JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, C11006, doi:10.1029/2012JC008263, 2012

The age of Yellow River water in the Bohai Sea
Zhe Liu,1 Haiyan Wang,1,2 Xinyu Guo,2 Qiang Wang,3 and Huiwang Gao1
Received 6 June 2012; revised 10 September 2012; accepted 21 September 2012; published 8 November 2012.

[1] To quantitatively understand the transport timescales of dissolved material
discharged from large rivers into a semienclosed sea, the age of Yellow River water inthe Bohai Sea was calculated with the constituent-oriented age and residence time theory(CART) and particle-tracking method. Yellow River water has a mean age of 3.0 years
for the entire Bohai Sea. The spatial variation of the water age is significant: 1.2 years near
the Yellow River estuary but 3.9 years in the Liaodong Bay. However, the temporalvariation in water age is insignificant. The water particles released at the river mouthneed only several days to reach the estuary area. The great water age (1.2 years) near the
Yellow River estuary is caused by the presence of old water particles that initially left
this area but returned to this area again. Without the reentry of Yellow River water from the
Yellow Sea to the Bohai Sea, the mean age of Yellow River water in the entire Bohai Sea
decreases to 1.2 years. Calculations without tidal forcing give a reduction in water age
by more than 50%, suggesting that tidal forcing plays the most dominant role in controllingthe age of Yellow River water in the Bohai Sea. Calculations without winds give an
increase in water age by 20–30%, suggesting that wind forcing is secondary factor to theage of Yellow River water. Changes in discharge of the Yellow River and in thermal
stratification have limited influence on the age of Yellow River water.
Citation: Liu, Z., H. Wang, X. Guo, Q. Wang, and H. Gao (2012), The age of Yellow River water in the Bohai Sea,
J. Geophys. Res., 117, C11006, doi:10.1029/2012JC008263.

1. Introduction[2] Advection and diffusion are two important processes
controlling material transport in coastal water. Because of
the complex spatiotemporal structure of these processes, it is
helpful to define auxiliary variables, such as water exchange
timescale and water age, to quantify their environmental
function in coastal water [Zimmerman, 1976; Takeoka, 1984;
Deleersnijder et al., 2001; Monsen et al., 2002; Delhez et al.,2004].
[3] Water age is defined as the time elapsed since thedeparture of a water parcel from an area, where its age isprescribed to be 0, to its arrival at a water body of interest[Bolin and Rodhe, 1973; Takeoka, 1984]. Transit time is theage of a water parcel at the outlet of a water body [Bolin andRodhe, 1973]. Transit time may be considered as a special
case of water age.
[4] Previous studies [Meier, 2007; Shen and Wang, 2007;
Gong et al., 2009; Zhang et al., 2010a] on water age have
1
Key Laboratory of Marine Environment and Ecology, Ocean
University of China, Ministry of Education, Qingdao, China.
2Center for Marine Environmental Studies, Ehime University, Matsuyama,
Japan.
3
North China Sea Marine Forecasting Center of State Oceanic Administration,
Qingdao, China.

Corresponding author: X. Guo, Center for Marine Environmental
Studies, Ehime University, 2-5 Bunkyo-Cho, Matsuyama 790-8577, Japan.
(guoxinyu@sci.ehime-u.ac.jp)©2012. American Geophysical Union. All Rights Reserved.
0148-0227/12/2012JC008263

typically used the concept of mean water age, which isdefined as the mass-weighted arithmetic average of the agesof all of the water parcels within a target domain. In principle, diffusion results in the complexity of water age structure. Without diffusion, the water particles inside a parcel are
isolated from the outside environment and therefore have thesame age. However, diffusion induces the exchange of particles inside and outside of the water parcel and consequently results in the coexistence of water particles withdifferent ages in a water parcel. In practice, the size of thegrid points in a numerical model cannot be infinitely small,and commonly, water parcels of different ages are found at
one grid point together. In this study, we also used theconcept of mean water age. Additionally, to better understand water age distribution, we also present a water age
frequency/spectrum for a target domain.
[5] Water age can be studied by field observations, theoretical analysis, and numerical simulation. Observational
techniques, including the isotope-tracer decaying method
and the lag time method, are widely used to measure meanwater age [e.g., Adkins and Boyle, 1997; Peeters et al., 2000;
Hansell et al., 2004; Kershaw et al., 2004; Anderson et al.,2010]. However, these methods may underestimate the true
mean water age if diffusion is considered [Deleersnijder
et al., 2001; Delhez et al., 2003; Delhez and Deleersnijder,2008]. Theoretical analysis is helpful for understanding
mean water age [e.g., Wunsch, 2002] because instructive
analytical solutions may be obtained. However, theoreticalanalysis is typically not sufficiently powerful when realistic
topography or nonlinear terms are considered. Compared to

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Figure 1. Bathymetry of the Bohai Sea and the Yellow Sea (unit: meter). The Bohai Sea is divided into
5 subregions: Laizhou Bay (LZB), Bohai Bay (BHB), Liaodong Bay (LDB), the central basin (CB), andBohai Strait (BS). The black dots represent the locations of the river mouths of the Yellow River, Haihe
River, Luanhe River, Liaohe River, and Yalu River. The black squares represent the location of Lijin
Station, where the Yellow River discharge is recorded. The Yellow River estuary (3  3 grids) is definedas the area surrounded by the blue line close to the Yellow River mouth. The black lines labeled with OB1
and OB2 are two open boundaries.
the aforementioned methods, numerical simulation includes
advection and diffusion processes in addition to realistic topography and forcing conditions [Chen, 2007; Liu et al., 2008;
Gong et al., 2009; Hong et al., 2010; Liu et al., 2011; de Bryeet al., 2012].
[6] There are two widely used numerical methods for calculating mean water age. One method is the particle-tracking
method (PTM) [Chen, 2007; Liu et al., 2011], and the othermethod is the constituent-oriented age and residence time
theory (CART, see www.climate.be/cart) [Deleersnijder et al.,
2001; Gong et al., 2009; de Brye et al., 2012]. These two
methods are essentially equivalent, although their simulation
results are not identical in practice. PTM is a Lagrangian
method and has the advantage of obtaining a spectrum ofwater age and the pathway of water parcels. However, thecomputational cost of PTM is high because a large amount ofparticles must be released to simulate the random walk due todiffusion. CART is a Eulerian method and has the advantage
of directly calculating mean water age without needing to know
the spectrum of water age in advance, although it is possible touse CART to obtain a spectrum of water age [Delhez andDeleersnijder, 2002; Zhang et al., 2010a; Cornaton, 2012].
However, the CART method cannot provide information on
the pathway of target water mass.
[7] The Yellow River is the largest river that feeds into the
Bohai Sea (Figure 1). The river brings freshwater, sediment[Fan and Huang, 2008], nutrients [Yang et al., 2009], andpersistent organic pollutants (POPs) [Sha et al., 2006] into
the sea. The Bohai Sea has an average depth of 18 m and isusually divided into 5 subregions, namely Laizhou Bay,
Bohai Bay, Liaodong Bay, the central basin, and the Bohai
Strait (Figure 1). Many studies have investigated the waterexchange between the Bohai Sea and the Yellow Sea throughthe Bohai Strait [e.g., Lin et al., 2002; Wei et al., 2003; Zhang
et al., 2010b]. The half-life time, which is defined as thenecessary time for the concentration of passive matter
reducing to 50% of its initial value [Luff and Pohlmann,
1996], was used as an index to evaluate the water exchange
capacity of the Bohai Sea [Wei et al., 2002]. However, no
study has considered the age of Yellow River water in the
Bohai Sea.
[8] In this study, the age of Yellow River water is definedas the time elapsed since the river water leaves the rivermouth, and the transit time of Yellow River water is water
age at the Bohai Strait, which is the sole outlet of Yellow
River water into the Yellow Sea. We use CART to obtain themean age of Yellow River water and to examine the processes controlling the mean water age; we use PTM to calculate the pathway of Yellow River water and the spectrumof water age.
[9] Mean water age in a target domain is influenced by the
return of water parcels that once left the target domain andstayed outside the target domain for a significant amount oftime. To consider the contribution of returned water parcels
to mean water age, we set open boundary for water age
calculations far from the target domain. Furthermore, we
compare the results of two calculations with and without
return of water parcels to the target domain for a quantitative
demonstration on the role of returned water parcels.
[10] The paper is organized as follows. Section 2 describes
the configuration of the hydrodynamic model and the calculation of water age. In section 3, we present the water age,transit time, age spectrum, and particle pathway results.
In section 4, we discuss the effects of nonreturning water and

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LIU ET AL.: AGE OF YELLOW RIVER WATER

C11006of several dynamic factors on water age. In section 5, wesummarize the entire study.

2. Model Description
2.1. Hydrodynamic Model[11] The hydrodynamic model used in this study is basedon the Princeton Ocean Model [Mellor, 2004]. This model
was initially developed by Guo et al. [2003] and has been
applied by Wang et al. [2008] to study the Yellow River
plume. The horizontal resolution was 1/18 degree in both
the zonal and meridional directions. In the vertical direction,
21 sigma levels were distributed. The time step was 9 s forthe external mode and 360 s for the internal mode.
[12] The hydrodynamic model was designed to reproduce theclimatological state with seasonal variations and was therefore
driven by monthly winds, monthly heat flux, monthly precipitation and evaporation rates, monthly river discharges from allof the rivers inside the model domain (Figure 1), monthly volume transports, and tidal forcing along all of the open boundaries. The monthly mean is defined at middle of each month anda linear interpolation from two monthly mean values was used
to obtain the value at a given time step between them. A fulldescription and validation of the hydrodynamic model has beenpresented by Wang et al. [2008]. For subsequent use in CART
and PTM calculations, we saved data regarding the sea level,
the three velocity components, and the horizontal and vertical
diffusivity coefficients for 1 year at an interval of 30 min.
2.2. Mean Water Age Calculation by CART
[13] To calculate water age using CART [Deleersnijder
et al., 2001], two equations were solved for the concentration of Yellow River water, which is treated as a passive
tracer and whose concentration ranges from 0 to unity in thedomain of interest, and age concentration of Yellow River
water a(t, x, y, z). The concentration of Yellow River waterC(t, x, y, z) was controlled by equation (1).
  ∂ðwC Þ
∂C
∂
∂C
!
þ rH  uC þ
 rH  ðKH rC Þ 
KV
¼ 0:
∂t
∂z
∂z
∂z
ð1Þ

[14] In this equation, t is time; x, y, z are three coordinates!
in space; u is the vector for two horizontal velocities; w is thevertical velocity; KH is the horizontal diffusivity coefficient;!
!
KV is the vertical diffusivity coefficient; and rH = i ∂x∂ + j ∂y∂ .
[15] The age concentration of Yellow River a(t, x, y, z)
was calculated by equation (2); the right-hand side of theequation consists of the concentration of Yellow River waterC(t, x, y, z).
  ∂ðwaÞ
∂a∂∂a!
þ rH  ua þ rH  ðKH raÞ 
KV
¼ C:
∂t
∂z
∂z
∂z
ð2Þ

[16] The age of Yellow River water a(t, x, y, z) was calculated as the ratio of the age concentration a and the concentration C of Yellow River water [Deleersnijder et al., 2001].
a ¼ a=C:

ð3Þ

C11006[17] A conversion from the z coordinate to the sigma
coordinate system used in Princeton Ocean Model (POM) is
necessary for the above equations. Because the conversion isexactly the same as equations for water temperature andsalinity, which can be found in Mellor [2004], we do notpresent them here.
[18] We developed new modules to solve equations (1)and (2) by referring to those for water temperature andsalinity in the POM. Because it is difficult to directly measure water age in an ocean to verify the calculated water age,
we used three analytical solutions for water age to check ourmodules that solve for equations (1) and (2). The first solution is for a spatially homogeneous, steady flow in a onedimensional channel. According to Deleersnijder et al. [2001],
the horizontal distribution of age in such a channel can be
described by x/u in which x is the distance to the source of thetarget water and u is the flow speed. This solution should
check the module that solves for advection process. A second
solution is designed to check the module that solves for thevertical diffusion process. The analytical solution for vertical
distribution of age in the water column of a material from thesea surface is given by equation (A11) in Appendix A. A third
solution is for water age in presence of both horizontal advection and horizontal diffusion in an one-dimensional space[Deleersnijder and Delhez, 2004]. This solution is used tocheck the module that solves for the horizontal diffusion. As
shown in Figures A1 and A2 in Appendix A, the numericalsolutions from our modules agree well with their corresponding
analytical solutions. Hence, we concluded that the new modules
used in this study for solving equations (1) and (2) are reliable.
[19] The model domain (Figure 1) for water age covers thecontrol volume (Bohai Sea) and its outer sea (Yellow Sea). We
set two open boundaries (OB1 and OB2 in Figure 1) in themodel domain. OB1 is at the Bohai Strait and is designed for
only one sensitivity simulation in which Yellow River wateroutside the Bohai Sea is not allowed to return to the Bohai Sea
across OB1. OB2 is for normal simulations in which Yellow
River water outside the Bohai Sea is allowed to return to the
Bohai Sea, but water outside the model domain was neverallowed to return to the model domain. The exact treatments of
the open boundary are as follows. If there is an outflow at theinterior gird point next to the open boundary, the concentration
C and age concentration of Yellow River water a at the open
boundary were set to those at the interior gird point. If there isan inflow at the interior gird point next to the open boundary,
the concentration C and age concentration of Yellow River
water a at the open boundary were set to 0.
[20] The concentration C and age concentration of Yellow
River water a at a grid point at a river mouth was set to 1
and 0, respectively, throughout the calculation of CART. The
initial values of the concentration C and age concentration of
Yellow River water a inside the model domain were set to 0.
The time step for solving equations (1) and (2) was 30 min,which is the same as the time interval for saving velocity anddiffusivity coefficient data from the hydrodynamic model.
The integration time for the CART calculation was 31 years,
during which the saved velocities and diffusivity coefficientswere repeated at the same time each year.
2.3. PTM Model[21] To study the frequency distribution of water age, thePTM module [Zhang, 1995] in the estuarine and coastal ocean

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LIU ET AL.: AGE OF YELLOW RIVER WATER

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Figure 2. Vertically averaged concentration of Yellow
River water (equals 1 at the river mouth) in (a) February,(b) May, (c) August, and (d) November. The concentration
inside each panel has been multiplied by a factor of 100.
The contour interval is 1.

model coupled with a sediment transport module (ECOMSED)[Blumberg, 2002] was implemented. The position of a particle
in this module is determined by two parts: a component representing advection and a random component representing diffusion. The calculation domain for the PTM module is the sameas that for water age (Figure 1). When a particle attempts tocross a land boundary, sea surface, or sea bottom, it is set toreflect back into the calculation domain. Consequently, a particle disappears from the model domain only when it flows out
from the open boundary (OB2).
[22] A new group of particles was released at the Yellow
River mouth every 30 min for only the first year of the PTM
calculation. The total time for the PTM calculation was
31 years. One particle was set to represent a volume of 3.6 
104 m3 of Yellow River freshwater, and the total numberof particles released in 1 day was determined by the daily
Yellow River discharge for that day. When a particle wasreleased, its age was set to 0. Subsequently, the particle age
was updated at every time step until it reached OB2, where
the particle was discarded. Consequently, the particle canfreely pass through the Bohai Strait regardless of which
direction it moved.
[23] Given a target region, the age frequency distributionfunction or age spectrum j(t, t) is defined by equation (4)[Bolin and Rodhe, 1973].
jðt; t Þ ¼

1 dM ðt; t Þ;
M0 ð t Þdtð4Þ

where M0(t) is the total number of particles at time t in a target
region; M(t, t) is the total number of the particles less thanor equal to an age t at time t in the target region. Notably,

C11006the original definition of the age frequency distribution function by Bolin and Rodhe [1973] applies to a steady case andis not a function of time t. Here, we applied the same idea to a
field with seasonal variations and therefore assumed the age
frequency distribution as a function of time t.
[24] We recorded the position of all of the particles
released in the first year at each time step during the 31 years
of calculation. For calculating the age frequency distributionfunction, we need the pathways of the particles released not
only in the first year, but also those in the second year andsucceeding years. Based on the fact that the velocity field anddiffusivity coefficients used for the PTM calculation wererepeated at the same time every year, we assumed that theparticles released in the second year and succeeding years
have the same pathways as those released in the first year.
The only difference is in the ages of the particles. In thismanner, we obtained the pathways of the particles released
after the second year without additional PTM calculations.
By counting the particle number defined by equation (4), we
obtained the age frequency distribution function of Yellow
River water in the target region.

3. Results
3.1. Age of Yellow River Water in the Bohai Sea[25] The horizontal distribution of vertically averaged
concentration of Yellow River water C demonstrates adecreasing trend throughout the year in the following order:
Laizhou Bay, Bohai Bay, the central basin, Liaodong Bay,and Bohai Strait (Figure 2). Inside the Laizhou Bay, theconcentration is higher in the western side than in the easternside, which reveals an inverse correlation with salinity
described by Wang et al. [2008]. A concentration front forms
along the western coast of the Laizhou Bay where a salinity
front also forms [Wang et al., 2008]. The inverse relationshipexists because most freshwater in the Laizhou Bay originatesfrom the Yellow River. In contrast, the concentration C does
not demonstrate an inverse relationship with salinity in the
Liaodong Bay, where freshwater primarily originates fromthe Liaohe River, not from the Yellow River.
[26] The seasonal variation in the distribution of concentration of Yellow River water is mostly found in the Laizhou
Bay and the central basin of the Bohai Sea. In the offshore areaof the Yellow River mouth, a northeastward spreading area ofhigh concentration occurs in August, which is consistent withlow-salinity water movement due to southeasterly winds [Wanget al., 2008]. In November, the high concentration area moves
to the southwestern area of the Laizhou Bay, corresponding
again to low-salinity area movement that is caused by the winddriven current along the coast of the Laizhou Bay [Wang et al.,2008].
[27] The age of Yellow River water is small at the offshore
area of the Yellow River and increases in proportion to the
distance away from the Yellow River mouth (Figure 3). The
volume-averaged annual age is 615 days for the Laizhou Bay,969 days for the Bohai Bay, 1101 days for the central basin,
and 1427 days for the Liaodong Bay (Table 1a). In general,
there is an inverse relationship between age (Figure 3) andconcentration of Yellow River water (Figure 2). The exception is at the Bohai Strait where the concentration is lowest(Figure 2) but the age is not greatest (Figure 3). Water

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Table 1a. Volume-Averaged Age of Yellow River Water in the
Bohai Sea and Subregions From Calculation With Boundary OB2a
Subregions

February

May

AugustNovember

AnnualBohai Sea
Laizhou Bay
Bohai Bay
Central Basin
Liaodong Bay
Bohai Strait

1079
571
997
1114
1427
1236

1125
731
984
1124
1444
1238

1101
732
986
1082
1422
1207

1024
500
914
1075
1415
1273

1082
615
969
1101
1427
1240

a

Units are days.

River water through the Bohai Strait (x = x0) were calculated
from the conservative matter concentration C.
VYR ¼

1
T

ZT ZZZC ðx; y; z; t Þdxdydzdt;
0

ð5Þ

Vol

8
ZZ
>

IN
>
ð
x
Þ
¼
fYR
ðx0 ; y; zÞdydz
F
>
0
YR
>
>
<
A
ZZ
;
>
>
þ
OUT
>
F
ð
x
Þ
¼
f
ð
x
;
y;
z
Þdydz
0
>
YR 0
>
: YR

Figure 3. Vertically averaged age of Yellow River water(unit: days) in (a) February, (b) May, (c) August, and(d) November. The contour interval is 100 days.

ð6Þ

A

exchange with the Yellow Sea likely affects the age of Yellow River water in that area.
[28] A front of water age is found offshore of the Yellow
River mouth and presents an apparent seasonal variation(Figure 3). This variation induces a relatively large seasonalvariation in volume-averaged ages of the Laizhou Bay(Table 1a). According to Table 1a, the range of seasonalvariation for volume-averaged age is 232 days for the
Laizhou Bay, 83 days for the Bohai Bay, 49 days for thecentral basin, and 29 days for the Liaodong Bay. The ratio of
seasonal variation range to annual age is 0.38, 0.09, 0.04,
and 0.02 for the Laizhou Bay, Bohai Bay, central basin, andLiaodong bay, respectively. If we treat the Bohai Sea as
one water body, its volume-averaged age is 1082 days witha seasonal variation range of 101 days (Table 1a), whichindicates weak seasonal variation (101/1082 = 0.09).
[29] The vertical variation in the concentration and age of
Yellow River water is small except for the area close to the
Yellow River mouth (figure not shown). As presented in
Figure 3 and Table 1a, the age of Yellow River water is on
the order of more than 1 year. With such time scale, tidal
mixing and wind mixing (especially in winter) easily produce a vertically homogenous distribution in concentration
and water age in the Bohai Sea.
3.2. Budget and Transit Time of Yellow
River Water in the Bohai Sea[30] Because the Bohai Sea has only one outlet (the Bohai
Strait) connecting with another water body (the Yellow Sea),
the freshwater and water age budget associated with waterexchange through the Bohai Strait is one of the key factors tounderstanding the mean age of Yellow River water in the
Bohai Sea (Figure 4).
[31] The annually averaged volume of Yellow River water
inside the Bohai Sea (VYR), the annually averaged inflow
IN
OUT
(FYR
(x0)) and outflow (FYR(x0)) volume transports of Yellow( 
fYR ðx0 ; y; zÞ ¼ fYR ðx0 ; y; zÞ if fYR ðx0 ; y; zÞ < 0þ
ðx0 ; y; zÞ ¼ fYR ðx0 ; y; zÞ if fYR ðx0 ; y; zÞ > 0
fYR

;

ð7Þ

ZT
fYR ðx0 ; y; zÞ ¼

uðx0 ; y; z; t ÞC ðx0 ; y; z; t Þdt:ð8Þ0[32] Here, T denotes the integral time (set to 1 year in thiscase); Vol the volume integral over the entire Bohai Sea;
A the area integral over the entire section across the Bohai
Strait; fYR(x0, y, z) the annually averaged Yellow River flux
at a grid point in which negative fYR(x0, y, z) contributes toinflow transport FIN
YR, whereas positive fYR(x0, y, z) conOUT
tributes to outflow transport FYR. The bar  in equation (8)denotes the procedure of detiding.
[33] The annually averaged volume of Yellow River water
inside the Bohai Sea (VYR) is 6.3  1010 m3 (Figure 4a),which occupies 4.3% of the total water volume in the Bohai
Sea (= a mean conservative matter concentration of 0.043
for the entire Bohai Sea). Every year, approximately 2.0 1010 m3 of Yellow River water is discharged into the Bohai

Table 1b. Volume-Averaged Age of Yellow River Water in the
Bohai Sea and Subregions From Calculation With Boundary OB1a
Subregions

February

May

AugustNovember

AnnualBohai Sea
Laizhou Bay
Bohai Bay
Central Basin
Liaodong Bay
Bohai Strait

420
214
450
427
708
348

463
284
447
451
723
457

441
250
445
420
706
411

378
166
398
399
702
421

424
218
434
426
710
393

5 of 19aUnits are days.

LIU ET AL.: AGE OF YELLOW RIVER WATER

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Figure 4. Budgets of (a) the Yellow River water and (b) its age concentration in the Bohai Sea. VBohai isvolume of the Bohai Sea. See section 3.2 for the definition and calculation methods of the other variables.
Sea from the river. However, approximately 6.0  1010 m3
of Yellow River water is transported out of the Bohai Sea
through the Bohai Strait, while approximately 4.0  1010 m3
of Yellow River water is transported into the Bohai Sea
through the strait. Therefore, the amount of returned old
Yellow River water from the Yellow Sea to the Bohai Sea
is twice that of the newly discharged river water from the
Yellow River mouth to the Bohai Sea. As shown later, such
returned old river water has an apparent influence on meanwater age of Yellow River water in the Bohai Sea.
[34] Similarly, we calculated the annually averaged age
concentration of Yellow River water inside the Bohai Sea(y YR), annually averaged Yellow River water inflow transOUT
port (PIN
YR(x0)) and outflow transport (PYR (x0)) through the
Bohai Strait by the following equations.
1y YR ¼T

ZTZZZ
aðx; y; z; t Þdxdydzdt;

ð9Þ

0 Vol

8
ZZ
>
IN
>
ð
x
Þ
¼
p
P
>
0
YR ðx0 ; y; zÞdydz
YR
>
>
<
A
ZZ
;
>
>
þ
OUT
>
P
ð
x
Þ
¼
p
ð
x
;
y;
z
Þdydz
0
>
YR 0
>
: YR

ð10Þ

A

( 
pYR ðx0 ; y; zÞ ¼ pYR ðx0 ; y; zÞ if pYR ðx0 ; y; zÞ < 0pþ
YR ðx0 ; y; zÞ ¼ pYR ðx0 ; y; zÞ if pYR ðx0 ; y; zÞ > 0

;

ð11Þ

ZT
pYR ðx0 ; y; zÞ ¼

uðx0 ; y; z; t Þaðx0 ; y; z; t Þdt:0ð12Þ[35] The transport of age concentration from the Yellow
River to the Bohai Sea is 0 because the age of Yellow River
water inside the river is 0 (Figure 4b). The annual transportof age concentration through the Bohai Strait into the Bohai
Sea is approximately 5.0  1013 m3 d and that out of theBohai Sea is approximately 7.0  1013 m3 d. The difference
between the two flows (approximately 2.0  1013 m3 d)
indicates an export of age concentration from the Bohai
Sea to the Yellow Sea. Clearly, Yellow River water inside
the Bohai Sea naturally increases by 1 year after a durationof 1 year. The net export of age concentration through the
Bohai Strait to the Yellow Sea is nearly balanced with theincreased 1 year of age concentration inside the Bohai Sea(approximately 2.3  1013 m3 d = multiplying 365 daysby the volume of Yellow River water inside the Bohai Sea[6.3  1010 m3]).
[36] The annual volume-integrated age concentration of
Yellow River water inside the Bohai Sea (y YR) is 6.8 1013 m3 d. Dividing this concentration by the volume of
Yellow River water inside the Bohai Sea (6.3  1010 m3)
gives a mean age of Yellow River water of 1079 days, which
is close to the 1082 days given in Table 1a.
[37] As stated in section 1, the age at the outlet of a control
volume is regarded as transit time. The calculated transit
time at the Bohai Strait is lower at the southern side than at
the northern side throughout a year (Figure 5). A general
understanding of the current patterns through the Bohai
Strait consists of an inflow in the northern area and an outflow in the southern area [Miao and Liu, 1988; Huang et al.,
1998; Zhao and Cao, 1998; Huang et al., 1999; Wei et al.,2003]. According to Figure 5, the inflow carries old riverwater, but the outflow carries young river water.
[38] The difference of water age from north to south at theBohai Strait depends on the season (Figure 5). The difference reaches a maximum (approximately 430 days) in winterwhen the minimum water age (approximately 960 days) and

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Figure 5. Vertical distribution of the age of Yellow River
water (unit: days) in the Bohai Strait in (a) February, (b) May,(c) August, and (d) November. The contour interval is 50 days.
Maximum value, minimum value, and mean value at the section
are given in each panel.
maximum water age (approximately 1390 days) in a year
appear in the southern area and northern areas, respectively.
Yellow River water is transported out of the Bohai Strait
in winter by the wind-driven coastal current along theLaizhou Bay [Wang et al., 2008]. The age difference acrossthe strait is at a minimum (approximately 180 days) insummer when the age in the southern area increases toapproximately 1090 day and that in the northern area
decreases to approximately 1270 days. Yellow River water
is transported northeastward from the river mouth to thecentral basin in summer and cannot reach the strait [Wanget al., 2008].
3.3. Movement of Particles[39] Because the daily number of particles released at theriver mouth in the PTM calculation was proportional to riverdischarge, its seasonal variation is apparent (Figure 6a). The
total number of particles released in a year is 5.5  105(Figure 6a), most of which stays inside the Bohai Sea in thefirst year (black line in Figure 6b). The total particle number
inside the Bohai Sea (Figure 6b) reaches a maximum at theend of the first year, decreases sharply in the winter andspring, and keeps nearly stable in the next summer andautumn. The sharp reduction in total particle number inside
the Bohai Sea in the winter and spring was resulted from theflowing out of numerous particles through the Bohai Strait
that is the only exit of particles leaving the Bohai Sea.
[40] To confirm the reentry of particles, we flagged eachparticle and counted the number of times that the particle
reentered the Bohai Sea. According to Figure 6b, the portionof particles not reentering (N = 0 in Figure 6b) decreases
with time after the first year. In contrast, the particles reentering once (N = 1 in Figure 6b) or more than once (N > 1 inFigure 6b) increases with time in the first several years anddecreases again after get its peak. The stable total particle
number in summer and autumn (black line in Figure 6b) was

C11006

resulted from combined effects of the returning of particles
to the Bohai Sea from the Yellow Sea (N = 1 in Figure 6b)
and the flowing out of particles from the Bohai Sea to the
Yellow Sea (N = 0 in Figure 6b).
[41] We present the horizontal distribution of particle
number in the water column (= sum of particle number frombottom to surface) at day 46 (Figure 7) and day 228 (Figure 8)of the fourth year of PTM calculation. Day 46 was chosenbecause it represents a typical situation when particles flowout of the Bohai Sea. Day 228 was chosen because it represents a typical situation when particles flow into the Bohai
Sea again. At day 46 (Figure 7), many particles distributeclosely to the Bohai Strait (Figure 7a) and easily flow out of
the Bohai Strait. The pathway of outflow is located on thesouthern side of the strait, as demonstrated by the distributionof particles with 0 times of reentry (Figures 7b). At day 228(Figure 8), in addition to amount of particles in the area close
to river mouth, a large number of particles distribute in
the northern part of the Bohai Strait and Liaodong Bay(Figure 8a). The particles in the northern part of the Bohai
Strait and Liaodong Bay are those reentering the Bohai Sea(Figures 8c and 8d).
3.4. Age Frequency Distribution[42] As shown in Figures 7 and 8, the particles inside theBohai Sea have different trajectory histories. Consequently,
the particles located at one grid point at a given time may havedifferent water age. An age spectrum (age frequency distribution) defined by equation (4) may be used to describe theage composition at a given area. Here, we focus on the Yellow
River estuary (see Figure 1 for the area definition) and theBohai Strait. The first area is where Yellow River water entersand concentrates in the Bohai Sea, and the latter area is where
Yellow River water leaves the Bohai Sea. As an example, we
present the age spectrum at day 46 at the estuary (Figure 9a)
and at the Bohai Strait (Figure 10a) that were calculated byequation (4) from the results of the PTM calculation in the lastyear when the composition of particles is annually repeatable.
We also present the age spectrums, daily ages, and particle
number during 1 year at the estuary (Figures 9c and 9e) and at
the Bohai Strait (Figures 10c and 10e).
[43] There is one major peak of frequency at approximately 0 in the age spectrum for the Yellow River estuary at
day 46 (Figure 9a). This peak corresponds to the young
freshwater that spreads into this area from the Yellow Rivermouth after several days. In addition to these young particles, we can also identify the presence of old particles thathave an age more than half year and even several years(Figure 9a). The frequency of old particles is low but the
total number of old particles is not low because they have awide distribution of age.
[44] Figure 9c is the extension of results at day 46 to
1 year. The presence of young water with an age ofapproximately 0 can be confirmed throughout the year
(Figure 9c). The percentage of this young water keeps large
from day 80 to day 130, becomes much smaller from day
140 to day 200, and becomes larger again from day
210 to day 330 (Figure 9c).
[45] The daily particle number and water age in the estuarychanges largely during a year (Figure 9e). The increasing ofparticle number before day 90 and before day 210 areaccompanied by decreasing of water age, indicating coming of

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Figure 6. (a) Daily number (red line) and accumulative number (black line) of particles released at theriver mouth in the first year. The range for daily number is given at left axis while that for accumulative
number is at right axis. (b) Number of all particles (black line) inside the Bohai Sea and that of particles(color lines) experiencing reentry process into the Bohai Sea during the first 10 years of the PTM calculation. N represents the reentry times. The ranges for N = 1, N = 2, N = 3, N = 4, and N > 4 are given at left
axis while the ranges for total number and N = 0 are at right axis. (c) The same as Figure 6b but for thecase without tidal forcing (Case 1). (d) The same as Figure 6b but for the case without winds (Case 4).
newly released particles from the river mouth. However, thepeaks of particle number around day 160 and day 280 areaccompanied by increasing of water age, indicating little
influence of newly released particles from the river mouth but
great influence of particles returned to the estuary from area
outside the estuary. The daily particle number and water age atthe estuary (Figure 9e) gives an annual mean age of Yellow
River water as 445 days. Apparently, this great age is a resultof coexistence of newly released particles from the river mouth
and the returned particles from the area outside the estuary.
[46] The age spectrum at the Bohai Strait at day 46(Figure 10a) presents multi peaks. The first peak is at
approximately half year and the subsequent ones appear withan interval of nearly 1 year (Figure 10a). According to
Figure 7, we know that day 46 is the time when the river waterparticles flow out from the Bohai Sea through the Bohai Strait.
The first age spectrum peak is due to the river water thatleaves the river mouth in summer and autumn, moves into andstays the Laizhou Bay in autumn, and passes through thesouthern part of Bohai Strait in winter and spring. The subsequent peaks are due to the river water that leaves the rivermouth in summer and autumn, moves inside or outside theBohai Sea for several years, and finally passes through thesouthern part of Bohai Strait in winter and spring. The large
river discharge in summer and autumn and its exiting throughthe Bohai Strait in winter and spring determine these age
spectrum peaks.
[47] The extension of spectrum at day 46 to 1 year demonstrates the presence of multi peaks in age spectrum throughout
a year (Figure 10c). The age of these peaks shows a naturally

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Figure 7. Distributions of (a) all particles, (b) particles
never reentering the Bohai Sea from the Yellow Sea acrossthe Bohai Strait (red line), (c) particles reentering once,and (d) particles reentering twice, at day 46 of the fourthyear of the PTM calculation (day 1141 from the beginning).
Colors represent the logarithm (based on 10) of the particle
number.
increasing with time during a year, suggesting that the particles
passing the Bohai Strait moves freely inside the model
domain. This situation is different from the estuary area where
the coming of newly released particles has a constant waterage (Figure 9c). The daily particle number and age show lessvariation at the Bohai Strait (Figure 10e) than at the estuary(Figure 9e). The daily age at the Bohai Strait is small(1000 days) from day 140 to day 200 and large(1500 days) from day 240 to day 340. As shown insection 4.1, if we do not allow the reentry of particles into the
Bohai Sea, the age spectrum at the Bohai Strait significantly
changes (Figure 10d).

C11006and Table 1c). A comparison of Figure 11 with Figure 3
indicates that the water age decreases from approximately
1400 days to 700 days in the Liaodong Bay, from 1100 days
to 400 days in the central basin, and from 600 days to 200 daysin the Laizhou Bay. Although the reduction in the absolutevalue of water age is great, the exclusion of the reentry process
does not change the spatial distribution of water age for thefour seasons. Therefore, seasonal variation in the spatial distribution of water age is primarily attributed to the movementof newly discharged Yellow River water.
[50] Without the reentry process, the water age at the Bohai
Strait decreases from approximately 1200 days (Figure 5) to400 days (Figure 12), but the spatial pattern with low water
age at the southern side and high water age at the northernside remains (Figure 12). The magnitude of the reduction isgreater at the northern side than at the southern side
(Figures 12 and 5). In this case, the age of Yellow River waterat the Bohai Strait is determined only by the outflow of tracer
concentration inside the Bohai Sea and therefore reflects thetransit time of the newly discharged Yellow River water inthe Bohai Sea.
[51] The influence of the reentry process also appears inthe spectrum of water age at the estuary and at the Bohai
Strait (Figures 9 and 10). If the particles are not allowed toreturn to the Bohai Sea in the PTM calculation, the particles
with an age longer than 5 years almost disappear at theestuary (Figure 9b); the daily age at the estuary apparently
decrease (Figure 9f) and its annual mean is only 294 days,
much less than 445 days in the case with reentry process(Figure 9e). Without reentry process, the particle number at
the Bohai Strait decrease significantly (Figure 10f). In particular, the particle number after day 230 approaches to 0
and such small number of particle makes the water age
spectrum to be hardly defined (Figure 10d). Since the particles returned to the Bohai Sea from the Yellow Sea haverelatively large water age, the young particles at the Bohai
Strait increases its ratio in the case without the reentry

4. Discussion[48] As we presented in section 3.3, reentering particles
occupy a portion of Yellow River water inside the Bohai Sea
and therefore affect the water age of Yellow River water in thesea. Additionally, because the water age is determined by thecurrent field, any change in the driving forces of the current
field, such as river discharge, winds, tide, and heating, mayalso affect water age. We therefore present water age without
the reentry process through the Bohai Strait in section 4.1 andwater age calculated by the current field obtained with artificially modified driving forces in section 4.2. These results andthe discussion of them will help to understand the process
related to the age of Yellow River water inside the Bohai Sea.
4.1. Water Age Without the Reentry Process[49] Setting an open boundary at OB1 (Figure 1), werepeated the water age calculation using CART and PTM.
Without the reentry process, the water age decreases by morethan 50% in all of the subregions in the Bohai Sea (Figure 11

Figure 8. The same as Figure 7 but with data for day 228of the fourth year (day 1323 from the beginning of thePTM calculation).

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Figure 9. (a) Total number (black line, M(t, t) in equation (4)) of the particles with ages less than orequal to an age (t) at day 46 (t = day 46); age spectrum (red line, j(t, t) in equation (4)) of Yellow River
water at the estuary (see Figure 1 for the position) from calculations using boundary OB2. (b) The same as
Figure 9a but from calculations using boundary OB1. (c) The age spectrum j(t, t) (unit: 103/d) of Yellow River water at the estuary during a year (t = day 1 to day 365) from calculations using boundary OB2.
The age range (t) is limited to 5 year since the frequency of particles with age larger than 5 years is too
small to be identified. (d) The same as Figure 9c but from calculations using boundary OB1. (e) Daily
number of particles (black line) and their mean age (red line) of Yellow River water at the estuary from
calculations using boundary OB2. (f) The same as Figure 9e but from calculations using boundary OB1.
process (Figure 10b). Consequently, the daily age at theBohai Strait significantly decreases in the case without thereentry process (Figure 10f ).
4.2. Influences of Dynamic Factors on Water Ages
[52] We designed 7 cases (Table 2) for examining thecontrol of dynamic factors on water age. In each of thesecases, we change only one physical process from the control
case (hereafter referred to as Case 0), for which the results
were given in section 3, and rerun the hydrodynamic modeland CART module to obtain a new water age. The open

boundary for water age in these cases is at OB2; therefore,
the reentry process was allowed in all of these cases.
[53] The exclusion of tidal forcing (Case 1, removing
tidal oscillation at open boundaries) significantly reduces theage of Yellow River water in the Bohai Sea (Table 3a andFigure 13b). Without tidal forcing, the annual mean age of
Yellow River water decreases by 57%, 34%, 43%, 50%,
52%, and 46% in the Laizhou Bay, Bohai Bay, central basin,
Liaodong Bay, Bohai Strait, and the entire Bohai Sea,
respectively (Table 3b). The reduction in water age is small

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Figure 10. The same as Figure 9 but for the Bohai Strait. The particle number in Figure 10f from day 230
to day 330 is very small and the spectrum during this period is essentially meaningless.
near the river mouth and gradually becomes larger with
distance from the river mouth (Figure 13b).
[54] The tidal forcing has two major hydrodynamic functions, which are tide-induced change in vertical mixing andtide-induced change in current field. To clarify which function is more important to the reduction of water age, we
designed Case 2 and Case 3 (Table 2). Both cases are thesame as Case 0 except that the vertical eddy diffusivity
coefficient for tracer and age concentrations in Case 2 were
replaced by those in Case 1, and the three components ofvelocity and sea level for tracer and age concentrations inCase 3 were replaced by those in Case 1. Therefore, the tideinduced change in vertical mixing was ignored in the water
age calculation in Case 2, whereas the tide-induced change
in current field was ignored in the water age calculation inCase 3.

[55] The reduction of water age in Case 1 compared toCase 0 (Figure 13b) is attributed primarily to the tideinduced change in current field (Figure 13d) and not to thetide-induced change in vertical mixing (Figure 13c). The
small change in water age in Case 2 (Figure 13c) suggested
that tide-induced change in vertical mixing has a negligible
role in the age of Yellow River water in the Bohai Sea.
[56] The tide-induced change in current field affects the
movement of particle of Yellow River water through the
Bohai Strait. Compared to Case 0 (black line in Figure 6b),the total particle number of Yellow River water inside theBohai Sea decreases sharply from the end of first year inCase 1 (black line in Figure 6c), indicating more particles
leaving the Bohai Sea in Case 1 than in Case 0. At the end of
second year, the total particle number inside the Bohai Sea is
3.5  105 in Case 0 but 1.3  105 in Case 1. In the summerof second and third years of Case 1, a large number of

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Figure 11. Vertically averaged age of Yellow River water(unit: days) in the Bohai Sea from calculation using boundary
OB1 in (a) February, (b) May, (c) August, and (d) November.
The contour interval is 100 days.
particles return into the Bohai Sea (green line of N = 1 inFigure 6c). However, the returned particles are much lessthan the particles leaving at the end of first year. Furthermore, they leave the Bohai Sea very soon, inducing anotherreduction in total particle number before the winter when the
major reduction due to leaving of the particles with N = 0
occurs.
[57] The reduction in total particle number due to returned
particles from late summer to early winter occurs only in
Case 1 (Figure 6c). To understand the reason for this, we
present the horizontal distribution of particles at day 167,
228, 320 in second year of Case 1 (Figure 14). At day 167,
the particles with N = 0 distribute along the southern coast of
Bohai Bay and Laizhou Bay. As suggested by the disconnection of particles with N = 0 around the Bohai Strait(Figure 14a), they already starts to move to the Laizhou Bay
from the strait. Following them, the particles with N = 1
distribute from the Bohai Strait to the southern coast of
Laizhou Bay (Figure 14b) and the particles with N = 0
accumulate outside the Bohai Strait (Figure 14a). With time
passing, the particles with N = 0 outside the Bohai Strait
enters the Bohai Sea and becomes the particles with N = 1
inside the Bohai Sea. At day 228, the particles with N = 0
distributes mainly in the Bohai Bay (Figure 14c) while theTable 1c. Relative Difference of Volume-Averaged Age of Yellow River Water Between Calculations With Boundary OB1 andOB2aSubregions

February

May

AugustNovember

AnnualBohai Sea
Laizhou Bay
Bohai Bay
Central Basin
Liaodong Bay
Bohai Strait

61
63
55
62
50
72

59
61
55
60
50
63

60
66
55
61
50
66

63
67
56
63
50
67

61
65
55
61
50
68

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Figure 12. Vertical distribution of age of Yellow River
water (unit: days) in the Bohai Strait from calculation using
boundary OB1 in (a) February, (b) May, (c) August, and(d) November. The contour interval is 50 days. Maximum
value, minimum value, and mean value at the section are
given in each panel.
particles with N = 1 distributes mainly in the Laizhou Bay(Figure 14d) and its total number reaches the maxima(>80000) (Figure 6c and Figure 14d). After that, the particles
start to move to the Bohai Strait and then leave the Bohai
Sea. At day 320, the particles with N = 0 come back the
Laizhou Bay from the Bohai Bay but does not reach the
Bohai Strait (Figure 14e). The particles with N = 1 distributefrom the Laizhou Bay to the Bohai Strait (Figure 14f). The
large number of particles with N = 1 outside the Bohai Strait(Figure 14f) indicate the exiting of particles through the
Bohai Strait up to day 320.
[58] According to Figure 14, the different pathway ofreturned particles in Case 1 from Case 0 is the cause of the
reduction in total particle number from late summer to early
winter in Case 1. The exiting pathway of particles is from thesoutheastern coast of Laizhou Bay to the Bohai Strait in both
Case 0 and Case1. With tidal forcing (Case 0), the particles
return to the Bohai Sea from northern side of the Bohai Strait
and distribute from the Bohai Strait to the Liaodong Bay(Figure 8c). These particles have to return to the Laizhou
Bay before exiting the Bohai Sea again. Without tidal

Table 2. Conditions Used in Sensitive Experiments for Case 1 toCase 7
Case

Yellow River
Discharge

Tidal
Current

Tidal
Mixing

Winds

ThermalStratification

1
2
3
4
5
6
7

Yes
Yes
Yes
Yes
Yes
0.5 times
2.0 times

No
Yes
No
Yes
Yes
Yes
Yes

No
No
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
No
Yes
Yes
Yes

Yes
Yes
Yes
Yes
No (10 C)
Yes
Yes

a

Units are percent.

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Table 3a. Volume- and Annually Averaged Age of Yellow River
Water in the Bohai Sea and Subregions From Sensitive Experimentsa
Subregions

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

Bohai Sea
Laizhou Bay
Bohai Bay
Central Basin
Liaodong Bay
Bohai Strait

586
264
641
630
708
591

1076
609
996
1093
1401
1213

580
250
449
648
802
617

1383
841
1194
1409
1778
1548

1127
628
979
1153
1513
1308

1097
631
976
1117
1450
1282

1080
614
975
1096
1413
1209

a
The results of control case are given in Table 1a. The sensitive experiments
are Case 1 to Case 7. Volume-averaged and annually averaged age units is indays.

forcing (Case 1), the particles returns to the Bohai Sea
from southern side of the Bohai Strait and distribute fromthe Bohai Strait to the southern coast of Laizhou Bay(Figure 14d). Since they are already at the exiting pathwayof particles, the returned particles in Case 1 can easily reachFigure 13. (a) Vertically and annually averaged age of
Yellow River water (unit: days) in the Bohai Sea calculated
for a control case (Case 0). (b–h) The same as Figure 13a but
for the differences between the Case denoted inside the panel
and Case 0. (i) The color bar shows the color range for
Figure 13a, and (j) the color bar shows the color range for
Figures 13b–13 h. The contour interval for Figures 13a,
13b, 13d, and 13e is 100 days, and the interval for
Figures 13c, 13f, 13 g, and 13 h is 20 days.

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Table 3b. Relative Difference of Volume- and Annually Averaged
Age of Yellow River Between Sensitive Experiments and Control
Casea
Subregions

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

Bohai Sea
Laizhou Bay
Bohai Bay
Central Basin
Liaodong Bay
Bohai Strait

46
57
34
43
50
52

1
1
3
1
2
2

46
59
54
41
44
50

28
37
23
28
25
25

4
2
1
5
6
5

1
3
1
1
2
3

0
0
1
0
1
3

a
The results of control case are given in Table 1a. The sensitive
experiments are Case 1 to Case 7. Relative difference is given in percent.

the Bohai Strait. Consequently, it is easier for the returned
particles to leave the Bohai Sea in Case 1 than in Case 0.
This is the cause why the water age of Yellow River water islower in Case 1 than in Case 0.
[59] The tide-induced change in current field includes
three major components. The tide-induced residual current
due to the asymmetry in the tidal currents generally acts toprevent Yellow River water from flowing out along the coastof the Laizhou Bay to the Bohai Strait [see Wang et al.,2008, Figure 11]. In addition, the presence or absence oftidal forcing also changes the response of Bohai Sea to thewind-forcing and buoyancy forcing and changes the winddriven current and density-driven current. All of them should
contribute to the tide-induced change in the current field aswell as the pathway of particles.
[60] Local winds are also important to the age of Yellow
River water in the Bohai Sea. Without local winds (Case 4;
Table 2), the age of Yellow River water in the entire Bohai
Sea and its subregions increased by 20–30% (Tables 3a and3b and Figure 13e), which indicates that local winds rank
second among all of the dynamic processes discussed here.
[61] The particles of Yellow River water with N = 0 areeasier to leave the Bohai Sea in Case 4 (Figure 6d) than inCase 0 (Figure 6b). The timescale for the total number ofparticles with N = 0 inside the Bohai Sea to decrease to 0 is
approximately two and half years in Case 4 (Figure 6d) but
10 years in Case 0 (Figure 6b). Therefore, the particles with
N = 0 do not contribute to the increasing of water age inCase 4. On the other hand, the returned particles (N > 0) are
more difficult to leave the Bohai Sea in Case 4 (Figure 6d)than in Case 0 (Figure 6b). Apparently, it is the returned
particles that increase the water age in the case withoutwinds.
[62] To know the movements of particles, we present thehorizontal distribution of particles at day 167, 228, 320 insecond year of Case 4 (Figure 15). From day 167 to day 320,
the particles with N = 0 continuously move from the Laizhou Bay toward the Bohai Strait and subsequently leave theBohai Sea (Figures 15a, 15c, and 15e). The movement ofparticles with N = 0 in opposite direction, which occurs inCase 0 (Figures 7a and 8a) from spring to summer whensoutherly or southeasterly winds prevails, does not occur inCase 4. Therefore, without winds, the particles with N = 0
lose the driving forcing for them to return the Laizhou Bay
and are kept in a one-way movement, i.e., leaving the Bohai
Sea. On the other hand, the returned particles in Case 4enter the Bohai Sea from northern part of Bohai Strait(Figures 15b, 15d, and 15f) and accumulate there to the

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Figure 14. Distributions of particles never reentering the Bohai Sea from the Yellow Sea across theBohai Strait (red line) at (a) day 167, (c) day 228, and (e) day 320 as well as particles reentering onceat (b) day 167, (d) day 228, and (f) day 320 of the second year of the PTM calculation in the case without
tidal forcing (Case 1). Colors represent the logarithm (based on 10) of the particle number.
Liaodong Bay. Without wind, it is difficult for them to moveto the southern coast of Laizhou Bay and therefore needmore time to leave the Bohai Sea again.
[63] Thermal stratification due to heating has been known
to influence the behavior of the Yellow River plume [Wanget al., 2008]. Without heating, the offshore spreading of theriver plume in spring and summer decreased, and surface
currents were weakened [Wang et al., 2008]. These changes,
however, have limited influences on the age of Yellow River
water (Case 5). Without heating, the water age increased byonly 0–80 days (Figure 13f), which is only a small percentage of the water age in Case 0 (Table 3).
[64] The changes in Yellow River discharge have slightinfluence on its water age (Table 3 and Figures 13g and13h). Halving (Case 6) or doubling (Case 7) Yellow River

discharges modified the water age on the order of 20–
40 days (Figures 13g and 13h), which is less than 5% of
the water age in Case 0 (Table 3).

5. Summary[65] The age of Yellow River water in the Bohai Sea wasevaluated by a three-dimensional model that was driven bymonthly forcing (wind stresses, heat flux, river discharge,
and ocean currents at the open boundary) and tidal forcing.
Two methods were used to calculate the water age. One
method is based on the constituent-oriented age and residence time theory [Deleersnijder et al., 2001], and the othermethod is a classic particle-tracking method [Zhang, 1995].
The former method presents the spatial distribution of water

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Figure 15. The same as Figure 14 but for the case without winds (Case 4).
age and a budget of tracer and age concentrations, whereas
the latter method reveals the trajectory and age spectrum ofriver water particles.
[66] Yellow River water has a mean age of 3.0 years forthe entire Bohai Sea. The water age varies significantly inthe horizontal direction but varies insignificantly in thevertical direction and in the temporal dimension. The water
age is approximately 1.2 years near the Yellow River estuary
but 3.9 years in the Liaodong Bay. The great water age(>1 year) induces a nearly homogeneous distribution in thevertical direction and a small temporal variation in spatiallyaveraged water age (a minimum value of 2.8 years inautumn and a maximum value of 3.1 years in spring).
[67] The mean age of Yellow River water reported in thisstudy is much greater than the mean age of river water inestuaries [Shen and Haas, 2004; Shen and Lin, 2006] andthe shelf sea [Zhang et al., 2010a]. The greater water age of
Yellow River water may be attributed to the large range ofBohai Sea (approximately 300–400 km from the rivermouth) and the weak current speed (0.05 m s1) in the Bohai
Sea. However, these factors are not the primary causes forthe greater age of Yellow River water found in this study.
For example, in an estuary in which the length is assumed
to be 400 km and the current is assumed to be a constant(0.05 m s1), the maximum age is approximately 90 days
without considering diffusion. This value is far less than that
we obtained.
[68] The return of old river water to the target area is theprimary cause for the greater age of Yellow River water inthe Bohai Sea found in this study. The target area of thisstudy is the entire Bohai Sea. The return of Yellow River
water from the area outside of the target area (i.e., the Yellow
Sea) has been demonstrated to increase the water age from
424 days (Table 1b) to 1082 days (Table 1a). The trajectoryof water particles released at the river mouth further proved
the role of returned old Yellow River water. Most of Yellow

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River water particles need only several days to reach theestuary area. This result is consistent with previous reports ofa short age of river water in an estuary [Chen, 2007; Liu et al.,2011]. However, the presence of old water particles in theestuary area results in a mean river water age on the order of
1 year. This fact, i.e., the composition of particles with different ages, was demonstrated by the age spectrum.
[69] The large spatial scale of the target domain (i.e., theBohai Sea) and the circulations there are the secondary
causes for the great water age because the combination ofthese two factors maintains the river water inside the target
domain for more than 1 year. If the target domain was limited to the Yellow River estuary or even to the Laizhou Bay,
we can obtain a shorter water age for Yellow River water.
[70] Among all of the dynamic processes associated withcirculations, the tide is the most dominant factor to affectthe age of Yellow River water. Without tidal forcing, themean age of Yellow River water was reduced by morethan 50%. The tide-induced change in current field, not the
tide-induced change in vertical mixing, was shown to be
responsible for the reduction in water age. The particles ofriver water return to the Bohai Sea from northern side of theBohai Strait in the presence of tide but from southern side of
the Bohai Strait in the absence of tide. Consequently, thereturned particles are easier to leave the Bohai Sea again in
the absence of tide than in the presence of tide because thesouthern side of the Bohai Strait is the exit for Yellow River
water to leave the Bohai Sea. The winds are a secondary
factor in controlling the age of Yellow River water. Withoutwinds, the mean age of Yellow River water increases by 20–
30%. The particles of river water return to the Bohai Sea
from northern side of the Bohai Strait in the absence ofwinds. Without winds, the returned particles are difficult tomove to the southern coast of Laizhou Bay and the southernside of Bohai Strait and therefore stay inside the Bohai Sea
for a long time. Changes in Yellow River discharge and inthermal stratification have only slight influences on the ageof Yellow River water.
[71] As shown in this study, the return of old river water tothe target region is an important factor in the mean age ofriver water. Both the water age with reentry process and thewater age without the reentry process have possible applications. The water age with the reentry process may be
applied to materials such as persistent organic pollutants(POPs) that move with water and stay in the sea with a timescale of several years or decades. The water age without thereentry process may be applied to materials such as nutrientsthat are rapidly used by phytoplankton and have a life spanof less than 1 year. Nevertheless, the link between riverwater age and terrigenous material transport and cycling inthe sea must be explored in our future studies.

With a constant velocity (0.01 m s1), the age increases by
11.57 days with every 10 km leaving the source. This featureis almost exactly given by the module (Figure A1a).
[73] The second analytical solution is for newly formed
passive dissolved conservative matter at the sea surface.
Assuming that only vertical diffusion applies here anddenoting time by t, vertical coordinate by z, water depth by H,
and a constant vertical diffusivity coefficient by K, the concentration of conservative matter C(z, t), and its age concentration a(z, t) are controlled by the following equations.

Appendix A: Comparison of Numerical Results
With Analytical Solutions[78] According to equation (A11), the age is inversely
proportional to the vertical diffusivity coefficient but is
proportional to water depth.
[79] We present vertical distribution of C(z, ∞), a(z, ∞), anda(z, ∞) in the case with a water depth of 60 m and a vertical
diffusivity coefficient of 0.001 m2 s1 in Figures A1b, A1c,and A1d, respectively. With the same parameters, we used thenumerical module for vertical diffusion to solve the above
problem defined by equations (A1)–(A8). The corresponding[72] According to Deleersnijder et al. [2001], the horizontal
distribution of age in the channel can be described by x/u inwhich x is the distance to the source of the target water and uis the speed of steady flow. This solution was used to checkour numerical module that solves for the advection process.
Figure A1a presents the relationship between water age anddistance in the analytical solution and in the module results.

∂C
∂2C
¼K 2
∂t
∂z

ðA1Þ

∂a
∂2a
¼ K 2 þ C ðz; t Þ
∂t
∂z

ðA2Þ

[74] The initial conditions for C and a are as follows.
C ðz; 0Þ ¼ 0

ðA3Þaðz; 0Þ ¼ 0

ðA4Þ

[75] The boundary conditions for C and a at the sea surface (z = 0) and sea bottom (z = H) are as follows.
C ð0; tÞ ¼ 1

ðA5Það0; t Þ ¼ 0

ðA6ÞC ðH; t Þ ¼ 0

ðA7ÞaðH; tÞ ¼ 0

ðA8Þ

[76] By neglecting solution for transient period, the analytical solution for the concentration of conservative matterC(z, ∞) at a steady state isC ðz; ∞Þ ¼ 1 

z
;
H

ðA9Þ

and the age concentration a(z, ∞) at a steady state isaðz; ∞Þ ¼

Hz 
z 
z
1
2
:
6K
H
H

ðA10Þ

[77] The analytical solution for water age a(z, ∞) at a
steady state isaðz; ∞Þ ¼

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aðz; ∞Þ Hz 
z
¼
2
:
C ðz; ∞Þ 6K
H

ðA11Þ

LIU ET AL.: AGE OF YELLOW RIVER WATER

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Figure A1. Comparison of the numerical results and analytical solutions for water age in (a) a case with aconstant current (0.01 m s1) and (b–d) a case with constant vertical diffusion coefficient (0.001 m2 s1).
See Appendix A for a description of each case.

numerical solutions at a steady state are also presented in
Figures A1b, A1c, and A1d. Again, a good agreement between
numerical results and analytical solutions is evidenced in the
figures.
[80] Finally, we consider the water age in a one-dimensional
flow with constant velocity u(>0) and horizontal diffusivity
K in a domain ∞ < x < ∞. Differing from first problem, thisproblem considers horizontal diffusion and therefore can beused to check the numerical module for horizontal diffusion.
According to Deleersnijder and Delhez [2004], the analyticalsolution for water age a(x, t) whose age is prescribed to 0 at
x = 0 isaðt; xÞ ¼ t 1  e2x I3=2 þ e2x I1=2 ;ðA12Þwhere,
Ib ðt; xÞ ¼

jxj
p1=2

Z t
0

qb eqx =q dq:
2

ðA13Þ

[81] In equations (A12) and (A13), t, a and x are dimensionless variables that are defined by dividing original timeand space variables by 4K/u2 and 4K/u, respectively.
[82] Assuming u = 0.01 m s1, K = 15 m2 s1, we
numerically solved the equations for water age in a onedimensional flow. Figure A2 presents the horizontal distribution of water age (a) along one-dimensional space (x) at
different time (t) from both numerical module and analyticalsolution (equation (A12)). Again, a good agreement between
numerical results and analytical solutions is obtained. At timet = 1/3, low water age is concentrated at x = 0 (Figure A2a).
As time increases, the maximum water age increases (seeordinate of each panel in Figure A2). Meanwhile, the low
water age propagates in positive direction of x with speed
larger than u. This occurs in the transition region where theslope of age to x is less than 1. However, in the region
upstream of the transition region (i.e., region close to x = 0),
the slope of age to x is equal to 1, indicating the propagation
speed of u. The distribution of low water age in region ofx < 0 is due to horizontal diffusion.

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Figure A2. Comparison of the numerical results and analytical solutions for the water age at time(a) t = 1/3, (b) t = 1, (c) t = 3, and (d) t = 9 in a case with a constant current (u = 0.01 m s1) and constanthorizontal diffusion coefficient (K = 15 m2 s1). The age a, time t, and coordinate x are dimensionless variables. See Appendix A for a description on the problem and solution.

[83] Acknowledgments. This study was funded by the Natural
Science Foundation of China (41176007 and 40706007). H. Wang thanks
the China Scholarship Council (CSC) for supporting her stay in Japan. X. Guois thankful for supports from JSPS KAKENHI (21310012) and from theOverseas, Hong Kong and Macao Scholars Collaborated Research Fundfrom the National Science Foundation of China (41028006). Discussions
with Jing Zhang at East China Normal University, Renjun Wang at the
Ocean University of China and Xiangyun Lin at Shandong University of
Science and Technology are highly appreciated. We are also grateful to theHigh Performance Center of Ocean University of China for the technicalsupport for our calculations.

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