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Modeling study of residence time and water age in Dahuofang Reservoir in China

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Understanding the dynamics of water renewal in a reservoir is essential when the transport and fate of dissolved substances are evaluated. A three-dimensional hydrodynamic model was implemented to compute average residence time and water age in Dahuofang Reservoir in China. The model was verified for a one-year time period in 2006. A simulation reproduced intraannual variation of mixing represented by the fall/winter mixing and the spring/summer stratification. The simulated variation of vertical thermal structures also matched observation. The spatially varying average residence times and age distribution were investigated through a series of numerical experiments using a passively dissolved and conservative tracer as a surrogate. Residence time estimations yield a broad range of values depending on the position. The average residence time for a tracer placed at the head of the reservoir under high-, mean-, and low flow conditions was found to be about 125, 236 and 521 days, respectively. The age simulation reveals that the age distribution is a function of the freshwater discharge. In the vertical direction, the age of the surface layers is larger than that of the bottom layers and the age difference between the surface and bottom layers decreases further downstream. The density-induced circulation plays an important role in the circulation in the reservoir, and can generate vertical age distribution in the reservoir. These findings provide useful information for understanding the transport process in Dahuofang Reservoir that can be used to assist the water quality management of the reservoir. KeywordsDahuofang reservoir–reservoir–three-dimensional model–residence time–age
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SCIENCE CHINA
Physics, Mechanics & Astronomy
© Science China Press and Springer-Verlag Berlin Heidelberg 2011 phys.scichina.com www.springerlink.com
*Corresponding author (email: ymshen@dlut.edu.cn)
Research Paper January 2011 Vol.54 No.1: 127–142
doi: 10.1007/s11433-010-4207-7
Modeling study of residence time and water age in Dahuofang
Reservoir in China
SHEN YongMing1*, WANG JinHua1, ZHENG BingHui2, ZHEN Hong3, FENG Yu3,
WANG ZaiXing4 & YANG Xu4
1 State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China;
2 Chinese Research Academy of Environmental Sciences, Beijing 100012, China;
3 Liaoning Academy of Environmental Sciences, Shenyang 110031, China;
4 Dahuofang Reservoir Administration Bureau, Fushun 113007, China
Received October 24, 2010; accepted November 29, 2010
Understanding the dynamics of water renewal in a reservoir is essential when the transport and fate of dissolved substances are
evaluated. A three-dimensional hydrodynamic model was implemented to compute average residence time and water age in
Dahuofang Reservoir in China. The model was verified for a one-year time period in 2006. A simulation reproduced in-
tra-annual variation of mixing represented by the fall/winter mixing and the spring/summer stratification. The simulated varia-
tion of vertical thermal structures also matched observation. The spatially varying average residence times and age distribution
were investigated through a series of numerical experiments using a passively dissolved and conservative tracer as a surrogate.
Residence time estimations yield a broad range of values depending on the position. The average residence time for a tracer
placed at the head of the reservoir under high-, mean-, and low flow conditions was found to be about 125, 236 and 521 days,
respectively. The age simulation reveals that the age distribution is a function of the freshwater discharge. In the vertical direc-
tion, the age of the surface layers is larger than that of the bottom layers and the age difference between the surface and bottom
layers decreases further downstream. The density-induced circulation plays an important role in the circulation in the reservoir,
and can generate vertical age distribution in the reservoir. These findings provide useful information for understanding the
transport process in Dahuofang Reservoir that can be used to assist the water quality management of the reservoir.
Dahuofang reservoir, reservoir, three-dimensional model, residence time, age
PACS: 92.40.qf, 92.40.Cy, 92.40.We, 47.85.Dh
1 Introduction
Since reservoirs serve multi-functions of production, elec-
tric power generation, living, and irrigation, reservoir pollu-
tion is gradually attracting government and public’s atten-
tion in China. The water quality of the reservoir system de-
pends crucially on its travel time scales. The determination
of these time scales is key to knowing the times required for
a pollutant discharged into a water body to be transported
out of the system under normal hydrological conditions, and
the times elapsed within the water body since the pollutant
entered the system. For example, Liu et al. [1] pointed that
the relative short residence time is likely to be one of the
limiting factors that result in a low phytoplankton biomass
in the Danshuei River estuary, Taiwan; Bricelj and Lons-
dale [2] used residence time to explain the occurrence of
harmful algal blooms.
With increasing awareness worldwide of all aspects of
aqua-environmental and ecological pollution, there has in
recent years been a marked increase in the development and
application of numerical models to predict transport time
128 Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1
scales in reservoir, estuarine waters and seas. For example,
Huang et al. [3] investigated the water age in a tidal river in
Florida, Little Manatee River, by the application of a
three-dimensional hydrodynamic model, and Huang and
Spaulding [4] studied the residence time in response to the
change of freshwater input in Apalachicola Bay. Shen and
Haas [5] used three-dimensional model experiments to es-
timate water ages and residence times in the tidal York Riv-
er. Shen and Wang [6] determine the age of water and
long-term transport timescale of the Chesapeake Bay by
conducting three dimensional modeling study. Ribbe et al.
[7] assessed water renewal time scales for marine environ-
ments from three-dimensional modeling in a case study for
Hervey Bay, Australia. Orfila et al. [8] using virtual La-
grangian particles to assess the residence time in a small
inlet in Cabrera National Park, Western Mediterranean Sea.
Meyers and Luther [9] examined the Lagrangian retention
and flushing time by advecting neutrally buoyant point par-
ticles within Tampa Bay.
Dahuofang Reservoir, located at Liaoning Province,
serves as the drinking water source area to the two major
cities of Fushun and Shenyang. It has been listed as one of
nine key water sources, and supplies water to Liaoyang,
Anshan, Yingkou, and Panjin. After 2010, Dahuofang Res-
ervoir will be the drinking water sources including seven
cities in Liaoning. Therefore, the water features have be-
come increasingly prominent in the central city of Liaoning
Province, and it stands in an important strategic position in
the construction and life of the people. To ensure environ-
mentally safe water sources is related to the survival of
people of the province and the overall development of the
national economy [10].
Since the 1990s, the pollution of water quality in Dahuo-
fang Reservoir has tended to increase, with the total phos-
phorus, permanganate index increased, and the obvious in-
crease of the total phosphorus year by year. The total phos-
phorus in the mid-1990s is about 6.5 times that of the early
1990s; with the total nitrogen and the permanganate index is
about 1.43 and 1.34 times, respectively. Overall the water
quality in recent years decreased gradually from Grade 2 to
Grade 3 [11]. As the transport time scale is important re-
lated to the water circulation, the quantitative interpretation
of water exchange time is necessary for better protecting
and utilizing the environmental resources in this area.
Hydrodynamic processes in reservoir often involve a
three-dimensional flow in the presence of complex geome-
try and bathymetry, especially with large water level varia-
tion [12]. The circulation and mass transport in reservoir
may be affected by complex geometry and bathymetry. For
the sake of accurately simulating reservoir hydrodynamic
due to rivers, wind, and density gradients, numerical models
must be able to resolve accurately and efficiently the dy-
namics of various vertical boundary layers and the complex
geometry and bathymetry.
In this study, a three dimensional high resolution hydro-
dynamic model was implemented and applied to estimate
residence time and water age distributions for a range of
inflow conditions in Dahuofang Reservoir. The hydrody-
namic model was previously calibrated and verified by field
observations to quantify the mixing and transport processes
in the reservoir under wind and freshwater inflows., The
average residence time and water age is then studied to
support water resources management, which helps quantify
the transport processes of dissolved substances and under-
stand the mechanisms that control their temporal and spatial
variations.
2 Information on Dahuofang Reservoir
The Reservoir, completed in 1958, is a type of river-valley
reservoir. It is located in the northeastern part of China
among 41°31N–42°15N and 120°20E–125°15E, as
shown in Figure 1. The length of the reservoir is about 35
km with the largest width about 4 km and minimum 0.3 km.
It has an initial design capacity of 21.87×108 m3, which is
the largest reservoir in Liaoning Province, with detailed
features represented in Table 1. As the water transfer project
was completed in 2008, 18.2×108 m3 water will be imported
to the reservoir annually. The reservoir is one of the most
monitored reservoirs in Liaoning province with the histori-
cal data monitored since 1975.
Flows into Dahuofang Reservoir may be divided into two
categories: gauged and distributed. Daily, gauged flows
were input to the model at the gauge locations (Figure 1).
The distributed flows entering at undefined locations are not
monitored. Based on precipitation and evaporation, distrib-
uted flows were computed and pooled into the locations.
Flows into Dahuofang Reservoir showed typical season-
ality. Highest flows occurred from June through September.
Lowest flows occurred in the remaining months. On the
bases of historic statistic data, the Hunhe River at the east
provided 52.7% of the runoff, followed by Suzihe River at
the southern end with 37.1%. The remainder was virtually
Shehe River.
Table 1 Characteristics of Dahuofang Reservoir
Drainage area (km2) 5437
Maximum surface area (km2) 114
Maximum volume (m3) 21.87×108
Effective volume (m3) 12.76×108
Constant storage level (m) 131.5
Mean depth (m) 12
Maximum depth (m) 37
Annual mean precipitation (mm) 840
Annual mean evaporation (mm) 950
Annual mean river runoff (m3) 15.97×108
Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1 129
Figure 1 Location and Map of Dahuofang Reservoir area: dotted lines are depths sections. A, B, C, D, E, and G are observation locations; F is Yinpan
station.
3 Numerical model description and model set
up
3.1 Description of the hydrodynamic model
A three-dimensional, finite volume coastal ocean model
FVCOM was selected for Dahuofang reservoir application.
FVCOM was originally developed by Chen et al. [13], and
is recently extended to include the wave effect by Wang and
Shen [14]. The model was selected based on its qualifica-
tion to meet the study objectives and requirements and on
their extensive application to estuarine eutrophication prob-
lems. The hydrodynamic model uses a “terrain following”
sigma coordinate transformation in the vertical direction to
accommodate irregular bathymetry, and a nonoverlapping
unstructured triangular grid in the horizontal direction to
resolve dynamics in regions with complex shorelines.
Unlike other coastal finite-difference and finite-element
models, FVCOM solves the hydrostatic primitive equations
by calculating fluxes resulted from a discretization of the
integral form of these equations on an unstructured triangu-
lar mesh. This approach not only takes advantage of finite-
element methods for grid flexibility and finite-difference
methods for numerical efficiency but also provides a good
numerical representation of momentum, mass, salt, and heat
conservation. It has been successfully applied to many wa-
ter bodies such as estuaries, lakes, and coastal bays [15–21].
A brief introduction and description of the hydrodynamic
model is described. After the Boussineq and hydrostatic
approximations the primitive equations transformed to
sigma coordinate can be written as:
22
0
0
d
UD U D UVD U gD D
tx y xDx
ς
ωρςρ
ς
ςρ ς
⎡⎤
∂∂ ∂ ∂
++++ −
⎢⎥
∂∂ ∂∂ ∂ ∂
⎣⎦
()
atm
0
mm
2,
px tx
x
P
D
fVD gD xx
UUV
A
HAH R
xxyyx
ηττ
ρς
∂∂
−+ + = +
∂∂
⎡⎤
⎛⎞
∂∂∂∂
⎡⎤
++++
⎢⎥
⎜⎟
⎢⎥
∂∂∂∂
⎣⎦ ⎝⎠
⎣⎦
(1)
22
0
0
d
VD UVD V D V gD D
tx y yDy
ς
ωρςρ
ς
ςρ ς
⎡⎤
∂∂ ∂ ∂
++++ −
⎢⎥
∂∂ ∂∂
⎣⎦
()
atm
0
mm
2,
py ty
y
P
D
fUD gD yy
VUV
A
HAH R
yyxyx
ηττ
ρς
∂∂
++ + = +
∂∂
⎡⎤
⎡⎤ ⎛
∂∂∂∂
++++
⎢⎥
⎜⎟
⎢⎥
∂∂∂∂
⎣⎦ ⎝
⎣⎦
(2)
130 Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1
0,
DU DV
xy t
ωη
ς
∂∂
+++=
∂∂ (3)
and the scalar transport equation is
h
h h source
1
,
S UDS VDS DS S
K
tx y D
SS
AH AH S
xxyy
ω
ς
ςς
⎛⎞
∂∂ ∂ ∂ ∂∂
+++ =
⎜⎟
∂∂ ∂ ∂ ∂∂
⎝⎠
⎡⎤
∂∂∂∂
⎡⎤
+++
⎢⎥
⎢⎥
∂∂∂∂
⎣⎦
⎣⎦
(4)
where U and V are the components of velocity in the hori-
zontal (x and y); f is the Coriolis parameter;
ω
is the velocity
component normal to sigma surfaces; the vertical sigma
coordinates ()/
z
D
η
ranges from 1
ς
=− at the bottom
to 0
ς
= at the free surface; z is the vertical coordinate
positive upwards with 0z= at the mean water level;
η
is
the wave-averaged free-surface elevation; D is the total wa-
ter depth DH
η
=+; H is the depth below the mean water
level of the bottom; P is the dynamic pressure, and atm
P
is
the air pressure;
ρ
and
ρ
0 are the total and reference densi-
ties for water; g is the acceleration due to gravity; ,
t
α
τ
p
α
τ
are the turbulence and wind pressure stress respectively;
h
K is the thermal vertical eddy diffusion coefficient; m
A
and h
A
are the horizontal eddy and thermal diffusion coef-
ficients, respectively, and they are determined using a
Smagorinsky eddy parameterization method; S represents a
tracer quantity (for example, dye tracer, temperature);
source
S are the tracer source/sink terms; ,
x
R
y
R
are the
radiation-stress terms caused by surface wave [22]:
()
() ,
() () ,
xy xy
xx xx
x
yx yy yx yy
y
SS
SS
DD
RDxy x y
SS S S
DD
RDxy x y
ς
ςςςς
ςς
ςςς
∂∂
⎛⎞⎛ ⎞
∂∂
∂∂
=− + + +
⎜⎟⎜ ⎟
∂∂ ∂
⎪⎝ ⎠
∂∂ ∂ ∂
⎛⎞⎛ ⎞
∂∂
=− + + +
⎜⎟⎜ ⎟
∂∂ ∂
⎝⎠⎝ ⎠
(5)
where ,
xx
S ,
yy
S xy
S are
2
2
[cosh 2 (1 ) 1]
() cos
sinh 2
[cosh 2 (1 ) 1]
,
sinh 2
[cosh 2 (1 ) 1]
() sin
sinh 2
[cosh 2 (1 ) 1]
,
sinh 2
[cosh 2 (1 ) 1]
() () sin
xx T D
T
yy T D
T
xy yx T
kkD
SE E
kD
kkD
EkD
kkD
SE E
kD
kkD
EkD
kkD
SSE
ς
ςθ
ς
ς
ςθ
ς
ς
ςς
++
=+
+−
++
=+
+−
++
== sin cos ,
h2kD
θ
θ
(6)
where 1
tan sin d / cos dEE
θθ
θ
θθ θθ
ππ
−π −π
=∫∫
is the domi-
dominant wave direction relative to the eastward direction;
E
θ
is the directional kinematic energy (divided by the
water density);
θ
is the wave propagation direction
relative to the eastward direction; (cos ,sin )kk
α
θ
θ
=is the
wave number vector and kk
α
=; T
E
is the total kinematic
wave energy per unit surface area; a modified delta
function D
E
is equal 0 if 0
ς
and 0
1d/2.
D
ED E
ς
=
A second-order turbulence closure model [23] was se-
lected to represent turbulent kinetic energy distribution
based on theoretical considerations and computational effi-
ciency.
222 2
22
2
m
3
h
10
22
hh
2
22
2
,
q
px py
qD UqD VqD q
tx y
KK
qUV
DD
UVDqg
K
Bl
qq
DA DA
xxyy
ω
ς
ςς ς ς
ρ
ττ
ς
ςρς
∂∂ ∂ ∂
+++
∂∂ ∂∂
⎡⎤
⎡⎤ ⎛⎞
∂∂ ∂ ∂
=++
⎢⎥
⎢⎥ ⎜⎟
∂∂ ∂ ∂
⎢⎥
⎝⎠
⎣⎦⎣⎦
⎛⎞
∂∂ ∂
+++
⎜⎟
∂∂ ∂
⎝⎠
⎛⎞⎛⎞
∂∂∂∂
++
⎜⎟⎜⎟
∂∂∂∂
⎝⎠⎝⎠
(7)
222 2
22
2
m
1
3
3h
01
22
hh
,
q
px py
qlD UqlD VqlD ql
tx y
KK
ql U V
El
DD
UVg Dq
E
KW
B
ql ql
DA DA
xxyy
ω
ς
ςς ς ς
ρ
ττ
ςςρς
∂∂ ∂ ∂
+++
∂∂ ∂∂
⎡⎤
⎡⎤ ⎛⎞
∂∂ ∂ ∂
=+ +
⎢⎥
⎢⎥ ⎜⎟
∂∂ ∂ ∂
⎢⎥
⎝⎠
⎣⎦ ⎣⎦
⎛⎞
∂∂ ∂
+++ −
⎜⎟
∂∂ ∂
⎝⎠
⎛⎞⎛⎞
∂∂∂∂
++
⎜⎟⎜⎟
∂∂∂∂
⎝⎠⎝⎠
(8)
where 11 1
()( );
L
zHz
η
−− −
=− + + 22
2
1/()WElL
κ
=+
is
the wall proximity function, 0.4
κ
= is the von Karman
constant; 1
E
, 3
E
and 1
B
are the close constant of the mode;
m
K is the vertical eddy viscosity coefficient; q
K is the
vertical eddy diffusion coefficient of the turbulent kinetic
energy; 22
2
1/()WElL
κ
=+
is a wall proximity function
where 11 1
()( )
L
zHz
η
−−
=− + + ; 2
/
2q is the turbulence
kinetic energy; 2
/
//
s
cp
ρ
ςρς ς
∂∂=∂∂−∂∂
, s
c is sound
velocity; lis the turbulence length scale;
p
τ
is the pres-
sure stress [24]; turbulent close parameters ( m,K h,K q
K)
have been given by Blumberg and Mellor [25].
3.2 Definition of transport time scales
While essentially four different names (residence time,
Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1 131
transit time, age, and flushing time) are used, the same
name quite often refers to parameters indicating dissimilar
sets of physical mechanisms and/or different approaches
and experimental procedures [26]. For avoiding misunder-
standings and even erroneous conclusions it is important to
introduce precise definitions and to use them with care [27].
It is only in recent years that sufficient attention has been
paid to the problem, e.g. by Monsen et al. [28] and Rueda et
al. [29]. Definitions have consequently become increasingly
detailed and precise, and at the same time the intrinsic dif-
ficulties of the problem and the causes of the unavoidable
approximation of the solutions have become even clearer
[30–34].
Let’s review that flushing time is an integrative system
measure, whereas both residence time and age are local
measures (i.e., spatially variable within the domain). Selec-
tion of the most appropriate transport time scale depends on
the guiding question [28]. Residence time is how long a
parcel, starting from a specified location within a waterbody,
will remain in the waterbody before exiting. It has an im-
portant implication to the fates of introduced substances,
and the primary productivity in the estuaries [35]. Age, the
complement to residence time, is the time required for a
parcel to travel from a boundary to a specified location
within a waterbody. In this paper we chose the residence
time and age to study the transport time scales of Dahuo-
fang reservoir.
The concept of water age was first developed for steady
flow problems. Assuming that the material transport
mechanism is a steady state (i.e., total mass and the statisti-
cal distributions do not vary with time), Bolin and Rodhe
[27] introduced the concept of age of each material as the
time that has elapsed since it entered the reservoir. ()M
τ
is defined as the mass of the material that has spent a time
less or equal to
τ
in the reservoir. The total mass of the
material in the reservoir is 0
M. The frequency function
()t
ϕ
of the material with respect to age is given as:
0
1d ()
,
d
M
M
τ
ϕ
τ
= (9)
where 0
M satisfies the end condition:
0lim ( ).MM
τ
τ
→∞
= (10)
The average age a
τ
can be defined as follows:
0()d.
a
τ
τϕ τ τ
= (11)
The residence time of each material element is defined
by Zimmerman [36] as the time taken for the element to
reach the outlet. Residence time is measured from an arbi-
trary start location within the water body. Defining the
amount of the material at 0
τ
= be 0
R
, and the amount of
the material which still remains in the reservoir at the time
τ
be ().R
τ
()
R
τ
is the amount of the material whose
residence time is larger than .
τ
The residence time distri-
bution function can then be defined as:
0
1d()
.
d
R
R
τ
φ
τ
=− (12)
It can be further assumed that:
Lim ( ) 0..M
τ
τ
→∞ = (13)
The average residence time of the material is defined as:
0()d.
r
τ
τφ τ τ
= (14)
Integrating the above equations by parts gives:
00
0
()
d()d,
r
Rrt
R
τ
τ
ττ
∞∞
==
∫∫
(15)
where 0
() ()/rRR
τ
τ
=
is called the remnant function [37].
Since the remnant function is defined for an individual ma-
terial considered, it can be directly applied to calculate the
residence time for a pollutant that is discharged into a water
body at a particular location and time if the remnant func-
tion of the material can be obtained.
Theoretically, the integration of eq. (15) should proceed
to the time when the residual mass reaches zero. It may take
an infinitely long time and is impractical for actual applica-
tions. In this application, a proper upper limit of integration
was used. For each simulation the model was run until the
relative error of the cumulative average residence time
(1) (1)
err ()/
nntntnt
rrr
t
ττ τ
++
=− for the studied segment was less
than 0.001, where n is the time steps. A similar method is
used in the previous works [30,35,38].
In an estuary or coastal sea, there are multiple pollutant
sources discharged to the water body including rivers, lat-
eral flows, and point sources. We are more interested in
knowing the elapsed time of a substance since it entered the
system from multiple discharge locations. More specifically,
we want to know the time that has elapsed since the sub-
stance is transported to a location of concern (i.e., the mean
age of the substance that is transported to the location of
concern). Deleersnijder et al. [39] introduced a general the-
ory for age. Suppose a water parcel located at xat time t
contains dissolved tracer having an age spectrum concentra-
tion distribution (, , )ct
τ
x, wheretis the age (i.e., the time
since the tracer was released into the water). The equation
for age spectrum concentration is
(),
cc
pd c c
t
τ
∂∂
=−⋅ −⋅
∂∂
uK (16)
where p and d are the rates of production and destruction,
132 Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1
respectively; u is the flow velocity; and
K
is the eddy
diffusivity tensor. The last term on the right-hand side ex-
presses the aging of the tracer. Eq. (16) can be used to
simulate the age spectrum concentration directly, but at
considerable computational cost if hundreds of tracers are
activated to resolve the age spectrum well.
The tracer concentration in the fluid is the integral of the
age spectrum with respect to age, 0
(, ) (, , )d ,Ctx ctx
τ
τ
=
whereas the mean age (, )at x is the first moment of the age
spectrum, 00
(, ) (, , ) / (, , )d .atx ct x d ctx
τ
ττ ττ
∞∞
=∫∫
If we
define an age concentration tracer, 0
(, ) (, , )d ,tx ctx
α
τττ
=
then
(, )
(, ) .
(, )
t
at Ct
α
=x
xx (17)
Integrating (16) and (16)*
τ
over
τ
gives the tracer
concentration equation and the age concentration equation,
respectively. Assuming that there is only one tracer dis-
charged to the system and neglecting sources and sinks of
the tracer, the transport equations for calculating the con-
centration and the age concentration can be written as:
(),
CCC
t
=−∇⋅ − ⋅
uK (18)
().C
t
α
α
α
=−⋅ −⋅
uK (19)
Eqs. (18) and (19) can be solved simultaneously with the
hydrodynamic fields. We set initial conditions for both
Cand
α
of zero and release the tracer after the initial time
from a source at the head of the three Rivers. Eq. (17) gives
the mean age of river source water everywhere. Where the
newly released tracer has not yet reached, C is zero and the
mean age is undefined.
4 Model configuration and verification
The model area is the reservoir region: up to Beizamu of
Hunhe river, Gulou of Suzhihe river, and Taigou of Shehe
river in the upstream, respectively. In order to better fit the
irregular coastline, the horizontal resolution is about 200 m.
The computation grid has 3041 nodes and 5042 triangular
elements as shown in Figure 2. In the vertical it comprises 5
uniformly distributed sigma layers, which result in a vertical
resolution of about 0.1–1 m in the coastal region, which is
shallower than 5 m, and about 7 m at 35 m isobaths. The
bathymetry used in this model is provided by the field ob-
servation carried out by the Department of the Dahuofang
Administration Bureau and Liaoning Academy of Environ-
mental Sciences (the dotted line shown in Figure 1), and
interpolated to the mesh grid by the distance weighted in-
terpolation method (The interpolated bottom topography is
shown in Figure 3). Based on the CFL condition, the exter-
nal time step is 8 seconds and the internal mode is 10 times
of the external mode. The simulation started on April 1,
2005, and ended on November 31, 2006 and the results of
year 2006 are analyzed and presented in this paper.
On the sidewalls and bottom, the normal gradients of
temperature were set to zero. The model area includes three
rivers and five outflows whose positions are shown in Fig-
ure 1. The discharge rates of these rivers and outflows were
shown in Figure 4. The bottom roughness z0 was chosen
equal to 0.001 m. The meteorological parameters (wind
Figure 2 Unstructured grid representing the modeling domain.
Figure 3 Interpolated bottom topography through the cross section in-
vestigation of water depth.
Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1 133
Figure 4 Inflow and outflow hydrograph of the reservoir.
components at 10 m above the water level, air temperature,
pressure, relative humidity, cloudiness and precipitation rate)
were obtained from the analysis of the National Center for
Environmental Prediction (NCEP), with a bilinear interpo-
lation in space and linear interpolation in time. Some mete-
orological conditions are shown in Figure 5. Using these
parameters, the heat forcing at the air-sea interface can be
calculated according to the formulas presented by Shen et al.
[40]. The initial temperature field was assumed uniform
based on the monitored data at the dam site, and the initial
water level and current were set to zero.
4.1 Water elevation
The model performance was verified by using the water-
surface elevation data collected from April 1, 2006 through
November 1, 2006. Figure 1 shows the locations of the
monitoring stations for water surface elevations used for the
model verification. Figure 6 presents the comparisons of
model-predicted surface elevations against the measured
data for Stations G. There was a good agreement between
the observed and predicted water-surface elevations, with
root-mean-square errors (RMSE) equal to 0.31 m for water-
Figure 5 Meteorological condition of Dahuofang Reservoir from April to November 2006. (a) The 10 m high wind speed; (b) the shortwave radiation flux
on the water surface; (c) the daily temperature at the station G; (d) the precipitation and evaporation rate at station F.
134 Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1
Figure 6 Comparison of the water level simulation and the actual value
at the dam survey station G.
surface elevations. The model captured the drying and wet-
ting processes in the reservoir. Generally, the model cap-
tures the water level variation reasonably well. The com-
parisons were sufficiently accurate to justify the use of the
model for transport time scales studies.
4.2 Water temperature
Water temperature data were used to evaluate the hydrody-
namic results from one-year model runs. Time series of
surface and bottom temperature at 6 stations confirmed that
the simulation reproduces observed annual cycling (Figure
7). At station E only the middle layer was measured and
only the surface layer was measured at station G. The varia-
tion of the modeled temperature during this time period was
similar to the observations. The model performance during
this interval indicates that the temporal variability in tem-
perature was correctly represented but that accuracy could
be improved via an improved evaluation of forcing func-
Figure 7 Time series of the surface, middle, and bottom temperatures at (a) station E, (b) station A, (c) station B, (d) station C, (e) station D, and (f) station
G.
Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1 135
Figure 8 Variation of the vertical thermal structure at station G.
tions. Additionally, the vertical stratification of temperature
in the reservoir is nicely reproduced by the model results.
Vertical profiles of calculated and measured temperature
at station G for 2006 are shown in Figure 8. Thermal strati-
fication is initiated in Dahuofang reservoir at the beginning
of spring (early May) and reaches its maximum during
summer. In late November, surface cooling and wind mix-
ing induce fall overturn. Computed timing of the initiation
and destruction of thermal stratification are obvious. The
thermocline restricts mixing between the warm upper layer
and the cold lower layer and, about 5 m below the still wa-
ter level. In September 15th, a complete vertical mixing is
again observed. These computations indicate the model re-
sponds correctly to major forcing functions: spring warming,
fall cooling and wind-induced mixing. Enhanced absolute
accuracy in temperature computations requires enhanced
accuracy in measured forcing functions. Accurate, local,
meteorological observations are required for enhanced
model accuracy.
5 Results and discussion
5.1 Calculation of the residence time
There are two different approaches to computing the resi-
dence time. We can compute the residence time from the
solution of an adjoint problem [41]. This provides a local
residence time, depending on space and time. However, it is
not easy to implement. We can also compute the residence
time by means of a direct approach that is easier to imple-
ment (it only requires solving advection-diffusion equations)
but too expensive to get the same results as those of the ad-
joint problem. That is because the direct approach merely
provides a global mean residence time, as an integral over
space and time. A compromise can be made by dividing the
domain into a small number of regions. The mean residence
time is then computed for each region. This approach is
adopted in this study.
Dahuofang reservoir was divided into 7 segments. Seven
segments are located in Dahuofang reservoir as shown in
Figure 9. A passive tracer was used in the experiments. The
initial tracer concentration is 1 at the segment where the
residence time is evaluated while 0 for other segments.
The freshwater discharge is one of the dominant factors
controlling long-term transport process [42]. A significant
variation of freshwater discharge exists in the inflows (see
Figure 4). To investigate the effect of the flow rates on the
transport timescale in the reservoir, we did three numerical
experiments. The 20th percentile low flow, mean flow, and
Figure 9 Segmentation for calculating residence time. The bold line is
the horizon place where the vertical section of age is plotted in Figure 14.
136 Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1
90th percentile high flow were selected for the model ex-
periments. The freshwater discharges used for model
experiments are listed in Table 2.
The model experiments were conducted for each segment
for high flow, mean flow and low flow conditions, which
results in a total of 21 model runs. The results for the aver-
age residence time with respect to different flow conditions
at each model segment are shown in Figure 10. Because of
the lower inflow rate of Shehe river, the residence time for
segment 2 is longer although it’s close to the outlet. From
the comparisons between the calculated residence time un-
der high-, mean- and low flow conditions, differences of the
residence time between the three conditions in the upstream
are more significant. The residence time at the segments 6
and 7 are nearly the same. For segment 7, it is about 125.42,
236.75 and 521.55 days under high-, mean-, and low flow
conditions, respectively. The differences between high flow
and mean flow are 111.33 days, and 284.8 days between
mean-and low flow conditions. In general, the results show
that the residence time decreases as the segment moves to-
wards the front of dam. We also note that the residence time
decreases as inflow rate increases, which indicates that the
influence of inflow rate on the transport is significant in
Dahuofang reservoir. As the inflow rate is high in summer
(Figure 4), it is beneficial for pollutant removal as a result
of short residence time.
5.2 Calculation of the age distribution
In this study, we use mean age to quantify the transport
process and estimate the time that the substance has spent in
the reservoir before it is transported to the location of con-
cern. Model experiments for high and mean flows as listed
Table 2 River discharges (m3 s1) at the upstream boundaries for various
scenarios of model simulations
River High flow Mean flow Low flow
Hunhe river 66.9 27.45 6.22
Shehe river 4.3 2.36 1.12
Suzihe river 90.2 33.27 7.18
Figure 10 Residence times for each segment with respect to different
flow conditions.
in Table 2 were conducted with respect to the tracer dis-
charged into the headwaters of Hunhe river, Shehe river and
Suzihe river.
A passive tracer without decay was simulated to repre-
sent transport of a dissolved substance. The tracer with a
concentration of 1 (a reference unit) was continuously re-
leased into the three headwaters of the reservoir. The in-
coming age tracer concentration
α
was set to zero. The
model was initially run for 2 months without tracer releas-
ing for each flow condition to obtain a dynamic equilibrium
condition. Model experiments were hot started using the
equilibrium flow fields as the initial condition.
Three model experiments were conducted to simulate
high-, mean-, and low conditions. As we are more interested
in the age distribution under the equilibrium condition, the
model is run barotropicly (with the temperature field fixed)
driven by the inflows only. The model experiments were
conducted for 2 years for the low flow, mean flow, and high
flow conditions. The equilibrium was attained at the end of
the 2 years simulation for the low flow condition. Therefore,
the averaged mean age is calculated after the equilibrium is
attained. The age of each vertical layer was calculated based
on eq. (17). The age at each vertical layer was averaged to
obtain the vertical mean age. The vertical mean age distri-
bution is shown as contour plots in Figure 11. The numbers
shown on the contour lines are the mean ages of the tracer
in days at that location. The results show that a substantial
time is required for a pollutant to be transported down-
stream in the reservoir. On the whole, the age of the tracer
near the northern bank of the reservoir is less than the age of
the tracer near the southern bank. This can be attributed to
the influence of bathymetry and Coriolis force.
The age distribution is a function of the freshwater dis-
charge. The pollutant released under the high flow condition
will take about 10 days to be transported to the confluence
of Hunhe river and Suzihe river, and about 100 days to be
transported in front of the dam of Dahuofang reservoir.
Under the mean flow condition, the age is increased sig-
nificantly. It takes 30 days and 200 days for the pollutant to
be transported to the confluence point and out of the reser-
voir, respectively. Under the low flow condition, it takes
more than 500 days for the pollutant to be transported out of
the estuary. It should be noted that these results were ob-
tained in the situation driven by the inflows only.
To evaluate the influence of density-induced circulation
caused by the season temperature variation and the influ-
ence of wind to the age distribution, we compare model
experiments under high and mean flow conditions driven by
the real meteorological conditions (EXP1), by the real case
without consideration of the wind effect (EXP2) and by the
inflows only (EXP3).
The age is less in the main channel than that in the shal-
low areas flanking the channel, especially in the branching
stream (Figure 12). This pattern can be explained by the
general circulation pattern in the branching stream. Figure
Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1 137
Figure 11 Vertically averaged age distributions (in days) under high-, mean-, and low flow conditions in Dahuofang Reservoir.
13 shows the circulation at the surface layer in Dahuofang
reservoir under the high and mean flow conditions. It can be
seen that the current occurring in the main channel of the
reservoir is stronger than that in the flanking area. The gra-
vitational circulation is more developed in the deep channel
and could enhance the transport [43]. The comparison
between the residence time under EXP1 (Figure 12(a) and
(b)) and EXP2 (Figure 12(c) and (d)) reveals that the
influence of wind is not significant to the model age
simulation. On the other hand, the age distribution is seri-
ously affected by the density circulation from the compari-
son between EXP1 (Figure 12(a) and (b)) and EXP3 (Figure
12(e) and (f)).
The computed vertical mean age with and without den-
sity-induced circulation under mean- and low flow condi-
tions are shown in Figure 14. It can be seen that the age of
the surface layers is larger than that of the bottom layers.
The age difference between the surface and bottom layers
decreases further downstream. This indicates that the verti-
cal age distribution is influenced by the gravitation circula-
tion. The model results also indicate that as the river dis-
charges increase, the vertical age distribution (i.e. the
transport time) is reduced.
Although the net transport is upstream at the surface
layer, it is downstream near bottom (Figure 15(a) and (b)).
The bottom current is larger than that in the surface layer.
Consequently, more substances are transported out of the
reservoir through the bottom layer. When the inflow rate is
low, weaker downstream velocities are seen from the com-
parison between Figure 15(e) and (f). Compared to the
model results with and without density induced circulation
under the high flow (Figure 15(a) and (e)), the current near
the bottom layer in EXP1 is about 0.05 m/s, larger than that
in EXP3 which is about 0.02 m/s. This means that the den-
sity-induced circulation plays an important role in the cir-
culation in the reservoir, and can generate vertical age dis-
138 Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1
Figure 12 Comparisons of the vertically averaged age distribution (in days) of Dahuofang Reservoir on October 15, 2006 under high/mean flow conditions
for EXP1 ((a)–(b)), EXP2 ((c)–(d)), and EXP3 ((e)–(f)).
tribution in the reservoir.
6 Conclusions
The application of a three-dimensional hydrodynamic mod-
model to Dahuofang reservoir is presented, which is one of
the first modeling efforts for Dahuofang reservoir accompa-
nied by a relatively comprehensive field program.
In keeping with established conventions for reservoirs,
transport processes were verified largely through a com-
parison of computed and observed temperatures. Overall,
Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1 139
Figure 13 Comparisons of the surface current of Dahuofang Reservoir on October 15, 2006 under high/mean flow conditions for EXP1 ((a)–(b)), EXP2
((c)–(d)), and EXP3 ((e)–(f)).
the computed temperature is generally consistent with the
ones observed. Improvement in computations requires im-
proved observations of forcing functions, notably the local
meteorology and the inflow temperature.
140 Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1
Figure 14 Comparisons of the vertical age distribution (in days) of Dahuofang Reservoir on October 15, 2006 along the section shown in Figure 9 under
high/mean flow conditions for EXP1 ((a)–(b)), EXP2 ((c)–(d)), and EXP3 ((e)–(f)).
Residence time and age provide different measures to
estimate transport scales in aquatic environments. In this
study we calculate both transport time scales through nu-
merical modeling. Using the verified model, a series of nu-
merical modeling experiments were made. The experiments
demonstrated the average residence time for a tracer placed
at the head of the reservoir under high-, mean-, and low
flow conditions was found to be about 125, 236 and 521
days, respectively. The age distribution is a function of the
freshwater discharge. In the vertical, the age of the surface
layers is larger than that of the bottom layers and age dif-
ference between the surface and bottom layers decreases
further downstream. The density-induced circulation plays
an important role in the circulation in the reservoir, and can
generate vertical age distribution in the reservoir.
This successful application of mechanistic models to
Dahuofang reservoir has provided insight into the response
of the water body to environmental conditions. While this
model does not include all of the processes and transforma-
tions that occur in the natural environment, it does capture,
in the case of Dahuofang reservoir, the major processes of
water transport. This modeling framework provides a useful
tool for developing management practices and protecting
the water quality in Dahuofang reservoir in the future.
Shen Y M, et al. Sci China Phys Mech Astron January (2011) Vol. 54 No. 1 141
Figure 15 Comparisons of the vertical current of Dahuofang Reservoir on October 15, 2006 along the transection shown in Figure 9 under high/mean flow
conditions for EXP1 ((a)–(b)), EXP2 ((c)–(d)), and EXP3 ((e)–(f)).
This research is supported by the National Science and Technology Major
Special Project of China on Water Pollution Control and Management
(Grant No. 2009ZX07528-006-01) and the National Natural Science
Foundation of China (Grant No. 50839001).
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... Renewal timescales have been defined to quantify the water renewal and transport processes of various water bodies, such as water age (Bolin and Rodhe 1973;Shen et al. 2011), residence time (Zimmerman 1976;Takeoka 1984;Arega et al. 2008) and exposure time (Delhez 2006;Delhez and Deleersnijder 2012). Many studies have analysed renewal timescales in bays (Huang and Spaulding 2002;Ribbe et al. 2008), estuaries (Liu et al. 2008;de Brauwere et al. 2011), lakes (Rueda and Cowen 2005;Pilotti et al. 2014), lagoons (Cucco andUmgiesser 2006;Gao et al. 2013) and other water bodies. ...
... where m(t) is the amount of the material whose residence time is larger than t, m 0 is the amount of the material at t 0 , and r(t) = m(t)/m 0 is the remnant function (Takeoka 1984) that physically represents the fraction of the initial mass of the tracer whose residence time is greater than or equal to t. The fraction r(t) can be obtained through a numerical simulation of the distribution of a tracer (or pollutant) concentration (Yuan et al. 2007;Arega et al. 2008;Shen et al. 2011). Because dividing lake systems into a number of smaller homogenous waterbodies is now common practice for monitoring and management purposes ), a comparable approach based on the forward Eulerian method can be used by dividing the domain into numbers of subregions Ω i , (i = 1,..... n). ...
... (1). One method is based on the relative error of the cumulative average residence time (Yuan et al. 2007;Arega et al. 2008;Shen et al. 2011). An appropriate upper limit of integration can be obtained when the relative error of the cumulative average residence time t err n = (t r (n + 1)t − t r nt )/t r (n + 1)t is less than 0.001, where n is the time step. ...
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The security of drinking water is a serious issue in China and worldwide. As the backup source of drinking water for the Changde City in China, the Huangshi Reservoir suffers from the threat of eutrophication due to the water quality of the reservoir ecosystem being affected by the tributaries that carry Non-Point Source (NPS) pollutants. The calculation of the water environmental capacity (WEC) can provide a scientific basis for water pollution control, which refers to the maximum amount of pollutants that the water can accommodate. In this paper, according to the hydrological characteristics of the river–reservoir combination system, a one-dimensional (1-D) water quality model and the Environmental Fluid Dynamics Code (EFDC) model were chosen to calculate the water environmental capacity of each functional zone in this basin. The quantity control of pollution from the tributaries was conducted based on the combined results of the water environmental capacity calculation from the EFDC model and a one-dimensional (1-D) river water quality model. The results show that total water environmental capacity of the tributaries included a chemical oxygen demand (COD) of 421.97 tons; ammonia nitrogen (NH3-N) of 40.99 tons; total nitrogen (TN) of 35.94 tons; and total phosphorus (TP) of 9.54 tons. The water environmental capacity of the Huangshi Reservoir region accounts for more than 93% of the total capacity. The reduction targets of the major pollutants in the Huangshi Reservoir and its four major input rivers, which are, namely, the Bamao River, the Longtan River, the Fanjiafang River, and the Dongtan River, have been determined to achieve the water quality objectives for the reservoir in 2020 and 2025. The results will be helpful for the local water quality management and will provide a valuable example for other similar water source reservoirs.
... Thus, an indicator related to the water parcel transport time will provide valuable information in evaluating the water ecological environment. Various timescales such as the flushing time, turnover time, residence time, and water age have been applied to many water bodies with the aim of assessing the transport process of nutrients (Li et al. 2010;Monsen et al. 2002;Shen et al. 2011). Water age is defined as Bthe time that has elapsed since the particle under consideration left the region in which its age is prescribed as being zero^ (Delhez et al. 1999), which has been regarded as a useful index for analyzing the distributions of pollutants under Fig. 1 The location of Poyang Lake, inflow tributaries, the proposed dam, and hydrological stations various conditions based on the spatio-temporal heterogeneity (de Brauwere et al. 2011;Li et al. 2011;Monsen et al. 2002;Liu et al. 2012). ...
... The constituent-oriented age and residence time theory (CART) method was developed by Deleersnijder et al. (2001) with the advantage of directly predicting the water age by simulating the change of tracer concentration. Also, it has been embedded in various hydrodynamic models and widely used in many water bodies (Gong et al. 2009;Liu et al. 2012;Shen and Haas 2004;Shen et al. 2011). ...
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The water quality in Poyang Lake, the largest freshwater lake in China, has deteriorated steadily in recent years and local governments have made efforts to manage the potential eutrophication. In order to investigate the transport and retention processes of dissolved substances, the hydrodynamic model, Environmental Fluid Dynamics Code (EFDC) was applied by using the concept of water age. The simulated results showed agreement with the measured water level, discharge, and inundation area. The water age in Poyang Lake was significantly influenced by the variations of hydrological conditions. The annual analysis revealed that the largest averaged water age was observed during the wet year (2010) with 28.4 days at Hukou, the junction of the Yangtze River and Poyang Lake. In the normal season (April), the youngest age with 9.1 days was found. The spatial distribution of water quality derived from the remote sensing images suggested that a higher chlorophyll-a concentration, lower turbidity, and smaller water age in the eastern area of Poyang Lake might threaten the regional aquatic health. The particle tracking simulation reproduced the trajectories of the dissolved substances, indicating that the water mass with greater nutrient loading would further lead to potential environmental problems in the east lake. Moreover, the water transfer ability would be weakened due to dam (Poyang Project) construction resulting in the rising water levels in periods of regulation. Generally, this study quantified an indicative transport timescale, which could help to better understand the complex hydrodynamic processes and manage wetland ecosystems similar to Poyang Lake.
... Water exchange rate represents how fast the water inside the reservoir is replaced by new water inflows, which is obtained by examining the spatially averaged dissolved tracer concentrations in all layers as a function of time. Specifically, the water exchange rate is defined as the percentage of the new water diverted into the reservoir that replaces the original water within the reservoir [31]. The water exchange rate is calculated based on tracer concentrations through the EFDC model in this study. ...
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Large shallow reservoirs control flooding, supply water, and protect the ecological environment, which are vital functions for societal development. As the largest artificial plain reservoir in China, Suyahu Reservoir is suffering from significant sedimentation and water quality deterioration in recent years. A three-dimensional (3-D) hydrodynamic and water quality model was developed based on the Environmental Fluid Dynamic Code (EFDC). The model was applied to seven scenarios for evaluating the response of in-reservoir hydrodynamics and water quality to the restoration measures, including expansion and sediment dredging project, external load reduction, and inflow regulation. The results show that: (1) the expansion and sediment dredging project has no notable improvement on the water quality of the reservoir; (2) the external load reduction can significantly improve the water quality of the reservoir; and (3) the optimal inflow condition occurred when the flows of Ru River’s two inlets were evenly distributed, and the hydrodynamics and water quality were best improved. Moreover, the increasing water exchange rate could not cause the same water quality improvement, showing that it may be unreliable to evaluate the effects of restoration measures using a single indicator. This study can provide useful information for developing and implementing effective restoration measures in large shallow reservoirs.
... It is defined as ''the time that has elapsed since the particle under consideration left the region in which its age is prescribed as being zero" (Delhez et al., 1999). The concept of water age has been extensively applied in coastal water areas and lakes/reservoirs with intense water exchange induced by tides, wind, or human regulations (Deleersnijder et al., 2001;Liu and Huang, 2009;Li et al., 2011;Shen et al., 2011;Liu et al., 2012;Wu et al., 2013). These studies focused on the characteristics and dominant controlling factors of water age. ...
Article
Integrated hydrologic and hydrodynamic modeling is useful in evaluating hydrodynamic characteristics (e.g. water exchange processes) in data-scarce water bodies, however, most studies lack verification of the hydrologic model. Here, water exchange (represented by water age) was investigated through integrated hydrologic and hydrodynamic modeling of the Hongfeng Reservoir, a poorly gauged reservoir in southwest China. The performance of the hydrologic model and parameter replacement among sub-basins with hydrological similarity was verified by historical data. Results showed that hydrological similarity based on the hierarchical cluster analysis and topographic index probability density distribution was reliable with satisfactory performance of parameter replacement. The hydrodynamic model was verified using daily water levels and water temperatures from 2009 and 2010. The water exchange processes in the Hongfeng Reservoir are very complex with temporal, vertical, and spatial variations. The temporal water age was primarily controlled by the variable inflow and outflow, and the maximum and minimum ages for the site near the dam were 406.10 d (15th June) and 90.74 d (3rd August), respectively, in 2010. Distinct vertical differences in water age showed that surface flow, interflow, and underflow appeared alternately, depending on the season and water depth. The worst water exchange situation was found in the central areas of the North Lake with the highest water ages in the bottom on both 15th June and 3rd August, in 2010. Comparison of the spatial water ages revealed that the more favorable hydraulic conditions on 3rd August mainly improved the water exchange in the dam areas and most areas of the South Lake, but had little effect on the bottom layers of the other deepest areas in the South and North Lakes. The presented framework can be applied in other data-scarce waterbodies worldwide to provide better understanding of water exchange processes.
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A three-dimensional hydrodynamic model of the Liaodong Bay was developed in the frame of Environmental Fluid Dynamics Code (EFDC) to study the effects of the artificial island layout on hydrodynamics and water exchange in the coastal waters. The results show that the island blocks water flow and the width of its upstream face is the most significant factor of the blocking effect. An island with a larger width has a greater blocking effect and forms a larger area of low-velocity flow, thereby resulting in a lower capacity of water exchange in the study area. Complexity of island shoreline is also a considerable factor of the flow hydrodynamics: A zigzag shoreline is easier to form a semi-enclosed area of very low flow and poor conditions of water exchange. We compared the blocking effects and flow velocities in the water region near the island in tidal flows of different intensities and found out that the impact of the island much depended on tidal intensity. The capacity of water exchange is described and compared using two parameters: half-life time and volume-exchange rate. The latter is found better describing the differences in water exchange produced by different island layouts.
... Xu et al. [9] also used a 3D hydrodynamic and eutrophication model to investigate the pollutant age distribution under different river discharges in the Pamlico River. Shen et al. [10] computed the water age using a 3D hydrodynamic model in Dahuofang Reservoir in China, especially different water layers. In the vertical direction, the age of the surface layers was higher than that of the bottom layers and the age difference between the surface and bottom layers decreased further downstream. ...
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Channel reservoirs have the characteristics of both rivers and lakes, in which hydrodynamic conditions and the factors affecting the eutrophication process are complex and highly affected by weather conditions. Water age at any location in the reservoir is used as an indicator for describing the spatial and temporal variations of water exchange and nutrient transport. The hyper-eutrophic Changtan Reservoir (CTR) in Southern China was investigated. Three weather conditions including wet, normal, and dry years were considered for assessing the response of water age by using the coupled watershed model Soil Water Assessment Tool (SWAT) and the three-dimensional hydrodynamic model Environmental Fluid Hydrodynamic Code (EFDC). The results showed that the water age in CTR varied tremendously under different weather conditions. The averaged water ages at the downstream of CTR were 3 d, 60 d, and 110 d, respectively in the three typical wet, normal, and dry years. The highest water ages at the main tributary were >70 d, >100 d, and >200 d, respectively. The spatial distribution of water ages in the tributaries and the reservoir were mainly affected by precipitation. This paper provides useful information on water exchange and transport pathways in channel reservoir, which will be helpful in understanding nutrient dynamics for controlling algal blooms.
... Water age, which is defined as ''the time that has elapsed since the particle under consideration left the region in which its age is prescribed as being zero" (Delhez et al., 1999), is a useful indicator for the temporal and spatial quantification of the transport time of pollutants (Takeoka, 1984;Boynton et al., 1995;Delhez et al., 1999;Shen and Wang, 2007;Li et al., 2011). The concept of water age has been extensively applied in coastal water areas with intense water exchange, which is induced by tides and wind (Deleersnijder et al., 2001;Liu and Huang, 2009;Liu et al., 2012), and lakes and reservoirs with intense water movement, which is induced by human regulations Shen et al., 2011;Wu et al., 2013). These studies also explored the dominant controlling factors of water age, such as the inflow/outflow and wind. ...
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Thermal stability (Schmidt stability) and water age, which are significantly related to water quality and algae bloom in deep reservoirs, are two crucial indicators of stratification strength and pollutant transport time, respectively. Here, the original Schmidt stability, which was derived from a one-dimensional assumption, was theoretically extended to a three-dimensional water body. In addition, a three-dimensional model was verified for the case study of Hongfeng Reservoir in China based on data from 2009 and 2010. Although the revised stability was similar to the original stability of Hongfeng Reservoir, which occurred at a relatively low level, the greater stratification in other deep water bodies would enhance their difference. Air temperature and water depth were the most important factors of the temporal variation in stability and the spatial variation in stability, respectively. The pollutant transport processes in the Hongfeng Reservoir was very complex with alternate appearances of overflow, interflow and underflow, depending on the season. The spatial water age was primarily determined by the morphometry and the inflow/outflow (with the highest water age in North Lake), whereas the vertical difference in the water age among the layers was primarily controlled by thermal stratification. Negative linear relationships between the average stability and the water ages of the bottom layers in three representative sites during summer were observed. Positive linear relationships between the average stability and the water ages of the surface layers were also observed. These findings enable a better understanding of the hydrodynamic and pollutant transport processes in a deep reservoir.
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Gangnan Reservoir is an important water source of Shijiazhuang, the seat of northern China’s Hebei Province. The irregular shape of the reservoir makes it easy for water to stop flowing in bays, forming dead water areas. Serious water quality problems will ensue. To disclose the influence of a water diversion project on the water exchange in Gangnan Reservoir, this paper sets up a hydrodynamic and water exchange model for the reservoir based on the convection–diffusion theory. According to different diversion flows and wind fields, a total of 12 working conditions was configured to numerically simulate the water exchange in the reservoir. The results show that: the diversion flow is the main factor affecting the water exchange rate. In the main reservoir areas, the water exchange rate increases gradually, finally, it can reach a relatively high level. In the bay areas, the water exchange rate is relatively small, and affected by the diversion flow and the bay location. The wind field has different impacts on the water exchange rate in the main reservoir areas and the bay areas. The impact is small in the former areas, yet significant in the latter areas. When it is not windy, the residence time decreases with the increase of the flow. When it is windy, the wind field of each direction shortened the residence time in the bay areas, while increased that in the main reservoir areas. Furthermore, the transport and diffusion law of water pollutants in Gangnan Reservoir was analyzed by the connectivity matrix: When the main reservoir areas are polluted, the pollutants greatly affect the main reservoir areas; When the bay areas are polluted, the pollutants only affect some adjacent water bodies. The research findings provide scientific reference for the diversion operation of Gangnan Reservoir.
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As an important indicator of pollutant transport and dispersion conditions in lakes, the water exchange capacity of large shallow lakes has always been a focus in research on lake hydrodynamic and water environment. Poyang Lake is a large shallow lake and also the largest freshwater lake in China, which is being given prominent environmental and ecological status. Poyang Lake’s hydrological situation fluctuates dramatically and the spatial and temporal characteristics and influencing factors of its water exchange capacity are complicated. In this paper, water age was selected to describe the water exchange capacity of Poyang Lake, and a water age model of Poyang Lake was established. With the water age model, the spatial and temporal characteristics and influencing factors of water age of Poyang Lake were studied and the law of response of the water age to the evolution of River-Lake relationship between Yangtze River and Poyang Lake and the proposed Poyang Lake Water Conservancy Hub was analyzed. The results showed that: (1) The water age of Poyang Lake demonstrates significant spatial and temporal heterogeneity, that is, the water age in summer and autumn is obviously higher than that in winter and spring and the water age in the disc-shaped lake and lake bay area is obviously higher than that in the main river channel and beach; (2) The water stage at Hukou and catchment inflow are the main factors affecting the water age of Poyang Lake and the influence of the water stage at Hukou on the water age of Poyang Lake is greater than that of the catchment inflow, and the higher water stage at Hukou, the higher the water age of Poyang Lake, while the higher the catchment inflow, the lower the water age of Poyang Lake; (3) After 2003, the water age of Poyang Lake decreases with the evolution of River-Lake relationship and the most significant decrease happens in autumn; (4) The proposed Poyang Lake Water Conservancy Hub may increase the water age of Poyang Lake to some extent while it alleviates the problem of low water in Poyang Lake. This study can provide a scientific base for the water environment management of Poyang Lake and provide a reference for research on water exchange capacity of other large shallow lakes.
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Applications of transport time scales are pervasive in biological, hydrologic, and geochemical studies yet these times scales are not consistently defined and applied with rigor in the literature. We compare three transport time scales (flushing time, age, and residence time) commonly used to measure the retention of water or scalar quantities transported with water. We identify the underlying assumptions associated with each time scale, describe procedures for computing these time scales in idealized cases, and identify pitfalls when real-world systems deviate from these idealizations. We then apply the time scale definitions to a shallow 378 ha tidal lake to illustrate how deviations between real water bodies and the idealized examples can result from: (1) non-steady flow; (2) spatial variability in bathymetry, circulation, and transport time scales; and (3) tides that introduce complexities not accounted for in the idealized cases. These examples illustrate that no single transport time scale is valid for all time periods, locations, and constituents, and no one time scale describes all transport processes. We encourage aquatic scientists to rigorously define the transport time scale when it is applied, identify the underlying assumptions in the application of that concept, and ask if those assumptions are valid in the application of that approach for computing transport time scales in real systems.
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The Hangzhou Bay faces frequent threats from typhoon-induced storm surge and has attracted considerable attentions of coastal researchers and environmental workers. A three-dimensional storm surge model system based on Finite-Volume Coastal Ocean Model (FVCOM) and analytical cyclone model is applied to investigate the hydrodynamic response in the Hangzhou Bay to tropical typhoon. This model has been used to reproduce the storm surge generated by Typhoon Agnes (No. 8114) and the simulated wind field and water elevations have been compared with the available field observations. A series of numerical experimental cases have been conducted to study the effects of land reclamation project (shoreline relocation and seabed deformation) and cyclonic parameters (minimal central pressure (MCP), radius to maximal wind (RMW) and translation speed (TS)) on the hydrodynamics in the Hangzhou Bay. The results show that the shoreline relocation and seabed deformation could generate much higher storm surge in the vicinity of reclamation project with the shoreline relocation making main contribution (about 70%) to this increase. It is found that among the cyclonic parameters, RMW is the most important factor affecting the peak surge in the Hangzhou Bay.