The TELEMAC system, developed by the Laboratoire National d Hydraulique Environnement of the Company Eletricit de France (CEDF), was used for the hydrodynamic simulations. The TELEMAC3D model solves the Navier-Stokes equations by considering local variations in the free surface of the fluid, neglecting density variations in the mass conservation equation and considering the hydrostatic pressure and Boussinesq approximations. The model is based on finite element techniques to solve the hydrodynamic equation [25] and relies on the sigma coordinate system to follow the surface and lower boundaries for vertical discretization [26] .

A time step of 90 s and a Coriolis coefficient of −7.70 × 10⁻⁵ rad·s⁻¹ (at 32˚S) were used in all of the simulations. The horizontal turbulence process was performed using the Smagorinsky model. This closure turbulent model is generally used for maritime domains with large-scale eddy phenomena. It calculates the mixing coefficient by considering the size of the mesh elements and the velocity field [27] .

The mixing length model for buoyant jets assessed the vertical turbulence processes and provided a better representation of the stratification. This model considers density effects via a damping factor that depends on the Richardson number to calculate the vertical diffusion coefficients.

The power of the ocean currents can be transformed using converters. Similar to the technology of wind converters, a submerged rotor is forced to rotate by the fluid surrounding it. A recent evaluation of the equipment available to capture hydrokinetic energy found that 76 pieces of equipment, including turbines, were in operation or were in the early stages of research [28] .

The hydrodynamic simulations used in this study were produced using the TELEMAC3D model. The investigations involving energy conversion from the currents into electrical power were performed with the energy module [14] . This module uses the turbine standard equation (Equation (1)) to calculate the electric power in watts (W) from the incident flow velocity (where: ρ is the water density; η is the efficiency coefficient; A is the blade area and v is the incident velocity). Table 1 indicates the turbine technical parameters used in the energy conversion module.

The water body boundaries used in this study were the Guaíba River, the Camaquã a River and the São Gonçalo Channel (Figure 2) based on the discharge time series obtained from the Brazilian National Water Agency¹ (ANA) web-site. The discharge of the São Gonçalo Channel was assumed to be constant at 760 m³/s due to the absence of the observed data series [29] .

The oceanic boundary was forced by the astronomical tides, water levels, current velocity, salinity and temperature fields. The salinity and temperature fields used as the initial conditions were obtained from the Ocean Circulation and Climate Advanced Modeling Project² (OCCAM).

The numerical model was initialized from the remaining parameters with a water level of 0.75 m, the approx- imate average tide in the region [30] . The amplitude and phase data on the oceanic border were calculated with the Grenoble Model FES95.2 (Finite Element Solution v. 95.6). The temporal and spatial variability of the winds and air temperature on the surface boundary were obtained from the National Oceanic and Atmospheric Administration (NOAA)³ website. The air temperature data on the ocean surface were also used to assess the heat exchange with the atmosphere in the model calculations.

The study was based on a two-year simulation (1998 and 1999). The first year represented anomalous conditions due to the ENSO influence, with moderate to high discharges occurring over the entire year. The second year represented normal conditions, when the freshwater discharge of the Patos Lagoon followed its natural pattern.

Monteiro et al. [31] - [33] presented results for the calibration and validation of the two-dimensional model in the Patos Lagoon estuary. Subsequently, Marques et al. [14] [23] [24] [34] performed a set of simulations for the calibration and validation of the three-dimensional numerical model along the area covered by the Patos Lagoon and the adjacent coastal region.

The results of these calibration and validation tests indicated that the TELEMAC3D model can be used for studies of the SBS with an acceptable degree of accuracy. As a result, the values for many physical parameters (such as the wind influence coefficient, friction coefficient and turbulence models) were available and were used to conduct this study.

The AHP is widely used for multi-criteria analysis [6] [7] [35] - [38] . This analysis evaluated all of the criteria/ factors which were considered relevant for decision, and compared against each other in a pair-wise comparison matrix. For the assemblage of this matrix, [39] and [40] suggested a scale for comparison that consisted of values ranging from 1 to 9 to describe the intensity of importance (preference/dominance).

The assigned preference values are synthesized to determine a ranking of the relevant factors in terms of a numerical value which is equivalent to the weights of the factors, where a value of 1 expressed equal importance

and a value of 9 was given to those factors that had an extreme importance over another factor. Therefore the eigenvalues and eigenvectors of the square preference matrix are calculated, revealing important details about patterns in the data matrix.

After the preference matrix is performed, each pair-wise match receives a consistency index, which is directly calculated from the matrix with the Equation (2), where λ_max is the greatest eigenvalue of the preference matrix, while n is the order of the matrix.

Therefore [39] provided the consistency ratio CR (Equation (3)) which is a single numerical index to check for consistency of the pair-wise comparison matrix. It is defined as the ratio of the consistency index (CI) to an average consistency index (RI), where RI depends on the order of the preference matrix [40] . Accordingly, a consistency ratio (CR) was provided after applying all of the criteria/factors in the comparison matrix. Saaty [40] recommended that the CR should never exceed a value of 0.1, otherwise the preference matrix should be reviewed.

This methodology was applied using the Geographic Information System (GIS) Software, which is a tool for geoprocessing information with high liability. The criteria/factors were divided into 3 themes called: 1) Positive Factors; 2) Negative Factors; and 3) Restraining Factors. Each group was filled with information from Internet geodatabases, such as ANEEL⁴, IBGE⁵, MMA⁶, IBAMA⁷, DHN⁸, GISMAPS⁹ and results from the hydrodynamic simulation from TELEMAC3D.

This information and their scale values are shown in Table 2, where the subclasses (factors) were chosen according to several studies [6] [7] [35] - [38] [41] - [45] . According to Brazil’s Policy, none installment may be per-

*: Classes with an asterisk were used to create a mask to identify the study track.

formed in a Conservation Unit, paleontological or archaeological sites. In addition, dredge discharge zones were included as a non-suitable spot for the study due to the constant dredging activities in the Rio Grande Harbor, turning these zones inappropriate due to navigation and sediment release. These factors (shown in Table 2 as an asterisk) were used as a mask in order to identify the forbidden places for the installment and also, the study track in which the factors were compared.

The possible installment locations of the turbines are highlighted in Figure 1. These locations are referred to in the following sections as the northern region (between the Solidão lighthouse and the Conceição Lighthouse) (Figure 1(b)) and the southern region (south of the Sarita lighthouse and north of the Albardão lighthouse) (Figure 1(c)).

In these regions, the average velocity of the current (Figure 3(a)) was analyzed. The mean values that reached extremes of 0.4 m/s were found with high standard deviations of the current velocity and appeared in the same regions as the mean values (Figure 3(b)). This result suggested that these regions were suitable for power conversion. However, these regions can also go through periods of low power generation because the velocity deviation had a value closer to the average.

The isobaths were closer in the northern region (Figure 4(a)) and presented a stronger vertical gradient. In this region it was possible to find an average power (Figure 4(a)) of approximately 7 kW/day. The power conversion was intensified in the region where the isobaths were farther apart (the 20 m isobath). The average power in this region reached 10 kW/day.

This area was characterized by complex topography, with the 50 m isobaths (the limit of the inner shelf) closer to the shoreline, where there was a high gradient. The gradient was reduced towards the Conceição Lighthouse, where this isobath moves away from the shore. Thus, the circulation pattern was modified when a current flowed from the region (with the 50 m isobaths near the coast) to where the coastal flow was more intense and concentrated in a shallower region near the 20 m isobath. The flow slowed down and spread out as this process occurred. Intensification occurred in the northern region when the current at the 20 m isobath encountered a topographic strangulation, diverting the current to the 30 m isobath and increasing its velocity.

The southern region (Figure 4(b)) had a distinct pattern of bathymetry in which the isobaths were far apart. However, the submarine floor had major irregularities. The high values of the average power were observed over almost the entire length of the inner shelf, between 10 and 20 m deep. Average power values (Figure 4(b)) near 3.5 kW/day were observed in this region.

The southern region had a complex bathymetry with significant linear banks, such as the Bank of Albardão, and a large depression (the Albardão Pit at a 75 m depth). The Bank of Albardão acts as a barrier to the coastal current (directed by the 20 m isobaths) causing the flow to diverge. Consequently, the meandering of the current intensified, suggesting that the intensification of power in this region was strongly influenced by the irregular topography.

This region relies on its oceanographic features, while the northern region was highly dominated by a strong vertical gradient which generated squeezing and stretching currents, enhancing the power generation. The south- ern region was forced by a topographic feature (e.g., the Bank of Albardão) that forced the flow to diverge, and, as a consequence, the meandering of the current intensified, increasing the power availability in this region.

The suitable installation areas were determined by the level of power density, the ease of accessibility and the number of environmental conflicts with the site selection methodology. Although the weight of each factor depends on the interference of the stakeholder, the AHP method relies on a very advanced consistency method to avoid misleading decisions.

The AHP was applied on each subclass and gathered them as a new class (their Consistency Ratio is shown on Table 2). Classes were intersected and reduced from the restraining factors to concatenate all of the information on a final map. The restraining factors consisted of: 1) desirable bathymetry for installation (0 to −50 m); 2) Endangered Species; and 3) Proximity to Conservation Units.

The positive factors were formed by gathering the energy information from the hydrodynamic model and the bathymetric data (especially the data above 50 m, see Figure 5(a)). The negative factors were formed by a convolution of the data that resulted from the three major shapes (Figures 5(b)-(d)) of the transmission and transport data, the socioeconomic influence data and the geological data.

The relative importance of location factors is also changing as the decision process stages proceed [46] . In the early stage of identifying preferred geographical areas, only a few priority items are considered to identify those regions that satisfy most important criteria, such as the availability of strong currents or the proper bathymetry according to the turbine settings.

When reaching the stage of selecting specific locations, site-specific factors such as grain size, endangered species or access to roads and power cables may dominate over another location. In the final stage of evaluating a few selected factors may escalate in favor of another factor, or even, decrease the importance of other factors.

All of the shapes showed the study track of this work, which meant that the suitable area had to be inside of these lines. This mask was made by applying all of the restraining factors, as the incidence of endangered species and Conservation Units inhibited the possibility of using any area. It is feasible to compare the possible and less possible areas according to the blue and red colors in the charts, respectively. The transmission and transport shape (Figure 5(b)) was dominated by the presence of the Rio Grande Harbor (30%), due to its navigation importance, followed by the electric transmission and substation (23%) that were necessary to reduce the cost of installation in a desirable site.

The sediment data (Figure 5(c)) showed a few possible areas and there was a dominance of medium possible areas. This slight divergence is the result of the influence of the gravel, which received a high weight (52%) due

to its importance for the installation process. The sand had a weight of 24%. The socioeconomic shape (Figure 5(d)) was greatly influenced by the urban areas (such as Rio Grande City at 45%), and the population concentration was the second most important factor at 30%.

We achieved the shapes of the positive and negative factors by integrating the prior results on themes. The positive factors (Figure 6(a)) were strongly dominated by the energy production (Figure 4(a) and Figure 4(b)) and had a greater mean energy. This area was likely the best area for installation. The southern region had a 60% acceptance, but due to the presence of geological sites and Conservation Units, this region was cut from the study track. The northern region had less influence from constraining factors than the southern region, and its energy peak was located inside the study track.

The negative factors (Figure 6(b)) shape showed that the area near the Rio Grande jets was the least possible installation area, due to the importance of navigation in this area. The northern region had less possible installation areas than the surroundings of the southern region. This negative influence was justified by the proximity of the northern region to fishing zones and Conservation Units.

A final AHP was created by using all of the shapes. Figure 7 represents the mixing between negative and positive factors, which resulted in a shape dominated by less possibility, the white zone inside the study track represents areas with less than 1% of installment possibility. A minor region inside the most energetic area in the northern region was the most viable region. This result was highly dominated by the positive factors, such as energy production, which counter balanced all of the negative influences from nearby locations.