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Upstream Extension of a Bottom-Advected Plume and Its Mechanism: The Case of the
Yellow RiverXIAOJIE YU,a,b XINYU GUO,a,c HUIWANG GAO,a,b AND TAO ZOUda

Key Laboratory of Marine Environment and Ecology, Ministry of Education, Ocean University of China, Qingdao, Chinab
Laboratory for Marine Ecology and Environmental Sciences, Qingdao National Laboratory for Marine
Science and Technology, Qingdao, ChinacCenter for Marine Environmental Studies, Ehime University, Matsuyama, Japand
Key Laboratory of Coastal Zone Environmental Processes and Ecological Remediation, Yantai Institute of
Coastal Zone Research, Chinese Academy of Sciences, Yantai, China(Manuscript received 29 September 2020, in final form 14 April 2021)

ABSTRACT: Hydrographic surveys have revealed that the Yellow River plume propagates in the direction opposite tothat of a Kelvin wave (upstream) under a low river discharge condition, but turns downstream as the river discharge
increases. A numerical model reproduced the upstream extension of the plume under the low river discharge condition andthe transition to the downstream direction under the high river discharge condition, and confirmed that the summer wind is
not the necessary condition for upstream extension of the plume. With the condition of low river discharge, the model also
indicated the dependence of the upstream extension of the plume on the tidal range: extending upstream in spring tide but turning
downstream in neap tide. The upstream movement of the plume results from the upstream transport of freshwater that depends on
the upstream tide-induced residual current around the river mouth and the downstream density-driven current around the offshore plume front. With the condition of high river discharge, the upstream tide-induced residual current cannot compete with thedownstream density-driven current and the plume turns downstream. Momentum analysis confirms the important roles of advection term and viscosity term in the condition of low river discharge and the shift to a Coriolis force–dominated system underhigh river discharge condition. An idealized model study suggests a dimensionless number for the river discharge changing theriver plume extension from upstream to downstream under a specific upstream ambient current around the river mouth.
KEYWORDS: Estuaries; Baroclinic flows; Buoyancy; Freshwater; Tides; Numerical analysis/modeling

1. Introduction
River discharge is a major buoyancy source in coastal regions. As the lighter freshwater encounters the denser seawater, a river plume with a sharp density front between the two
types of water is formed. In terms of the structure of the density
front, the river plume can be categorized as bottom advectedor surface advected (Yankovsky and Chapman 1997). For thebottom-advected plume, the low-salinity water occupies the entire
water column and turns immediately downstream (in the form of
Kelvin wave) after it flows out of the estuary mouth. For thesurface-advected plume, the lighter water primarily remains in thesurface layer and detaches from the bottom. In this case, theplume has two distinct features: an anticyclonic bulge near theriver mouth and a downstream coastal current. A realistic river
plume should be somewhere between the two extreme types depending on a variety of factors such as river discharge, bathymetry, and vertical mixing induced by tides and winds.

Denotes content that is immediately available upon publication as open access.
Supplemental information related to this paper is available atthe Journals Online website: https://doi.org/10.1175/JPO-D-200235.s1.
Corresponding author: Xinyu Guo, guoxinyu@sci.ehime-u.ac.jp

Many numerical simulations produced the upstream extension of a plume, which spread in a direction opposite to thatof a Kelvin wave (e.g., Chao and Boicourt 1986; Chapman andLenz 1994; Garvine 2001; Matano and Palma 2010). Various
mechanisms have been proposed for the upstream extension,
including unrealistic model configurations of a simple inlet or adeep coastal wall (Garvine 2001), oversimplification of theboundary condition (Yankovsky 2000), geostrophic adjustment (Chapman and Lenz 1994; Matano and Palma 2010), andnongeostrophic acceleration (Kourafalou et al. 1996). A universal effective remedy to arrest the upstream development is
to add a downstream ambient current (Chapman and Lenz
1994; Yankovsky and Chapman 1997).
The tides have been reported to be important to the behavior of a river plume. Isobe (2005) demonstrated that
unstable freshwater accumulating in a bulge can be restricted
to the alongshore direction by the alongshore tidal currents.
Li and Rong (2012) also found that the tidal currents could
stabilize the Changjiang River plume bulge and force theplume water to move in the direction of the tidal currents.
Using numerical experiments with and without tide, Guo andValle-Levison (2007) found that the upstream extension of
the plume in the Chesapeake Bay is well inhibited after
considering the effect of the tide. Wu et al. (2011) also
pointed out that with tidal forcing, the unrealistic upstream
extension of the Changjiang River plume in the no-tidalforcing case is restricted. All these studies demonstrated theeffect of tidal current or tidal mixing on the extension of river

DOI: 10.1175/JPO-D-20-0235.1
Ó 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright
Policy (www.ametsoc.org/PUBSReuseLicenses).
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plume, but paid no attention on the possible influence oftide-induced residual current as an ambient current on theriver plume.
There is a fundamental problem: is the upstream extensionof a river plume a consequence of model configuration or anaturally existing phenomenon? Some observational evidence
for the upstream extension of a river plume in real oceans
exists. Magome and Isobe (2003) observed an upstream extension in the bulge after a peak value of river discharge in SuoNada, Seto Inland Sea, and deduced that the onshore current in
the bottom layer beneath the bulge transported the bulge in the
upstream direction. Beardsley et al. (1985) observed the upstream extension of the Changjiang River plume. Wu et al.
(2014) suggested that the coastal current from Changjiang estuary due to tide-induced Stokes drift is the major mechanism
driving such upstream extension.
The Yellow River is the second largest river in China and isfamous for its huge sediment load contribution to the sea. In
recent decades, however, it has experienced a dramatic decreasing in freshwater and sediment fluxes into the sea due toclimate change and anthropogenic activities (Wang et al. 2006).
Subsequently, a series of consequences have occurred, suchas a frequent occurrence of no water events in some parts of
the river, accumulation of sediment in the river, and increasingof salinity in the Bohai Sea, its receiver (Lin et al. 2001; Wu
et al. 2004). Since 2002, the Yellow River Conservancy Commission(YRCC) has implemented a water–sediment regulation
scheme (WSRS) to reshape the relationship between thewater and sediment in the river by releasing a large amount ofwater in a short time in summer to flush out sediments from theriver into the Bohai Sea.
The WSRS provides us an opportunity to observe how theriver discharge affects the movement of a plume. During theimplementation of the WSRS, the Yellow River discharge increases from less than 500 m3 s21 to larger than 3500 m3 s21 in aperiod of less than 2 weeks. Wang et al. (2011) conducted threefield surveys, one each before, during, and after the implementation of the WSRS in 2009. They found that the plume
propagated upstream before the water release, and turned
downstream during and after it. However, the mechanism forthe upstream extension of the Yellow River plume when theriver discharge was low, the reason for the change in the direction of the plume to downstream after the river discharge
was increased, and the role of summer wind in the upstream
extension of the plume remain unknown.
Our objectives are to examine whether the upstream extension of the Yellow River plume occurs occasionally or
regularly by analyzing historical field survey data, and to clarify
the mechanism responsible for the upstream extension under
low river discharge condition and downstream extension underhigh river discharge condition by numerical modeling. To
generalize the influence of variation in river discharge on theplume extension direction, idealized numerical studies are alsoneeded. Previous studies on the Yellow River plume weremainly concerned about the seasonal variation in the distribution of low-salinity water, and included observational surveys (Guan and Chen 1964; Zhou et al. 1991, 1997) andnumerical modeling (Wang et al. 2008). All the results showed

VOLUME 51

TABLE 1. Dates of the observations and the corresponding Yellow
River discharges.
Year

Date

River discharge (m3 s21)2009

19 Jun
1 Jul
19 Jul24–26 Jun
26–28 Jul
23–25 Sep
12–14 Jun
7–8 Jul
17–20 Jul

173
3600
478
2100
3310
345
400
3000
300

2013

2014

that the low-salinity water from the Yellow River extends
southward into the Laizhou Bay in winter and propagatesnortheastward into the central Bohai Sea in summer. However,studies about the influence of sharp variations in river discharge on the Yellow River plume are limited, although there
are some studies in other river plume showing that the sharp
variation in river discharge can induce a partially detachedplume (Yankovsky et al. 2001; Jurisa and Chant 2012).
The remainder of this paper is organized as follows.
Section 2 describes the observational data and model configuration, and section 3 presents the observations and model results
about the extension of the Yellow River plume. Section 4 examines the mechanism for the upstream extension of the Yellow
River plume through numerical experiments and analyzes how
the river discharge and summer wind influence the upstream extension. The results of this study are summarized in section 5.

2. Observational data and model description
Yantai Institute of Coastal Zone Research, Chinese Academyof Sciences, carried out field surveys around the Yellow Riverestuary before, during, and after the implementation of the
WSRS in 2013 and 2014 using similar stations as Wang et al.
(2011), who reported the results of a similar survey in 2009.
The observational dates and corresponding Yellow River discharges in the three years are shown in Table 1. The observational stations (positions shown in section 3a) comprise six
sections from the river mouth. Each section has 5–9 stations,where water temperature and salinity are measured byconductivity–temperature–depth profilers (CTDs) over theentire depth. In 2009, three fishing boats were employed, witheach covering two sections. The boats started observations at
the same time in the early morning and covered all thesections within ;12 h. In 2013 and 2014, only one fishing boat
was employed. The survey was conducted for three days on
average, with each day starting from early morning and lasting
for approximately 12 h. The tidal current around the Yellow
River mouth has a semidiurnal period and a magnitude of;0.5 m s21 that can induce an intratidal movement of plume by;10 km. As shown later, such distance does not affect thedifference of salinity in the surveys in 2009 as well as those in2013 and 2014. On the other hand, the three fishing boats in2009 started at the same time and the one fishing boat in 2013
and 2014 observed every two sections at almost the same time

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every day. Since the phase difference between three boats in2009 and that between different days in 2013 and 2014 aresmall, our observed salinity field does not contain its maximum
intratidal motion, which also guarantee the little influence of
intratidal variation on the difference among the observed salinity fields from different surveys.
The river discharge recorded at Station Lijin, the hydrological station nearest to the river mouth (;100 km away),
was obtained from www.yrcc.gov.cn. In general, the river discharge was low in the first survey (150–400 m3 s21), increased
significantly in the second survey (.3000 m3 s21), and decreased again in the third survey (300–500 m3 s21) (Table 1).
Although the wind velocity over the sea was not recorded
during the surveys in the three years, the reanalysis data fromthe European Centre for Medium-Range Weather Forecasts(ECMWF) shows that the prevailing winds were southerly
during most surveys in the three years, with the wind speed
ranging from 3 to 7 m s21. Only during the survey in September
2014, which was the third survey in 2014, the wind was northerly with a speed of approximately 9 m s21.
The numerical model we adopted is a three-dimensional
primitive equation ocean model, the Princeton Ocean Model(POM) (Blumberg and Mellor 1987; Mellor 2003). It uses a
second momentum turbulent closure scheme to calculate thevertical eddy viscosity and diffusivity (Mellor and Yamada
1982) and the Smagorinsky formulation to parameterize thehorizontal eddy viscosity and diffusivity (Smagorinsky 1963).
The model domain and bathymetry are shown in Fig. 1a. The
horizontal resolution is ;1 km (1/908), which is nested by theratio of 1:5 to a coarse grid model (1/188) (Fig. 1b; Wang et al.
2008). The coarse grid model covers the Bohai Sea, Yellow
Sea, and East China Sea, and focuses on the seasonal variationin the Yellow River plume. Being the same as the coarse gridmodel, we set 21 sigma layers in the vertical direction in the finegrid model, with the sigma values of 0, 20.002, 20.004, 20.01,
20.02, 20.04, 20.06, 20.08, 20.10, 20.12, 20.14, 20.17,
20.20, 20.30, 20.40, 20.50, 20.65, 20.80, 20.90, 20.95, and21 from the sea surface to the sea bottom. The bathymetry andforcing conditions for the fine grid model were interpolated
linearly from those of the coarse grid model, except for thebathymetry near the Yellow River mouth that was modified by
the chart in 2009 to represent the recent changes in the geography of the Yellow River delta.
The forcing conditions for the model to reproduce a climatological state included monthly wind stress, monthly heat
flux, monthly river discharge, monthly precipitation, monthly
evaporation, and monthly sea surface pressure (Wang et al.
2008). Four rivers were considered in the fine grid model:
Yellow River, Liaohe River, Luanhe River, and Haihe River(Fig. 1a). The open boundary was set along 122.38E, where thebathymetry and monthly temperature, salinity, residual currents, and sea level in every five grids were set to be equal tothose at the corresponding grid of the coarse grid model. Fourtidal constituents (M2, S2, K1, and O1), whose information was
also provided by the coarse grid model, were considered. The
currents were specified at the open boundary using a linear
combination of the tidal current and residual current (Wanget al. 2008). The fine grid model under the abovementioned

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FIG. 1. Model domain and bathymetry of (a) the fine grid modeland (b) the coarse grid model. The red triangles in (a) denote thepositions of rivers.

forcing reached a quasi-equilibrium state after 3 years of integration (case 0) from the initial condition on 1 December,which was obtained from the coarse grid model.
After finishing the spinup of the fine grid model with theabovementioned climatological forcing, we carried out thecalculations for 2009 (case a), 2013 (case b), and 2014 (case c),in which the daily Yellow River discharge (Fig. 2a) and6-hourly wind stress were used to replace those applied in the
spinup. In both 2009 and 2014, the river discharge increased
from less than 500 m3 s21 to more than 3500 m3 s21, and thendecreased to less than 500 m3 s21 during one month (Fig. 2a). In
2013, the WSRS was conducted twice, and each lasted for one
month. The 6-hourly wind stress for the fine grid model was
spatially linearly interpolated from the ECMWF, whose spatial
resolution is 0.1258 3 0.1258. The daily mean wind stress near
the Yellow River mouth is shown in Fig. 2b. In summer, thearea around the Yellow River mouth is covered mostly bysoutherly wind and occasionally by weak northerly wind. The
calculations for 2009, 2013, and 2014 were started from thesame initial condition, that is, the climatological model resultson 1 January in the third year (case 0), and performed for one
year using realistic Yellow River discharges and winds tosimulate the Yellow River plume in each year.
We set a series of numerical experiments (Table 2) to examine the effects of the Yellow River discharge, tide, and wind
forcing on the movement of Yellow River plume. In case 1, theYellow River discharge in 2009 and tide were considered. Case
2 examined the tide and tide-induced residual current aroundthe Yellow River mouth. To know influences of wind forcing,
we chose three types of winds and applied them to the cases
designed for spring tide (9–11 June, cases 3–5) and neap tide
(17–19 June, cases 6–8). The three types of winds are monthly
wind stress in June 2009 (eastward component of wind stress

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FIG. 2. (a) Daily Yellow River discharges recorded at Station Lijin in 2009, 2013, and 2014,
and (b) daily mean wind stress from the ECMWF near the Yellow River mouth in 2009, 2013, and2014 (shown from top to bottom). The dots in (a) indicate the river discharges on the surveyed
days in different years, and the red arrows in (b) denote the wind stresses on the same days.

was 0.001 N m22 and northward component was 0.02 N m22,
corresponding to a wind speed of 3.8 m s21), the strong
southwesterly wind stress appearing on 1 June 2009 (eastward
component was 0.03 N m22 and northward component was
0.05 N m22, corresponding to a wind speed of 6.5 m s21), andthe strong northeasterly wind stress appearing on 9 May 2009
(eastward component was 20.06 N m22 and northward component was 20.05 N m22, corresponding to a wind speed of
7.1 m s21). The model results were saved hourly, and a low-passfilter (Hanawa and Mitsudera 1985) was used to remove thetidal components.
We also set an idealized numerical model to generalize theinfluence of variation in river discharge on the river plume
extension direction under an ambient current. The model domain has a meridional range of 80 km and a zonal range of
200 km and the water depth linearly increases from 1 m inside ariver course at the western boundary to 15 m at the easternboundary (their figure is presented in section 4b). The model

TABLE 2. List of numerical experiments. All the cases except case 2 considered the surface heat flux.
Realistic cases

Yellow River discharge

Case 0Case aCase bCase cMonthly climatology
Daily in 2009
Daily in 2013
Daily in 2014

Sensitivity cases

Yellow River discharge

Case 1Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Case 8

Daily in 2009
No discharge
Daily in 2009
Daily in 2009
Daily in 2009
Daily in 2009
Daily in 2009
Daily in 2009

Idealized cases
Cases 9–488
Cases 489–968

River discharge
3 21

100:100:3000 (m s )100:100:3000 (m3 s21)

Wind forcing
Monthly climatology
Hourly in 2009
Hourly in 2013
Hourly in 2014
Wind forcing

Tide

No wind
No wind
Average in June 2009
Strong southwesterly on 1 Jun 2009
Strong northeasterly on 9 May 2009
Average in June 2009
Strong southwesterly on 1 Jun 2009
Strong northeasterly on 9 May 2009

Spring tide
Spring tide
Spring tide
Neap tide
Neap tide
Neap tide

Ambient current

Tidal current amplitude

21

20.05:0.01:0.10 (m s )20.05:0.01:0.10 (m s21)

0.1 m s21
1 m s21

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FIG. 3. Horizontal distributions of observed sea surface salinity (top) before, (middle) during, and (bottom) after implementation of the
WSRS in (a),(d),(g) 2009; (b),(e),(h) 2013; and (c),(f),(i) 2014. The black dots denote the survey stations. The distribution in 2009 is
directly derived from Wang et al. (2011). Characters A–F in (a) and A1–F1 in (c) represent the sections in 2009 and 2014, respectively,
along which the vertical distributions of salinity are shown in Fig. 4.

resolution is 1 km in the horizontal direction and 21 sigma
layers in the vertical direction. The angle between the rivercourse and the northward direction is 908. The river discharge
is imposed as vertical freshwater flux to the surface layer over
the river course. Only the M2 tide is included in the model.
Because the tide-induced residual current around the rivermouth is negligible small, an ambient current resembling thetide-induced residual current around the Yellow River mouth
is applied along both southern and northern boundaries of themodel domain.
We set a series of numerical experiments to examine how theriver discharge, ambient current and tidal current affect theriver plume in this idealized case (Table 2). In these experiments, the river discharge varies from 100 to 3000 m3 s21 withan interval of 100 m3 s21; the specified ambient current varies
from 20.05 m s21 (southward) to 0.10 m s21 (northward) withan interval of 0.01 m s21. We considered two situations for the
tidal current amplitude around the river mouth (0.1 or 1 m s21).
In each experiment, the model was run for 30 days from rest,

and we obtained the subtidal results on the 25th day by
applying a low-pass filter (Hanawa and Mitsudera 1985) to thehourly model results from the 20th day to the 30th day.

3. Resultsa. Field observations
The horizontal distributions of the observed sea surface
salinity before, during, and after the implementation of the
WSRS in the 3 years are shown in Fig. 3. In 2009, the lowsalinity water was concentrated in the direction upstream of
the Yellow River mouth on 19 June (Fig. 3a) when the riverdischarge was 173 m3 s21. However, it became symmetricalaround the river mouth on 1 July (Fig. 3d) when river discharge
increased to 3600 m3 s21. After the river discharge subsided to478 m3 s21 on 19 July, the plume turned downstream (Fig. 3g).
The change in the Yellow River plume pattern before andduring the WSRS also occurred in 2013, when low-salinity

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FIG. 4. Vertical distributions of salinity along the sections where observed low-salinity water concentrated (top)before, (middle) during, and (bottom) after implementation of the WSRS in (a),(c),(e) 2009 and (b),(d),(f) 2014.
Salinity distributions shown for section A in (a), section C in (c), section E in (e), section B1 in (b), section D1 in (d),and section C1 in (f). The distribution in 2009 is derived directly from Wang et al. (2011).

water was found to be distributed upstream on 24 June
(Fig. 3b), and symmetrically near the river mouth on 26 July(Fig. 3e). Owing to the lack of data in the stations near theriver mouth on 25 September, the distribution of lowsalinity water after the reduction in the river discharge
was not clear (Fig. 3h). In 2014, the coverage of the observational stations was narrower than those in 2009 and2013. However, the results also showed that the plume wasdistributed in the upstream area (Fig. 3c) when the riverdischarge was low (400 m 3 s 21), and extended northeastward (Fig. 3f) when the discharge increased to 3000 m 3 s 21 .
After the river discharge subsided, the low-salinity water
was not easily confirmed from the observation (Fig. 3i)
because the low-salinity water possibly extended beyond

the survey region. The wind conditions before the WSRS wereupwelling favorable in 2009 and 2013, but downwelling favorable in 2014 (Fig. 2b). After the WSRS, they were upwellingfavorable in 2009 and 2014, but downwelling favorable in2013 (Fig. 2b).
Therefore, under normal conditions when the river discharge was low, the Yellow River plume likely extended upstream in summer, which is different from the downstream
extension of the Kelvin wave. Under abnormal conditions
when the river discharge increased sharply, the Yellow River
plume gradually turned downstream.
We have shown the vertical distributions of salinity along
the sections where low-salinity water concentrated in 2009
and 2014 (Fig. 4); this information is not shown for 2013 when

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FIG. 5. Horizontal distributions of modeled sea surface salinity at the observational stations before (top) before, (middle) during, and(bottom) after implementation of the WSRS in (a),(d),(g) 2009 (case a); (b),(e),(h) 2013 (case b); and (c),(f),(i) 2014 (case c), respectively.

only surface data were available. The salinity was almost
homogeneous in the vertical direction when the river discharge
was low in both 2009 and 2014 (Figs. 4a,b), except for that near
the river mouth. However, strong salinity stratification wasformed when the river discharge reached a value larger than3000 m3 s21 (Figs. 4c,d). It remained stratified even after theriver discharge decreased (Figs. 4e,f).

b. Model results
We performed numerical simulations to examine themechanism for upstream extension of the Yellow River plumeunder the low river discharge condition in summer, as well as
the transition to the downstream direction after the river discharge increased. First, we calculated the climatological salinity in the Bohai Sea (case 0), and compared it with theobservations and results of the coarse grid model reported by
Wang et al. (2008). The water salinity calculated by our modelis closer to the observations than that calculated by the coarse
grid model, especially the salinity front near the Yellow Rivermouth in summer. Since we used the same forcing as Wanget al. (2008), the change in model resolution is likely the reason
for this improvement.
Then, we simulated the Yellow River plume in 2009 (case a),2013 (case b), and 2014 (case c) using daily Yellow River discharges and 6-hourly wind stress data from the ECMWF ineach year. The modeled surface and bottom salinity at theobservational stations were compared with the observational
data (Fig. S1 in the online supplemental material). As theobservations were not synchronous, we compared the modeledsalinity at the same hour of each CTD casting. The root-meansquare error is 3.4 for surface salinity and 1.1 for bottom salinity, respectively, and the correlation coefficient is 0.63 forsurface salinity and 0.63 for bottom salinity (Fig. S1). Except
for model resolution that cannot resolve the realistic bathymetry, the exact local winds over the sea and the realistic Yellow
River discharge before and during observation period are actually not available. These factors strongly affect the salinity
distribution near the river mouth where the salinity gradient islargest. Therefore, it is difficult for the model to reproduce theexact distribution of salinity and even a shift in spatial pattern

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FIG. 6. (a),(b) Horizontal distributions of sea surface salinity (color) and residual current (arrow) and (c),(d)vertical distributions of salinity (color) and residual current (arrow) along the upstream section [red line in (a)] in(left) spring tide and (right) neap tide in June 2009 in case 1. The black lines in (a) and (b) show the 25 isohaline on
11 and 19 Jun, respectively, while the white line in (b) shows the 25 isohaline on 11 Jun. The red point in (a) and(b) denotes the position of the Yellow River mouth.

should also cause a large error in a direct salinity comparison
between model results and observations.
However, although the specific value of modeled salinity is
not perfectly consistent with the observed salinity, the distribution of the plume is consistent. The modeled lowsalinity water was distributed in the upstream direction on
19 June 2009 (Fig. 5a), symmetrically around the Yellow
River mouth on 1 July (Fig. 5d), and in both upstream anddownstream directions on 19 July 2009 (Fig. 5g). On 24 June
2013, as the river discharge was large (2100 m3 s21), theplume was mainly in the upstream direction but also partially distributed in downstream direction (Fig. 5b). As theriver discharge increased, the plume was distributed aroundthe river mouth on 26 July 2013 (Fig. 5e). Although the observational station coverage was smaller in 2014, the observed pattern of low-salinity water was reproduced quite
closely by the model, showing little low-salinity water in the
upstream direction on 12 June (Fig. 5c), and a relatively
narrow area of low-salinity water in the northeast direction
on 7 July (Fig. 5f).
The model results confirm the observed low-salinity water in
upstream area of the Yellow River plume under the low riverdischarge condition, and the transition to the downstream
direction under the high river discharge condition. Consequently,
the model can be used to analyze the evolution processes anddynamics between these situations and the influences of bothriver discharge and winds on them.

4. Discussion
a. Reason for upstream extension of the Yellow
River plume in summer
To investigate the behavior of the Yellow River plume under the condition of low river discharge, we considered the casein 2009 as an example and designed a new case (case 1) in which
the effect of wind was excluded, and only tide, heat flux, andriver discharge in 2009 (black line in Fig. 2a) were considered.
Except for the time when the Yellow River discharge was large
from 23 June to 20 July, the low-salinity water from the Yellow
River was distributed mainly in the area upstream of the rivermouth in case 1. However, the distribution of the Yellow River
plume shows significant spring and neap tidal variations(Fig. 6). During spring tide (Fig. 6a), the Yellow River plume

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FIG. 7. (a) The low-salinity area A1 (m2) inside the 25 isohaline north of the 37.98N section and the freshwater
volume VR1 (m3) inside the northern part of target domain in case 1. (b) The temporal variation rate of freshwater
volume (m3 s21) inside the northern part of target domain (dVR1/dt), the freshwater volume transport (m3 s21)
across the 37.98N section (F1) and northern 25 isohaline on 11 Jun (2F2), and the sum of both volume transport(F1 1 F2). The dVR1/dt and F1 1 F2 share the left axis, while F1 and 2F2 share the right axis. (c) The freshwater volumetransports (m3 s21) across the 37.98N section (F1) and northern 25 isohaline on 11 Jun (F2), and the contributions ofsubtidal process and intratidal process to them. The left axis is for those across the 37.98N section, and the right axis is
for those across the northern 25 isohaline on 11 Jun. (d) The freshwater volume transport (m3 s21) by the tide-induced
residual current and density-driven current across the 37.98N section and northern 25 isohaline on 11 Jun, with theformer two sharing the left axis and the latter two sharing the right axis. The black dashed lines with ‘‘N’’ refer to thedays of neap tide, while the red dashed lines with ‘‘S’’ refer to the days of spring tide.

(salinity , 25) distributes in a narrow area from river mouth tothe upstream area north of the river mouth, with a northward
velocity of ;0.06 m s21 inside the plume; during neap tide
(Fig. 6b), it forms an anticyclonic bulge and occupies a large
area from river mouth to the downstream area south of theriver mouth.
The vertical distribution of salinity along a section fromthe river mouth to the upstream area (red line in Fig. 6a)shows that the isohalines are almost vertical to the surface inspring tide (Fig. 6c) but tilt with the surface in neap tide
(Fig. 6d), which is due to the strong tidal mixing in spring tide
and weak tidal mixing in neap tide. According to Yankovsky

and Chapman (1997), the plume with freshwater occupying theentire water column is categorized as a bottom-advected
plume, while that with lighter water distributing above thedenser water is classified as a surface-advected plume. In ourcase, the Yellow River plume in spring tide resembles abottom-advected plume, while that in neap tide is similar to asurface-advected plume.
The residual current along the section shows that except
in the area very close to the river mouth, the current flows
northward in both the surface and bottom layers in springtide (Fig. 6c). However, in neap tide (Fig. 6d), except for
the northward residual current near the river mouth, there

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FIG. 8. (a) The low-salinity area A2 (m2) inside the 25 isohaline south of the 37.98N section and the freshwater
volume VR2 (m3) inside the southern part of target domain in case 1. (b) The temporal variation rate of freshwater
volume (m3 s21) inside the southern part of target domain (dVR2/dt), the river discharge (riv), the northward
freshwater volume transport across the 37.98N section (2F1) and southern 25 isohaline on 11 Jun (F3), and the sumof them (riv 2 F1 1 F3). The dVR2/dt and riv 2 F1 1 F3 share the left axis, while riv, 2F1 and F3 share the right axis.
(c) The freshwater volume transport (m3 s21) across the southern 25 isohaline on 11 Jun (F3), and the contributionsof subtidal process and intratidal process to it. (d) The freshwater volume transport by the tide-induced residual
current and density-driven current across the southern 25 isohaline on 11 Jun. The black dashed lines with ‘‘N’’ referto the days of neap tide, while the red dashed lines with ‘‘S’’ refer to the days of spring tide.

is no obvious northward current in the surface layer. In
particular, the surface current in the area around 37.98N issouthward.
We calculated the surface area of the plume with surface
salinity less than 25 (Figs. 7a and 8a ). Because of the alternation in the direction of surface residual current around37.98N from spring tide to neap tide (Figs. 6c,d), we divide theplume into northern and southern parts by the 37.98N section(blue line in Fig. 6a). In the northern part, the area (A1)reaches a maximum value in neap tide and a minimum value
one or two days before spring tide (blue line in Fig. 7a). In thesouthern part, the area (A2) reaches a maximum value ;2 days
after neap tide and a minimum value near spring tide (blue line
in Fig. 8a).

To explain the variation of low-salinity area during spring–
neap tidal cycles over the two months of ÐÐÐ
calculation in case 1, we
calculate the volume of freshwater (VR 5 [(s0 2 s)/s0 ] dx dy dz)
inside the 25 isohaline on 11 June when the low-salinity area
was at a minimum level in both the northern and southernparts (Figs. 7a and 8a). Being the same as the area, we also
divide this fixed target domain into two parts by the 37.98N
section. In the equation for VR, s0 is a background salinity
with a value of 32, s is the salinity at each grid point inside thetarget domain, the integration in the x direction is from thecoastline to the 25 isohaline, the integration in the y direction
is from the 37.98N section to the 25 isohaline in the northernarea and from the 25 isohaline to the 37.98N section in thesouthern area, respectively, and the integration in the z

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direction is from the sea bottom to the sea surface. The
overbar denotes the detiding procedure using a low-passfilter (Hanawa and Mitsudera 1985).
The VR in the northern part of the target domain (VR1,orange line in Fig. 7a) increases from neap tide to spring tide,
reaches a maximum value after spring tide, decreases toward
neap tide, and reaches a minimum value after neap tide. As
comparing the two lines in Fig. 7a, we found a time lag of
3–4 days between the peak values of freshwater volume in
the northern part of target domain VR1 and the area with asurface salinity less than 25 north of 37.98N section (A1, blueline in Fig. 7a). In addition, as passing each spring tide toward next neap tide, both VR1 and A1 increase, showing an
in-phase variation. There is also a short time for both VR1 and
A1 to decrease. Apparently, the horizontal transport offreshwater through the fixed lateral boundary defined by the
25 isohaline on 11 June (Fig. 6a) is a key process to understand the relation between VR1 and A1 as well as the temporal change of A1.
The temporal variation rate of VR1 (black line in Fig. 7b) isapproximately determined by the horizontal transport offreshwater through the 37.98N section and the northern 25
isohaline on 11 June. This relation is expressed as following
equation:
dVR1
5 F1 (t) 1 F2 (t) 1 HDIF1 ,
(1)
dt
ÐÐ
and
F2 (t) 5
where
F1 (t) 5 [(s0 2 s)/s0 ]y dx dz
ÐÐ[(s0 2 s)/s0 ]u(y) dy( dx) dz are the freshwater volume transport across the 37.98N section and the northern 25 isohalineon 11 June, respectively, HDIF 1 is the freshwater volumetransport across the 37.98N section and the northern 25
isohaline caused by horizontal diffusion. In this calculation, the 25 isohaline on 11 June is represented by a steplike line composed by some meridional and zonal grid lines.
If the line at a grid point is at meridional direction, thefreshwater
volume transport at that grid point is given byÐÐ[(s
0 2 s)/s0 ]u dy dz; if the line is at zonal direction, it isÐÐ
by [(s0 2 s)/s0 ]y dx dz.
The dVR1/dt is positive (20 m3 s21) around spring tide andnegative (230 m3 s21) near neap tide (black line in Fig. 7b).
The positive value has a longer duration than negativevalue, indicating a slow increasing but fast decreasing of
freshwater volume inside the target domain. The freshwater transport through the 37.98N (F1 ) is persistently northward (blue dashed line in Fig. 7b, acting as an influx offreshwater), and that through the northern 25 isohaline of
11 June (F2 ) is persistently outward (2F2 by the green
dashed line in Fig. 7b, acting as an outflux of freshwater).
Both values of transport are larger in spring tide than inneap tide. Around spring tide, the former is larger than thelatter, thus, the freshwater volume inside the northern area
increases; ;3 days before neap tide, the former becomes
smaller than the latter, thus, the freshwater volume inside
the northern area becomes to decrease. Therefore, thefreshwater volume inside the northern area reaches thepeak value ;3 days before neap tide (orange line in Fig. 7a).
It must be noted that the sum of F1 and F2 is close to dV R1/dt

in Fig. 7b, indicating the negligible role of horizontal diffusion HDIF1 on lateral transport of freshwater.
In the southern part of the target domain, the freshwater
volume VR2 also starts increasing after neap tide, keeps increasing after spring tide; after reaching a maximum value
before next neap tide, it starts decreasing and reaches a minimum value after next neap tide (orange line in Fig. 8a). There isalso a time lag of ;4 days between the peak values of the lowsalinity water area south of the 37.98N section and the freshwater volume in the southern part of target domain (Fig. 8a).
Their in-phase and antiphase variations as well as their time lag
indicate a close relation between them.
Being similar to the northern part of target domain, thetemporal variation of freshwater volume VR2 can be expressedby the budget of the horizontal transports of freshwater
through the 37.98N section and the southern 25 isohaline on
11 June, and the direct input of river water through theequation
dVR2
5 riv 2 F1 (t) 1 F3 (t) 1 HDIF2 ,dt(2)

where riv, F1(t), and F3(t) are the river discharge, northward
freshwater transport across the 37.98N section, and the horizontal freshwater transport across the southern 25 isohaline on
11 June, respectively; HDIF2 is the freshwater volume transport across the 37.98N section and the southern 25 isohalinecaused by horizontal diffusion.
The dVR2/dt is positive (100 m3 s21) around spring tide andnegative (2170 m3 s21) near neap tide (black line in Fig. 8b).
Again the duration is longer for positive values than for negative values. The river discharge ranges from 100 to 400 m3 s21
and naturally has no spring–neap tidal cycle (black dashed line
in Fig. 8b). The freshwater transport across the southern 25
isohaline on 11 June (F3) is positive around spring tide(100 m3 s21) but negative near neap tide (2150 m3 s21) (green
dashed line in Fig. 8b). The sum of riv, 2F1, and F3 is positivearound spring tide and negative around neap tide (red line in
Fig. 8b), coinciding well with dVR2/dt and demonstrating again
the negligible role of horizontal diffusion on freshwatertransport.
From above analysis, we found that the freshwater transport
across the 37.98N section is an essential factor for keeping thelow-salinity water in the northern area. In the southern area,
the lateral transport of freshwater across the 25 isohaline on
11 June is a key process for the expanding or shrinking of lowsalinity water area on the other days. For example, as theoutward freshwater transport across the 25 isohaline on
11 June (green dashed line in Fig. 8b) increases from two days
before neap tide, the low-salinity water area in the southernarea (A2, blue line in Fig. 8a) also increases. When the former
decreases and approaches zero 2 days after neap tide (green
dashed line in Fig. 8b), the latter reaches the maximum value(blue line in Fig. 8a). When the freshwater transport across the
25 isohaline on 11 June becomes positive (inward, green
dashed line in Fig. 8b), the area (A2) decreases sharply (blueline in Fig. 8a).
To clarify the processes responsible for the freshwater volume transport across the 37.98N section and the 25 isohalines

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on 11 June, we divide the transport into the subtidal process and intratidal process. The salinity s and velocity y aresubsequently divided into two parts: one is the subtidal
component (s, y), and the other is the anomaly (s 0 , y0 ).
Following this decomposition, the freshwater volume transport
is given asððs0 2 sy dx dz 5s0ðð

s0 2 sy dx dz 2s0

ðð 0 0sy
dx dz.
s0(3)

The first term on the right-hand side of Eq. (3) denotes thetransport contributed by the subtidal process, and the second
term by the intratidal process.
The freshwater transport across the 37.98N section (F1) ismainly attributed to the subtidal process (red line in Fig. 7c),whose value is ;400 m3 s21 in spring tide and ;250 m3 s21 inneap tide and shows a similar spring–neap tidal variationas F1. The freshwater transport by the intratidal process(red dashed line in Fig. 7c) shows a small negative value(250 m3 s21) with a slight temporal variation. This feature isalso true for the freshwater transport through the northern
25 isohaline on 11 June (F2, ;2300 m3 s21, blue line in
Fig. 7c), which is mainly contributed by the subtidal process(2300 m3 s21, green line in Fig. 7c) because the transport by
the intratidal process is much smaller (50 m3 s21, green
dashed line in Fig. 7c). The freshwater transport through thesouthern 25 isohaline on 11 June (F3, black line in Fig. 8c) isalso attributed to the subtidal process (red line in Fig. 8c)
because the transport by the intratidal process (red dashedline in Fig. 8c) is small. Because the salinity field has only
slight change during a spring–neap tidal cycle, the subtidal
current is likely the reason for the different freshwatertransport in spring and neap tides.
An apparent spring–neap tidal cycle in the subtidal current
prompts us to examine the tide-induced residual current byrunning the model forced only by tide (case 2). The cotide
map (Figs. 9a,b) and tidal ellipse (Figs. 9c,d) given by themodel results are consistent with those in previous studies(Dou et al. 1981; Fang and Yang 1985; Fang 1986). The tide
near the Yellow River mouth is dominated by M2 and K1
whose combination forms an irregular semidiurnal tide. The
tidal current near the Yellow River mouth is rectilinear,which flows southward during flood and northward during
ebb (Fig. 9c). The tide-induced residual current near the
Yellow River mouth flows northward, and its maximum speed
is ;0.07 m s21 in spring tide (Fig. 9e) and ;0.02 m s21 in neap
tide (Fig. 9f). This northward tide-induced residual current
near the Yellow River mouth has been reported in many
previous studies (Dou et al. 1981; Fang and Yang 1985; Zhao
et al. 1995; Huang et al. 1999; Wei et al. 2004). In addition,
Zhao et al. (1995) and Wei et al. (2004) observed that the
sediment from the Yellow River was transported northward,
and attributed this northward transport of sediment to thenorthward tide-induced residual current near the Yellow
River mouth.
As an approximation of the density-driven current, we
calculate the difference in residual current between case 1
and case 2. In the surface layer, the density-driven current

FIG. 9. (a),(b) Cotide map and (c),(d) tidal ellipse of M 2 andK 1 tide constituent off the Yellow River mouth, and thehorizontal distribution of tide-induced residual current in(e) spring tide and (f) neap tide. In (a) and (b), the black solidlines denote the amplitude (cm) and the red dashed lines show
the phase.

inside the plume flows northward from the river mouth andthen turns southward in both spring tide and neap tide
(Figs. 10a,b). Furthermore, the current is stronger in neap
tide (Fig. 10b) than in spring tide (Fig. 10a). At the 37.98N
section where we examined the freshwater transport, thedensity-driven current is southward in the surface layer andnorthward in the bottom layer (Figs. 10c,d). Both the surface
southward current and the bottom northward current arestronger in neap tide (Fig. 10d) than in spring tide (Fig. 10c).
For example, the surface southward current is 0.01 m s21 inspring tide and 0.05 m s21 in neap tide. In both the estuary(Wong 1994) and the offshore shelf area (Kasai et al. 2000),
the density-driven current is inversely correlated to thevertical eddy viscosity, which is stronger in spring tide thanin neap tide.
The northward tide-induced residual current is stronger
in spring tide than in neap tide (Figs. 9e,f). The southwardsurface density-driven current is stronger in neap tide thanin spring tide (Figs. 10a,b). To quantify their contribution
to freshwater transport, we use the same method as those in
Eqs. (1) and (2) to calculate the freshwater transport acrossthe three sections by the tide-induced residual current anddensity-driven current, respectively. At the 37.98N section,
the freshwater transport by the tide-induced residual current

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FIG. 10. Horizontal distribution of surface density-driven current, which is approximated by the difference ofresidual currents between case 1 and case 2 on (a) 11 Jun and (b) 19 Jun. Vertical distribution of northward densitydriven current across the section denoted by the blue line in (a) and (b) on (c) 11 Jun and (d) 19 Jun. The black linein (a) and (b) shows the 25 isohaline of the bulge in case 1.

shows apparent spring tide (270 m3 s21) and neap tidal variations (150 m3 s21) (black line in Fig. 7d), and is stronger thanthat by the density-driven current (;100 m3 s21) (red line in
Fig. 7d). At the northern 25-isohaline on 11 June, the outward freshwater transport by the tide-induced residual
current (2250 m3 s21, blue dashed line in Fig. 7d) is stronger
than that by the density-driven current (2100 m3 s21, green
dashed line in Fig. 7d) in spring tide, but is smaller(2150 m3 s21) than that (2200 m3 s21) in neap tide. At thesouthern 25 isohaline on 11 June, the freshwater transport
by the tide-induced residual current is always positive(;100 m3 s21, black line in Fig. 8d), showing a slight spring–
neap tidal variation, while that by the density-driven current
is generally negative, showing a relatively larger spring–
neap tidal variation (red line in Fig. 8d). Consequently, thefreshwater transport across the 37.98N section is likely
dominated by the tide-induced residual current, while thatacross the 25 isohaline is controlled by tide-induced residual
current in spring tide and by density-driven current in neap
tide. For this reason, we suggest that the upstream extensionof the plume is promoted by the upstream tide-induced residual current around the river mouth in spring tide, while
the downstream extension is attributed to the downstream

density-driven current around the offshore plume front inneap tide.
The above consideration on the fortnightly variations oftide-induced residual current and density-driven current
needs supports from a viewpoint of momentum balance, inwhich the advection term is necessary for the tide-induced
residual current while the vertical eddy viscosity term isnecessary for the density-driven current. We then calculate
the momentum equation for the surface northward velocity
using Eq. (4):›y5 adv 1 cor 1 pre 1 vert_vis 1 hori_vis.
›t(4)

In Eq. (4), y is the northward component of the velocity, adv
is the advection term, cor is the Coriolis force, pre is thepressure gradient term, vert_vis is the vertical eddy viscosity
term, and hori_vis is the horizontal eddy viscosity term. The
overbar above each term denotes detiding procedure by a lowpass filter (Hanawa and Mitsudera 1985).
In spring tide, the advection term in the north area of theriver mouth (Fig. 11a) is positive, which is favorable to theacceleration of the northward current, whereas the Coriolis

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FIG. 11. Horizontal distribution of the (a),(e),(i) advection term; (b),(f),(j) Coriolis force; (c),(g),(k) pressure gradient term; and(d),(h),(l) vertical viscosity term in the momentum equation [Eq. (4)] for the northward component of velocity on (top) 11 Jun (spring tide,
154 m3 s21), (middle) 19 Jun (neap tide, 173 m3 s21), and (bottom) 26 Jun (spring tide, 3250 m3 s21) in case 1. The units of all the values arem s22. The black line in each panel shows the 25 isohaline of the plume. The red rectangle in (i) shows the area where averaged surface
momentum terms are calculated inside the plume in Fig. 12.

force is relatively small inside the plume (salinity smaller than25) (Fig. 11b). The advection term inside the plume is balancedby the pressure gradient term (Fig. 11c) and vertical eddy
viscosity term (Fig. 11d). In neap tide, the Coriolis force becomes negative inside the plume (Fig. 11f), and is likely balanced by the pressure gradient term (Fig. 11g) and verticaleddy viscosity term (Fig. 11h).
To quantitatively evaluate the change of these terms within
the spring–neap tidal cycle, we spatially average the surface
momentum terms in an area north of the Yellow River mouth(the red rectangle in Fig. 11i). The time series shows significant
spring–neap tidal variations in the advection term, Coriolis
force, and vertical eddy viscosity term before 19 June when the
Yellow River discharge was small (Fig. 12). The advection
term (red solid line in Fig. 12) is positive (0.4 3 1025 m s22)
around spring tide but decreases to a negative value (20.1 31025 m s22) in neap tide. The vertical eddy viscosity term (reddashed line in Fig. 12) is negative (20.4 3 1025 m s22) in springtide but positive (0.4 3 1025 m s22) in neap tide, acting todecelerate both the northward residual current in spring tideand the southward residual current in neap tide. The pressure
gradient (blue solid line in Fig. 12) is always positive and shows
little fortnightly variation. The Coriolis force (blue dashed line
in Fig. 12) is always negative but shows a large fortnightly variation (20.9 3 1025 m s22 in neap tide and 20.2 3 1025 m s22 inspring tide).
The combination of above four terms is positive in springtide but negative in neap tide (black line in Fig. 12), indicating an acceleration of a northward current in spring tideand that of a southward current in neap tide. The magnitudeof advection term and its fortnightly variation indicate an
acceleration of the northward current in spring tide and its
deceleration in neap tide, which confirms our interpretationof the tide-induced residual current. The magnitude of vertical eddy viscosity term demonstrates its important role inmomentum balance, supporting our interpretation on the
inverse correlation of density-driven current with verticaleddy viscosity.

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FIG. 12. Time series of surface momentum terms (m s22) averaged inside the bulge to thenorth of the Yellow River mouth (within the red rectangle in Fig. 11i) in May and June 2009 incase 1. The red triangles with ‘‘N’’ refer to the days of neap tide, while those with ‘‘S’’ refer tothe days of spring tide.

b. Transition to downstream extension underhigh river discharge
As mentioned in section 3, both the observations and model
results showed that the low-salinity water from the Yellow
River was mainly concentrated in the upstream area when theriver discharge was low, but turned to downstream area when
the river discharge increased in all three years (2009, 2013, and2014). To investigate the reason for the transition of the lowsalinity water from the upstream area to the downstream area,
we consider case 1 in 2009 to examine the dynamics responsiblefor different movement directions under different river discharges in spring tide. The days of spring tide (and corresponding river discharge) are 11 June (154 m3 s21), 26 June
(3250 m3 s21), 11 July (338 m3 s21), and 25 July (543 m3 s21),
from which 11 June and 26 June are chosen for a comparison of
low river discharge and high river discharge.
The Yellow River plume shows significantly different patterns under different river discharges in spring tide, which
propagates upstream on 11 June (Fig. 13a), but forms a large
anticyclonic bulge near the river mouth on 26 June (Fig. 13b).
The vertical distribution of salinity also exhibits different
characteristics, which is vertically homogeneous on 11 June
(Fig. 13c), but strongly stratified on 26 June (Fig. 13d). Garvine(1995) suggested that for a small-scale plume, advection wasstronger than the Coriolis force, while for a large-scale plume,
Coriolis force was stronger than the advection. The relative
importance of the advection term for the small-scale plume on
11 June has been verified in section 4a, whereas the relative
importance of the Coriolis force for the large-scale plume on
26 June needs to be confirmed.

Following Eq. (4), we also calculated the momentum balance in the same spring tide but for different river discharges.
The results under low river discharge condition have beenpresented in Figs. 11a–d and described in section 4a. The results under high river discharge condition are presented in
Figs. 11i–l. Under the low river discharge condition on 11 June,
the advection term (Fig. 11a) and pressure gradient term
(Fig. 11c) are larger than the Coriolis force (Fig. 11b).
However, the situation changes on 26 June, when the Coriolis
force and pressure gradient terms (Figs. 11j,k) are much larger
than the advection term (Fig. 11i). The time series of the surface momentum terms averaged in the area north of the rivermouth also show that the advection term (20.2 3 1025 m s22)
and vertical eddy viscosity term (0.3 3 1025 m s22) were
smaller than the Coriolis force (21.1 3 1025 m s22) and pressure gradient term (1.1 3 1025 m s22) on 26 June (Fig. 12),which means that the Yellow River plume in the high riverdischarge condition is controlled mainly by a geostrophic
balance.
The plume extension directions under different river discharge conditions are further examined from the idealized
numerical model. We calculate the volume of freshwater VR
in the upstream area by dividing the model domain into twoparts using the section denoted by the dashed line in Fig. 14a.
The ratio of VR in the upstream area to that in the entire
domain is calculated for all the sensitivity experiments(Figs. 14b,c). In the situation with a tidal current amplitude of
0.1 m s21 (Fig. 14b), this ratio is smaller than 22.5% under thesouthward downstream ambient current, and decreases synchronously with the increasing of downstream ambient current(from 0 to 20.05 m s21). Under the northward upstream

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FIG. 13. (a),(b) Horizontal distribution of salinity (color) and residual current (arrow) and (c),(d) vertical
distribution of salinity along the section denoted by the blue line in (a) on (left) 11 Jun and (right) 26 Jun in case 1.
The black line in (a) and (b) shows the 25 isohaline of the bulge.

ambient current, this value increases with the speed of ambient
current (0–0.1 m s21), but is also dependent on river discharge.
For example, under the ambient current of 0.1 m s21, it is 75%
for the river discharge of 100 m3 s21, but becomes 50% for theriver discharge of 3000 m3 s21.
To define the upstream extension of plume, we specify acritical value of 50% that means half of freshwater distributing
in the upstream area. According to Fig. 14b, the river discharge
and the speed of upstream ambient current are closely linked
for the alternation of upstream and downstream extension of
the plume. There is a critical river discharge for a specificambient current. For example, the critical river discharge is3000 m3 s21 for an upstream ambient current of 0.1 m s21.
Under such ambient current (0.1 m s21), the river plume willturn upstream with a river discharge R less than the criticalriver discharge (R , 3000 m3 s21), but turn downstream if theriver discharge is larger than the critical river discharge (R .
3000 m3 s21).
As the tidal current amplitude increases to 1 m s21 (Fig. 14c),
the relation between the river discharge and the speed of upstream ambient current is kept for the upstream extension of
the plume. However, as compared to Fig. 14b, under the sameambient current (e.g., 0.1 m s21), the critical river dischargethat turns the river plume downstream decreases (2500 m3 s21).
Therefore, a strong tidal current is favorable to the downstream movement of rive plume due to strong tidal mixing,
which is consistent with previous reports (Isobe 2005).

According to these experiments, we want to find a thresholdriver discharge that changes the plume direction from upstream to downstream under a specified upstream ambient
current. Following the idea in Whitney and Garvine (2005)
who considered the competition between a buoyancy driven
current and a wind-driven current, we define a dimensionless
number Wd 5 Vdis/Vamb to consider the competition between
the buoyancy driven current Vdis and the upstream ambient
current Vamb.
The buoyancy driven current corresponding to a speci1/4
0fied river discharge are calculated by Vdis 5 (1/K)(2gr Qf )(Whitney and Garvine 2005), in which K is the internal Kelvin0
number (K 5 Ly/R), gr is the reduced gravity of river water0(gr 5 gDrr /ra , where Drr 5 ra 2 rr, ra is the ambient density
outside the plume, rr is the density of river water), Q is the riverdischarge, and f is the Coriolis parameter.
pﬃﬃﬃﬃﬃﬃﬃ Also, Ly is theacross-shore width of plume, R (R 5 g0 h/f ) is the internal
Rossby radius, g 0 is the reduced gravities of buoyant outflow(g 0 5 gDr/ra, where Dr 5 ra 2 r, r is the density inside theplume), and h is the plume depth. These parameters are derived from the idealized model result on the 25th day. For
example, when the river discharge is 1000 m3 s21 and the amplitude of tidal current is 0.1 m s21, Ly is 23 543 m, g0 is00.152 m s22, h is 5.8 m, R is 10 558 m, gr is 0.239 m s22, and thus
Vdis is 0.20 m s21.
For a specific river discharge, the plume can extend upstream or downstream under different ambient currents. We

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FIG. 14. (a) Model domain and bathymetry of the idealized numerical model. The percent of low-salinity water inthe upstream direction [denoted by the dashed line in (a)] under the condition of ambient current ranging from20.05 to 0.1 m s21 and river discharge varying from 100 to 3000 m3 s21 with the tidal amplitude of (b) 0.1 and(c) 1 m s21 around the river mouth. (d) The Wd variation with river discharge under different tidal current
amplitudes.

define Vamb as the critical ambient current corresponding to
50% of freshwater proportion in the upstream area (50% line
in Figs. 14b,c). For example, Vamb is 0.086 m s21 for the riverdischarge of 1000 m3 s21 in the case when the amplitude of tidal
current is 0.1 m s21.
Finally, we obtain the values of Wd for the river discharges
ranging from 100 to 3000 m 3 s21 in the cases with two different amplitudes of tidal current (Fig. 14d). When the tidal
mixing is weak, i.e., in the case with an amplitude of tidal
current as 0.1 m s21, Wd varies around ;2.5 after river discharge is larger than 500 m3 s21 (black line in Fig. 14d). As
the tidal mixing becomes stronger in the case with an amplitude of tidal current as 1 m s21, Wd becomes a little larger,
but decreases to ;2.5 after river discharge is larger than
700 m3 s 21 (red line in Fig. 14d). Therefore, the value of ;2.5
can be a critical number for the downstream buoyancy
driven current to overcome the upstream ambient current
and induce the river plume extension from upstream direction to downstream direction under a specific upstream
ambient current.

As for the Yellow River, the northward tide-induced residual current acts as the upstream ambient current in the idealized model. The tide-induced residual current north of the rivermouth is ;0.03 m s21 in spring tide. From the dimensionless
number Wd of ;2.5, we can infer that when the buoyancy
driven current is larger than ;0.08 m s21, the plume will turndownstream. We then modeled the Yellow River plume underriver discharges ranging from 100 to 1000 m3 s21 with an interval of 100 m3 s21. As an approximation to the buoyancy
driven current, we calculate the differences in residual current
between these cases and that in case 2, which are approximately 0.04, 0.05, 0.06, 0.07, 0.09, 0.10, 0.11, 0.11, 0.12, and0.13 m s21 around the river mouth in spring tide. Therefore,
according to the critical value of Wd, the plume will turn todownstream direction when the Yellow River discharge islarger than 500 m3 s21 and the buoyancy driven current aroundthe river mouth is larger than 0.08 m s21.
We then calculate the proportion of the freshwater volume in the upstream area (separated by a northward section
originated from the river mouth) in spring tide, which are

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FIG. 15. The variation in the proportion of freshwater volume inthe upstream area with the Yellow River discharge ranging from100 to 1000 m3 s21 with an interval of 100 m3 s21.

64%, 60%, 55%, 52%, 48%, 46%, 42%, 38%, 34%, and
29% for the cases with river discharge increased from 100
to 1000 m3 s21 with an interval of 100 m3 s21 (Fig. 15).
Apparently, the proportion of freshwater volume in the

VOLUME 51

upstream area decreases with the increasing of river discharge, which is consistent with the results of the idealized
model. Because of the temporal variations in ambient current (tide-induced residual current around the Yellow Rivermouth), we cannot obtain the exact values for the proportion of the freshwater volume in the upstream area as thosein the idealized model. However, the proportion becomes
smaller than 50% after the Yellow River discharge is larger
than 500 m3 s21, which is consistent with the river discharge
inferred from the Wd and suggest the application of Wd in
the Yellow River.
From above analysis, we also note that the effect of tide on
the river plume has two aspects. As mentioned in the introduction and indicated from the idealized model result, tidal
mixing plays an important role in prohibiting the upstream
extension of river plume. However, the tide-induced residual
current in the Yellow River, which plays a similar role as an
upstream ambient current in the idealized model, can promote
the upstream extension of the river plume. In the condition of
low Yellow River discharge, the role of tide-induced residual
current is more important than that of tidal mixing in springtide, which induces the upstream extension of the plume.
Moreover, under such specified tide-induced residual current,
there exists a critical Yellow River discharge that determines
the extension direction of the plume. As the Yellow River

FIG. 16. Horizontal distribution of sea surface salinity (color) and residual current (arrow) in (a) case 3, (b) case 4, and (c) case 5 on 11 Jun
and (d) case 6, (e) case 7, and (f) case 8 on 19 Jun.

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discharge is larger than the critical value, the plume turns
downstream.

c. Influence of summer wind on the upstream
extension of the plumeThe influences of tide and river discharge on the upstream
extension of the Yellow River plume have been presented in
sections 4a and 4b. Here, we examine the influence of winds on
the upstream extension of the Yellow River plume using cases
3–8 (Table 2).
Generally, the pattern of upstream extension of the
Yellow River plume in spring tide does not change under the
influence of southerly wind (Fig. 16a), southwesterly wind
(Fig. 16b), and northeasterly wind (Fig. 16c). In all threecases, the Yellow River plume still moves in upstream direction. Furthermore, the wind-induced residual current appears mainly outside the plume, which flows northeastward incases 3 and 4, and southwestward in case 5. Consequently,
summer wind has little influence on the upstream extension of
the Yellow River plume under the low river discharge condition in spring tide.
We also check the influence of the same three wind conditions on the river plume in neap tide (Figs. 16d–f). Results showthat the influence of wind on the plume is larger than that inspring tide. The low-salinity water is moved eastward by thesoutherly and southwesterly wind (Figs. 16d,e), and distributes
closely to the coast by the northeasterly wind (Fig. 16f).
Furthermore, the wind-driven currents inside the plume arealso stronger in neap tide than in spring tide due to the smaller
vertical eddy coefficient in neap tide and therefore reduction of
Ekman layer thickness.

d. General discussion on the upstream extensionof river plumes
As mentioned in the introduction, upstream extension of
the river plume has been frequently found in numericalsimulations (Chao and Boicourt 1986; Chapman and Lenz
1994; Kourafalou et al. 1996; Yankovsky and Chapman 1997;
Yankovsky 2000; Garvine 2001; Guo and Valle-Levison 2007;
Matano and Palma 2010; Wu et al. 2011). Different mechanisms have been proposed, including model configuration(Yankovsky 2000; Garvine 2001), geostrophic adjustment(Chapman and Lenz 1994; Matano and Palma 2010), andnongeostrophic acceleration (Kourafalou et al. 1996). Tide
has been considered as an important effect to restrict the
upstream extension of the river plumes (Isobe 2005; Guo andValle-Levison 2007; Wu et al. 2011). In both the Chesapeake
Bay (Guo and Valle-Levison 2007) and Changjiang River(Wu et al. 2011), the plumes extend upstream in the numerical experiment without tide, but turn downstream when thetide is considered.
However, in our study, the strong tidal current has the effectto promote the upstream extension of the Yellow River plumeunder low river discharge condition. The strong tidal current
in spring tide intensifies the upstream tide-induced residual
current, and the strong tidal mixing weakens the downstream density-driven current. The combination of weakened
downstream density-driven current and intensified upstream

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tide-induced residual current promotes the upstream extensionof the plume in spring tide under low river discharge condition.
The opposite situation occurs in neap tide when the plumemoves in the downstream direction. It must be noted that suchtransition from spring tide to neap tide cannot be maintained
under high river discharge condition when the tidal mixing andtide-induced residual current cannot compete with the buoyancy effect given by the river discharge.
Although these points are specific to our study area, they are
different from the previous understanding on the effects of tide
on river plume (Isobe 2005; Guo and Valle-Levison 2007; Wu
et al. 2011). Furthermore, tide-induced residual current has
been reported in many coastal regions, such as the East China
Sea (Tang 1988), the North Sea (Lwiza et al. 1991), and theSeto Inland Sea (Chang et al. 2009). In the regions of riverwater influence, coastline and bathymetry usually change
largely, which is favorable to the generation of tide-induced
residual current, which, as shown in this study, probably influences the river plume as an ambient current. Therefore, it isnecessary to put this mechanism in mind when examining the
behavior of river plume in a tide-dominated area with a largely
changed coastline or bathymetry.

5. Conclusions
Both the hydrographic data and modeling results show that
the Yellow River plume propagates upstream under the low
river discharge condition in summer, but turns downstream
under the high river discharge condition. The numerical experiments demonstrate that the upstream extension under the
low river discharge condition has significant spring and neap
tidal variations. In spring tide, the Yellow River plume extends
in the upstream direction, whereas in neap tide, the plume
propagates in the downstream direction. Freshwater volumetransport analysis shows that the different transport of freshwater in spring tide and neap tide are mainly contributed by thesubtidal process. The strong (weak) northward tide-induced
residual current and the weak (strong) southward densitydriven current cause the upstream (downstream) extension of
the plume in spring (neap) tide. Momentum analysis confirms
the important roles of advection term and viscosity term in thecondition of low river discharge. Therefore, both the tideinduced residual current and tidal mixing are important for the
upstream extension of the Yellow River plume under low riverdischarge condition. Summer wind has little influence on the
upstream extension of the Yellow River plume in spring tide,whereas its influence on the plume in neap tide is a little
stronger.
River discharge can change the upstream extension of the
Yellow River plume, which turns downstream when the riverdischarge increases. The upstream tide-induced residual current cannot compete with the downstream density-driven
current and the plume consequently turns downstream.
Momentum balance demonstrates that the Yellow River
plume in the high river discharge condition is controlled mainly
by a geostrophic balance. An idealized model study suggeststhat a dimensionless number of ;2.5, the ratio of buoyancy
driven current to upstream ambient current, can be used to

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know the river discharge that changes the plume extension
from upstream to downstream under a specific upstream ambient current.
This study emphasizes the importance of tide and river discharge on the river plume. Differing from previous studies,
which suggested that tide can prohibit the upstream extensionof river plume, our study find that tide can promote the upstream extension of the plume. Therefore, the effect andmechanism of tide on the river plume should be examined caseby case. On the other hand, the river discharge can also influence the extension of the river plume. As the river discharge islarge enough, it can overcome the effect of an upstream ambient current and turn the plume downstream.
Acknowledgments. The authors thank the two anonymous
reviewers for their helpful suggestions on original manuscript.
This study was supported by the National Natural Science
Foundation of China (41906010), the National Natural Science
Foundation of China-Shandong Joint Fund (U1906215,
U1806211), the Postdoctoral Research Foundation of China(2018M642701). X. Guo thanks support from the Fundamental
Research Funds for Central Universities of the Ministry of
Education of China (201512004). T. Zou thanks support fromthe National Natural Science Foundation of China (41406029).
We also thank support from the Youth Foundation of the
Shandong Academy of Sciences (2019QN0026).
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