Analysis of currents on the continental shelf off the Santa Catarina Island through measured data

The coastal currents and forcing agents that conduct them are still little-known in the internal continental shelf of Santa Catarina. Therefore, this work aimed to analyze the data of currents measured off the Island of Santa Catarina in order to better comprehend its patterns and forcing agents. The three measuring stations were installed in shallow water near the Arvoredo Biological Marine Reserve (ST01), Jurerê Beach (ST02) and Ingleses Beach (ST03). Data were collected by a current meter from January 22, 2014 to December 17, 2014. In the consisted data set, it was performed a basic statistical analysis, spectral decomposition and harmonic analysis in the tide components. All the stations presented a resulting southward flow, especially the station next to Arvoredo Marine Biological Reserve (ST01). The meteorological forcing has a strong contribution to the magnitude and direction of component v (alongshore). While the tidal component has greater importance in the cross-shore flow (component u). The wind showed a strong correlation with currents and the local level, indicating to be the main forcing agent of the flow in the subtidal frequency.


INTRODUCTION
Hydrodynamic patterns of the continental shelf conduct the environmental and economic aspects of coastal regions such as fishing, sedimentary dynamics, nutrient availability, navigation, dispersion of pollutants, among others (Halpern et al., 2008;Mann & Lazier, 2006). However, the circulation in these regions is forced by agents of different scales (temporal and spatial), natures and intensities, besides the influence of bottom and coastal morphology (Mitchell et al., 2015;Noernberg & Alberti, 2014). It makes the knowledge of processes in shallow environments much more complex.
The circulation of the oceans in the South Brazilian Bight (SBB, which comprehend the region between Cabo Frio/RJ and Cabo de Santa Marta/SC) has been well studied and documented in recent years, especially through regional numerical models (Stech & Lorenzzetti, 1992;Mesquita & Harari, 2003;Souza & Robinson, 2004;Palma et al., 2004;Calado et al., 2008;Palma et al., 2008;Oliveira et al., 2009;Matano et al., 2010;Lima et al., 2013;Pereira et al., 2013). On the other hand, hydrodynamic studies with measured data on the South Brazilian Bight (SBB) remain scarce. In the 1990s, the project entitled "Estudos Ambientais em Áreas Oceânicas e Costeiras da Região Sul do País" (Environmental Studies in Oceanic and Coastal Areas of the Southern Region of the Country) carried out by PETROBRAS in partnership with universities raised the first series of data with more consistency for the region. There were 11 months of data collected by 3 current logs at 30, 75 and 130 meters deep (Casares Pinto, 1998;Hirata, 2008). After this survey, indirect measurements (Pimenta et al., 2006) or of short length (Cirano & Lessa, 2007) were documented. In 2014 a survey of oceanographic data was carried out around the north/northeast region of Santa Catarina Island in order to generate funds for the implantation of a submarine emissary in the region Bleninger et al., 2016). Part of this dataset is used in this study.
The SBB comprises an extension of approximately 350 km between latitudes 26° and 29° 20'S and it is inserted in the SBB. The current in the SBB has a dominant flow to southwest, with weaker currents during autumn and more intense in spring (Casares Pinto, 1998;Palma et al., 2008). In summer, predominant flows to southeast generate resurgence, whereas in autumn and winter more periods of inversion of this pattern occur, with currents flowing to north and generating subsidence (Pimenta et al., 2006;Cecílio, 2006).
Currently, it is believed that the meteorological forcing is the one that controls the currents in the region, and the transient meteorological conditions (like the passage of cold fronts) are more important than seasonal wind patterns (Harari et al., 2011). However, wind loses importance in less exposed environments, such as the west region of Santa Catarina Island, where the astronomical tide becomes more relevant in the local outflow . For Casares Pinto (1998), the longshore flow to the bathymetry is dominated by subtidal frequency events, whereas the cross-shore flow presents a greater influence of the tide. However, other authors also attribute to the Brazilian Current (BC) an important role in determining the circulation in SBB (Hirata, 2008;Palma et al., 2008).
Although the studies cited indicate a relationship between the pattern of currents in the SBB and forcing agents that rule it, there is still a need for more direct and concrete analysis of these relationships. This study therefore aims to describe the behavior of currents in the SBB and to analyze its relationship with wind and local level.

MATERIALS AND METHODS
The study region is located in the Internal Continental Shelf of Santa Catarina and comprises the north of Santa Catarina Island (SCI) and Arvoredo Marine Biological Reserve (ReBioMar Arvoredo). Current velocity, sea level, and background temperature data were obtained from the measurement of three ADCPs (Acoustic Doppler Current Profile). One ADCP (ST01) was anchored at ReBioMar Arvoredo and the other two (ST02 and ST03) in the north of SCI (Figure 1 and Table 1). Data from the north of SCI were collected by the Companhia Catarinense de Águas e Saneamento (CASAN) to elaborate studies for the implantation of submarine outfalls in the region Bleninger et al., 2016). The ADCP funded at Arvoredo Reserve is part of the Environmental Monitoring Project of the Arvoredo Reserve -MAArE Project (Segal et al., 2017). The project was executed between 2013 and 2017 with fundings from PETROBRAS in partnership with the Federal University of Santa Catarina (UFSC) and the Arvoredo Reserve technical team.
All three devices were installed on the seabed with transducers pointed to the surface. The ADCP of ST01 station was anchored to a depth of 21.4 meters in a metal structure of approximately 1 meter. It has been configured to record data in 1-meter cells along the water column with 0.5 m blank distance, 1 Hz acquisition rate, 300 second sampling time and 1-hour sampling interval. With these settings the first measured cell was 2 meters from the bottom (structure + blank distance + ½ cell size). Because this first cell was excluded in the consistency analysis, the first valid cell from ST01 collected data at a depth of 3 meters ( Table 2).
The ADCPs of ST02 and ST03 stations were installed in 0.86 m metal structures at a depth of 11 and 20 meters, respectively. Differing the sampling settings of station ST01 only in sampling interval, which was 30 minutes. The first cell measured by these ADCPs was at a distance of 1.86 m from the bottom ( Table 2).
The measured data went through a consistency analysis and quality control, as well as correction in the magnetic declination. For ST01, ST02 and ST03, 16, 6 and 15 cells were validated, respectively. From the dataset, the period between 01/22/2014 and 12/17/2014 (328 days) was cut for analysis because it is the

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After data consistency, basic statistical analysis and spectral decomposition of the series were performed. For the spectral decomposition of the observed current velocity time series (Yo) was used a classical frequency decomposition technique. The hourly series of currents measured by the ADCP were decomposed into independent components. Initially the tidal component (Yt) was identified through the t_tide package (Pawlowicz et al., 2002) developed for use in MATLAB. Subtracting the tidal component from the total signal, we have the non-tidal component (Ynt = Yo -Yt). This component contains important contributions in the day and week range (synoptic scale) and seasonal scale, but it still maintains high frequency residual (Yres). To identify and exclude this high frequency component, the low-pass filter LP33 (Flagg et al., 1976;Beardsley et al., 1985) was applied, resulting in the subtidal component (Ysubt = Ynt -Yres). The filtered subtidal component (without the high frequency residual) now represents scales of meteorological and seasonal processes.
Energy distribution of the observed current series, non-tidal and subtidal, was analyzed by estimating power spectrum. For this, it was used the consolidated Welch's method, with 50% overlap and Hamming window. As the three measured data series (ST01, ST02 and ST03) have significant holes, for each series a 114-day period was extracted with consistent data and few failures to perform this analysis. A 38-day window has been set.
After descriptive and spectral analysis of currents, linear correlation analysis (Pearson) was performed for the total period of measured data, in order to better understand the relationship  period with the largest number of data collected simultaneously by the three stations. The currents were analyzed in their barotropic condition (mean value for the entire measured water column) and baroclinic condition (layer analysis) ( Table 2).

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between local hydrodynamic patterns and atmospheric and astronomical forcing, and cross correlation for a cutout time series.
The excerpt of the series to be analyzed was defined aiming to understand a period of influence of two atmospheric systems that act in the region: wind N-NE (South Atlantic Subtropical Anticyclone -SASH) and wind S (Anticyclone of polar origin, which originates the called cold front). It was used the methodology proposed by Rodrigues et al. (2004) to identify cold fronts on the time series of wind data. After identifying cold fronts, a period was chosen in which currents had been measured simultaneously in the three stations.
Wind data with a 6-hour temporal resolution were obtained from version 2 of the Climate Forecast System reanalysis model (CFSv2 -NCEP; Saha et al., 2014). The series was extracted at the closest possible point to the ADCP's anchored stations (STW, Figure 1). And, to check the temperature pattern along the water column at the points measured by the ADCP, a surface temperature series was also extracted from the STW point. The sea surface temperature series was collected from the OSTIA database provided by the National Oceanic and Atmospheric Administration (NOAA). The data have daily and spatial temporal resolution of 0.05 ° (~ 6 km).

RESULTS AND DISCUSSIONS
Time series of measured data, already validated, showed temporal coverage of 66.8% for ST01, 67.8% for ST02 and 80.8% for ST03. The most significant periods of data shortages at all three stations occurred because of equipment configuration problems or equipment loss due to trawling activity common in the region. Figure 2 shows the barotropic current velocity series (mean of the entire water column) in component u (zonal, east-west) and component v (southern, north-south). For ST01, located in ReBioMar Arvoredo, the current presented higher intensity in component v (alongshore) with predominance of southward flow. The average current magnitude at this station was 0.177 m/s, with a contribution of 68.47% in component v and 31.53% in component u. This directional pattern of current in ST01, flowing predominantly in the north-south axis, can be seen in Figure 3.
For component u, the maximum positive velocity (to the east) was 0.37 m/s and the negative maximum velocity (to the west) was 0.44 m/s. In addition to similar intensities, these currents (east/west) also had balanced percentage of occurrence (Table 3 and Figure 2). By analyzing the component u along the water column ( Figure 4) it was found that the balance between east/west currents is not in a distribution over time, but in a reversal of direction between  the layers. The currents were predominantly east on the surface and west on the bottom layer. Component v presented positive mean velocity (north) of 0.762 m/s and negative velocity (south) of 1.013 m/s. In addition to being more intense, the southward component v was also the most frequent in the measured period. Throughout the layers (Figure 4) it can be noticed that southward flowing currents (negative) have greater intensity on the surface that will be gradually reduced to the bottom. Flowing north current (positive) has a constant intensity along the water column.
In ST02, the current had a maximum magnitude of 0.491 m/s and an average of 0.113 m/s, with balanced contribution of components u and v (Table 3). For component u, the positive values (to the east) were more intense. For component v, the negative (south) currents were stronger and more frequent (55.70%). The directional pattern of this station occurs northeast-southwest (Figure 3), resulting in mean runoff to the south quadrant. Along the water column, as in ST01, it was possible to identify predominance of currents to northeast in the surface and southwest in the bottom (Figure 4).
The current at ST03 presented the highest average magnitude (0.194 m/s) and the highest intensities in the u component (east-west) among three analyzed stations. For component u, maximum speed to the east was 0.798 m/s, and to the west was 0.601 m/s. In addition to being more intense, the eastward current was also approximately 2 times more frequent than the westward currents throughout the measured period (Table 3 and Figure 2). Component v presented very similar average south and north speeds of 0.677 and 0.629 m/s respectively, with higher frequency for southward currents. The flow at this station was northwest-southeast direction (Figure 3). In contrast to ST01 and ST02, ST03's current was uniform across the layers in both magnitude and direction (Figure 4). There is a natural weakening of the magnitude of the current in cells closer to the bottom, but in the analyzed period, no inversions of direction along the water column were identified.
Because these measurements are performed in shallow environment and near islands and mainland, velocity and direction of measured flow were strongly influenced by local geomorphology. Percentages of contribution of components u and v in the current's magnitude (Table 3), quite different for 3 stations, portray this. In ST01, the current flows in north-south directions, alongshore, and suffers interference from the islands that form the ReBioMar Arvoredo. Due to its proximity to the north of Santa Catarina Island and North Bay channel, ST02 has its flow in northeast-southwest direction, being part of the ebb and flood current. As to ST03 being in a narrow region between the coast of Santa Catarina Island and a promontory and two small islands to east and south (Figure 1). This configuration causes runoff at this station to be limited mostly to northwest-southeast direction (Figure 3). The geomorphology only draws the main flow paths (north-south axis) and softens or intensifies velocities (Cecílio, 2006;Palma et al., 2008). Other forcing agents, which will be discussed later, are responsible for the characterization of the flows themselves.
The average velocity of component v found in ST01 (0.14 m/s) was similar to those found by Zavialov et al. (2002) in the external platform of Rio Grande do Sul (0.16 m/s) and Casares Pinto (1998) in the internal platform of Santa Catarina (0.12 m/s). The ST03 has its intensity divided between components u and v, however in average, the magnitude is close to the values found in ST01. The mean magnitude found in ST02 (0.10 m/s) approximates the values measured by Garbossa et al. (2014) in the North Bay of Santa Catarina Island (0.11 m/s).
In seasonal analysis, it was observed that in ST01 and ST03 there was greater variation in velocity and directional pattern between stations (Table 3 and Figure 5).
In these two stations, the highest intensities occurred in spring, with predominance of currents flowing to the south quadrant, corroborating the seasonal pattern identified by Casares Pinto (1998) and Palma et al. (2004). In autumn, in addition to milder currents, the currents showed a resulting average northward flow in all measured cells ( Figure 6). In ST02, in all seasons of the year, the current maintained its magnitude and direction pattern, with values more intense in summer (Table 3 and Figure 5). This indicates the highest degree of protection of this region, especially the forcing agents coming from the south and east, typical from autumn and winter (Monteiro, 2001).
Seasonal modulation identified in current data can be observed most intensely in surface and bottom water temperature series (Figure 7). It is possible to notice an intense stratification of the water column in summer and spring months, and homogenization of the column during winter and autumn. Seasonality of water thermal patterns is directly related to seasonality of current patterns. As previously mentioned, in summer and spring the currents to south and southeast intensify in baroclinic character. The higher velocity of surface currents, and declination by Ekman.
In consequence, surface water flows into ocean region, generating subsidence zones along the coast. In order to correct the formed sea level gradient, current flows toward the shore through the bottom layer, also leading low-temperature water, that commonly occupy the middle and outer shelf. Thus, generating the observed thermal gradient. This seasonal pattern of stratification and homogenization of the water column has been previously identified by studies in the continental shelf of Santa Catarina (Hille et al., 2008;Carvalho et al., 1998;Bordin et al., 2019). The power density spectra for the u and v components of the currents measured at the three stations are shown in Figure 8. When performing spectral decomposition, the contributions of   the tidal component in the semidiurnal band, 1/3 diurnal and 1/4 diurnal, were evident. The tidal component was less intense in the diurnal band. Also, the subtidal component peaks around 3 days, that corresponds to the duration of the passage of frontal systems in the region. (Gregorio, 2014).
In ST01, in the subtidal range presented variance (energy) almost 2 times greater than component u (east-west). Moreover, the energy level in the tidal and subtidal bands in component v was very distinct, with the subtidal band having greater importance (Table 4 and Figure 8).
In ST02 it was possible to verify a diurnal peak higher than in other stations, and also a greater balance between energy levels of components u and v. And unlike ST01, the tidal band in ST02 is the most important component in the composition of the final  magnitude of the local current. In ST03 it was possible to identify two well marked peaks around the period of 6 and 10 days for components u and v. Also, greater energy balance between the tidal and subtidal bands was observed.
In the variance decomposition of the subtidal component, it is possible to verify the portions attributed to the meteorological and low frequency component ( Table 4). The component in the meteorological band dominates (around 80% of the explained variance) the subtidal frequency. However, the low frequency component also plays an important role, reaching 23% of the variance explained in ST03.
The influence of the different energy bands, for the u and v components at each measurement point and at different depths, can be better seen in Figure 9 and Figure 10. The importance of the subtidal band for the predominant north/south flow to ST01 is evident, as well as the irrelevance of the subtidal band to the intensity of currents in ST02, and the balance between the tidal and subtidal bands in the composition of the flow patterns in ST03.
It is also clear the importance of the tidal current for the cross-shore flow (u component), already identified in previous studies (Casares Pinto, 1998;Mesquita & Harari, 2003). In all stations, tidal current in the cross-shore component was more significant than the subtidal current. This fact results an amplification of the tidal current in this component (in ST03, due to local morphology), associated with a lower influence of the subtidal band (in ST01 and ST02). The intensification of tidal currents in shallower areas and with a geomorphology that generates bottlenecks or channels (ST02 and ST03), occurs basically due to mass conservation (Harari & Camargo, 1998). As to the main influence of the subtidal band on the component v (north-south), especially in non-sheltered areas, is related to the characteristics of two main atmospheric systems that act in the region: the South Atlantic Subtropical Anticyclones (SASH) and movements of Front Meteorological Systems (FMSs) (Castro & Miranda, 1998).
The SASH, a high-pressure system located in the Atlantic between South America and Africa, is the determining system in defining the atmospheric condition for the study area (Ito & Ambrizzi, 2000). The zonal displacement throughout the year sometimes intensifies northeast winds, sometimes weakens them allowing greater penetration of FMSs (Tchernia, 1981). Wind data collected from the STW (Figure 1) indicated that the local wind pattern for the period is characteristic of southern Brazil    ( Figure 11). It happens with higher occurrence of N-NE sector winds, but higher wind intensity associated with cold fronts (FMSs). On average, the number of cold fronts is quite similar in all stations, with a slight decrease in summer and a slight increase in winter (Oliveira, 1986;Stech & Lorenzzetti, 1992;Lemos & Calbete, 1996;Rodrigues et al., 2004;Barletta et al., 2016). Linear correlation analyzes between wind (Figure 11), level ( Figure 12) and currents allowed us to better understand the relationship among the local hydrodynamic pattern and the atmospheric and astronomical forcing agents.
Understanding, more specifically, the local runoff under the influence of usual atmospheric conditions (N-NE wind) and during the cold fronts (S wind), cross-correlation analyzes were performed in a section extracted from the total series: from April 22, 2014 to May 03, 2014 (Figures 11 and 12).
Only by visual verification of the selected excerpt it was possible to observe sea level rising and currents flowing north during the cold front, and local level lowering and mean southward flow under usual atmospheric condition ( Figure 13). Components v current and wind (subtidal frequency) presented linear and in-phase correlation in the expressive value of 0.78 for ST01, 0.75 for ST03 and 0.56 for ST02. This high subtidal frequency of  energy in the parallel-to-coast current, especially at stations ST01 and ST03, had already been demonstrated in the spectral analyzes previously performed (Table 4 and Figures 8, 9 and 10). The strong influence of wind on currents over the internal continental shelf has been widely studied (Scott & Csanady, 1976;Brink, 1991;Lentz, 1994;Palma et al., 2004;Palma et al., 2008). Despite the strong relationship always found between current, wind direction and magnitude, defining that wind blows longshore and currents only flow proportionally in the same direction is an oversimplification (Winant, 1980;Cecílio, 2006). Wind blowing in the ocean generates a surface current initially in the same direction as the wind, but already in the second moment it deflects, due to the Ekman spiral (Ekman, 1905). This Ekman transport or pumping, as it is known, acts along the water column generating a deflection of the current in relation to the wind direction that increases as it moves away from the surface (Csanady, 1976;Scott & Csanady, 1976). This explains, for example, the strong correlation found between the bottom cross-shore current and the surface longshore current (Figure 14 -A). Since this deflection goes to the left in the southern hemisphere, winds from the south quadrant generate currents flowing towards the coast, while northeast winds favoring the formation of a coastal jet to the oceanic region. Sea level changes in the coastal region then arise as the pressure field adjusts in geostrophic balance to longshore velocities (Cecílio, 2006).
The relationship between wind, current and sea level was identified in the correlation analyzes performed. The linear correlation between sea level and wind direction (in subtidal frequency) resulted in an average value of 0.48 for the three measured data stations. Cross-correlation analysis started on April 22 (first day of south wind) between level and component longshore wind indicated increasing correlation with sea level rise, peaking on the third day (0.64) south wind incidence (Figure 14 -B) indicating a significant, and out of phase, relationship. Cross-correlation of level with current indicated the same behavior, an increase in local sea level with currents blowing north (Figure 14 -C). On the other hand, the current also has a high frequency correlation with sea level. This is the influence of the semidiurnal cycle of the tide on the currents, especially in the transverse direction of the coast (Figure 14 -D).

CONCLUSIONS
The geomorphology of Santa Catarina Island and its surroundings provides the development of environments with diverse hydrodynamic characteristics. The forcing agents that dictate the magnitude and direction of the flow are impacted according to the shoreline designs, bathymetry and degree of protection of the ocean region. Coastal flow in the region is more dependent on transient weather conditions in the wind pattern than seasonal variations. The fixed high-pressure ocean system that generates a predominance of northeast quadrant winds is interrupted during the entry of cold fronts (frontal systems) with southern quadrant winds. Nevertheless, the intensification and/or displacement of both systems ends up generating a seasonal flow, especially in the outermost regions of Santa Catarina Island.
The resulting flow to the south makes the northern region of Santa Catarina Island a recipient of waters from the Arvoredo Biological Marine Reserve region, as well as supplier to North Bay. This predominant southward flow is most easily reversed during the fall.
Through the spectral decomposition of velocities, it was possible to identify larger contributions of the subtidal frequency in component v (north-south, longshore). In component u (east-west, cross-shore), the flow was conducted mainly by the tidal stream.
Current and local level presented a strong relation with the local wind pattern, indicating that the wind is the main forcing agent of the subtidal frequency. In the region, SASH and FMSs alternate the prevailing wind regime between northeast (SASH) and south (FMSs or cold fronts). The northeast wind drains the flow to the south and causes local level lowering by geostrophic balance. Wind from the south, on the other hand, forces the currents to the north and stacks water on the coast, raising the local sea level.
Long monitoring campaigns with measured data are extremely important for understanding the processes that conduct the coastal hydrodynamics. Not only because they allow a detailed realistic analysis of each spectrum that forms that signal, but also, can serve as input or calibration data for numerical models that can evaluate flow at wider scales.