(cunha 2006) hydrodynamics and water quality models applied to sepetiba bay_sisbahia

7/31/2019 (Cunha 2006) Hydrodynamics and Water Quality Models Applied to Sepetiba Bay_SiSBaHia

1/14

Continental Shelf Research 26 (2006) 19401953

Hydrodynamics and water quality models applied

to Sepetiba Bay

Cynara de L. da N. Cunhaa,, Paulo C.C. Rosmanb, Aldo Pacheco Ferreirac,Teo filo Carlos do Nascimento Monteirod

aNational School of Public HealthENSPFIOCRUZ, Rua Leopoldo Bulhoes, 1480 5 andar, CEP: 21041-210, Rio de Janeiro, BrazilbCoastal & Oceanographic Engineering, Ocean Engineering Department COPPE/UFRJ, Federal University in Rio de Janeiro,

PO Box, 68508, CEP: 21945-970, Rio de Janeiro, BrazilcNational School of Public HealthENSP- FIOCRUZ, Rua Leopoldo Bulhoes, 1480 6 andar, CEP: 21041-210, Rio de Janeiro, Brazil

dSustainable Development and Environmental Health Area, PAHO/WHO

Received 19 January 2005; received in revised form 21 June 2006; accepted 28 June 2006

Available online 30 August 2006

Abstract

A coupled hydrodynamic and water quality model is used to simulate the pollution in Sepetiba Bay due to sewage

effluent. Sepetiba Bay has a complicated geometry and bottom topography, and is located on the Brazilian coast near Rio

de Janeiro. In the simulation, the dissolved oxygen (DO) concentration and biochemical oxygen demand (BOD) are used

as indicators for the presence of organic matter in the body of water, and as parameters for evaluating the environmental

pollution of the eastern part of Sepetiba Bay. Effluent sources in the model are taken from DO and BOD fieldmeasurements. The simulation results are consistent with field observations and demonstrate that the model has been

correctly calibrated. The model is suitable for evaluating the environmental impact of sewage effluent on Sepetiba Bay

from river inflows, assessing the feasibility of different treatment schemes, and developing specific monitoring activities.

This approach has general applicability for environmental assessment of complicated coastal bays.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Coastal areas; Water quality model; Sepetiba Bay; Numerical simulation

1. Introduction

Sepetiba Bay is located on the coast of Rio de

Janeiro State, Brazil. The bay constitutes an

important natural breeding place for molluscs,

crustaceans, and fish; fishing has become an

important economic activity, together with tourism,

stimulated by the natural environment. However,the proximity of the metropolitan region of Rio de

Janeiro City has brought several environmental

problems to the Bay, including reduced water

quality due to sewage effluent and urban solid

residues, mainly on the eastern part of the bay.

Since the local depths are small and stratification

patterns are weak, the tidal currents are expected to

be well represented by depth-averaged variables.

Consequently, in the study of pollution transport

ARTICLE IN PRESS

www.elsevier.com/locate/csr

0278-4343/$- see front matterr 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.csr.2006.06.010

Corresponding author. Tel.: +55 21 2598 2747;

fax: +5521 2270 7352.

E-mail addresses: [email protected] (C.L.N. Cunha),

[email protected] (A.P. Ferreira).
http://www.elsevier.com/locate/csrhttp://dx.doi.org/10.1016/j.csr.2006.06.010mailto:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.csr.2006.06.010http://www.elsevier.com/locate/csr


2/14

and hydrodynamic circulation in Sepetiba Bay, two-

dimensional depth-integrated models were em-

ployed. The present paper describes hydrodynamic

and water quality models.

Hydrodynamic and water quality models are

developed to simulate the long-term transport andto evaluate pollution by sewage effluent. Validation

of the water quality model is carried out through the

analyses of two examples. The first example presents

a comparison between the results furnished by the

present model and the analytical solution, consider-

ing a channel with a simple geometry. In the second

example, application of the proposed model to

Sepetiba Bay illustrates practical problems in

estuaries with complicated geometry and bottom

topography, and aims to evaluate the dispersion of

sewage effluent brought by local rivers. Thus, such a

water quality model can be employed to support thechoice of strategic decisions concerning sewage

effluent in rivers, and even in coastal areas. In the

simulations conducted here, despite the possibility

using other substances, the dissolved oxygen (DO)

and biochemical oxygen demand (BOD) water

quality parameters were adopted. This choice was

motivated by the availability of measurement data.

The models belong to the Hydrodynamic Envir-

onmental System called SisBAHIAs (Sistema Base

de Hidrodinamica Ambiental), developed by the

Coastal and Oceanographic Engineering Depart-ment, Oceanic Engineering Program, Federal Uni-

versity in Rio de Janeiro (COPPE/UFRJsee

www.sisbahia.coppe.ufrj.br). In the development

of SisBAHIAs, finite elements and finite differences

were adopted, respectively, in the spatial and time

discretization. Turbulent stress is parameterized

according to filtering techniques derived from the

approach known as large eddy simulation (LES)

(Rosman, 2005). The water quality model takes the

oxygen, nitrogen, and phosphorus cycles into

account. Since the modelled kinetic reactions are

heavily dependent on temperature and salinity

(Sellers, 1965), the model was developed regarding

the following water quality parameters: salinity,

temperature, DO, BOD, organic nitrogen, ammonia

nitrogen, nitrate nitrogen, chlorophyll a, algal

biomass, organic phosphorus, and inorganic phos-

phorus.

One of the most important consequences of

dumping organic and inorganic residues into the

body of water relates to the oxygen deficit. Oxygen

is important in the process of organic matter

oxidation in waste material. Oxygen sources include

reaeration from the atmosphere, photosynthetic

oxygen production, and DO in incoming effluents.

DO sinks include: oxidation of carbonaceous and

nitrogenous waste material, sediments demand in

the body of water, and use for respiration by

aquatic plants (Thomann and Muller, 1987). Thereare thus many uncertainties concerning the trans-

formation processes. These processes are generally

modelled using first-order reactions, with coeffi-

cients experimentally computed and the values

belonging to a specific range. Calibration of the

water quality model requires correct definition of

these coefficients. Advection and diffusion, which

also affect DO and BOD concentrations, are also

taken into account.

Numerical models that simulate the spatial and

temporal distributions of non-conservative water

quality parameters have been used in recent years asa scientific and managerial tool (QUAL2E, Brown

and Barnwell, 1987, WASP4, Umgiesser et al., 2003;

MIKE 21, 2001). The water quality model devel-

oped here uses the same basic transformation

equations as the WASP model, as reported in Sheng

et al. (1996), and also uses the same spatial grid as

the hydrodynamics model (note that a different time

step length can be employed in the analyses). Flow

velocities and turbulence coefficients, already com-

puted by hydrodynamics model, can be used

directly by the water quality model without anyspace averaging.

2. Mathematical model

The water quality model is coupled with the

hydrodynamic model to provide the advective and

diffusive components of the water quality equa-

tions. Two-dimensional shallow water equations in

their depth-integrated form can be written in a

Cartesian system (x,y), aligned in the east, north,

and vertical directions, using hydrostatic approx-imation for the pressure distribution and the

Boussinesq approximation, as

qz

qt qUh z

qx qVh z

qy 0, (1)

qU

qt UqU

qx VqU

qy g qz

qx

1d

q

qx

dtxx

rr

qqy

dtxy

rr

!fV t

Sx

drr bU,

2

ARTICLE IN PRESS

C.L.N. Cunha et al. / Continental Shelf Research 26 (2006) 19401953 1941
http://www.sisbahia.coppe.ufrj.br/http://www.sisbahia.coppe.ufrj.br/


3/14

qV

qt UqV

qx VqV

qy g qz

qy 1

d

q

qx

dtyx

rr

qqy

dtyy

rr

!fU t

Sy

drr bV. 3

In (2) and (3), one has

b Cf U2 V2

1=2d

, (4)

where: d(x,y,t) h(x,y)+z(x,y,t); z(x,y,t) is the freesurface elevation with respect to the mean water

level; h(x,y) is the water depth, d(x,y,t) is the total

water depth; U and V are the depth-averaged

components of the horizontal velocity;tij represent

the turbulent stresses components, f is the Coriolis

factor, and rr is a reference density. The bottom

friction coefficient, Cf, is written in terms of theChezy coefficient (C) according to

Cf g

C2with C 18 log 6d

, (5)

where e is the amplitude of the equivalent bottom

roughness that corresponds to double the roughness

height.

According to Daily and Harleman (1966), the

surface stresses may be expressed as follows:

tsi rairCDU

210 cos yi, (6)

where CD is a wind drag coefficient (Wu, 1982);

U10 is the wind speed 10 m above the free sur-

face, yi the angle between the wind velocity

vector and the xi direction, and rair is the air

density.

Turbulent stresses can be written in a para-

metric form following the approach by Cunha

and Rosman (2005), which was based on the

filtering techniques. The resultant expressions

are

tij

rr KVij KHij q

Ui

qxj qUjqxi

L2k

24

qUi

qxk

qUjqxk

qUi

qxk

qUj

qxk

, 7

where i;j 1; 2 and k 1; 2; 3, with k 3 corre-sponding to time t (in this context x3 t), KVij is adepth-averaged turbulent viscosity coefficient in the

horizontal plane, KHij is a horizontal dispersion

coefficient of momentum, and Lk represent the

widths of the spatial and temporal Gaussian filters.

A simple formulation for the overall effect of

(KH+KV) is adopted:

KH KV 0:1ud; with u ffiffiffi

gpCh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2 V2

p.

(8)

The width of the Gaussian filter Lk, in the xkdimension is defined as Lk akDxk, where akis a homogeneous scaling parameter in the xkdimension. The value of ak calibrates the mag-

nitude of the filtering terms. Usual values of ak lie

between 0.25 and 2.0; most often the value 1.0

gives satisfactory results. The filtering terms, as

displayed in Eq. (7), behave as self-adjusting sub-

grid scale turbulent stresses. In a non-structured

finite element discretization mesh, the magnitude of

these terms is a function of the local resolvable

scale.

The basic mass-balance equation for a non-

conservative substance, with advection and

diffusion terms and kinetic processes, may be

expressed as

qCm

qt Uiq

Cm

qxi 1

d

q

qxjd Dijdjk L

2k

12

qUj

qxk

!qCm

qxk

kinetic processes, 9

where Cm is the concentration of m substances and

Dij is the turbulent diffusivity. In Eq. (9), i, j 1,2

and k 1, 2, 3, with k 3 corresponding to time t.The following interpretation is valid for the indexcoefficient Cm: C1 ammonia nitrogen (mg N/L),C2 nitrate nitrogen (mg N/L), C3 inorganicphosphorus (mg P/L), C4 algal biomass (mg P/Lor mg N/L), C5 biochemical oxygen demand (mgO2/L), C6 dissolved oxygen (mg O2/L),C7 organic nitrogen (mg N/L), C organicphosphorus (mg P/L), C9 chlorophyll a (mg/L),CT temperature (1C), and CS salinity (psu).

2.1. Kinetic processes

Details of the kinetic reactions involved in the

transformation processes for the above-mentioned

substance can be found in Rosman (2005). In the

present work, the kinetic processes of the substances

involved in the Sepetiba Bay application, i.e.,

biochemical oxygen demand, C5, dissolved oxygen,

C6, and temperature, CT, are shown; salinity is

considered a conservative substance and conse-

quently does not undergo reaction or transforma-

tion. The kinetic reactions were obtained according

to the equations below (Sheng et al., 1996):

ARTICLE IN PRESS

C.L.N. Cunha et al. / Continental Shelf Research 26 (2006) 194019531942


4/14

Biochemical oxygen demand (C5):qC5

qt aocK1DC4 KDYT20D

C6

KDBO C6

C5

Vs31 fD5d

C5 4014

K2DYT202D

KNO3KNO3 C6

C2.

10

Dissolved oxygen (C6):qC6

qt KaYT20a Cs C6 KDYT20D C6KDBO C6

C5

6414

K12YT2012

C6

KNIT C6

C1

GPI32

12 48

121 PNH3

C4

32

12 K1RYT201R C4

SOD

d YT20s .

11

Temperature (CT) (Sellers, 1965):qCT

qt Hnrcd

. (12)

The coefficients used in the model are given in

Table 1.

3. Numerical model

The numerical implementation of the two

models, hydrodynamic and water quality, are not

discussed here; the interested reader is referred to

Rosman (2005) for additional information on thehydrodynamic model; the numerical model devel-

oped for the advective and diffusive transport is

described in detail by Cunha et al. (2002). The

current article merely presents the time discretiza-

tion of the equations that describe the kinetic

reactions. The water quality model employs the

same spatial grid as the hydrodynamic models; in

other words, the model uses finite differences in the

time discretization and finite elements in the spatial

(Abbot and Basco, 1989). These equations can be

written as

qCm

qt K1;mCm K2;m, (13)

where K1,m and K2,m are the coefficients related to

the transformation processes. Taking as an example

the biochemical oxygen demand (C5), the values of

K1,5 and K2,5 are given by

qC5

qt K1;5C5 K2;5, (14)

ARTICLE IN PRESS

Table 1

Parameters employed in the water quality model and values adopted in the Sepetiba Bay analysis

Var. Description Units Sepetiba Bay

K1D Algal biomass death rate Day1 0.02

aoc Oxygencarbon ratio mg O2/mg C 2/12

KD De-oxygenation rate at 20 1C Day1 0.05

KDBO Half-saturation constant for oxidation of BOD mg O2/L 0.5

VS3 Organic matter settling velocity m/day 0.0

fD5 Fraction of dissolved DBO in the water column 0.5K2D Denitrification rate at 20 1C Day

1 0.09

KNO3 Half-saturation constant for DO limitation in the denitrification process mg N/L 0.1

Ka Re-aeration rate at 20 1C Day1 1.38

K12 Nitrification rate at 20 1C Day1 0.02

KNIT Half-saturation constant for DO limitation in the nitrification process mg O2/L 0.3

GPI Algal biomass growth rate Day1 0.30

K1R Algal biomass respiration rate at 20 1C Day1 0.12

SOD Sediment oxygen demand g/mg day 0.2

PNH3 Ammonia preference factor Variable

YD, Yay Temperature correction coefficient for de-oxygenation, re-aeration,y

Cs Saturation concentration of DO mg O2/L Variable

Hn Energy flux passing the airwater interface Cal/cm2/day Variable

C Specific heat of water Cal/ kg

o

C 1000.0



5/14

where

K1;5 KDYT20DC6

KDBO C6

Vs31 fD5

d

and

K2;5 aocK1DC4 40

14K2DY

T202D

KNO3KNO3 C6

C2.

If one follows the implicit factored scheme in the

time discretization (Beam and Warming, 1978), a

non-linear equation such as the equation below:

q

qtCx;y; t L1CL2C, (15)

where C is a scale function and L1and L2 are linear

operators ofC, is rewritten at the time step (n+1) in

the approximate form

Cn1 CnDt

12

Ln11 Ln2 Ln1Ln12

O Dt2 (16)with a truncation error of order Dt2.

Using the approximations defined in the implicit

factored scheme, the time discrete equation is given

by

Cn1m CnmDt

12

Kn11;m Cnm Kn1;mCn1m

1

2Kn12;m Kn2;m

, 17

where Cn1m is the concentration of substance m attime t Dt, Cnm the concentration of substance m attime t, Kn11;m and K

n12;m are the coefficients of

substance m at time t Dt and Kn1;m and Kn2;m arethe coefficients of substance m at time t.

The coefficients are calculated explicitly as:

Kn1;5 KDYTn20

DCn6

KDBO Cn6

Vs31 fD5d

,

(18)

Kn11;5 KDYTn120

D

C6KDBO C6

Vs31 fD5

d,

(19)

Kn2;5 aocK1DCi4 40

14K2DY

Tn202D

KNO3KNO3 Cn6

Ci2,

(20)

Kn12;5 aocK1DCi4 40

14K2DY

Tn1202D

KNO3KNO3 C6

Ci2, 21

where C6 is the DO concentration extrapolated attime t+1/2Dt, Ci4 is the algal biomass concentration

in the initial condition, Ci1 is the ammonia nitrogen

concentration in the initial condition, Tn+1 is the

temperature at time t Dt, Cn6 is the DO concentra-tion at time t, Tn is the temperature at time t.

For each substance, the values of the coefficients

K1,5 and K2,5 are explicitly calculated, extrapolating

the variables at time t 1=2Dt when necessary. Forthe extrapolated variables, with a second-order

scheme, the following quadratic approximations

with three time levels are used:

G 1:875G 1:25G 0:375G, (22)where G are variables at time t, G are variables at

time tDt, and G are variables at time t2Dt.It can be observed that the DO concentration,

which was not calculated yet in this time t Dt,needs to be extrapolated for time t 1=2Dt.Temperature, which was already calculated, does

not need to be extrapolated, and the adopted values

correspond exactly to the computed values. The

final system of equations presents a bandwidthsmaller than the bandwidth corresponding to the

classic scheme. As a consequence, the adopted

ascheme is less computer memory consuming.

4. Verification of the water quality model

Thomann and Muller (1987) have presented a

one-dimensional analytical solution to a problem

with a simple geometry under the assumption of

BOD waste discharge concentration. The test

problem consists of a channel aligned with x-axis,

15.0km total length, 200.0 m width, and 3.0 m

depth. In the analysis conducted in this study, a

mesh with 300 elements and 1505 nodes was

adopted, with Dx Dy 50,0 m, characterizing aone-dimensional flow. The equation of the BOD

DO model, which describes the BOD waste dis-

charge, considers the steady, uniform, and one-

dimensional flows can be written as

U

qC5

qx Dq2C5

qx2 KrC5, (23)

ARTICLE IN PRESS



6/14

UqC6

qx D q

2C6

qx2 KaCs C6 KDC5, (24)

where Kr is the BOD decay rate constant and D is

the dispersion coefficient. The analytical solutions

of Eqs. (23) and (24) are

C5x; t

C5;0 exp

U

2D 1

arx !, (25)

C6x; t C6;0KD

Ka Krexp U=2D1 arx

ar

&

exp U=2D1 aax

aa

', 26

where

ar ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 4KrDU2

r; aa

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 4KaD

U2

r,

x is the distance from the upstream boundary in the

flow direction and C5,0 and C6,0 are the initial

concentrations of BOD and DO, respectively. The

conditions used in the simulation are given by:

U 0.03 m/s, D 0.1m2/s, KD 0.20/day, Ka 1.25 /day, Kr 0.12/day, C5,0 10.0 mg/L, andC6,0 8.3 mg/L.

Fig. 1 shows the comparison between the

analytical solution for BOD and DO concentrations

and the results obtained by SisBAHIAs along the

channel. A good agreement among the analytical

and numerical solutions can be observed. Fig. 2

depicts an estimate of the mean quadratic error for

the BOD and DO concentrations. The order of

3.0% demonstrates the models good performance.

5. Description of Sepetiba Bay

Sepetiba Bay is located at longitude 441 W and

latitude 231 S, near Greater Metropolitan Rio de

Janeiro. The bay has a plan area of approximately305 km2 and extends 40 km from east to west and

20km from north to south. The perimeter is

approximately 130 km. Water depths are about

20m in the main channel but less than 10m in

most of the Bay. The drainage basin has catchments

of 2617 km2 with 22 separate sub-watersheds. The

region is under a hot-humid tropical limit with the

mean annual precipitation ranging from 1400 mm to

2500 mm. Environmental preservation and urban

areas correspond to 20% and 9.2% of the catch-

ment areas, respectively. Fig. 3 depicts Sepetiba

Bay, indicating watercourses that discharge into the

bay. As shown in Fig. 3, the bay is separated from

the Atlantic Ocean by a sandbar. The main

connection with the ocean is between Marambaia

Island and Ilha Grande. Several studies have

focused on water quality assessment in Sepetiba

Bay (Copeland et al., 2003; Paraqueti et al., 2004)

and ecological disturbances (Magalha es et al., 2003;

Magalha es and Pfeiffer, 1995; Pessanha and Ger-

son, 2003). Studies on heavy metals in fish and algae

are also available (Karez et al., 1994; Lima Junior

et al., 2002).

ARTICLE IN PRESS

0.0

2.0

4.0

6.0

8.0

10.0

0 1500 3000 4500 6000 7500 9000 10500 12000 13500 15000

x (m)

C(mg/L)

DO - Analytic solution BOD - Analytic solution

DO - SisBAHIA BOD - SisBAHIA

Fig. 1. Comparison of analytical solution for BOD and DO concentrations with results obtained by SisBAHIAs along the channel.



7/14

Due to the areas industrial development, the bay

has suffered different environmental impacts, in-

creasing the organic and industrial pollution (Ma-

galha es et al., 2003). The bay is subject to sewage

effluent emanating from 1.4 million inhabitants out

of the total for Greater Metropolitan Rio de Janeiro

City and from 12 neighbouring cities, mostly

concentrated along the northeastern shore as a

result of industrial growth. Unplanned development

has resulted in severe contamination of the bay,

ARTICLE IN PRESS

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 1500 3000 4500 6000 7500 9000 10500 12000 13500 15000

x (m)

Error(%)

BOD DO

Fig. 2. Mean quadratic error between analytical solutions for BOD and DO concentrations and results obtained by SisBAHIAs

.

Fig. 3. Map of Sepetiba Bay with bathymetry, showing the principal rivers and four water quality and current stations from which

measured data were used to compare with numeric results.



8/14

with organic loading produced by the contribution

basin. Unfortunately, direct measurements of these

loads are not available, yet. Effluent sources used in

the model were defined using the DO and BOD

concentrations measured in certain rivers of each

drainage basin and from the economic activitydeveloped in each region. Approximately 70,000 kg

BOD/day is dumped untreated into the rivers and

channels that carry mainly untreated waste into the

bay. In the City of Rio de Janeiro (which contains

most of the urban population of the Sepetiba Bay

basin) there are effectively no sewage treatment

plants. The contributions of organic loading from

domestic waste discharge can be categorized ac-

cording to FEEMA (1998) as follows:

West region: provides a small percentage of

organic loading, compared to the remainder ofthe contribution basin. Point sources comprising

small shore strips can occur. However, these

discharges do not pose a water quality problem.

Central region: this region is responsible forapproximately 64% of the organic loading input

in the Bay. The GuanduMirim River comprises

approximately 31% of this amount. However,

this area of Sepetiba Bay contains a circulation

zone that helps mitigate water quality problems.

East region: although this region receives 34.5%

of the organic loading, water recycling is veryslow due to lack of hydrodynamic flushing. As a

consequence, this region has low water quality,

and the shoreline has become heavily polluted,

failing to meet the water quality standards set by

the prevailing Brazilian legislation.

The effluents include another source of pollution

from agriculture and cattle-raising. Unfortunately,

there are no data available for characterizing these

effluents. As for industrial waste discharge, the

Sepetiba Bay drainage basin has more than 100

factories, constituting one of the largest industrial

complexes in the State of Rio de Janeiro. Mose of

these factories are small or medium-sized. For many

years these factories have dumped highly toxic,

cumulative waste that contains high concentrations

of heavy metals, mainly zinc and cadmium (Lima

Junior et al., 2002). Industrial organic pollution is

less relevant as compared to pollution from

domestic waste discharge. Worthy of note is that

the factories with the potential to generate such

loads have a good environmental record. The

present study concerns organic pollution of Sepeti-

ba Bay, so only loads from domestic waste

discharge are considered.

5.1. Water quality evaluation in Sepetiba Bay basin

The main Sepetiba Bay basin tributaries are the

Guandu River (known as the Sao Francisco Canal

near the Bay), Guarda River, Ita Canal (connected

to the GuanduMirim River), Piraque River,

Portinho River, Mazomba River, and Cac-a o River.

The remaining rivers have low discharges. Fig. 3

show the location of all the rivers whose waters

flows into Sepetiba Bay. There is no substantial

seasonal variation in the fluvial discharge into the

bay. The largest contribution comes from the Sa o

Francisco Canal, which is artificially controlled by awater treatment plant located upstream from the

main industrial area. Most of the water originates

from an adjacent basin, the Paraba do Sul system.

Table 2 shows the mean discharge.

From 1990 to 1997, observations of DO, BOD,

ammonia nitrogen, Kjeldahl nitrogen, and total

phosphorus were conducted in some of the rivers,

aimed at water quality monitoring in the recepient

channel. The concentrations showed significant

fluctuations according to the season, precipitation,

saline intrusion observed in some of these rivers.

Despite the variation in concentration, only the

mean values for concentrations are available.

Therefore, only these values will be presented.

Table 3 shows the median value of the data

collected during the observation period. With the

exception of Sa o Francisco Canal, the rivers have

very poor water quality. The Sao Francisco Canal

presents representative organic loads corresponding

to 22.56% of the total load, but has a high mean

discharge of 89 m3/s which aids a mixing process

and depuration of the organic matter. The remain-

ing rivers and canals have high organic loads and

ARTICLE IN PRESS

Table 2

Average discharge of the rivers as contribution to the Sepetiba

Bay basin

Discharge (m3/s)

Guarda River 6.8

Sa o Francisco Canal 89.0

Guandu Canal 8.8

Ita Canal 3.3

Saco do Engenho River 0.5

Piraque River 2.5

Cac-ao River 1.1



9/14

low discharge; thus suffering accelerated degrada-

tion of their water quality.

6. Hydrodynamics

The transport of a given substance in a body of

water is dominated by advection, thus suggesting a

strong interdependence between hydrodynamic si-

mulation and the transport process (Oliveira et al.,

2000). In this context, all target contaminants are

modelled as passive scalars. This means that the

hydrodynamic circulation in the Bay area is the

same, regardless of the presence of any contami-

nant. As a consequence, modelling of hydrody-

namic patterns in Sepetiba Bay and modelling of the

transport of a given contaminant by such patterns

are uncoupled problems.

Two numerical tidal models of Sepetiba Bay were

developed. Considering the extreme complexity in

hydrodynamic circulation in Sepetiba Bay and

assuming that the relevant circulation is due to long

period forces, the most adequate model for char-

acterization of the hydrodynamic circulation can be

defined. The long period forces result from the

interactions between tides and winds. In the model,

spatial discretization in the horizontal xy plane is

carried out through sub-parametric Lagrangian

finite elements, using nine nodes quadrilaterals. In

a sub-parametric element, the elements geometry is

linear and is defined only by the vertices. However,

the variables are quadratic, and in addition to the

ARTICLE IN PRESS

Table 3

Median of the water quality parameter collected of the tributaries of the Sepetiba Bay basin during the period from 1990 to 1997

BOD DO N-Ammonia N-Kjeldahl P-Total

(mg O2/L) (mg O2/L) (mg N/L) (mg N/L) (mg P/L)

Piraque River 10.0 1.2 3.0 7.0 1.0

Portino River 2.0 6.8 0.2 0.8 0.1

Ita Canal 20.0 o0.1 5.5 8.0 1.5

Sao Francisco Canal o 2.0 8.0 0.09 0.6 0.1

Guarda River 7.0 2.2 1.0 2.0 0.2

Guandu-Mirim River 12.0 1.2 2.6 4.5 1.0

Fig. 4. Sepetiba Bay modelling domain: FEM.



10/14

values at the vertices, values at the middle of each

side are also needed; in the case of quadrilaterals, a

node at the centre of the element is also necessary.

The mesh consists of 497 elements and 2314

nodes and is shown in Fig. 4. The time step equal to150 s was adopted. The bathymetry of the Bay,

presented in Fig. 3, was obtained from the nautical

maps from the Directorate for Hydrography and

Navigation (DHN) numbers 1607 (scale 1:80,000)

and 1622 (scale 1:40,122). Fig. 5 illustrates the

measured tidal elevation curve at the entrance to the

bay at Guaba Island, when a typical springneap

tide occurred from April 20 to May 5, 1996. During

that period, measurements of water quality para-

meters and currents were obtained at four locations

in Sepetiba Bay by FEEMA/GTZ (State Environ-

mental Engineering Foundation and Brazil

Germany Technical Cooperation, Project PLANA-

GUA/GTZ).

In the numerical model, wind conditions are

considered unsteady but spatially homogeneous; the

input data used in the model were the time series of

wind speeds and directions measured hourly at

Santa Cruz Station, near the Bay. The tide curve is

imposed at open boundaries of the computational

domain. Discharges from the rivers into the bay are

taken to be the same as in Table 2. At all water-land

boundary nodes, the null tangential velocity com-

ponent is imposed. The bottom friction coefficient

can be written in terms of the Chezy coefficient,

which depends on the amplitude of the equivalent

bottom roughness. The amplitude of the equivalent

bottom roughness, e, was defined on the basis of thecharacterization and distribution of bottom sedi-

ment (Abbot and Basco, 1989). Sand is predomi-

nant in the western portion (effi0.030 m) and in theregion near Ilha Grande and the Marambaia

Shoals. In the eastern portion the mud to fine sand

sediments predominate (effi0.015 m).Based on the data, the tidal current in Sepetiba

Bay presents strong quarter-diurnal variations

(Copeland et al., 2003). Peak flood currents reached

values of 0.40 m/s, and the maximum ebb speed

measured is 0.60 m/s at station 1. The shallow water

effect is appreciable in the current variations and is

responsible for large asymmetries in the ebb-flood

current distribution.

The numerical model was run from April 20 to

May 5, 1996, using the observed tides presented in

Fig. 5. Fig. 6 presents the time series of the east

west component of the current for the stations

indicated in Fig. 3, from April 22 to 26, 1996. At

Station 1, where the depth is 21 m, reasonable

agreement can be observed between the computed

and measured data. This station is located near an

island, where the bathymetry of the main channel is

ARTICLE IN PRESS

-1.0

-0.5

0.0

0.5

1.0

1.5

4/20/96 4/21/96 4/22/96 4/23/96 4/24/96 4/25/96 4/26/96 4/27/96 4/28/96 4/29/96 4/30/96 5/1/96 5/2/96 5/3/96 5/4/96 5/5/96

Time

Tidalelevation(m)

Fig. 5. Tidal elevation at Guaiba Island from April 20 to May 5, 1996.



11/14

very irregular. Hence, the current has large spatial

gradients, so that a small difference in spatial

position can lead to a large difference in velocity.

At Station 4, where the depth is 12 m, the computedEW components of the velocities are in close

agreement with the measured ones. The agreement

is better for weaker currents. A small phase

difference can be observed near day April 23,

1996. From the observation at Station 3 (depth

6 m), located on the inner part of the bay, the

currents are weaker than those generated at the

narrowing. The same pattern is repeated at Station

2 (depth 8 m), also located at the inner part of the

Bay. At Stations 4 and (mainly) 1, where the area is

reduced and there is a natural deep channel, the

currents are more intense.

7. Water quality model

The main objective of this paper is the develop-

ment of a water quality model to simulate the long-

term transport. DO and BOD are used as indicators

of the presence of organic matter, and also as

parameters for the evaluation of the environ-

mental pollution of the eastern part of Sepetiba

Bay. Table 4 lists the in loco concentrations used in

the simulations. Values estimated from the dilution

coefficient for each river were used as boundary

conditions. The simulations covered the same

period as that of the hydrodynamic simulation,

from April 20 to May 5, 1996.

The values of the parameters and constants are

well-defined in the literature and were used in the

application considering that there are no studies

available for water quality modelling in Sepetiba

Bay. This is the main difficulty in performing

the analysis proposed in this article. The field

data are not sufficient for a complete calibration,

and the adjustments were carried out to obtain the

ARTICLE IN PRESS

Fig. 6. Eastwest component of the current measured (FEEMA/GTZ) at the stations and computed numerically (SisBAHIAs

).

Table 4

DO, BOD, salt concentration, and temperature values in the

rivers

DO BOD Temperature Salinity(mg O2/L) (mg O2/L) (1C) (psu)

Sa o Francisco

Canal

8.0 2.1 25.0 30.0

Ita Canal 0.1 20.0 25.0 28.0

Guarda River 2.5 8.2 25.0 23.0

Piraque River 1.5 11.6 23.0 25.0

Mazomba River 2.2 8.5 23.0 25.0

Guandu Canal 1.2 12.0 23.0 25.0

Portinho River 1.2 1.0 23.0 25.0

Sepetiba Beach 0.5 30.0 23.0 25.0



12/14

numerical results close to the measured data, within

a specified variation limit; some adjustments proved

necessary, mainly in the re-aeration and de-oxyge-

nation rates.

The field data for temperature and salinity

present few variations, with temperature valuesbetween 24 and 25 1C and salinity approximately

32 psu at the four stations. Thus, two cases were

defined for this study, considering different initial

conditions for temperature and salinity: (i) case 1:

Cs (x,0) 32.0 psu (salinity), CT (x,0) 25.0 1C(temperature), (ii) case 2: Cs (x,0) 30.0 psu, CT(x,0) 20.0 1C. In both cases, the initial conditionsare: C5 (x,0) 2.0 m g O2/L (BOD) and C6(x,0) 8.0 mg O2/L (DO). The following waterquality parameters were prescribed as constant

values throughout the computational domain: C1(x,t) 0.02 mg N/L (ammonia nitrogen); and C2(x,t) 0.04 mg N/L (nitrate nitrogen). Table 1 liststhe model coefficients and constants employed in

the numerical simulation for the two cases.

Data available from FEEMA/GTZ were used in

the Sepetiba Bay water quality analysis. During the

study period, data related to DO, salinity, and

temperature were collected. Measurements were

taken at four stations in Sepetiba Bay (see Fig. 3)

at two time intervals. At Stations 1 and 4, data were

obtained at two points in the vertical direction. At

Stations 2 and 3, measurements were obtained at a

single point in the vertical direction. Fig. 7 shows

the large variation in DO concentrations at the

stations. The variations in DO concentrations can

be explained according to the fluctuating supply ofsewage effluent from rivers in the area.

However, the model did not reproduce the large

variation in concentrations at stations near the

estuary. This can be explained as follows: These

stations are under the direct influence of the rivers

flowing into the bay, mainly the Sa o Francisco

Canal, which present significant discharges and

probably large time variations. In order to ade-

quately reproduce these variations, time variable

boundary conditions would have to be taken

into account. The stations located on the Bay are

not under the direct influence of the rivers, so thereis better agreement between the results. Observing

the differences between numerical (SisBAHIAs)

and measured values for DO concentration, the

mean values are 14.0% for Station 1, 12.0% for

Station 2, 11.0% for Station 3, and 18.0% for

Station 4, allowing one to conclude that the

proposed model can predict changes in DO during

the oxidation of organic matter in the waste

material.

ARTICLE IN PRESS

Fig. 7. DO concentration measured (FEEMA/GTZ) at the stations and computed numerically (SisBAHIAs).



13/14

Analysing the differences between numerical

(SisBAHIAs) and measured values for salinity

and temperature (see Table 5), the maximum value

is 4.4% for temperature and 10.4% for salinity,

considering case 1. For case 2, the maximum errors

are 6.2% for temperature and 12.3% for salinity.These values show that the model tends towards

stabilization, assuming the values attributed for the

boundary conditions.

Stations 1 and 4, located on the central part of the

Bay, show quite similar behaviour and values

related to DO and salt concentrations, and tem-

perature. In general, the mean salinity in the bay is

some 32 psu, with variations only at the estuary of

the main rivers. Mean water temperature is some

25 1C, with little thermal stratification. The mea-

surements show a mean DO concentration of8.0 mg/l. Note that the data were obtained in only

one study period, during the months of April and

May, representing a considerably reduced study of

the behaviour by these substances in Sepetiba Bay.

8. Conclusions

Water quality in Sepetiba Bay was examined

using a coupled hydrodynamic and water quality

model to evaluate pollution by sewage effluent. The

combined model, SisBAHIAs, adopts finite ele-

ments and finite differences, respectively, in the

spatial and time discretization. In the simulation,

DO and BOD concentrations were used as indica-

tors of the presence of organic matter in the body of

water and as parameters for evaluating the environ-

mental pollution in the eastern part of the bay.

Sepetiba Bay water quality is predominantly

affected by local effluent sources. With respect to

hydrodynamics, the shallow water effect is appreci-

able in the current variations and is responsible for

large asymmetries in the ebb-flood current distribu-

tion. In general, the mean salinity in the bay is

around 32 psu, with variations only at the estuaries

of the main rivers. Mean water temperature is some

25 1C, and mean DO concentration is 8.0 mg/L. A

larger temporal series would be necessary for a

better model calibration. Results from the combined

numerical model are in satisfactory agreement withthe measured data, demonstrating that this ap-

proach has general applicability for environmental

assessment in complicated coastal bays.

References

Abbot, M.B., Basco, R., 1989. Computational Fluid Mechanics:

An Introduction for Engineering. Longman Group, UK.

Beam, R.M., Warming, R.F., 1978. An implicit factored scheme

for the compressible Navier-Stokes Equations. AIAA journal

16, 393402.

Brown, C.L., Barnwell, T., 1987. Documentation and usermanual for the enhanced stream water quality model

QUAL2E and QUAL2E-UNCAS. Documentation and user

manual. Resp. EPA/600/3-87/007. Environmental Research

Laboratory, United States.

Copeland, G., Monteiro, T., Couch, S., Borthwick, A., 2003.

Water quality in Sepetiba Bay, Brazil. Marine Environmental

Research 55, 385408.

Cunha, C.L.N., Rosman, P.C.C., 2005. A semi-implicit finite

element model for natural water bodies. Water Research 39,

20342047.

Cunha, C.L.N., Monteiro, T.C., Rosman, P.C.C., 2002. Two-

dimensional modelling of scalars transport. Revista Brasileira

de Recursos Hdricos 7 (2), 6379 (in Portuguese, with

English Abstr).

Daily, J.W., Harleman, D.R.F., 1966. Fluid Dynamics. Addison-

Wesley, Reading, MA.

FEEMA, 1998. Avaliac-a o da qualidade da a gua da Bacia da Baa

da SepetibaOutubro de 1995 a Julho de 1998Projeto de

Cooperac-a o Te cnica BrasilAlemanha, FEEMA/GTZ (in

Portuguese).

Karez, C.S., Magalhaes, V.F., Pfeiffer, W.C., 1994. Trace metal

accumulation by algae in Sepetiba Bay, Brasil. Environmental

Pollution 83, 351356.

Lima Junior, R.G.S., Araujo, F.G., Maia, M.F., Pinto, A.S.S.B.,

2002. Evalution of Heavy Metals in Fish of Sepetiba and Ilha

Grande Bays, Rio de Janeiro, Brazil. Environmental Research

89, 171179.Magalhaes, V.F., Pfeiffer, W.C., 1995. Arsenic concentratin in

sediments near a metallurgical plant (Sepetiba Bay, Rio de

Janeiro, Brazil). Journal of Geochemical Exploration 52,

175181.

Magalhaes, V.F., Marinho, M.M., Domingos, P., Oliveira, A.C.,

Costa, S.M., Azevedo, L.O., Azevedo, S.F.O., 2003. Micro-

cystins (cyanobacteria hepatotoxins) bioaccumulation in fish

and crustaceans from Sepetiba Bay (Brasil, RJ). Toxicon 42,

289295.

MIKE 21, 2001. User Guide and Reference Manual. DHI,

Horsholm, Denmark.

Oliveira, A., Fortunato, A.B., Batisis, A.M., 2000. Mass Balance

in EulerianLagrangisn transport simulations in estuaries.

Journal of Hydraulic Engineering 126 (08).

ARTICLE IN PRESS

Table 5

Mean quadratic error between numerical (SisBAHIAs) and

measured values of temperature and salinity at the stations

Stations Temperature Salinity

Case 1 Case 2 Case 1 Case 2

1 3.8 5.0 3.5 3.8

2 1.7 6.2 5.9 12.3

3 4.4 6.0 10.4 7.3

4 3.6 4.5 3.5 2.8



14/14

Paraqueti, H.H.M., Ayres, G.A., Almeida, M.D., Molinasi,

M.M., Lacerda, L.D., 2004. Mercury distribution, speciation

and fluxe in the Sepetiba Bay, tributaries, SE Brazil. Water

Research 38, 14391448.

Pessanha, A.L.M., Gerson, F., 2003. Spatial, temporal and diel

variations of fish assemblages at two sandy beaches in the

Sepetiba Bay, Rio de Janeiro, Brazil. Estuarine, Coastal andShelf Science 57, 817828.

Rosman, P.C.C., 2005. Referencia Te cnica do SISBAHIA

SISTEMA BASE DE HIDRODINA MICA AMBIENTAL,

Programa COPPE: Engenharia Oceanica, A rea de Engenhar-

ia Costeira e Oceanogra fica, Rio de Janeiro, Brasil

(in Portuguese). Access in: /www.sisbahia.coppe.ufrj.br/

SisBAHIA_TecRef_V4.pdfS.

Sellers, W.D., 1965. Physical Climatology. The University of

Chicago Press, Chicago, London.

Sheng, Y.P., Yassuda, E.A., Yang, C., 1996. Estuarine and

Coastal. American Society of Civil Engineers.

Thomann, R.V., Muller, J.A., 1987. Principle of Surface

Water Quality Modeling and Control. Harper and Row,

New York.Umgiesser, G., Canu, D.M., Solidoro, C., Ambrose, R.A., 2003.

A finite element ecological model: a first application to the

Venice Lagoon. Environmental Modelling & Software 18,

131145.

Wu, J., 1982. Windstress coefficients over sea surface from

breeze to hurricane. Journal of Geophysical Research 87 (12),

97049706.

ARTICLE IN PRESS

http://www.sisbahia.coppe.ufrj.br/SisBAHIA_TecRef_V4.pdfhttp://www.sisbahia.coppe.ufrj.br/SisBAHIA_TecRef_V4.pdfhttp://www.sisbahia.coppe.ufrj.br/SisBAHIA_TecRef_V4.pdfhttp://www.sisbahia.coppe.ufrj.br/SisBAHIA_TecRef_V4.pdf

(cunha 2006) hydrodynamics and water quality models applied to sepetiba bay_sisbahia

Documents