This study used hydrodynamic modeling to investigate the hydrodynamic circulation and pollutant transport of the Guajará Bay-PA. The hydrodynamic modeling was performed using the classical Saint-Venant model for shallow waters. The pollutant dispersion was described using a Lagrangian deterministic model that simulates advective–diffusive transport with kinetic reactions for two-dimensional flow. The finites elements method was used to solve the Saint-Venant and transport equations. The bathymetry data were obtained by combining the data from nautical charts provided by the Directorate of Hydrography and Navigation of the Brazilian Navy. The substrate grain size data for the determination of rugosity were obtained from literature. Data on the tides, the wind and the flowrate of the rivers that form the Guajará bay were used as the boundary conditions in the simulation of the hydrodynamic circulation and the pollutant dispersion scenarios. Flood and ebb tide patterns were simulated, which enabled the contaminant plumes of the Guajará Bay to be simulated. An analysis of the simulated fecal coliform plumes indicated that these pollutants that are produced in the metropolitan region of Belém flow towards the beaches in the North, especially those in the Icoaraci and Outeiro districts, affecting the bathing water quality.

INTRODUCTION

Increasing urbanization in Brazilian cities and the absence of a proper sanitary infrastructure have contributed to the degradation of the water quality in rivers, lakes, ponds and estuaries that are used as domestic and industrial wastewater receptors as a short-term solution that has been adopted by public agencies for basic sanitation. This action has compromised the water quality not only at the site of sewage disposal but also over the entire hydrographic basin. Although developed countries have addressed this issue with a sustainable solution, given their available sanitary infrastructure and more developed environmental laws, there are numerous current studies on global pollutant dispersion.

For instance, Lopes et al. (2005) modeled the hydrodynamics and water quality of the Ria de Aveiro Lagoon in the Northwest of Portugal. The hydrodynamic pattern consisted of semi-diurnal tides. The following parameters were used to analyze the water quality: dissolved oxygen (DO), biochemical oxygen demand (BOD), ammonia, nitrate, nitrite and phosphate. Cunha et al. (2006) used the coupled model for shallow waters, 2DH, to describe the hydrodynamics and water quality of the Sepetiba Bay in the state of Rio de Janeiro. The DO and BOD were used to simulate the water quality. Lee & Seo (2007) studied pollutant transport in the Han River (South Korea). These authors used a two-dimensional (2D) advection–diffusion model. The velocity fields that were required for the pollutant transport simulation were obtained from a 2D hydrodynamic model. Montaño-Ley et al. (2007) investigated the tidal hydrodynamics of the coastal lagoon system of Topolobampo on the Northwest coast of Mexico. The shallow waters hydrodynamic model was used, and the 2D equations were solved using the finite difference method. The advective–diffusive process was simulated by releasing a hypothetical pollutant in the coastal lagoon. Barros et al. (2011) used computational modeling to analyze the hydrodynamics of the estuary system of the Guajará Bay. The 2D longitudinal-transversal shallow waters model was applied. The results successfully described the flow patterns in the Guajará Bay, and the calculated water levels were comparable to those observed in experimental studies. Periáñez (2012) developed a 2D numerical model to study the behavior of pollutants in the Algeciras Bay in the South of Spain in the Strait of Gibraltar. Hydrodynamic and sediment transport and pollutant dispersion moduli were considered in the model. The results of the hydrodynamic model were combined with tidal current data to evaluate the interaction between water and sediments and the behavior of pollutants in the bay.

The present study is a continuation of a study by Barros et al. (2011) on the Guajará Bay. The bay is located in the Northern region of Brazil (Figure 1), in the state of Pará, between parallels 01° 28′03″ S and meridians 48° 29′18″ W and is an integral part of a larger estuary that is associated with the mouth of the Amazon River. The Guajarino Estuary is characterized as a fluvial environment with a marine influence. The Guajarino Estuary is formed at the confluence of the Pará, Acará and Guamá Rivers, thus delimiting the area in the South to form the Guajará Bay, which in the North is mistaken for the Marajó Bay from the Pará River (Gonçalves & Filho 2005). This area encompasses a continental region in the West, where Belém, the capital city of the state of Pará, is located, and an insular region that is separated by numerous rivers, wells, streams and channels. Only approximately 50% of the population of the municipality of Belém is estimated to have has access to sewage collection and treatment services. The remainder of the population disposes of the residues in septic tanks or directly and untreated in the channels and streams (Braz 2003) that flow into the Guajará Bay.
Figure 1

Geographic location of the area of study (adapted from Blanco et al. 2013).

Figure 1

Geographic location of the area of study (adapted from Blanco et al. 2013).

Industries and important residential areas in the metropolitan region of Belém are concentrated along the Guajará Bay waterfront. This area contains highly ecologically significant environments, including floodplains and rivers that are used by the local population as economic and food subsistence sources. These water resources are supplied to the city of Belém via a potable water collection system. The long-standing but slow environmental degradation processes in Guajará Bay have been accelerated in recent decades by urban expansion and industrial activities. The disposal of often untreated domestic and industrial wastewater has affected the water quality of the bay, especially the bathing water quality. It has been speculated that the beaches surrounding the city are being polluted by effluent disposal from the municipality of Belém (Barros 2005). A few studies have been conducted on the Guajará Bay area to understand the discharge standards for and the behavior of the constituents in the estuary water bodies in an integrated manner: we cite studies by Pinheiro (1987), Batista (2005), Barros et al. (2011) and Blanco et al. (2013) among these studies.

MATERIAL AND METHODS

Hydrodynamic modeling

In this study, a set of 2D shallow water equations, known as the vertically averaged model (the 2DH model), was obtained by vertically integrating the Navier–Stokes three-dimensional (3D) equations for incompressible flow, including the seafloor and surface boundary conditions. The primary limitation of the 2DH model is that effects resulting from variations in the velocity and the density in the vertical direction are neglected. However, the 2DH model is adequate as long as the flow of the layer located between the seafloor and the free surface is homogeneous and the velocities are predominantly horizontal. Therefore, the flow can be fairly well estimated in 2D and the primary results, i.e., the velocities and depths, can be used as input data for pollutant dispersion modeling. The resultant equations for the momentum conservation in the x- (Equation (1)) and y- (Equation (2)) directions and mass conservation (Equation (3)) are given below: 
formula
1
 
formula
2
 
formula
3
wherein
  • U – velocity in the x-direction (m/s);

  • V – velocity in the y-direction (m/s);

  • t – time (s);

  • g – acceleration of gravity (m/s2);

  • ζ- free surface elevation (m);

  • ρ - density of water (kg/m3);

  • H –liquid column height (m);

  • τij - Reynolds stress tensor (Pa);

  • - bottom or wind stress tensor (Pa);

  • - Coriolis force in the x-direction (N);

  • - Coriolis force in the y-direction (N).

Further details on the derivation of these equations can be found in Rosman (2001).

Bathymetry

Bathymetry data were obtained from Batista (2005) by combining the datasets from nautical charts and navigation sketches of the Guamá river that were obtained for mean low water spring levels (MLWS). The following nautical charts and sketches were obtained from the Directorate of Hydrography and Navigation of the Brazilian Navy (Diretoria de Hidrografia e Navegação da Marinha do Brazil – DHN): North Coast bathymetry from Salinópolis to Belém: nautical charts DNH: n. 310, scale 1:200,000; river bathymetry from Belém to Mosqueiro: nautical chart DHN: n. 316, scale 1:49,990; and river bathymetry for the Port of Belém: nautical chart DHN: n. 320, scale 1:15,000. Figure 2 illustrates the resulting bathymetry.
Figure 2

Bathymetry used in modeling.

Figure 2

Bathymetry used in modeling.

Substrate

A few sedimentological studies have been performed on the Guajará Bay. The sedimentological data that were obtained by Pinheiro (1987) were used in the present study. Pinheiro determined that the average diameter of the sediment particles ranged between 0.062 and 0.25 mm (Figure 3). From Figure 3, the predominance of medium grain sand may be observed north of Onças Island, in the region around the Da Barra Island. Coarse sands are also found at the confluence of the Guamá and Acará rivers. Fine sands occur in a considerable area in front of Belém city. This information is needed to estimate the mean Manning coefficient.
Figure 3

Distribution of diameters of sediment particles from Guajará Bay (Pinheiro 1987).

Figure 3

Distribution of diameters of sediment particles from Guajará Bay (Pinheiro 1987).

Tide

The Guajará Bay model was simulated using tidal dates that were generated from the harmonic constants for the Port of Belém. Table 1 presents the 29 harmonic constants with the highest amplitudes for the Port of Belém using the data from the DHN. Figure 4 illustrates the typical tidal curves for the Port of Belém that were used as boundary conditions for the simulations of the Guajará Bay hydrodynamic model.
Table 1

Harmonic constants for Port of Belém tide station

Constant Period (sec) Amplitude (m) Phase (rad) 
Mm 2,380,713.137 0.042 0.6632 
MSf 1,275,721.388 0.083 0.6807 
Q1 96,726.08402 0.007 1.7977 
O1 92,949.62999 0.090 5.1138 
P1 86,637.20458 0.024 5.6723 
K1 86,164.090760 0.095 5.5327 
J1 83,154.516370 0.001 3.4558 
OO1 80,301.867110 0.003 0.6981 
2N2 46,459.348130 0.043 4.9742 
mu2 46,338.327480 0.059 0.8901 
nu2 45,453.615880 0.048 5.1662 
M2 44,714.164390 1.163 5.8294 
L2 43,889.832740 0.065 5.7596 
T2 43,259.217110 0.026 6.0563 
S2 43,200.000000 0.333 0.2094 
K2 43,082.045240 0.091 0.1920 
MO3 30,190.690690 0.044 3.0543 
M3 29,809.442930 0.013 3.1591 
MK3 29,437.703880 0.038 3.5779 
MN4 22,569.026070 0.051 4.1364 
M4 22,357.082200 0.122 4.4157 
SN4 22,176.694020 0.008 4.6775 
MS4 21,972.021400 0.076 4.8695 
M1 89,399.694090 0.009 2.5482 
Sa 31,556,955.922 0.036 5.6025 
Ssa 15,778,458.751 0.067 0.1047 
Mf 1,180,292.2880 0.026 1.1868 
MNS2 42,430.07141 0.006 1.5533 
N2 45,570.05300 0.223 5.5676 
Constant Period (sec) Amplitude (m) Phase (rad) 
Mm 2,380,713.137 0.042 0.6632 
MSf 1,275,721.388 0.083 0.6807 
Q1 96,726.08402 0.007 1.7977 
O1 92,949.62999 0.090 5.1138 
P1 86,637.20458 0.024 5.6723 
K1 86,164.090760 0.095 5.5327 
J1 83,154.516370 0.001 3.4558 
OO1 80,301.867110 0.003 0.6981 
2N2 46,459.348130 0.043 4.9742 
mu2 46,338.327480 0.059 0.8901 
nu2 45,453.615880 0.048 5.1662 
M2 44,714.164390 1.163 5.8294 
L2 43,889.832740 0.065 5.7596 
T2 43,259.217110 0.026 6.0563 
S2 43,200.000000 0.333 0.2094 
K2 43,082.045240 0.091 0.1920 
MO3 30,190.690690 0.044 3.0543 
M3 29,809.442930 0.013 3.1591 
MK3 29,437.703880 0.038 3.5779 
MN4 22,569.026070 0.051 4.1364 
M4 22,357.082200 0.122 4.4157 
SN4 22,176.694020 0.008 4.6775 
MS4 21,972.021400 0.076 4.8695 
M1 89,399.694090 0.009 2.5482 
Sa 31,556,955.922 0.036 5.6025 
Ssa 15,778,458.751 0.067 0.1047 
Mf 1,180,292.2880 0.026 1.1868 
MNS2 42,430.07141 0.006 1.5533 
N2 45,570.05300 0.223 5.5676 
Figure 4

Tidal curve for Port of Belém during September 2003.

Figure 4

Tidal curve for Port of Belém during September 2003.

Wind

The wind data that were used in the simulation were obtained from the website of the Center for Hydrometeorology of the Executive Secretariat of Science, Technology and Environment of the state of Pará (Secretaria Executiva de Ciência, Tecnologia e Meio Ambiente do estado do Pará – SECTAM 2007). The aforementioned station is located in the municipality of Barbacena, in the state of Pará, at a latitude of –1.54° and a longitude of –48.74° and an altitude of 10 m and belongs to the National Institute of Space Research (Instituto Nacional de Pesquisas Espaciais – INPE). Only this station was used because of its proximity to the region of study. The data from September (the dry period) 2003 were used in the model. Uniform wind fields were considered over the region of study, where the intensity was varied every 3 hours using typical patterns, as presented in Figure 5. The arrows represent the modulus, which is proportional to wind the velocity, as indicated by the color pattern. The direction and orientation of the wind are indicated by the arrows corresponding to the compass rose.
Figure 5

Graph of wind time series, which is used as input data to the model.

Figure 5

Graph of wind time series, which is used as input data to the model.

Estimated flowrate from contributing basins and organic load from Belém

The hydrographic basins that contribute directly to the formation of the Guajará Bay for the domain of this study are the basins of the Guamá-Capim and Acará-Mojú rivers, as illustrated in Figure 6. In this case, the hydrographic region exhibits superficial water availability at a flowrate of 1.485 m3/s. The dry period flowrate, which is considered to be the flow with 95% permanence, is 480 m3/s, according to the Plan for Water Resources of the Tocantins and Araguaia river basins (ANA 2009). Sixty percent of this flowrate originates from the Guamá-Capim basin, and 40% of the flowrate originates from the Acará-Mojú basin. September (the dry period) 2003 was considered for the model in this study.
Figure 6

Basins that flow into Guajará Bay (source: Böck 2010).

Figure 6

Basins that flow into Guajará Bay (source: Böck 2010).

The flowrate data of the Belém channels are not well known being difficult to acquire, primarily because the tidal action that reaches its median point or even its head during the high tide. Thus, the flow values were estimated for some of the primary hydrographic basins of the channels in the municipality of Belém. The results for the flowrate and the organic load estimations were obtained from Barbosa & Silva (2002) and are presented in Table 2.

Table 2

Estimated load and flowrates generated by hydrographic basins and discharged into Guajará Bay

Hydrographic Basin Paracuri Mata Fome Val-de-cans Una Reduto Tamandaré 
Population (hab) 110,438 56,637 70,001 449,986 20,759 25,619 
Flowrate (m3/s) 0.0630 0.0510 0.2710 1.1040 0.1390 0.1720 
Organic load (ton/day BOD) 6.00 3.10 3.80 24.3 1.10 1.40 
Hydrographic Basin Paracuri Mata Fome Val-de-cans Una Reduto Tamandaré 
Population (hab) 110,438 56,637 70,001 449,986 20,759 25,619 
Flowrate (m3/s) 0.0630 0.0510 0.2710 1.1040 0.1390 0.1720 
Organic load (ton/day BOD) 6.00 3.10 3.80 24.3 1.10 1.40 

The limits of the hydrographic basins in the municipality of Belém are illustrated in Figure 7. The adopted fecal coliform (FC) concentration equal to 108 NMP/100ml, decay rate equal to 21,600s and lifetime equal to 18 hours were obtained from Batista (2005). The data in Table 2 show that the Una basin contributes approximately 60% of the total sewage that is generated by the basins under consideration, which is reasonable because of the large population that is associated with this basin. Figure 8 shows the effluent discharge sites in the hydrographic basins of the metropolitan region of Belém that flow directly into Guajará Bay and were considered in the present study.
Figure 7

Limits of hydrographic basins (source: Jesus & Paranhos 2003).

Figure 7

Limits of hydrographic basins (source: Jesus & Paranhos 2003).

Figure 8

Sites of effluent discharges into Guajará Bay.

Figure 8

Sites of effluent discharges into Guajará Bay.

RESULTS AND DISCUSSION

Hydrodynamics

Figure 9 shows the hydrodynamic circulation for a typical flood and neap tide cycle in September 2003.
Figure 9

Hydrodynamic circulation for flood and neap tides for September 2003.

Figure 9

Hydrodynamic circulation for flood and neap tides for September 2003.

The characteristically high velocities of the Onças Island Channel can be attributed to the acceleration of the flow because of the peculiar bathymetry of the channel. The channel has much deeper regions (Figure 2) than the other regions of the Guajará Bay, thus becoming a preferred flow path. A low-velocity zone originates close to the Port of Belém and advances in the Northern direction, ending at the coastal zone of the city. As the Guamá River flows into the Guajará Bay, the low-velocity stream tends to flow to the East, where it is obstructed by Onças Island and continues a course to the North. Hence, the city waterfront area is protected from the influence of this low-velocity stream.

Contaminant plumes

In this section, we present results showing the impact of the sewage effluent discharge, i.e., the FC levels, as previously cited, for the following hydrographic basins that pollute the Guajará Bay in the metropolitan region of Belém: Paracuri, Mata Fome, Val-de-Cans, Una, Reduto and Tamandaré. Table 2 presents the parameters that were used in the simulations. Figure 10 shows the FC dispersion in the Guajará Bay as a function of the elapsed time after disposal. Figures 1113 show the FC concentrations at 48 hours (Figure 11), 120 hours (Figure 12) and 168 hours (Figure 13) after disposal.
Figure 10

Plume for FC disposal in Guajará Bay.

Figure 10

Plume for FC disposal in Guajará Bay.

Figure 11

FC concentration 48 hours after disposal.

Figure 11

FC concentration 48 hours after disposal.

Figure 12

FC concentration 120 hours after disposal.

Figure 12

FC concentration 120 hours after disposal.

Figure 13

FC concentration 168 hours after disposal.

Figure 13

FC concentration 168 hours after disposal.

These figures demonstrate that the pollutant plumes flow from Belém towards the beaches in the North, particularly those located in the Icoaraci and Outeiro districts, thereby affecting the bathing water quality. Thus, the pollution in these areas is not localized as Braz (2003) has suggested. The pollutant plumes also flow very close to the city waterfront because of the low velocities in this region, as was discussed for the hydrodynamics results. Hence, the pollutants tend to remain confined longer in the regions around the waterfront. In these regions, the effects of turbulent diffusion are less intense, reducing pollutant dispersion, because dispersion depends strongly on the local flow velocities. One of the possible applications of the model is to determine the optimum locations and times for pollutant disposal that promote local turbulence action. The model could be used to project future disposal schemes through channels and submarine outfalls to decrease the pollution at the Belém waterfront.

The simulated FC concentrations were comparable to results in the literature. For instance, Ribeiro (2002) presented quantitative data for FCs in the Paracuri stream that were obtained in the wet and dry periods, with average values of 2.5 × 105 and 2.8× 105 in MPN/100 ml, respectively. Berredo et al. (2000) verified that the FC values were on the order of 106 MPN/100 ml at sites in the Guajará Bay (Figure 8).

CONCLUSION

We simulated the hydrodynamic circulation for a typical neap tide scenario with a flood cycle. These results were used to simulate FC plumes as a function of the time after disposal in the Guajará Bay. The simulated FC concentrations were in satisfactory agreement with values found in the literature. The analysis of the simulated plumes demonstrated that the FCs that are produced in the metropolitan region of Belém flow towards the beaches in the North, especially those in the Icoaraci and Outeiro districts, thereby affecting the bathing water quality. The dispersion of only one species was simulated in the present study. However, hydrodynamic and pollutant dispersion models of the Guajará Bay are available and can be used to simulate other species. The methodology is sufficiently robust and can be applied to other waterbodies to improve water resource management.

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