(cunha 2006) hydrodynamics and water quality models applied to sepetiba bay_sisbahia
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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
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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).
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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
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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):
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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)
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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
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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)
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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).
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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.
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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,
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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.
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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
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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
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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
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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.
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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
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-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.
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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
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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
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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.
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Fig. 7. DO concentration measured (FEEMA/GTZ) at the stations and computed numerically (SisBAHIAs).
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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.
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Table 5
Mean quadratic error between numerical (SisBAHIAs) and
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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
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