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MARINE
Marine Environmental Research 60 (2005) 171–193
www.elsevier.com/locate/marenvrev
ENVIRONMENTAL
RESEARCH
Three-dimensionalhydrodynamic-eutrophication model (HEM-3D):
application to Kwang-Yang Bay, Korea
Kyeong Park a,*, Hoon-Shin Jung b, Hong-Sun Kim b,Sung-Mo Ahn c
a Department of Marine Sciences, University of South Alabama, Dauphin Island Sea Lab,
101 Bienville Blvd., Dauphin Island, AL 36528, USAb GeoSystem Research Corp., 7301 Dongil Techno Town 7th, 823 Kwanyang-2-dong, Dongan-gu, Anyang,
Kyonggi-do 431-716, Republic of Koreac Samsung Engineering & Construction, Samsung PO Box 32, 263 Samsung Plaza Bldg., Seohyun-dong,
Bundang-gu, Sungnam, Kyonggi-do 463-721, Republic of Korea
Received 1 January 2004; received in revised form 7 July 2004; accepted 21 October 2004
Abstract
The purpose of this paper is twofold: to describe the water quality model of Three-Dimen-
sional Hydrodynamic-Eutrophication Model (HEM-3D) and to present an application of
HEM-3D to a coastal system in Korea. HEM-3D, listed as a tool for the development of Total
Maximum Daily Load by US Environmental Protection Agency, is a general-purpose model-
ing package for simulation of the flow field, transport, and eutrophication processes through-
out the water column and of diagenetic processes in the benthic sediment. This paper describes
the water quality model of HEM-3D with emphasis on its unique features. Excessive loadings
of organic wastes have significantly deteriorated water quality conditions of Korean coastal
waters. This paper presents an application of HEM-3D to Kwang-Yang Bay, a coastal system
in Korea, which is one of the first water quality modeling efforts for Korean coastal waters
0141-1136/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.marenvres.2004.10.003
* Corresponding author. Tel.: +1 251 861 7563; fax: +1 251 861 7540.
E-mail address: kpark@jaguar1.usouthal.edu (K. Park).
172 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
accompanied by a relatively comprehensive field program. The current status of data availabil-
ity for water quality modeling in Korea is discussed.
� 2004 Elsevier Ltd. All rights reserved.
Keywords: HEM-3D/EFDC; Physical transport; Eutrophication; Numerical model; Kwang-Yang Bay
(Korea)
1. Introduction
Numerical water quality models have been extensively used to study and manage
water quality conditions in aquatic systems. Deterministic models for the water col-
umn conditions are based on mass balance equations for dissolved and particulate
substances in water column, which consist of physical transport (advective and tur-bulent diffusive transport) processes and biogeochemical processes. Information on
physical transport processes is usually obtained by applying hydrodynamic models.
Depending on the characteristics of a system, one may choose an appropriate hydro-
dynamic model. For a large coastal system where both horizontal and vertical gra-
dients are significant, one needs to employ a three-dimensional hydrodynamic
model. Some examples of three-dimensional hydrodynamic models are Princeton
Ocean Model (POM; Blumberg & Mellor, 1987), Environmental Fluid Dynamics
Computer Code (EFDC; Hamrick, 1992), and Curvilinear Hydrodynamics in ThreeDimensions-Waterways Experiment Station (CH3D-WES; Johnson, Kim, Heath,
Hsieh, & Butler, 1993).
For eutrophication modeling of Chesapeake Bay, Cerco & Cole (1993) developed
a three-dimensional eutrophication model (Corps of Engineers Water Quality Inte-
grated Compartment Model; CE-QUAL-ICM), which receives information on phys-
ical transport processes from CH3D-WES through an external interface. The
interface filters intratidal CH3D-WES results and transfers Lagrangian residual
transport information to CE-QUAL-ICM (Dortch, Chapman, & Abt, 1992), whichfacilitates long-term simulations of water quality conditions. The first-order
Lagrangian residual transport, however, is applicable only to weakly non-linear sys-
tems (Hamrick, 1994). For highly non-linear systems, the Eulerian residual transport
with a time step much shorter than one tidal cycle or a higher-order Lagrangian
residual transport may be required for simulation of physical transport processes.
CE-QUAL-ICM is directly coupled to a predictive sediment diagenesis model (DiT-
oro & Fitzpatrick, 1993) to simulate the interactions between water column and ben-
thic sediment.Virginia Institute of Marine Science has developed EFDC (Hamrick, 1992), a gen-
eral purpose three-dimensional hydrodynamic model. The EFDC subsequently has
been internally integrated with a water-column eutrophication model and a sedi-
ment-diagenesis model (Park, Kuo, Shen, & Hamrick, 1995) to develop Three-dimen-
sional Hydrodynamic-Eutrophication Model (HEM-3D). HEM-3D, also referred to
as EFDC, has been listed as a tool for the development of Total Maximum Daily
Load by US Environmental Protection Agency (1997). The hydrodynamic model,
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 173
hereinafter referred to as EFDC, has been employed for many studies. Examples
include studies of estuarine processes (Ji, Morton, & Hamrick, 2001; Kuo, Shen, &
Hamrick, 1996; Shen, Boon, & Kuo, 1999), wetlands in Everglades (Moustafa &
Hamrick, 2000), shelf areas (Kim, Wright, Maa, & Shen, 1998), and Lake Okeecho-
bee (Jin, Hamrick, & Tisdale, 2001). The water quality model also has been employedfor many studies (e.g., Kim, Shen, & Kuo, 2000; Tetra Tech, 1999) but their results
have not been presented in peer-reviewed journals. The first objective of this paper
is to describe the water quality model portion in HEM-3D.
Since the 1980s, water quality conditions in coastal waters of Korea have been sig-
nificantly deteriorated due to excessive organic loadings of domestic, industrial, agri-
cultural, maricultural, and storm water origins. Construction of large-scale dikes to
isolate coastal embayments has deteriorated water quality inside and outside of dikes
and land reclamation has destroyed intertidal mud flats and their ecosystems (e.g.,Shihwa Lake). Heavy development along the coast to build industrial and residential
complexes has worsened water quality problems for many coastal systems in Korea.
Since the establishment of the Ministry of Maritime Affairs and Fisheries in 1996, the
Korean government has just started to apply systematic management of water qual-
ity for Korean coastal waters, which in most cases are based on numerical models.
Kwang-Yang Bay is a coastal system in southern Korea. Because of recent active
development in Kwang-Yang Bay, the establishment of a modeling framework as a
management tool has been suggested. HEM-3D has been applied to Kwang-YangBay, which is one of the first water quality modeling efforts for Korean coastal
waters accompanied by a relatively comprehensive field program. The second objec-
tive of this paper is to present the application of HEM-3D to Kwang-Yang Bay. The
current status of data availability for water quality modeling and management in
Korea is also discussed.
2. Water quality model in HEM-3D
HEM-3D consists of a hydrodynamic model and a water quality model linked
internally. A brief description of the hydrodynamic model (EFDC) in HEM-3D is
given first, and then, a rather detailed description of the water quality model follows.
EFDC is a three-dimensional hydrodynamic model based on continuity, momen-
tum, salt balance, and heat balance equations with hydrostatic and Boussinesq
approximations. For turbulent closure, the second moment turbulence model, devel-
oped by Mellor & Yamada (1982) and modified by Galperin, Kantha, Hassid, & Ro-sati (1988), is used. EFDC also includes a sediment transport model (Kim et al.,
1998; Lin & Kuo, 2003) and a wetting and drying scheme (Ji et al., 2001). EFDC uses
orthogonal curvilinear or Cartesian horizontal coordinates and a stretched sigma
vertical coordinate. One of the unique features in the numerical solution of EFDC
is an internal–external mode splitting for the momentum equation. EFDC solves
both modes at the same time step by solving the external mode semi-implicitly with
respect to barotropic pressure gradient term in depth-averaged momentum equa-
tions, which allows large time steps and facilitates the wetting-and-drying scheme
174 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
(Lee, Park, & Oh, 2000). Detailed description of EFDC, including the governing
equations and numerical solution method, can be found in Hamrick (1992), Hamrick
& Wu (1997), and Ji et al. (2001).
2.1. Water column eutrophication model
The water column eutrophication model in HEM-3D solves mass balance equa-
tions for the 21 state variables in the water column, simulating three algal groups,
cycles of organic carbon, phosphorus, nitrogen and silica, dissolved oxygen dynam-
ics, and fecal coliform bacteria (Table 1 and Fig. 1). The mass balance equation for a
state variable may be expressed as:
oCot
þ oðuCÞox
þ oðvCÞoy
þ oðwCÞoz
¼ o
oxKx
oCox
� �þ o
oyKy
oCoy
� �
þ o
ozKz
oCoz
� �þ SC; ð1Þ
where C is the concentration of a state variable; u, v, and w are the velocity compo-
nents in the x, y, and z directions, respectively; Kx, Ky, and Kz are the turbulent dif-
fusivities in the x, y, and z directions, respectively; SC is the internal and external
sources and sinks per unit volume. The model state variables, except fecal coliform
bacteria, are identical to those in CE-QUAL-ICM (Cerco & Cole, 1993). Total phos-phate in the present model is defined to include dissolved phosphate and particulate
(sorbed) phosphate only, while that in CE-QUAL-ICM includes algal phosphorus as
well.
The kinetic formulations in the present model are mostly from CE-QUAL-
ICM. Detailed description of the kinetic formulations is given in Park et al.
(1995) and only those that are different from CE-QUAL-ICM are described be-
low. Since the hydrodynamic model has an option of simulating total suspended
solids, the formulation for the light extinction includes the extinction due to totalsuspended solids as well as the background extinction and algal self-shading.
HEM-3D has an option of using either total suspended solids or total active me-
tal as sorption sites for phosphate and dissolved silica. For the phosphorus cycle,
the total phosphate in HEM-3D is defined to include dissolved phosphate and
particulate phosphate and thus the mass balance equation for total phosphate
contains terms to account for the effects of uptake and basal metabolism of algae.
The corresponding terms do not appear in CE-QUAL-ICM, where total phos-
phate includes algal phosphorus as well as dissolved and particulate phosphate.For the reaeration coefficient of dissolved oxygen, HEM-3D includes the effect
of turbulence by bottom friction using the relationship in O�Connor & Dobbins
(1958) and that by surface wind stress using the relationship in Banks & Herrera
(1977). HEM-3D includes fecal coliform bacteria as a state variable. It has no
interaction with other state variables and has only a sink term with a first-order
die-off rate. An exponential function is employed to account for temperature
adjustment of the die-off rate.
Table 1
Model state variables
Water column:
(1) Blue-green algae (Bc)
(2) Diatoms (Bd)
(3) Green algae (Bg)
(4) Refractory particulate organic C (RPOC)
(5) Labile particulate organic C (LPOC)
(6) Dissolved organic C (DOC)
(7) Refractory particulate organic P (RPOP)
(8) Labile particulate organic P (LPOP)
(9) Dissolved organic P (DOP)
(10) Total phosphate P (PO4t)
(11) Refractory particulate organic N (RPON)
(12) Labile particulate organic N (LPON)
(13) Dissolved organic N (DON)
(14) Ammonium N (NH4)
(15) Nitrite + nitrate N (NO3)
(16) Particulate biogenic silica (SU)
(17) Available silica (SA)
(18) Dissolved oxygen (DO)
(19) Chemical oxygen demand (COD)
(20a) Total suspended solida (TSS)
(20b) Total active metala (TAM)
(21) Fecal coliform bacteria (FCB)
Benthic-sedimentb:
(1)–(3) Particulate organic C, G1, G2 and G3 classes in Layer 2
(4)–(6) Particulate organic N, G1, G2 and G3 classes in Layer 2
(7)–(9) Particulate organic P, G1, G2 and G3 classes in Layer 2
(10) Particulate biogenic silica in Layer 2
(11)–(12) Sulfide/methanec, Layers 1 and 2
(13)–(14) Ammonium N, Layers 1 and 2
(15)–(16) Nitrate N, Layers 1 and 2
(17)–(18) Phosphate P, Layers 1 and 2
(19)–(20) Available silica, Layers 1 and 2
(21) Ammonium N flux
(22) Nitrate N flux
(23) Phosphate P flux
(24) Silica flux
(25) Sediment oxygen demand
(26) Release of chemical oxygen demand
(27) Sediment temperature
a Total active metal may not be modeled by using total suspended solid as sorption sites for phosphate
and dissolved silica.b Bottom sediments in the model consist of the oxic upper layer (Layer 1) and the permanently anoxic
lower layer (Layer 2).c Sulfide is modeled for seawater whereas methane is for freshwater.
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 175
2.2. Solution method of mass balance equations in water column
HEM-3D employs an innovative solution method of mass balance equations for
the 21 state variables. The governing mass balance equation Eq. (1) consists of
PO4p
RPOC
DOSOD photosynthesis
respirationreaeration
LPOC
DOC
RPON
NO23
NH4
LPON
DON
TSS
TAMFCB
COD Bg BdBc
SU
SA
PO4d
orlight
RPOP
LPOP
DOP
PO4t
PO4d
PO4p
Fig. 1. Kinetic interactions among the 21 water quality state variables in water column: each box
represents a state variable and the arrows represent kinetic interactions among state variables.
176 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
physical transport and biogeochemical processes. The physical transport and biogeo-
chemical terms are decoupled in HEM-3D (Park et al., 1995). The mass balance
equations for physical transport only (advective and turbulent diffusive terms), here-
inafter referred to as physical transport equations, take the same mathematical formas the salt balance equation in the hydrodynamic model. The equations for biogeo-
chemical processes only, hereinafter referred to as kinetic equations, include kinetic
processes and external loads. The decoupling of the governing mass balance equa-
tions not only simplifies the solution scheme but also makes the model more flexible
with respect to the addition of new state variables and to the modification of kinetic
formulations (Park & Kuo, 1996). Detailed description of the solution method and
interfacing with EFDC is given in Park et al. (1995) and only a brief description is
given below.In HEM-3D, the physical transport and kinetic equations are solved separately in
a multi-step scheme employing alternate computation of each equation (Park et al.,
1995). The time integration of both equations employs a two-time level finite differ-
ence scheme. In the physical transport equation, horizontal advective transport
terms are solved using a second-order accurate upwind advection scheme with
anti-diffusive correction (Smolarkiewicz & Margolin, 1993) and vertical diffusive
transport terms are represented implicitly. The kinetic equation is solved using a sec-
ond-order accurate trapezoidal Crank–Nicholson scheme (see Eq. (4)). Since thephysical transport processes have shorter time scales than the kinetic processes in
intratidal models, the kinetic equation may not be solved as often as the physical
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 177
transport equation. HEM-3D can employ different time steps in the solutions of
physical transport and kinetic equations. The kinetic equation is solved once over
a relatively large time interval with multiple steps of computation of the physical
transport equation over the same time interval without degrading accuracy (Park,
Shen, & Kuo, 1998).The kinetic equations for the 21 state variables can be expressed in a 21 · 21
matrix:
o½C�ot
¼ ½K� � ½C� þ ½R�; ð2Þ
where [C] is the concentration (mass volume�1); [K] is the kinetic rate (time�1); [R] is
the source/sink term (mass volume�1 time�1). Eq. (2) is obtained by linearizing someterms in kinetic equations, mostly Monod type expressions. In reality, most kinetic
processes are non-linear, especially when viewed over a long time period. Over a rel-
atively short time increment, however, at which intratidal numerical models advance
their computation, these processes may be approximated by linear representation.
Therefore, [K] and [R] in Eq. (2) are known quantities in each step of numerical com-
putation, though they may vary with time (Park et al., 1998).
Since the settling of particulate matter from the overlying cell acts as a source for
a given cell, when Eq. (2) is applied to a cell of finite volume, it may be expressed as:
o½C�kot
¼ ½K1�k � ½C�k þ k � ½K2�k � ½C�kþ1 þ ½R�k; ð3Þ
where the subscript k designates a cell at the kth vertical layer. The vertical layer in-
dex k increases upward: with KC vertical layers, k = 1 for the bottom layer and
k = KC for the surface layer. The matrix [C] is a 21 · 1 column vector with state vari-
ables as elements. The matrix [K1] is a 21 · 21 coefficient matrix including terms of
internal kinetic processes. The matrix [K2] is a 21 · 21 diagonal matrix with the non-zero elements accounting for the settling of particulate matter from the overlying
cell: then, k = 0 for k = KC, otherwise k = 1. The matrix [R] is a 21 · 1 column vector
including terms of external loads, benthic fluxes and surface reaeration of DO.
A second-order accurate trapezoidal Crank–Nicholson solution of Eq. (3) over a
time step of h may be expressed as:
½C�Nk ¼ ½I � � h2½K1�Ok
� ��1
� ½C�Ok þ h2
½K1�Ok � ½C�Ok þ k½K2�Ok � ½C�Akþ1
n oþ h½R�Ok
� �;
ð4Þwhere h (=m Æ Dt) is the time step for kinetic equation; m is the positive integer; Dt isthe time step for physical transport equation; [I] is the unit matrix;
[C]A = [C]O + [C]N with the superscripts O and N designating the variables beforeand after being adjusted for the relevant kinetic processes. Since Eq. (4) is solved
from the surface layer downward, the term with ½C�Akþ1 is known for the kth layer
and thus placed on the right-hand side. In Eq. (4), inversion of a matrix can be
avoided if the 21 state variables are solved in a proper order: the kinetic equations
are solved in the order of the variables listed in Table 1.
178 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
2.3. Sediment diagenesis model
HEM-3D has a sediment diagenesis model, internally linked with the water col-
umn eutrophication model, to simulate the processes in the benthic sediment and
at the sediment–water interface. The sediment diagenesis model developed by DiT-oro & Fitzpatrick (1993) and coupled with CE-QUAL-ICM (Cerco & Cole, 1993)
is slightly modified and incorporated into HEM-3D. The sediment diagenesis model
has 27 water quality related state variables and fluxes (Table 1). The sediment model
incorporates three basic processes: depositional flux of particulate organic matter,
their diagenesis and the resulting sediment flux. The sediment model is driven by
net settling of particulate organic carbon, nitrogen, phosphorus, and silica from
the overlying water as calculated by the water column eutrophication model. The
model simulates the diagenesis of deposited particulate organic matter, producinginorganic nutrients and oxygen demand as sulfide or methane. The end products
of diagenesis exert sediment fluxes of nutrients and sediment oxygen demand
depending on the ambient conditions. The governing mass balance equations and
their solution method in the sediment diagenesis model in HEM-3D are identical
to those in DiToro & Fitzpatrick (1993) and are given in Park et al. (1995). The only
difference is the representation of the hysteresis effect of benthic stress due to low
oxygen conditions on benthic population and thus particulate mixing. A first-order
differential equation is employed for benthic stress, the form of which is differentfrom that in DiToro & Fitzpatrick (1993), and the benthic stress accumulates only
when the overlying oxygen is low and is dissipated at a first-order rate (Park
et al., 1995, Eq. (4-14)).
3. Application of HEM-3D to Kwang-Yang Bay
3.1. Modeling domain
Kwang-Yang Bay, a semi-enclosed bay system in southern Korea, is connected in
the south to the coastal sea (South Sea) and in the east to Jin-Joo Bay through the
narrow No-Ryang Strait (Fig. 2). Tidal ranges at the Bay mouth (T3 in Fig. 2) are
about 3.5 and 1.5 m during periods of spring and neap tides, respectively. The largest
freshwater input is from Seom-Jin River with the median discharge rate of 42 m3 s�1,
and Kwang-Yang and Soo-Eo streams are the next most important freshwater in-
puts. Because of recent active development in Kwang-Yang Bay such as the con-struction of coastal industrial complexes and channel dredging, the establishment
of a modeling framework as a management tool was suggested.
The Kwang-Yang Bay area between latitudes 34�44 0–35�05 0N and longitudes
127�34 0–127�54 0E has been selected as the modeling domain (Fig. 3). An orthogonal
curvilinear grid was used to resolve the complex shoreline and highly varying bottom
topography for the inner portion of the Bay and narrow tributaries, while a Carte-
sian grid was used for the rest of the domain. A varying-size grid of 70–300 m was
Fig. 2. Lowest low water depth (m) at Kwang-Yang Bay in Korea with the insert showing Korean
Peninsula: ·, nine stations for tidal harmonic constants; +, six stations for tidal current harmonic
constants; d, three stations for time-series surface elevation (T1–T3); j, two stations for time-series
current velocity (C3 and C4); and m, seven stations for water quality (C1–C7).
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 179
used and five sigma-layers were considered vertically. The number of total water cells
at the surface layer is 9002, including 994 intertidal cells.
3.2. Field data
A field program was conducted in May–July of 2001 to collect data for model
application, of which only the measurements presented in this paper are described
below. Time-series data for surface elevation were obtained using tide gauges at threestations (T1–T3 in Fig. 2). Measurements at two open boundary stations (T2 and
T3) covered the entire modeling period from May 18 to July 31 in 2001, while mea-
surement at station T1 lasted 36 days from May 16. Time-series data for the vertical
profiles of current velocity were obtained from May 15 to June 14 using ADCPs at
127.60 127.65 127.70 127.75 127.80 127.85
East Longitude (degrees)
34.75
34.80
34.85
34.90
34.95
35.00
35.05N
orth
Lat
itude
(de
gree
s)
Yeo-Soo
Kwang-YangStream
Kwang-Yang
Seom-Jin River
No-Ryang Strait
Soo-EoStream
0 1 2 3 4 5(km)
Fig. 3. Grid map for Kwang-Yang Bay in Korea.
180 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
two stations (C3 and C4 in Fig. 2). Four surveys were conducted on May 15–18,
May 23–26, June 20–22, and July 29–31 to obtain the vertical profiles of salinity
and temperature using CTDs at seven stations (C1–C7 in Fig. 2), with hourly
CTD casting over a 13-h period at each station. The reported values for daily fresh-
water discharge rates from Seom-Jin River were compiled (Fig. 4). The daily dis-
charge rates from Kwang-Yang and Soo-Eo streams were estimated based on the
ratios of their drainage basin areas to that of Seom-Jin River. Daily wind data
and other meteorological data related to surface heat exchange were compiled fromthe meteorological station at Yeo-Soo Airport.
In the four surveys for salinity and temperature, water quality parameters were
measured from surface and bottom waters at the same seven stations (C1–C7 in
Fig. 2), with two to three measurements taken over a 13-h period at each station
for each parameter. Parameters measured include chlorophyll-a, particulate organic
carbon, dissolved organic carbon, particulate phosphorus, phosphate, particulate
nitrogen, ammonia, nitrate, nitrite, and dissolved silica. For the loads from tributar-
ies, concentrations of the afore-mentioned water quality parameters were measured
5/21/01 5/31/01 6/10/01 6/20/01 6/30/01 7/10/01 7/20/01 7/30/01
Time (days)
0
500
1000
1500
2000D
isch
arge
(m
3 s-1
)
Fig. 4. Daily freshwater discharge rate from Seom-Jin River: black arrows indicate the times of four water
quality surveys.
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 181
in the four surveys from surface waters at nine tributary stations. For the six small
tributaries (not indicated in Fig. 1) excluding Seom-Jin River and Kwang-Yang and
Soo-Eo streams, freshwater discharge rates were also measured in the first and last
surveys to estimate their loads. For ten point source facilities, the reported values
for discharge rates and the concentrations of monthly 5-day biochemical oxygen de-
mand (BOD5), ammonia, nitrate, nitrite, and phosphate were compiled.
3.3. Application of hydrodynamic model
The hydrodynamic model was calibrated with respect to bottom roughness height
by simulating mean tide characteristics. The open boundary conditions were speci-
fied using the harmonic constants of five major constituents (M2, S2, N2, K1, and
O1) reported in the Tide Tables. The model results calculated with a bottom rough-
ness height of 0.3 cm were compared with the harmonic constants for tides and tidal
currents in Tide Tables. Table 2 lists the absolute relative errors and mean errors
averaged over nine tidal stations (· in Fig. 2) for the amplitude and phase of tidalconstituents. Table 3 lists the errors averaged over six stations (+ in Fig. 2) for the
amplitude and phase of tidal current constituents. The results show that the present
model application is capable of reproducing tidal dynamics not only for the ampli-
tude but also for the propagation (phase) of tidal waves and tidal currents through-
out the modeling domain.
To verify the hydrodynamic model, a model run was conducted for the period of
76 days from May 18 to July 31 in 2001. Open boundary conditions for surface ele-
vation were specified with the observed time-series data at stations T2 and T3, andthose for salinity were specified with the data at stations C6 and C7. Freshwater dis-
Table 2
Mean tide calibration results for tide: absolute relative error (ARE) and mean error (ME) averaged over
nine tidal stations
Tidal constituents M2 S2 K1 O1 N2
Amplitude
ARE (%) 1.6 1.9 2.4 3.7 2.7
ME (cm) �0.6 �0.6 �0.0 �0.5 �0.5
Phase
ME (deg.) �0.1 0.7 0.7 0.5 �0.7
Table 3
Mean tide calibration results for tidal current: absolute relative error (ARE) and mean error (ME)
averaged over six tidal current stations
Tidal current constituentsa M2 S2 K1 O1
U-component
Amplitude
ARE (%) 32.5 11.9 27.0 34.7
ME (cm s�1) 1.1 �0.3 �0.7 �0.5
Phase
ME (deg.) 5.5 10.5 �7.2 6.5
V-component
Amplitude
ARE (%) 17.4 8.8 19.6 63.2
ME (cm s�1) 3.8 1.0 0.1 0.1
Phase
ME (deg.) 6.6 8.1 12.2 �0.6
a The N2 component was not considered with the time-series data for only 15 days long.
182 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
charge rates were specified with the daily data. Daily values of equilibrium temper-
ature and heat exchange coefficient estimated from meteorological data (Edinger,
Brady, & Geyer, 1974) were specified to account for air–sea heat exchange. The mod-
el-data comparison for surface elevation at station T1 is shown in Fig. 5 for both
instantaneous and residual (a cut-off period of 48 h) components. The model calcu-
lated instantaneous and residual components of current velocity are compared with
the data at station C3 in Fig. 6. The model is capable of reproducing surface eleva-
tion and current velocity not only for instantaneous components but also for theresidual components. The model gives a reasonable reproduction of the observed
salinity (Fig. 7) and temperature (Fig. 8), except the overestimation of the observed
salinity at stations C3 and C4 from the last survey on July 29–31. All four surveys
were conducted during the low flow conditions for safety consideration (Fig. 4)
5/18/01 5/22/01 5/26/01 5/30/01 6/3/01 6/7/01 6/11/01 6/15/01 6/19/01
Time (days)
-0.3-0.2-0.10.00.10.20.3
Surf
ace
Ele
vatio
n (m
)
(b)
-3-2-10123
(a)
Fig. 5. Instantaneous (a) and residual (b) surface elevation at station T1: model results (solid line) and
field data (· or dashed line).
-30
-15
0
15
30
(e) filtered U-component (surface)
-100
-50
0
50
100
(a) U-component (surface)
-100
-50
0
50
100
(b) V-component (surface)
-100
-50
0
50
100
(c) U-component (bottom)
-100
-50
0
50
100
Vel
ocity
(cm
s-1
)
(d) V-component(bottom)
5/18/01 5/22/01 5/26/01 5/30/01 6/3/01 6/7/01 6/11/01
Time (days)
-30
-15
0
15
30
(f) filtered U-component (bottom)
Fig. 6. Instantaneous (a)–(d) and residual (e)–(f) current velocity at station C3: model results (solid line)
and field data (· or dashed line).
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 183
and little spatial gradient existed in the observed surface salinity between stations C2,
C3, and C4. The last survey, however, showed that the observed surface salinity was
higher at station C2 than those at stations C3 and C4. Station C2 is closer to Kwang-
Yang Stream (Fig. 2), the second largest freshwater input, and the last survey also
was conducted during the low flow condition (Fig. 4). Hence, the lower salinity at
stations C3 and C4 on July 29–31 cannot be due to the discharge from Kwang-Yang
Stream but is likely to be due to local freshwater input that was not captured by the
20
30
40
(a) Station C2: surface
20
30
40
(c) StationC3: surface
5/18 5/28 6/7 6/17 6/27 7/7 7/17 7/27
Time (days in 2001)
20
30
40
Salin
ity (
psu)
Salin
ity (
psu)
Salin
ity (
psu)
(e) Station C4: surface
(b) Station C2: bottom
(d) Station C3: bottom
5/18 5/28 6/7 6/17 6/27 7/7 7/17 7/27
Time (days in 2001)
(f) StationC4: bottom
Fig. 7. Salinity at stations C2, C3, and C4: model results (solid line) and field data (·: maximum, mean,
and minimum over a 13-h period).
0
10
20
30
(a) Station C2:surface
0
10
20
30
(c) Station C3:surface
5/18 5/28 6/7 6/17 6/27 7/7 7/17 7/27
Time (days in 2001)
0
10
20
30
T (
ºC)
T (
ºC)
T (
ºC)
(e) StationC4: surface
(b) Station C2:bottom
(d) Station C3:bottom
5/18 5/28 6/7 6/17 6/27 7/7 7/17 7/27
Time (days in 2001)
(f) StationC4:bottom
Fig. 8. Same as Fig. 7 except for temperature.
184 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 185
current field program. There are several industrial complexes and sewage treatment
plants along the coastline near stations C3 and C4 and only the design values were
reported for the discharge rates from point source facilities. The present application
of the hydrodynamic model gives information of physical transport processes in
good agreement with the observations, which can be used for water qualitymodeling.
3.4. Application of water quality model
Prior to the present study, there have been no systematic water quality measure-
ments, for example, simultaneous measurements of both physical transport and
water quality parameters, which can be used for modeling purposes. The water qual-
ity model was applied over the period of May 18–July 31 in 2001, a period that wasdictated by the field data collected in the present study. Since diatoms are dominant
in Kwang-Yang Bay during the modeling period (i.e., late spring to early summer),
two groups of algae were simulated with each representing diatoms and other algae.
With diatoms modeled as a separate group, the silica cycle was simulated. Fecal coli-
form bacteria were not simulated. Sorption/desorption of phosphate and dissolved
silica was not considered and thus neither total suspended solids nor total active me-
tal were simulated. Although the model incorporates a sediment process model, it
was not activated in the present application due to the relatively short modeling per-iod (76 days) and constant values based on previous measurements were specified for
benthic fluxes (Table 5).
Data from the field program were used to estimate the external loads from ten
point source facilities and nine tributaries. For all point source facilities, only the de-
sign values for discharge rates and the monthly effluent concentrations of BOD5,
inorganic nitrogen, and inorganic phosphorus were available with no data on efflu-
ent concentrations of organic matter. Such lack of data for effluents is not unusual
for the point source facilities in Korea. In the present model application, BOD5 con-centrations were converted to total organic carbon using the empirical relationship
Table 4
Summary of loads from point sources and tributaries
Loads TOCa (kg d�1) TNa (kg d�1) TPa (kg d�1)
Point source loads
Yeo-Chun-2 2082 1930 450
Other 9 facilities 1572 1852 393
Sub total (10 facilities) 3654 3782 843
Tributary loads
Seom-Jin river 62,622 62,712 1549
Other 8 rivers 5933 4068 100
Sub total (9 rivers) 68,555 66,780 1649
Total 72,209 70,562 2492
a TOC, total organic carbon; TN, total nitrogen; TP, total phosphorus.
Table 5
Summary of kinetic coefficients employed in the present model application
Coefficient Value
Maximum algal growth rate (d�1) 2.25, 2.0a
Optimum temperature for algal growth (�C) 15.0, 27.0a
Effect of temperature on algal growth below optimum temperature (�C�2) 0.008, 0.006a
Effect of temperature on algal growth above optimum temperature (�C�2) 0.008
Algal basal metabolism rate at 20 �C (d�1) 0.03
Half-saturation constant for:
Nitrogen uptake of algae (g N m�3) 0.01
Phosphorus uptake of algae (g P m�3) 0.001
Silica uptake of diatoms (g Si m�3) 0.05
Algal predation rate at 20 �C (d�1) 0.16, 0.20a
Algal settling rate (m d�1) 0.10
Decay rate of:
Organic carbon at 20 �C (d�1) 0.005, 0.075, 0.01b
Organic phosphorus at 20 �C (d�1) 0.005, 0.075, 0.10b
Organic nitrogen at 20 �C (d�1) 0.005, 0.075, 0.015b
Settling rate of particulate organic matter (m d�1) 1.0
Maximum nitrification rate at 27 �C (g N m�3 d�1) 0.07
Dissolution rate of particulate silica at 20 �C (d�1) 0.03
Sediment oxygen demand (g O2 m�2 d�1) 0.64
Benthic flux of:
Ammonia (g N m�2 d�1) 0.1
Nitrate (g N m�2 d�1) 0.005
Phosphate (g P m�2 d�1) 0.005
Dissolved silica (g N m�2 d�1) 0.075
a For diatoms and other algae, respectively.b For refractory particulate, labile particulate, and dissolved organic matter, respectively.
186 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
developed for New York City municipal plants (Cerco & Cole, 1994, Eq. (V-1)).
Concentrations of organic nitrogen and organic phosphorus were estimated based
on the default concentrations depending on the levels of treatment of each facility(Cerco & Cole, 1994, Table 5-3). The loads from tributaries were estimated from a
few measurements only: four measurements for concentrations and two for dis-
charge rates. Since no data were available, nonpoint source loads along the shoreline
and atmospheric loads were not considered (the latter may not be significant due to
the relatively small surface area). These uncertainties in the estimation of external
loads will limit the applicability of the present model results for water quality. A
comprehensive data set including detailed data for all external loads is essential
for a reliable water quality modeling. A watershed modeling approach may be nec-essary to reasonably estimate the tributary and nonpoint source loads. More com-
plete measurements including discharge rates and effluent concentrations of
organic and inorganic nutrients are necessary to reasonably estimate the point source
loads. Table 4 summarizes the loads employed in the present model application.
Kwang-Yang Bay is dominated by tributary loads, which comprise 95% of total
loads for carbon and nitrogen and 66% for phosphorus. Seom-Jin River is responsi-
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 187
ble for 91–94% of total tributary loads. Of point source loads, the Yeo-Chun-2 facil-
ity (Fig. 2) is the largest one. The estimated loads for total organic matter were split
into refractory particulate, labile particulate and dissolved organic matter following
Cerco & Cole (1994, Tables 6-3 to 6-6).
Initial conditions were specified with the data from the first survey on May 15–18and open boundary conditions were specified with the data at stations C6 and C7.
The coefficient values in Cerco & Cole (1994, Chapter 9) served as a starting point
for the present model calibration. Several kinetic coefficients that may vary for dif-
ferent systems were adjusted by comparing the model results with the survey data
collected in the present study. Table 5 shows a summary of the kinetic coefficients
employed in the present application. Kinetic coefficients not listed in Table 5 are
the same as those in Cerco & Cole (1994). Figs. 9–12 compare the model results with
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.4
0.8
1.2
Dis
solv
ed S
i(g
Si m
-3)
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.1
0.2
PO4 (
gP
m-3)
0.0
0.1
0.2
0.3
0.4
TP
(g P
m-3)
0.0
0.2
0.4
0.6
0.8
NO
3 (g
Nm
-3)
0.0
0.2
0.4
0.6
0.8
NH
4 (g
Nm
-3)
0
1
2
3
TN
(g
Nm
-3)
0
1
2
3
4
DO
C(g
C m
-3)
0
2
4
6
8T
OC
(g
C m
-3)
0
10
20
30
Chl
. (m
g C
HL
m-3)
Fig. 9. Daily maximum (dashed line), mean (solid line), and minimum (dashed line) model results
compared with field data (·, 2–3 data over a 13-h period) for the surface water of station C3.
188 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
the field data for the surface and bottom waters of stations C3 and C4 for chloro-
phyll-a, total organic carbon (TOC), dissolved organic carbon (DOC), total nitrogen
(TN), ammonia nitrogen (NH4), nitrate + nitrite nitrogen (NO3), total phosphorus
(TP), dissolved phosphate (PO4), and dissolved silica.
The model overall gives a reasonable reproduction of observed chlorophyll con-centrations. Kwang-Yang Bay, at least during the simulation period, is so eutrophic
that the algal growth is mainly controlled by light availability: note the relatively
high nutrient concentrations (Figs. 9–12) compared to the half-saturation constants
for algal uptake (Table 5). Underestimation of phosphorus are apparent at station
C3, which may be attributable to the uncertainties in the estimation of the external
loads described above. For station C3, quite close to the largest point source facility
(Yeo-Chun-2 in Fig. 2 and see Table 4), the underestimation of phosphorus probably
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.4
0.8
1.2
Dis
solv
ed S
i(g
Si m
-3)
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.1
0.2
PO4 (
gP
m-3)
0.0
0.1
0.2
0.3
0.4
TP
(g P
m-3)
0.0
0.2
0.4
0.6
0.8
NO
3 (g
Nm
-3)
0.0
0.2
0.4
0.6
0.8
NH
4 (g
Nm
-3)
0
1
2
3
TN
(g
Nm
-3)
0
1
2
3
4
DO
C(g
C m
-3)
0
2
4
6
8
TO
C (
g C
m-3)
0
10
20
30
Chl
. (m
g C
HL
m-3)
Fig. 10. Same as Fig. 9 except for the bottom water of station C3.
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.4
0.8
1.2
Dis
solv
ed S
i(g
Si m
-3)
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.1
0.2
PO4 (
gP
m-3)
0.0
0.1
0.2
0.3
0.4
TP
(g P
m-3)
0.0
0.2
0.4
0.6
0.8
NO
3 (g
Nm
-3)
0.0
0.2
0.4
0.6
0.8
NH
4 (g
Nm
-3)
0
1
2
3
TN
(g
Nm
-3)
0
1
2
3
4
DO
C(g
C m
-3)
0
2
4
6
8
TO
C (
g C
m-3)
0
10
20
30C
hl. (
mg
CH
L m
-3)
Fig. 11. Same as Fig. 9 except for the surface water of station C4.
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 189
is due to the insufficient point source loads. For all point source facilities, only the
design values for discharge rates and the monthly effluent concentrations of
BOD5, inorganic nitrogen, and inorganic phosphorus were available with no data
on effluent concentrations of organic matter. In addition to the data for external
loads, more data for water quality conditions certainly are required for more thor-
ough calibration and verification of the water quality model.
4. Summary and conclusion
This paper describes the water quality model in HEM-3D. In the water column
eutrophication model, the state variables and kinetic formulations in general are
similar to those in CE-QUAL-ICM (Cerco & Cole, 1993). The water column
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.4
0.8
1.2
Dis
solv
ed S
i(g
Si m
-3)
5/16 5/31 6/15 6/30 7/15 7/30
Time (days in 2001)
0.0
0.1
0.2
PO4 (
gP
m-3)
0.0
0.1
0.2
0.3
0.4
TP
(g P
m-3)
0.0
0.2
0.4
0.6
0.8
NO
3 (g
Nm
-3)
0.0
0.2
0.4
0.6
0.8
NH
4 (g
Nm
-3)
0
1
2
3
TN
(g
Nm
-3)
0
1
2
3
4
DO
C(g
C m
-3)
0
2
4
6
8
TO
C (
g C
m-3)
0
10
20
30
Chl
. (m
g C
HL
m-3)
Fig. 12. Same as Fig. 9 except for the bottom water of station C4.
190 K. Park et al. / Marine Environmental Research 60 (2005) 171–193
eutrophication model is internally linked with a sediment diagenesis model, which is
slightly modified from the model developed by DiToro & Fitzpatrick (1993). One of
the unique features of HEM-3D is the internal linkage of the eutrophication model
with its hydrodynamic counterpart (EFDC) and the subsequent solution method of
the governing mass balance equations. The mass balance equations are decoupled
into physical transport and biogeochemical equations, which are solved separately
in a multi-step scheme employing alternate computation of each equation (Park
et al., 1995). The decoupling simplifies the solution scheme and makes the modelmore flexible with respect to the addition of new state variables and to the modifica-
tion of kinetic formulations (Park & Kuo, 1996). The decoupling also allows a sec-
ond-order accurate Crank–Nicholson solution of the kinetic equation Eq. (4), by
which the numerical solution of the kinetic terms does not degrade the accuracy
of the solution scheme of mass balance equations. Shanahan & Harleman (1982)
K. Park et al. / Marine Environmental Research 60 (2005) 171–193 191
have pointed out the necessity of an even-handed treatment of both hydrodynamics
and biogeochemistry in water quality models. In the multi-step solution method, dif-
ferent time steps can be employed in the solutions of physical transport and kinetic
equations. The kinetic equation is solved once over a relatively large time interval
with multiple steps of computation of the physical transport equation over the sametime interval without degrading accuracy (Park et al., 1998).
The application of HEM-3D to Kwang-Yang Bay in Korea is presented, which is
one of the first water quality modeling efforts for Korean coastal waters accompa-
nied by a relatively comprehensive field program. A field program was conducted
in May–July of 2001 to collect data for model application. The physical transport
processes were rather thoroughly validated with the data. The model gave a good
reproduction of tidal dynamics (Tables 2 and 3), both instantaneous and residual
components of surface elevation (Fig. 5) and current velocity (Fig. 6), salinity(Fig. 7), and temperature (Fig. 8). The model overall gives a reasonable reproduction
of water quality conditions including chlorophyll, but lack of data was apparent for
both external loads and water quality conditions in Kwang-Yang Bay (Figs. 9–12).
The water quality model results could be substantially improved, particularly for
phosphorus, if more data were available for external loads and for more thorough
model calibration and verification.
Systematic management of water quality for Korean coastal waters based on
numerical models has just started since the establishment of the Ministry of Mar-itime Affairs and Fisheries in 1996. A comprehensive monitoring program has not
yet been in place for Korean coastal waters including Kwang-Yang Bay. The exist-
ing monitoring program and almost all other measurements for external loads and
water quality conditions have focused on inorganic nutrients only, not including
organic matter. Few studies have been made for the external loads into Korean
coastal waters from tributaries and nonpoint sources. A systematic and long-term
monitoring program including measurements of organic matter and estimation of
external loads is necessary for Korean coastal waters for the accurate evaluation ofwater quality conditions and for the reasonable application of a water quality
model.
Acknowledgements
HEM-3D was developed in the Virginia Institute of Marine Science as a part of the
Three-Dimensional Model Project funded by the Virginia Chesapeake Bay InitiativePrograms. Partial support of the model application to Kwang-Yang Bay was from
Samsung Engineering & Construction and from the Basic Research Program of the
Korean Science and Engineering Foundation (Grant No. R01-2001-000-00076-0).
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