
Although the impacts of tides on shelf water export are complicated, considering the tidal effect isessential for correctly simulating the process of shelf water export in climate models. Meanwhile, theresults of the extra experiments in section 4.2 show that the parameterization of tidal bottom friction
could improve the water export rate of the entire shelf sea for the models without tides. However,
due to the difference in the spatial distribution of WRTs between the models with the parameterizedtides and the explicitly described tides, the test and comparison of different parameterizations of thetidal effect on the bottom friction should be pursued in the following studies. Moreover, the effect of
the oscillating tidal currents on the water export rate still needs to be quantiﬁed for understanding
the potential of the improvement on the model by tidal parameterization.
Besides the tides, other high‐frequency phenomena, for example, diurnal forcing, or small‐scale processes
could inﬂuence the hydrodynamics in shelf seas (e.g., Graham et al., 2018; Yu et al., 2017) and thus on
the water export from shelf seas to deep oceans. In this study, monthly mean forcings were used in thehydrodynamic model to characterize the shelf circulation in the ESSC and drive the WRT model. An extra
experiment with six hourly forcings (winds and heat ﬂuxes) shows that the average change in the WRT was~17% compared to the monthly mean forcings (the results of this numerical experiment were not presented
in order to focus on the tidal effect), which suggest that the forcing frequency could also have some inﬂuences on the water export rate in ESSC, although much weaker than that of the tides. Therefore, more attention should be paid to the effect of high‐frequency processes and forcings in climate models, in spite of theirsmall‐time and small‐space scales.
Shallow shelves are especially important for the global carbon cycle. For instance, Dunne et al. (2007)
estimated that depths shallower than 50 m could account for 48% of the global ﬂux of organic carbon to
the seaﬂoor. The signiﬁcant tidal effect on the water export rate from shelf seas implies that tides
could play an important role in shelf carbon export and climate models that do not consider the tidal
effect could overestimate the carbon export rate from shallow shelves to the deep oceans.
Nevertheless, in the future, it will be necessary to couple the hydrodynamic model with a biogeochemical model so as to enable a more thorough analysis of the impacts of tides on shelf carbon export to thedeep oceans.

5. Conclusions
Using the WRT as an indicator and a regional hydrodynamic model, we quantitively evaluated the tidal
effect on the water export rate in the ESSC. The model results show that the average WRT in the ESSC
was 2.12 years, which decreased to 0.63 year when tides were removed from the hydrodynamic model.
This suggests a signiﬁcant effect of tides on the modeled water export rate from the shelf. The tidal effecton the WRTs in the inner and middle shelves (roughly water depth <80 m) was >70%, which was muchstronger than that in the outer shelf (~10%), thereby indicating a high spatial variability of the tidal effecton the water export rate across the shelf. Compared to the case without tides, it is the signiﬁcantly weakened shelf circulation in the inner and middle shelves in the case with tides that slows the water export
rate in the shelf, while the change in the water transport across the shelf boundary in the cases with andwithout tides is very limited. This can explain the stronger effect of tides on the inner and middle shelves
than the outer shelf. The effect of tidal mixing on the WRT in ESSC was very small, while the effect oftides on the bottom friction was a dominant factor for the tidal effect on the WRT. When tides areincluded in the model, they intensiﬁed bottom resistance and thus decreased coastal currents. The
reduced coastal currents induce a smaller gradient of the water level across the shelf and thus a weaker
YSWC in winter in the control case than in the case without tides. The reduced coastal currents andYSWC in the YS and BS therefore induced a much slower water exchange and water export rate forthe inner and middle shelves compared to the case without tides. The results of this study imply that
there could be a considerable simulation error for the water exchange between shelf seas and deep oceansin the climate and Earth system models that do not consider the tidal effect, which could introduce biases
in the projections of the global carbon cycle.
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Appendix A: List of Abbreviations

Acknowledgments
This study was supported by the China
Postdoctoral Science Foundation(Project 2017M621409), the National
Natural Science Foundation of China(Grants 41706011 and 41876127), andthe Ministry of Science andTechnology, China (2016YFE0133700
and 2016YFA0600904). The authors
would like to thank the two anonymous
reviewers for their very constructive
comments that helped us improve themanuscript. Original data used for theﬁgures are available at https://doi.org/
10.6084/m9.ﬁgshare.11788917.

LIN ET AL.

WRT

Water residence time

WET
ESSC
BS
YS
ECS
TS
SH
CE
YSWC
TVDal
CART

Water exposure time
The eastern shelf seas of China
The Bohai Sea
The Yellow Sea
The East China Sea
The Taiwan Strait
Shelf break
The east of Cheju Island
Yellow Sea Warm Current
Total variation diminishing scheme with an alternating ﬂux limiter
Constituent‐oriented Age and Residence time Theory

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