Three-dimensional hydrodynamic-eutrophication model (HEM ... hydrodynamic... · CE-QUAL-ICM is...

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: [email protected] (K. Park).

mailto:[email protected]

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


(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.


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.


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


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.


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).


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.


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.


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.


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).


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.



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.


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-


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.


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.


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.


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)


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).

References

Banks, R. B., & Herrera, F. F. (1977). Effect of wind and rain on surface reaeration. ASCE Journal of the

Environmental Engineering Division, 103, 489–504.


Blumberg, A. F., & Mellor, G. L. (1987). A description of a three-dimensional coastal ocean

circulation model. In N. S. Heaps (Ed.), Three dimensional coastal models (pp. 1–16). Washington,

DC: AGU.

Cerco, C. F., & Cole, T. M. (1993). Three-dimensional eutrophication model of Chesapeake Bay. ASCE

Journal of Environmental Engineering, 119, 1006–1025.

Cerco, C. F. & Cole, T. M. (1994). Three-dimensional eutrophication model of Chesapeake Bay: Volume

1, main report. Technical Report EL-94-4, US Army Engineer Waterways Experiment Station,

Vicksburg, MS.

DiToro, D. M. & Fitzpatrick, J. J. (1993). Chesapeake Bay sediment flux model. Contract Report EL-93-

2, US Army Engineer Waterways Experiment Station, Vicksburg, MS.

Dortch, M. S., Chapman, R. S., & Abt, S. R. (1992). Application of three-dimensional Lagrangian

residual transport. ASCE Journal of Hydraulic Engineering, 118, 831–848.

Edinger, J. E., Brady, D. K., Geyer, J. C. (1974). Heat exchange and transport in the environment. Report

No. 14, Johns Hopkins University, Baltimore, MD.

Galperin, B., Kantha, L. H., Hassid, S., & Rosati, A. (1988). A quasi-equilibrium turbulent energy model

for geophysical flows. Journal of the Atmospheric Sciences, 45, 55–62.

Hamrick, J. M. (1992). A three-dimensional environmental fluid dynamics computer code: theoretical and

computational aspects. Special Report in Applied Marine Science and Ocean Engineering (SRAM-

SOE) No. 317, Virginia Institute of Marine Science (VIMS), VA.

Hamrick, J. M. (1994). Linking hydrodynamic and biogeochemical transport and transformation models

for estuarine and coastal waters. In M. L. Spaulding, K. W. Bedford, A. F. Blumberg, R. T. Cheng, &

J. C. Swanson (Eds.). Estuarine and coastal modeling III (pp. 591–608). New York: ASCE.

Hamrick, J. M., & Wu, T. S. (1997). Computational design and optimization of the EFDC/HEM3D

surface water hydrodynamic and eutrophication models. In G. Delich & M. F. Wheeler (Eds.), Next

generation environmental models and computational methods (pp. 143–161). Pennsylvania: Society for

Industrial and Applied Mathematics.

Ji, Z.-G., Morton, M. R., & Hamrick, J. M. (2001). Wetting and drying simulation of estuarine processes.

Estuarine, Coastal and Shelf Science, 53, 683–700.

Jin, K.-R., Hamrick, J. H., & Tisdale, T. (2001). Application of three-dimensional hydrodynamic model

for Lake Okeechobee. ASCE Journal of Hydraulic Engineering, 126, 758–771.

Johnson, B. H., Kim, K. W., Heath, R. E., Hsieh, B. B., & Butler, L. (1993). Validation of a three-

dimensional hydrodynamic model of Chesapeake Bay. ASCE Journal of Hydraulic Engineering, 119,

2–20.

Kim, S.-C., Wright, D. L., Maa, J. P.-Y., & Shen, J. (1998). Morphodynamic responses to extratropical

meteorological forcing on the inner shelf of the middle Atlantic Bight: Wind wave, currents, and

suspended sediment transport. In M. L. Spaulding & A. F. Blumberg (Eds.). Estuarine and coastal

modeling V (pp. 456–466). New York: ASCE.

Kim, S.-C., Shen, J., & Kuo, A. Y. (2000). Application of VIMS HEM-3D to a macrotidal environment.

In M. L. Spaulding & A. F. Blumberg (Eds.). Estuarine and coastal modeling VI (pp. 238–249). New

York: ASCE.

Kuo, A. Y., Shen, J., & Hamrick, J. M. (1996). The effect of acceleration on bottom shear stress in tidal

estuaries. ASCE Journal of Waterways, Ports, Coastal and Ocean Engineering, 122, 75–83.

Lee, K.-S., Park, K., & Oh, J.-H. (2000). Development of a three-dimensional, semi-implicit hydrody-

namic model with wetting-and-drying scheme. Journal of Korean Society of Coastal and Ocean

Engineers, 12, 70–80 (in Korean with English abstract).

Lin, J., & Kuo, A. Y. (2003). A model study of turbidity maxima in the York River estuary, Virginia.

Estuaries, 26, 1269–1280.

Mellor, G. L., & Yamada, T. (1982). Development of a turbulence closure model for geophysical fluid

problems. Review of Geophysics and Space Physics, 20, 851–875.

Moustafa, M. Z., & Hamrick, J. M. (2000). Calibration of the wetland hydrodynamic model to the

Everglades Nutrient Removal Project. Water Quality and Ecosystem Modeling, 1, 141–167.

O�Connor, D. J., & Dobbins, W. E. (1958). Mechanism of reaeration in natural streams. Transactions of

the American Society of Civil Engineers, 123, 641–684.


Park, K., Kuo, A. Y., Shen, J., Hamrick, J. M. (1995). A three-dimensional hydrodynamic-eutrophication

model HEM-3D: Description of water quality and sediment process submodels. SRAMSOE No. 327,

VIMS, VA.

Park, K., & Kuo, A. Y. (1996). A multi-step computation scheme decoupling kinetic processes from

physical transport in water quality models. Water Research, 30, 2255–2264.

Park, K., Shen, J., & Kuo, A. Y. (1998). Application of a multi-step computation scheme to an intratidal

estuarine water quality model. Ecological Modelling, 110, 281–292.

Shanahan, P., Harleman, D. R. F. (1982). Linked hydrodynamic and biogeochemical models of water

quality in shallow lakes. Report No. 268, Ralph M. Parsons Laboratory, MIT, MA.

Shen, J., Boon, J. D., & Kuo, A. Y. (1999). A modeling study of a tidal intrusion front and its impact on

larval dispersion in the James River estuary, Virginia. Estuaries, 22, 681–692.

Smolarkiewicz, P. K., & Margolin, L. G. (1993). On forward-in-time differencing for fluids: extension to a

curvilinear framework. Monthly Weather Review, 121, 1847–1859.

Tetra Tech. (1999). Three-dimensional hydrodynamic and water quality model of Potomac Estuary.

Report for Peconic Estuary Program, Suffolk County, NY, Tetra Tech, Inc., VA.

US Environmental Protection Agency. (1997). Compendium of tools for watershed assessment and

TMDL development. EPA841-B-97-006, Office of Water, Washington, DC.

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