Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022
https://doi.org/10.5194/hess-26-5207-2022© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Effect of tides on river water behavior over the eastern
shelf seas of China
Lei Lin1,2 , Hao Liu1 , Xiaomeng Huang2 , Qingjun Fu1 , and Xinyu Guo3
1 College of Ocean Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China
2 Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science,

Tsinghua University, Beijing 100084, China
3 Center for Marine Environmental Study, Ehime University, Matsuyama 790-8577, Japan
Correspondence: Lei Lin (llin@sdust.edu.cn, linlei24@126.com)
Received: 29 June 2022 – Discussion started: 25 July 2022
Revised: 29 September 2022 – Accepted: 30 September 2022 – Published: 18 October 2022

Abstract. Rivers carry large amounts of freshwater and terrestrial material into shelf seas, which is an important part of
the global water and biogeochemical cycles. The earth system model or climate model is an important instrument for
simulating and projecting the global water cycle and climatechange, in which tides however are commonly removed. Fora better understanding of the potential effect of the absenceof tides in the simulation of the water cycle, this study compared the results of a regional model with and without considering tides, and evaluated the effect of tides on the behavior of three major rivers (i.e., the Yellow, Yalujiang, andChangjiang rivers) water in the eastern shelf seas of China
from the perspectives of transport pathways, timescales, andwater concentration. The results showed that the tides induced more dispersed transport for the water of the Yellow
and Yalujiang rivers, but more concentrated transport for the
Changjiang River water. The effect of tides on the transit
areas of the Yellow, Yalujiang, and Changjiang rivers was
13 %, 40 %, and 21 %, respectively. The annual mean water
age and transit time of the three rivers in the model with tides
were several (∼ 2–10) times higher than those in the no-tidemodel, suggesting that tides dramatically slow the river water transport and export rate over the shelf. By slowing theriver water export, tides induced a three-fold increase in riverwater concentration and a decrease in shelf seawater salinity
by > 1. Moreover, the effect of tides on river behavior wasstronger in relatively enclosed seas (i.e., the Bohai and Yellow seas) than in relatively open seas (i.e., the East China
Sea). The change in the shelf currents induced by tides is themain cause of the difference in the river water behavior be-

tween the two model runs. Tides can increase bottom stressand thus weaken shelf currents and decrease the water transport timescales. The improvement in tidal parameterizationin the no-tide model in the simulation of river water behavior was very limited. Given the important role of river runoff
on the global water cycle and the effect of changes in riverwater behavior on ocean carbon cycling, it is important to include the tidal effect in earth system models to improve theirprojection accuracy.

1

Introduction

Rivers carry large amounts of freshwater and terrestrial material into shelf seas, which plays a crucial role in the global
water cycle and the global biogeochemical cycle. For instance, on a global scale, river runoff contributes to about
10 % of the global meridional water fluxes, modulating theocean circulation by affecting the water balance and salinity of the oceans (Oki et al., 1995, 2004). Approximately
400 Mt of organic carbon, 54 Mt of terrestrial nitrogen, and
8.5 Mt of phosphorus are annually discharged into the shelfseas by rivers (Mackenzie et al., 2002; Schlünz and Schneider, 2000; Hopkinson and Vallino, 2005), which have an important impact on marine primary productivity and carbon
cycling (Dittmar and Kattner, 2003; Gong et al., 2011). The
continental shelf sea is the first stop for the river water toenter the ocean. As the shelf seas connect the rivers anddeep oceans, and are the most productive part of the world’s
oceans, the river water behavior over the shelf seas is criti-

Published by Copernicus Publications on behalf of the European Geosciences Union.

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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

cal for the processes of the global water and biogeochemical
cycle.
Earth system models or climate models are important tools
to represent and project the global water and biogeochemical
cycles and climate change (e.g., Winkelbauer et al., 2022;
Brady et al., 2019; Dufresne et al., 2013; Clark et al., 2015).
An accurate simulation of the river water behavior over the
shelf seas is one of key steps for accurate simulation in thesemodels, but is usually hard to be achieved in earth systemmodels or climate models (Feng et al., 2021). On one hand,climate models used relatively large grid cells which are toocoarse for shelf seas with relatively small spatial scales (Graham et al., 2018; Feng et al., 2021; Holt et al., 2017). Thisissue would be addressed in the future as the computation
power increases. On the other hand, climate models usually
do not explicitly consider the tidal process since the tides
have much shorter timescales than the ocean circulation andwater cycle, and could induce numerical instability of models(Lee et al., 2006; Luneva et al., 2015; Voldoire et al., 2013;
Müller et al., 2010). However, tides are the major motions ofshelf seawater and play a crucial role in hydrodynamic processes in shelf seas. A model without considering tides may
induce a large bias in the simulation of the river water behavior. Thus, to better understand the potential consequences of
the absence of tides in climate models, it is necessary to firstquantitatively evaluate the impact of tides on the behavior ofriver water on the shelf.
Previous studies have suggested that tides can significantly
influence shelf hydrodynamics, and thus river water behavior. For instance, Guo and Valle-Levinson (2007) found thattidal mixing intensifies the salinity gradient and restricts the
upstream extension of the river plume off the Chesapeake
Bay. Wu et al. (2011, 2014) pointed out that tidal forcing
increases vertical mixing and results in a strong horizontal
salinity gradient at the northern edge of the Changjiang River
plume and restricts its northward extension, while the tideinduced Stokes drift along the coast facilitates the northwardtransport of the Changjiang River water to the Jiangsu coast.
A numerical study by Liu et al. (2012) suggested that tidal
forcing plays the most dominant role in controlling the ageof the Yellow River water in the Bohai Sea. Further, Yu etal. (2021) found that upstream tide-induced residual currents
induced the upstream transport of freshwater around the Yellow River mouth. All these studies demonstrate that tides caninfluence the current or mixing processes, and thus modulate river water behavior over the shelf. However, most ofthese studies have focused on the effect of tides on river water transport in estuaries and their adjacent seas, while few
studies have evaluated the effect of tides on river water behavior at the spatial scale of the entire shelf sea.
The eastern shelf seas of China (ESSC) with energetic
tides have wide continental shelves (Fig. 1). The ESSC includes the Bohai, Yellow, and the East China seas. It connects
the rivers of China and the Korean Peninsula to the western
Pacific Ocean. Among these rivers, the Yellow, Yalujiang,
Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022

and Changjiang rivers are the three with the largest discharge.
The Changjiang River, located on the west coast of the East
China Sea, has an annual mean runoff of ∼ 30 000 m3 s−1 ,accounting for more than three-quarters of the total amountof river runoff discharged to the ESSC (Liu et al., 2010).
The Yalujiang and Yellow rivers are located on the northern coast of the Yellow Sea and the southern coast of theBohai Sea, with annual runoffs of ∼ 1000 and ∼ 650 m3 s−1 ,respectively. Terrigenous materials from the three rivers aredischarged into the ESSC, playing an important role in its
ecosystem and biogeochemical cycling (Liu et al., 2010;
Yang et al., 2018; Ding et al., 2020). As mentioned previously, several studies have investigated the characteristics ofwater transport in the three rivers and highlighted the roleof tides in river water behavior (Wu et al., 2011, 2014; Liuet al., 2012; Yu et al., 2021). However, they commonly focused on only one aspect of the river water behavior (i.e.,either the transport direction, the pattern of the river plume,or transport timescale) at the spatial scale of the estuary or
its adjacent area. The present study aimed at a comprehensive
understanding of the effects of tides on the river water behavior over the entire shelf and selected the Yellow, Yalujiang,
and Changjiang rivers located in the Bohai, Yellow, and East
China seas, respectively, as the study objects. Using numerical modeling and sensitivity experiments, this study assessed
the effect of tides on river water behavior in the ESSC fromthe perspectives of transport pathways, transport timescales,
and water concentration distribution.
The remainder of this study is organized as follows: Sect. 2
introduces the models and diagnostic methods for river watertransport pathways, timescales, and concentration. Section 3
presents the results of the impact of tides on the water behavior of the three rivers over the shelf. By analyzing thechange in the shelf circulation and the results of sensitivity
experiments, Sect. 4 discusses the dynamic mechanism on
the tidal effect on the river water behavior. The potential effect of the absence of tides on climate modeling is also discussed in Sect. 4. Finally, Sect. 5 provides a brief conclusionof the study.

2
2.1

Models and methods
Hydrodynamic model

The hydrodynamic model used in this study was the Princeton Ocean Model (Blumberg and Mellor, 1987). The model
for ESSC was initially set up by Guo et al. (2003) and
Wang et al. (2008). The model included four major tidal
constituents (M2 , S2 , K1 , and O1 ) and covered the entire
ESSC (Fig. 1). Its horizontal grid resolution was ∼ 5–6 km.
The model had 21 non-uniform sigma layers in the vertical direction with finer resolution in the upper layer. This
study focused on the climatological state results, and thus themodel was driven by climatological mean forcings, includhttps://doi.org/10.5194/hess-26-5207-2022

L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

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efficients with a time interval of 0.5 h, were used to drive
the particle-tracking and passive tracer models as both theparticle-tracking and tracer models were decoupled from thehydrodynamic model. It should be noted that though surface
evaporation was considered in the hydrodynamics model
which could be the surface sink for the river water, that was
not considered in the particle-tracking and tracer models.
2.2

Figure 1. Model domain, locations of the Yellow, Yalujiang, andChangjiang rivers, and the primary shelf circulation in the eastern
shelf seas of China. The red and blue arrows denote the primarywarm currents (TWC: Taiwan Warm Current; YSWC: Yellow Sea
Warm Current) and coastal currents (KWCC: Korea west coastal
current; JSCC: Jiangsu coastal current; ZMCC: Zhe–Min coastal
current), respectively. The blue dashed arrow denotes the JSCC insummer. The red dashed lines are the open boundary for the calculation of the transit time (see Sect. 2.4).

ing winds, heat fluxes, precipitation, and evaporation (Wanget al., 2008). The monthly mean river runoff values of the
Changjiang, Yellow, and Yalujiang rivers (Table 1) were derived from measurements of river hydrological stations andthe marine atlas, and were linearly interpolated to each time
step during the model run. This model has been successfully
applied to simulation studies of riverine nutrient transportand cycling in the ESSC (Zhao and Guo, 2011; Zhang etal., 2019; Wang et al., 2019; Zhang et al., 2021), the Yellow River age and plume in the Bohai Sea (Liu et al., 2012;
Yu et al., 2020), the Yellow Sea cold water mass (Zhu et al.,2018), and the water residence time of the shelf sea (Linet al., 2020). These studies have well validated the modeland demonstrated the model reliability and applicability inthe ESSC. The readers are referred to Wang et al. (2008)
and Guo et al. (2003) for more detailed descriptions. The
hydrodynamic fields from the hydrodynamic model, including the sea level, water depth, velocity, and diffusivity cohttps://doi.org/10.5194/hess-26-5207-2022

Particle-tracking and passive tracer models fordiagnosing river water behavior

In this study, the particle-tracking method used to obtainthe trajectory of river water over the shelf is from the estuarine and coastal ocean model coupled with a sedimenttransport module (ECOMSED) (Blumberg, 2002), which has
been used in the study of the Yellow River water transport in
the Bohai Sea (Liu et al., 2012; Wang et al., 2013). In the
numerical experiments, we released 1000 particles at each of
the three river boundaries at 00:00 GMT+8 every day andran the particle-tracking model for 30 years. The location ofeach particle and its time after release were recorded for the
analysis of the particle trajectory and calculation of the riverwater age.
To quantify the concentration of river water in the shelfseas, three passive tracers were released at the three riverboundaries with a dimensionless concentration of 1. Thus,
the passive tracers of each river were equivalent to the freshwater concentration, that is the tracer concentration was 1
for freshwater and 0 for pure seawater. Tracer concentrations
were calculated using an offline advection–diffusion module from the Marine Environment Research and Forecastingmodel (MERF) (Liu et al., 2016; Lin and Liu, 2019a; Tanget al., 2021), in which the TVDal (Total variation diminishing scheme with alternating limiters) and central-difference
algorithms were used in the discretization of the advection
and diffusion terms, respectively (Lin and Liu, 2019b). The
tracer model ran for 30 years and the results of the last year
were outputted and analyzed.
2.3

Characterizing the pathway and transit area ofriver water

Based on the results of the particle-tracking model, the emergence probability of the particles at each grid over the shelf
was used to characterize the river water pathways and was
calculated at 0.5◦ × 0.5◦ grid cells by dividing the verticallyintegrated number of particles emerging in the grid cell by
the total number of particles released per day (i.e., 1000). A
particle can re-enter a grid more than once, in which case thesame particle is counted only once for a given grid. In thisway, we obtained the results of the emergence probability
for particles released on each day of 1 year. The annual mean
emergence probability was used in the analysis of the riverwater transport pathway, which was calculated by averaging
the emergence probability on all days of the year. The main
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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

Table 1. The monthly mean river runoff (m3 s−1 ) of the Changjiang, Yellow, and Yalujiang rivers in the hydrodynamic model.
Rivers

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

10 834656
378

12 017657
296

17 171709
299

25 282693
209

33 188695
216

39 942828
271

52 8401353
907

44 9522117
1481

40 3231158
1345

32 117699
1084

22 136678
619

13 776685
440

water transport pathway is indicated by locations with highparticle emergence probabilities.
Then, the transit area of the river water was calculated as
the particles’ emergence probability in each grid multipliedby the area of the corresponding grid and summed over the
shelf to quantify the magnitude of the influence range of theriver on shelf seas. A larger (smaller) transit area indicatesmore dispersed (concentrated) transport of the river water.

2.5

Changjiang
Yalujiang
Yellow

2.4

Transport timescales of river water

Water age and transit time were used to quantify the transport
timescales of river water over the shelf.
2.4.1

Water age

Water age is defined as the time elapsed since a river waterparticle enters the domain of interest (Deleersnijder, 2001),
and can quantify the transport rate of the river water overthe shelf. For a particle released at time t0 , it moves to someposition at time t, and the water age at this position is t–t0 .
Then, the mean water age for each grid cell was calculatedusing a weighted average of all the particle ages at a gridcell at time t. Once one particle had left the ESSC, it would
no longer participate in the calculation of the mean waterage. Because the same number of particles was released every day, particles released on different days denoted different
water masses due to variation of the river discharge. Thus,
the weighted average of the mean water age was calculatedusing the river discharge on the particle release day as theweight coefficient. The mean water age used in the analysis
was calculated by averaging the particle age at 0.5◦ × 0.5◦
grid cells. Due to space limitations, this study only shows theannual mean of the vertical average results for the water ageof the three rivers.
2.4.2

Transit time

The transit time of the river water over the shelf is defined as
the time the river water particle spends from the river boundary to the shelf boundary (red dashed lines in Fig. 1), which
can quantify the total retention time of the river water in the
shelf seas. A river particle released at time t0 leaves for the
first time the shelf at time t1 , and its transit time according to
the definition is t1 –t0 . The re-entry process was not considered in the calculation of the transit time and water age.
Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022

Physical meanings of the indicators

Overall, five indicators (i.e., the emerging probability, transit area, water age, transit time, and tracer concentration)
were used to characterize the behavior of the river waters.
The emerging probability of the particles reflects the proportion of river water that passes through the region, which ismainly related to the shelf currents. The regions with higher
emerging probability indicate a greater amount of river water
passing through them, and thus are the main pathway of riverwater transport. The transit area can be an approximate representation of the area through which the river flows. Water
age reflects how long the river water has been on the shelfafter leaving the estuary, while the transit time reflects thetotal time the river water takes from entering to leaving theshelf. The tracer concentration reflects the stock of the riverwater over the shelf, which can influence the salinity field. It
should be noted that the magnitudes of the emerging probability, water age, and tracer concentration may not be directly
related. For instance, a small proportion of one river water
may stay in region A for a long time while the most proportion of the river water may quickly leave the shelf throughregion B. Then, region A would obtain a relatively large water age but a relatively small emerging probability comparedwith region B. However, the tracer concentration in region
A could be either high or low which is determined by theaccumulated amount of river water in this region.
2.6

Sensitivity experiments

Numerical experiments were designed to explore the effectof tides on the river water fate in the ESSC, which were conducted by using the model run with tides (hereafter termed“control run”) and the model run without tides (hereaftertermed “no-tide case”), respectively. In both experiments,
the hydrodynamic model was run for 3 years which waslong enough for the model to get steady seasonal cycles (seeFig. S1 in the Supplement), and the model data output of thelast year were used for analyzing and driving the particletracking and passive tracer models. Then, the water transport
pathways and timescales and the water concentrations of therivers in the ESSC were determined using the same procedures described in Sect. 2.3 and 2.4.

https://doi.org/10.5194/hess-26-5207-2022

L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China
3

Results

By comparing the model’s control run and no-tide case results, the effect of tides on the behavior of the three rivers’
waters in the ESSC was analyzed for three aspects: the effecton river water transport pathways, transport timescales, andconcentrations.
3.1

Effect on transport pathways

Significant differences in the water transport pathways of thethree rivers between the control run and no-tide case wereobserved (Fig. 2). As shown in the results of the control run,most of the Yellow River water passes through the Bohai
Strait, enters the Yellow Sea, and finally leaves through the
Cheju Strait (Fig. 2a). This emergence probability suggeststhat the Yellow River water passes through most of the Yellow Sea. The Yalujiang River water passes mainly throughthe eastern Yellow Sea and leaves it through the Cheju Strait(Fig. 2b). The Changjiang River water flows northeastward
after leaving the Changjiang estuary and leaves China’s eastern shelf through the Korea–Tsushima strait, with a probability of ∼ 10 %–20 % of it passing through the Yellow Sea(Fig. 2c). The Changjiang River water is concentrated in theSouth Yellow Sea and north of the East China Sea. In addition, the emerging probability for the Changjiang River
showed spatial discontinuity (Fig. 2c), which could be dueto the northward transport of the river water by the Yellow
Sea Warm Current. The northward transport brought part of
the Changjiang River into the Yellow Sea, and thus rapidly
reduced the emerging probability of the river water in the
middle of the Yellow Sea.
In comparison to the control run, the water transport pathways of the Yellow River and Yalujiang River for the no-tidecase were more concentrated in the western coastal region of
the Yellow Sea, as shown in the map of their emergence probability (Fig. 2d and e). However, the emergence probabilityof the Changjiang River water for the no-tide case increasedin the Yellow Sea and East China Sea, particularly at the
Jiangsu and Zhemin coasts (Fig. 2f). In comparison, the transit areas of the Yellow, Yalujiang, and Changjiang rivers forthe control run are 2556, 2027, and 1537 km2 , respectively,
while they are 2224, 1214, and 1851 km2 , respectively, forthe no-tide case. As compared with the control run, the transit areas of the Yellow and Yalujiang rivers for the no-tidecase decreased by 13 % and 40 %, respectively, while that of
the Changjiang River increased by 21 %. The above results
suggest that the tidal effect induced more dispersed transport
for the Yellow and Yalujiang rivers’ waters but more concentrated transport for the Changjiang River water.
3.2

Effect on transport timescales

The transport timescales of the river water for the no-tidecase were significantly decreased as against the control run.
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The water age for the three rivers showed high values (4–10 years) in the Bohai Sea and the Yellow Sea, and much
lower values (less than 1 year) in the East China Sea (Fig. 3a–c). The mean age of the Yellow and Yalujiang rivers water was 4.7 and 4.5 years in the Bohai Sea and 5.5 and3.1 years in the Yellow Sea, respectively. The water age of
the Changjiang River in the Yellow and East China seas was
1.3 and 0.3 years, respectively. Moreover, the relatively highwater age of the three rivers is concentrated in the central
Yellow Sea (123–126◦ E, 34–39◦ N), where the Yellow Sea
Cold Water Mass (YSCWM) occurs every summer, suggesting that the YSCWM region could trap river water and terrigenous materials for several years. However, the emergencepossibility in the YSCWM region was relatively low (Fig. 2),
as only a small proportion of the river water was trapped in
the region of the YSCWM and most of the river waters weretransported along the west coast of the Korean Peninsula.
The YSCWM occurred at the bottom of the central Yellow
Sea during the stratified season. It formed mainly due to theretention of the winter cold water (Zhang et al., 2008), while
the water in winter is well mixed in the Yellow Sea (e.g., Zhu
et al., 2018; Lin et al., 2019). Thus, the river water trappedby the YSCWM during the stratified season should be mainly
from the river water in the Yellow Sea in winter.
In comparison, when the tides were removed, the rivers’
water age decreased significantly (Fig. 3e–f). For the notide case, the average age of the Yellow and Yalujiang rivers
water was 1.6 and 0.5 years in the Bohai Sea and 1.0 and
0.3 years in the Yellow Sea, respectively, and decreased byaveragely more than 80 % as compared with the control run.
The mean water age of the Changjiang River in the Yellow
Sea decreased to 0.5 years (by ∼ 60 %) in the no-tide case,while in the East China Sea it remained basically unchanged.
The dramatic decrease in the river water age for the no-tidecase suggests that the tides could significantly slow down thetransport of river water over the shelf, especially in the relatively enclosed Yellow and Bohai seas.
The shorter transport timescales of the rivers’ waters forthe no-tide case are also shown in the transit time results(Fig. 4). The annual mean transit time of the Yellow, Yalujiang, and Changjiang rivers are 9.4, 5.6, and 2.2 years, respectively, while they decreased to 2.4, 0.4, and 1.2 years,
respectively, in the no-tide case. The apparent decrease intransit time indicated a much shorter retention in the shelfseas and a faster export rate of river water from the shelfseas for the no-tide model than for the control model considering tides. The mean transit time of the waters of the Yellow and Yalujiang rivers for the no-tide case decreased by
75 % and 93 %, respectively, which is larger than that of the
Changjiang River (45 %), suggesting that the effects of tides
on the river water export rate could be more strong for rivers
in relatively enclosed seas than those in relatively open seas.
Moreover, as against the control run, the river water transit
time for the no-tide case showed a different seasonal variation pattern and a decreased variance.
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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

Figure 2. The annually averaged emergence probability of the particles released at the three rivers’ boundaries for the control run (a–c) andno-tide case (d–f), which are indicated by the emergence probability of the particles in the grids (in percent).

3.3

Effect on river water concentrations

Given their effect on river water pathways and timescales, it
is expected that tides would influence the river water concentrations over the shelf. As indicated in Fig. 5, the water
concentrations of the three rivers in the no-tide case wereapproximately one order lower in magnitude than those in
the control run, especially in the Yellow and Bohai seas. As
against the control run, when the tides were excluded, theannual mean river water concentrations of the Yellow, Yalujiang, and Changjiang rivers over the entire shelf were reduced by 73 %, 84 %, and 76 %, respectively. The mean reduction in the water concentration of the three rivers in the
Bohai and Yellow seas is over 75 %, which is several times
more than that in the East China Sea, suggesting that the tidal
effect on river water concentrations is more significant in relatively enclosed seas than in relatively open seas. In addition, relatively low tracer concentrations but relatively highemerging probabilities occurred in Cheju Strait (Figs. 5 and2). This is because when the river water was transported to
Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022

the Cheju Strait, it had been mixed with shelf seawater which
decreased the river water concentration. However, since the
Cheju Strait is an important outlet for river water, most of
the river particles would pass through the strait which induced the high emerging probabilities of the river water at
the Cheju Strait.
A change in river water concentration can directly induce achange in seawater salinity over the shelf. As shown in Fig. 6,
the salinity in the estuaries and coastal waters is lower than
30 because of the input of freshwater from the rivers, while
the salinity in the East China Sea is relatively high (> 33)
because of the salty water input from the Kuroshio Current(Fig. 6a). The seawater salinity in the no-tide case increased
significantly as against the control run, particularly in the areas adjacent to the estuaries and in the Bohai and Yellow seas
(Fig. 6b and c). This can be understood as the faster exportof the river water in the no-tide case (Figs. 3 and 4) leaving asmaller proportion of river freshwater in the shelf sea (Fig. 5)
and resulting in higher salinity over the shelf. The increase insalinity was more than 3 in the estuaries of the Yellow, Yaluhttps://doi.org/10.5194/hess-26-5207-2022

L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

5213

Figure 3. The annually and vertically averaged water age of the three rivers for the control run (a–c) and no-tide case (d–f). Only results at
locations with particle emergence probability of > 1 % have been presented.

jiang, and Changjiang rivers and more than 1 (on average) in
the Yellow and Bohai seas (Fig. 6c), while in the East China
Sea, the magnitude of salinity change was smaller than 0.5,
suggesting that the tidal effect on seawater salinity is moresignificant in relatively enclosed seas than in relatively open
seas.
4
4.1

Discussion
Role of tidally induced change in the mixing andadvection on the river water behavior

Changes in the river water transport pathways andtimescales, and thus the river water concentrations and seawater salinity in the shelf seas, indicate a significant effectof tides on the behavior of the river water over the shelf.
The river water behavior over the shelf is determined by two
processes, namely advection and mixing. Tides can affectshelf current and water mixing, and thus influence river water transport over the shelf (Moon et al., 2009; Palma et al.,https://doi.org/10.5194/hess-26-5207-2022

2004; Lin et al., 2020; Wang et al., 2013; Wu et al., 2018).
To assess the respective effects of the changes in mixing andcurrents (changes in shelf currents and mixing are shown in
Sect. 4.2 and in Fig. S2, respectively), induced by tides onriver water transport, we designed two additional numericalexperiments similar to the no-tide case, except that in one,the diffusivity coefficients driving the particle-tracking andpassive tracer models were replaced by those in the control
run (hereafter termed “tidal–mixing case”), and in the other,
the velocity and sea level driving the particle-tracking andtracer transport models were replaced by those in the control
run (hereafter termed “tidal–advection case”). The effect of
the tidally induced change in the mixing and current on riverwater transport could be identified by comparing the resultsof the tidal–advection and tidal–mixing cases with those of
the no-tide case and control run.
The river water transport pathways in the tidal–advection
and tidal–mixing cases show a similar result to that in thecontrol run and no-tide case, respectively (Fig. 7), suggestingthat tidally induced changes in the shelf currents are more

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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China
4.2

Figure 4. The daily mean water transit time over the shelf of thethree rivers for the control run (blue) and no-tide case (red). SD in
the figure label denotes the standard deviation of the transit time forparticles released on the same day.

important than those induced by water mixing for the riverwater pathways in the shelf sea. This is reasonable because
the currents usually dominate horizontal transport, whereas
mixing influences vertical transport.
For the transport timescales, the water age of the tidal–
advection case was much higher than that of the no-tide caseand even higher than that of the control run, whereas the water age of the tidal–mixing case was slightly lower than thatof the no-tide case (Fig. 8). Similar to the results of the waterage, the annual mean transit times of the tidal–mixing casewere 2.4, 0.65, and 1.0 years for the Yellow, Yalujiang, andChangjiang rivers, respectively, which are very close to theresults of the no-tide case (Fig. 9); however, the transit timeof the tidal–advection case was much higher than that of theno-tide case. The water age and transit time results suggestthat the tidally induced changes in currents and mixing had
opposite effects on the river water transport timescale, which
decreased and increased the river water transport rate, respectively. As the transport timescales of the control run (withtides) were much higher than those of the no-tide case, we
can infer that the change in shelf currents induced by tides
plays a dominant role in the transport rate of river water overthe shelf.

Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022

Tidally induced changes in the shelf current and its
effect on river water transport

To further understand the effect of tidally induced changes
in currents on river water transport, we compared and analyzed the shelf currents of the control run and the no-tidecase (Fig. 10). When the tides were removed, the change inthe shelf currents mainly occurred in the coastal region andthe central Yellow Sea (Fig. 10a–d), and the change in winterwas more significant than that in summer (Figs. 10e–f and
S3 in the supplementary material). During winter, the coastal
currents along the Jiangsu and west Korea in the no-tide casewere several times stronger as against those in the control
run (see Fig. 10d). The Yellow Sea Warm Current (YSWC)
was also significantly strengthened in the model without tides(Fig. 10b). The analysis of water transport fluxes by Lin etal. (2020) showed the winter season accounted for ∼ 73 %of the volume transport for the entire year and suggested thatthe winter processes dominate the water exchange of the Yellow Sea. Due to the strong surface cooling, the coastal water(even in the central Yellow Sea) in winter was well mixed.
Thus, the change in the barotropic process could dominate
the change of the shelf currents. In addition, the change in the
coastal current along the Jiangsu and Zhejiang coasts showedsouthward in winter and northward in summer (Fig. 10e andf), which are consistent with the directions of the seasonal
wind-driven currents (northerly wind in winter and southerly
wind in summer). This consistency indicates that the winddriven coastal current was significantly weakened by tides,
which can be explained by the nonlinear interaction betweentides and wind-driven current in a quadratic bottom friction
term (e.g., Moon, 2005; Wu et al., 2018). When consideringtides, the period–mean bottom resistance becomes about oneorder larger due to the quadratic nature of the bottom friction, and thus greatly reduces the wind-driven coastal currents (Wu et al., 2018).
The relatively weak YSWC in the control run is mainly
related to the weakened coastal current and enhanced bottom
friction. Several studies have interpreted the formation of theYSWC using the upwind theory (e.g., Hsueh and Yuan, 1997;
Isobe, 2008; Lin and Yang, 2011). In the semi-enclosed Yellow Sea, the wind stress is the dominant forcing in winterand thus the currents along the eastern and western coasts arein the same direction as the northerly wind. The southward
coastal currents on both sides can reduce the water elevation
inside, pile up water mass at the downwind end, and form
the negative pressure gradient (decrease to the north). Alongthe deep trough of the central Yellow Sea, the depth-averaged
wind stress is small and too weak to counter the northward
pressure gradient force. This imbalance results in a pressuredriven flow that is opposite to the direction of the surface
wind along the trough of the Yellow Sea. Under the effect of
the Coriolis force, the upwind current is further geostrophically adjusted and slightly shifted to the western side of thetrough to satisfy the balance of the potential vorticity (Lin
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Figure 5. The annually and vertically averaged river water concentrations of the three rivers for the control run (a–c) and no-tide case (d–f)(the maps show the logarithmic distribution of the obtained river water concentrations).

Figure 6. The annually and vertically averaged salinity of the shelf water for the control run (a), no-tide case (b), and their difference (c).
Positive (negative) values denote the salinity of the no-tide case as being higher (lower) than that of the control run.

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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

Figure 7. The annually averaged water transport pathways of the three rivers over the shelf for the tidal–advection case (a–c) and tidal–mixing
case (d–f), indicated by the emergence probability of the particles in the grids (in percent).

and Yang, 2011). When considering tides, enhanced bottom
friction weakened the coastal currents, and thus decreased
the water elevation difference and thus the pressure gradient (Moon, 2005; Lin et al., 2020). Meanwhile, the enhanced
bottom friction below the YSWC further countered a part of
the northward momentum (Moon, 2005). Thus, the weaker
YSWC was presented in the model with tides.
Besides the tidally enhanced bottom resistance, the tidally
enhanced mixing and induced residual current and residualtransport could also modulate the shelf currents, especiallyduring the stratified season (e.g., Moon, 2005; Lie and Cho,2016; Moon et al., 2009; Wu et al., 2011, 2014; Wu and Wu,
2018). Moon et al. (2009) suggested that the tidal forcing
induces a strong southward residual flow along the western
slope of the Yellow Sea in summer, which can explain thechange of northward current in the no-tide case in the middle of the Yellow Sea (Fig. 10f). Wu et al. (2011) suggested
that tidally enhanced mixing resulted in a strong horizontal
Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022

salinity gradient at the north of the Changjiang River mouth,
which acted as a dynamic barrier and restricts the northwardtransport of the Changjiang River water to the Jiangsu coastin summer. In addition, strong tidal mixing induced a mixing
front along the Zhe–Min coast and maintained a down-shelf
frontal current (Wu and Wu, 2018), which was important forthe southward transport of the Changjiang River water. Overall, the mechanism of the tidal effect on the shelf current iscomplicated and diverse. However, the tidally enhanced bottom friction should be the dominant mechanism due to theimportant role of winter currents in the water exchange andthe significant change in the winter coastal current in the control run and no-tide case.
In contrast to the Bohai and Yellow seas, there was a relatively small difference in the shelf currents in the central
East China Sea between the control run and no-tide case(Fig. 10d). The different effects of tides on the Bohai andYellow seas and the East China Sea could be related to both
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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

5217

Figure 8. The annually and vertically averaged water age of the three rivers for the tidal–advection case (a–c) and tidal–mixing case (d–f).

the geometry and the water depth, as both of them can influence the water exchange and the strength of the tidal current.
The semi-enclosed geometry in the Bohai and Yellow seas
induced relatively weak water exchange compared to the relatively open East China Sea. Thus, the coastal currents areimportant dynamics for the water exchange in the Bohai andYellow seas, and the tidal effect on the coastal currents significantly influenced the river water behavior in the Bohai
and Yellow seas. On the other hand, the change in the bottom
friction induced by the tides is an important mechanism forthe tidal effect on the shelf currents. Due to the larger inertia and stronger stratification, the shelf currents in relatively
deep water could be less influenced by changes in bottom
friction than that in relatively shallow water. Thus, the effectof tides on the shelf current and river water concentration in
the East China Sea was relatively smaller than those in the
Yellow and Bohai seas.
The changes in the shelf currents further changed the behavior of the river water over the shelf. For the Yellow andhttps://doi.org/10.5194/hess-26-5207-2022

Yalujiang rivers, the significantly intensified coastal currents
in the Yellow and Bohai seas in the no-tide case accelerated water transport along the coasts to the Cheju Strait
and induced much smaller transport timescales than thoseof the control run. Likewise, the enhanced coastal currents
and shelf circulations of the no-tide case can accelerate riverwater transport over the shelf, and thus induce much shorter
water transport timescales in the Changjiang River. However,
the tidal effects on the pathways of the Yellow and Yalujiang rivers and the Changjiang River were different. Tides
induced more dispersed transport for the water of the Yellow and Yalujiang rivers, but more concentrated transport for
the Changjiang River water (Fig. 2). The different tidal effects should be related to the different water transport patterns of the rivers (Fig. 11). For the Yellow and Yalujiang
rivers water, the west coast of the Korean Peninsula withstrong tides and cross-shelf tidal currents (see the tidal current ellipses and cotidal map in Fig. S4 in the Supplement)
was their main transport pathway. Without considering tides,
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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

Figure 9. The daily mean water transit time over the shelf of thethree rivers for the tidal–advection case (blue) and tidal–mixing case(red), along with the control run (black) and no-tide case (dottedblack).

the southward coastal current along the west coast of the Korean Peninsula was intensified, especially in winter, which
accelerated the river water export and reduced the transport
timescales of the Yellow and Yalujiang rivers’ waters. Whenconsidering the tides, on one hand the cross-shelf tidal currents along the coast could increase the cross-shelf water
dispersion as the magnitude of tidal dispersion is proportional to the tidal velocity (Geyer and Signell, 1992). On
the other hand, the weakened coast current slowed down
the along-shore transport of the river waters and further promoted cross-shelf water dispersion. Thus, compared to theno-tide case, the control run obtained a more dispersed transport for the Yellow and Yalujiang rivers’ waters. For the
Changjiang River, there are three major branches for the riverwater transport, i.e., the northeastward branch to Cheju Island, the northward branches to the Jiangsu coast, and thesouthward branch to the Zhejiang coast (Wu et al., 2014).
The northeastward branch to Cheju Island is the dominant
one for the Changjiang River water transport. In the no-tidecase, the intensified coastal currents could increase the riverwater transport to the Yellow Sea along the Jiangsu coast insummer and to the East China Sea along the Zhejiang coastin winter, which intensified the northward and southward
branches of the Changjiang River water transport. In addition, the flow field at the offshore water of the Changjiang estuary in the control run showed a pattern of a mesoscale eddy
which might trap some river water and reduce the disperHydrol. Earth Syst. Sci., 26, 5207–5225, 2022

Figure 10. Comparison of the shelf currents between the control run
and no-tide case. (a) and (b) are the annual mean and vertically averaged velocities for the control run and no-tide case, respectively.
The arrow and color in (a) and (b) denote the direction and magnitude of the velocity, respectively. (c) and (d) show the change andrelative change in the magnitude of the shelf currents after removing tides in the model. (e) and (f) show the changes in shelf currents
in February and August, respectively.

sion of the water. Thus, the water particles of the ChangjiangRiver in the no-tide case were more dispersed than those in
the control run.
The experiential results also suggested that, under the effect of tides, the transit time of the three rivers water in thehttps://doi.org/10.5194/hess-26-5207-2022

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Figure 11. Schematic map of the shelf currents and the major pattern of the river water transport for the control run (a) and no-tide case (b).
The blue and red arrows denote the coastal currents and warm currents, respectively. The blue dashed arrow at the Jiangsu coast denotes thecoastal current in summer. The thickness of the arrows denotes the intensity of the shelf currents. The black dashed wavy line in (a) denotes
the cross-shelf dispersion induced by tides. The black arrows denote the direction and the branches of the river water transport.

control run showed a high standard deviation (SD) (Fig. 4),
which could be related to the strong water dispersion andthe high spatial variation in the water residence time. As
shown in Lin et al. (2020), there is significant spatial variation in the water residence time (WRT) on the eastern shelfof China. The WRT can reach 15 years in the Bohai Sea, 4–
10 years in the Yellow Sea, and about 1 year in the East China
Sea. The particles released at the estuaries were continuously
dispersed as they move under the effect of tidal dispersion
and mixing. Dispersed particles can go into different seas
and get significantly different residence times over the shelf,
which can explain the high SD of the transit time. In addition,
the seasonal variability of the transit time of the ChangjiangRiver water could be related to the seasonal variation in the
shelf currents. In spring, part of the Changjiang River water is prone to be transported into the Yellow Sea under theeffect of the southerly wind and thus obtained a longer retention time over the shelf than in other seasons. Meanwhile, thelarge range of the residence time of the Yellow Sea induced
the large SD in spring.
4.3

Whether a tidal parameterization can improve thesimulation in a no-tide model?

The present study shows that tides could have a significant
effect on river water transport, concentration, and seawatersalinity in shelf seas by changing the bottom resistance andhttps://doi.org/10.5194/hess-26-5207-2022

reducing the shelf currents. Tidal parameterization can include the tidal effect on hydrodynamics in a no-tide model
to some extent. To examine the availability of tidal parameterization in no-tide models for the simulation of river watertransport on the shelf, we added a parameterized–tide experiment (PMT–tide case), wherein linear-type bottom friction
considering the tidal effect proposed by Lee et al. (2000) wasapplied to the hydrodynamic model. The method has beenused in studies on the shelf currents in the Yellow Sea and
ESSC (Moon et al., 2009; Lin et al., 2020). The details of theparameterization were presented by Moon et al. (2009) and
Lin et al. (2020). Then, using the hydrodynamic forcing of
the parameterized–tide model, the water transport pathways
and timescales, and the water concentrations of the rivers
in the ESSC were diagnosed using the same procedures described in Sect. 2.3 and 2.4.
The experimental results showed that the tidal parameterization could not significantly improve the simulation of theriver water transport pathways and the pattern of the river water age over the shelf. As compared with the control run, theriver water pathways of the Yellow and Yalujiang rivers in
the PMT–tide case were still very concentrated in the coastal
region, and that of the Changjiang River was more dispersedin the Yellow Sea (Fig. 12). The transit time of the Yellow
River for the PMT–tide case was close to the result of thecontrol run (∼ 0.2 years bias), while those of the Yalujiang
and Changjiang rivers still showed a large bias (more thanHydrol. Earth Syst. Sci., 26, 5207–5225, 2022

5220

L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

Figure 12. The three rivers’ waters transport pathways, age, and concentration for the PMT–tide case. The annually averaged emerging
probability of particles (a–c). The annually and vertically averaged water age (d–f). The annually and vertically averaged river water concentration (g–i).

Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022

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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

Figure 13. The daily mean water transit time over the shelf of thethree rivers for the control run (blue) and PMT–tide case (red). SD
in the figure label denotes the standard deviation of the transit time
for particles released on the same day.

3.4 years) as compared to the control run (Fig. 13). When
compared with the no-tide case, the PMT–tide case could increase the water concentration of the Yellow and Changjiang
rivers (Fig. 12) and thus improve the simulation of salinity
over the shelf to some extent; however, there was still a large
bias in the simulated salinity (> 3) in the estuarine zones(Fig. 14). Therefore, the tidal parameterization in a no-tidemodel could not adequately consider the effect of tides onriver water transport, implying that a better tidal parameterization for no-tide ocean models needs further development
and examination in future work, or explicitly considering thetides in ocean models is necessary.
4.4

Implications on climate modeling

The present study demonstrated that tides have a significant
effect on river water transport pathways, timescales, river water concentration, and shelf seawater salinity. Moreover, theimprovement of tidal parameterization in the simulation ofa no-tide model could be very limited. Therefore, if earthsystem models or climate models do not explicitly consider
tides, the model results will have a large bias in the river water transport process over shelf seas. Consequently, such biases may seriously affect the accuracy of global model predictions of global water and carbon cycles and even climatechange for the following reasons. First, river runoff which accounts for about 10 % of the global meridional water fluxes
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plays a significant role in the ocean circulation through affecting the water balance and salinity of the oceans (Okiet al., 1995, 2004). The absence of tides in global models
could accelerate the freshwater export from shelf seas to deep
oceans and influence the salinity balance and circulations inoceans. Second, river water is rich in terrigenous nutrients,
which are an important source of nutrients for phytoplankton in shelf seas. Shelf seas contribute to approximately 1/3of the marine primary productivity and 40 % of the ocean
carbon storage, and the carbon pumping of shelf seas is
an important way of global carbon sequestration, thus shelfseas play a critical role in the global carbon cycle (Thomas,
2004; Laruelle et al., 2018; Dunne et al., 2007). The absence of tides will change the nutrient transport pathways
and timescales and reduce the concentration of terrigenous
nutrients, which will directly change the primary productivity of shelf seas. Meanwhile, the absence of tides significantly increased the seawater salinity of the shelf seas. The
total alkalinity of seawater is controlled mainly by salinity(Millero et al., 1998), dominating the air–sea CO2 flux (Kantha, 2004). Thus, the change in primary productivity and thebias in seawater salinity could ultimately lead to errors in thesimulation of the CO2 flux and carbon cycle in shelf seas inclimate models. Third, the terrigenous organic and inorganiccarbon carried by rivers is over 0.8 PgC yr−1 (1 Pg = 1015 g)
and is input into shelf seas (Bauer et al., 2013). The simulation of the export rate of river water and terrigenous carbon
in shelf seas in a no-tide model would be falsely accelerated,which may reduce terrigenous carbon burial and emission in
the shelf sea and thus increase the amount of terrigenous carbon entering the open ocean (Schlünz and Schneider, 2000).
In these ways, the absence of tides in climate models could
induce a strong uncertainty in the simulation of the carbon
cycle and thus affect the accuracy of the climate projectionof the climate models and the earth system models. However,
the effect of the change of the river water behavior in no-tidemodels on the bias of the carbon cycle simulation and climate
projection still needs to be further quantitatively studied using a high-resolution earth system model.

5Conclusions

Using numerical modeling and sensitivity experiments, thisstudy assessed the effect of tides on river water transport
pathways and timescales and the water concentration of threemajor rivers (i.e., the Yellow, Yalujiang, and Changjiang
rivers) in the ESSC. The model results suggest that tides induced more dispersed transport pathways for the Yellow and
Yalujiang rivers, but more concentrated transport pathways
for the Changjiang River. By weakening the shelf currents,tides increased the water transport timescales of the threerivers by 2–10 times and thus significantly slowed the transport and export of the river water over the shelf. The slow
export of river water induced by tides increased the river waHydrol. Earth Syst. Sci., 26, 5207–5225, 2022

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L. Lin et al.: Effect of tides on river water behavior over the eastern shelf seas of China

Figure 14. The annually and vertically averaged salinity of the shelf water for the control run (a), the PMT–tide case (b), and their difference (c). Positive (negative) values denote the salinity of the no-tide case higher (lower) than that of the control run.

ter concentration by approximately one order in magnitude
and decreased seawater salinity in the ESSC. Moreover, theeffects of tides on river water behavior were stronger in relatively enclosed seas (i.e., the Bohai and Yellow seas) thanin relatively open seas (i.e., the East China Sea). Given theimportant role of river water in water and carbon cycling, climate and earth system models without tides may be biased insimulating and predicting the global water and carbon cycle.
Therefore, the effects of tides on river water behavior should
be carefully considered in climate and earth system modeling.

Code availability. The source code of numerical model usedin this study is available on request. Please contact Lei Lin(llin@sdust.edu.cn).

Data availability. The model data are shown in the figures in themain text which is available on request. Please contact Lei Lin(llin@sdust.edu.cn).

Disclaimer. Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims in published maps andinstitutional affiliations.

Acknowledgements. The authors thank Hui Wu and the two anonymous reviewers for their very constructive comments that helped us
improve the paper. This study was supported by the National Key
Research and Development Program of China(2020YFA0607900)
and the National Natural Science Foundation of China (grantnos. 42125503 and 41706011). Xinyu Guo was supported by
Grants-in-Aid for Scientific Research (MEXT KAKENHI grantno. 20H04319).

Financial support. This research has been supported by the National Key Research and Development Program of China (grantno. 2020YFA0607900), the National Natural Science Foundation ofChina (grant nos. 42125503 and 41706011), and the Grants-in-Aid
for Scientific Research (MEXT KAKENHI grant no. 20H04319).

Review statement. This paper was edited by Louise Slater and reviewed by Hui Wu and two anonymous referees.
Supplement. The supplement related to this article is available online at: https://doi.org/10.5194/hess-26-5207-2022-supplement.

Author contributions. LL, HL, and QF conducted the numerical experiments and analyzed the data. LL, HL, and XH wrote the initial draft, and all authors have contributed to editing the paper. XG
provided the hydrodynamic model. All authors contributed to discussing and interpreting the results.

Competing interests. The contact author has declared that none of
the authors has any competing interests.

Hydrol. Earth Syst. Sci., 26, 5207–5225, 2022

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