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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°31′N–42°15′N and 120°20′E–125°15′E, 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

,

D

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 s−1) 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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