Laboratório de Oceanografia Física Estuarina e Costeira, Departamento de Oceanografia, Universidade Federal de Pernambuco, Recife, Brazil
CEERMA-Centro de Estudos e Ensaios em Risco e Modelagem Ambiental, Universidade Federal de Pernambuco
Corresponding author: D. Veleda, Laboratório de Oceanografia Física Estuarina e Costeira, Departamento de Oceanografia, Universidade Federal de Pernambuco, Av. Arquitetura s/n, 50740-550, Cidade Universitária, Recife, PE, Brazil. (firstname.lastname@example.org)
Corresponding author: D. Veleda, Laboratório de Oceanografia Física Estuarina e Costeira, Departamento de Oceanografia, Universidade Federal de Pernambuco, Av. Arquitetura s/n, 50740-550, Cidade Universitária, Recife, PE, Brazil. (email@example.com)
 Intraseasonal signals with periods of 2 to 3 weeks in near-surface alongshore current measurements are detected from four moorings (K1–K4) deployed from 2000 to 2004 at the 11°S section close to the Brazilian coast as part of the German CLIVAR Tropical Atlantic Variability Project. This section crosses the path of the North Brazil Undercurrent, the most powerful western boundary current in the South Atlantic Ocean. We investigate the origin of this intraseasonal variability of the North Brazil Undercurrent by relating the oceanic oscillation of the alongshore currents to its atmospheric counterpart, the meridional wind stress. On average, the results indicate a well-defined lagged (10 days) correlation (∼0.6) structure between meridional wind stress and alongshore currents. The oceanic region with the highest cross-correlations is identified as a relatively narrow band along the Brazilian coast, from 22°–36°S and 40°–50°W, bounded in the north by an eastward change in coastline orientation. The cross-wavelet transform establishes the common power between the time series of meridional wind stress and alongshore currents, predominantly during austral winter and spring. These signals propagate equatorward with an alongshore speed of 285 ± 63 km day−1, consistent with Coastal Trapped Wave theory.
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 Over the past few decades, the western boundary currents of the tropical South Atlantic and their associated scales of variability have been investigated by numerous researchers [Molinari, 1983; Stramma, 1991; Schott and Böning, 1991; Mayer and Weisberg, 1993; Schott et al., 1993; Rhein et al., 1995; Stramma et al., 1995; Dengler et al., 2004; Schott et al., 2005]. While the Deep Western Boundary Current (DWBC) transports cold North Atlantic Deep Water far into the southern hemisphere, the North Brazil Undercurrent (NBUC) and North Brazil Current (NBC) serve as a northward warm-water conduit as part of the thermohaline overturning cell [Gordon, 1986; Schmitz, 1995]. The South Atlantic Central Water (SACW), located at depths between 100 and 500 m, is transported westward within the southern band of the South Equatorial Current (sSEC) until it reaches the Brazilian shelf. After the sSEC bifurcates, its southward limb becomes the Brazil Current (BC) and merges into the South Atlantic subtropical gyre system. The northward limb feeds into the NBUC [Stramma and Schott, 1999; Stramma et al., 2005] and - as a western boundary current - carries warm waters of South Atlantic origin across the equator and into the northern hemisphere. It also supplies the eastward flow of the South Equatorial Countercurrent (SECC) which partially recirculates into the central band of the SEC (cSEC). In addition, in the 50–300 m depth range, the NBUC seems to play an important role in the Atlantic Equatorial Gyre [Schott et al., 2005] and in the coupled ocean-atmosphere system. This strong western boundary current has a nearshore core position approximately 50 km from the Brazilian coast, reaching down to about 900 m in depth, with a maximum speed of about 65 cm s−1 at 180 to 250 m on average. At 11°S, the mean flow structure of the NBUC is already well developed, indicating that the bifurcation of the sSEC is located well south of this section with a maximum northward NBUC flow in July and a minimum in the October–November period [Schott et al., 2005]. The sSEC bifurcation has a southernmost position in July and a northernmost position in November [Rodrigues et al., 2007; Silva et al., 2009].
 While the dominant fluctuation in the NBUC core, approx. 50 km from the coast, has a period of about two months [Schott et al., 2005], biweekly signals are the dominant modes along the western (onshore) flank of the NBUC, about 10 km from the coast [von Schuckmann, 2006].
 The cause of these intraseasonal fluctuations in the upper-ocean circulation may be found in several dynamic processes, such as local wind-forcing, remote wind-forcing via waveguide dynamics, mean flow instability, and resonance due to the coastline geometry [von Schuckmann, 2006]. Furthermore, if these fluctuations are in reasonable proximity of the coast, the motion of oceanic waters over the continental shelf and slope may also be influenced by the earth's rotation, density stratification, the offshore current regime, sloping bottom topography and the presence of the coastline [Allen, 1980], causing coastal-trapped waves (hereafter CTWs). The existence of CTWs depends entirely on the presence of a shallow shelf between the coast and the deep ocean. CTWs propagate along the continental slopes and shelves of the world's coastlines, with the coast to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. They have periods of days to 2–3 weeks and wavelengths on the order of 2000 km, determined by the atmospheric weather patterns. The impact of CTWs on shelf currents and sea level varies with seasonal changes in stratification over the coast. For arbitrary topography and stratification, there is a free-wave mode (similar to the barotropic Kelvin wave) plus an infinite set of higher mode, more slowly propagating waves [Brink, 1991]. These perturbations induce variations in sea level and alongshore currents over the continental shelf for typical periods ranging from the inertial period to about 20 days. Winds and tides in coastal regions at sub-inertial frequencies force these waves with periods ranging from days to weeks. Since the continental shelf is a transition zone between the coastal waters and the open ocean, the CTWs transport materials (e.g., nutrients and pollutants) from regions near the coastline to and from the open ocean, and along the continental margins. Thus, CTWs modulate the upwelling system and primary productivity in the coastal regions.
 This paper investigates the relationship between observed intraseasonal fluctuations in alongshore current measurements near the Brazilian shelf and the large-scale wind stress field over the South Atlantic through the use of cross-correlations and continuous wavelet transforms.
2.1. Moored Array Observations at 11°S
 The ocean data set used here was obtained between March 2000 and August 2004 as part of the German CLIVAR Tropical Atlantic Variability Project [Schott et al., 2005]. The data were collected in an array of five moorings (K1–K5) stretching 225 km across the NBUC (10°S–11.5°S) (Figure 1). Data sources, positions and sampling periods are presented in Table 1. Since the offshore mooring K5 was deployed for only two years, and observations were confined to depths below 1500 m. this mooring was not used in the present analysis. Additional details of this data set are given by Schott et al. .
Table 1. Location and Sampling Periods for Moorings and Wind Stress Data
Moorings, German CLIVAR Project
10° 16.0′S 35° 51.7′W
10°22.8′S 35° 40.8′W
10° 36.7′S 35° 23.4′W
10° 56.5′S 34° 59.5′W
Wind stress data, NOAA/NCDC
2.2. Wind Stress Data
 The wind stress data set used in this study was obtained from NOAA/NCDC (National Oceanic and Atmospheric Administration/National Climatic Data Center) and is available at www.ncdc.noaa.gov/oa/rsad/seawinds.html. The domain used here covers the area 40°S to 0°N and 60°W to 20°W (Figure 2). In this database, surface wind stresses (N m−2) are estimated from blended sea surface wind speeds at 10 m above sea level, generated from six satellites, on a global 0.25° regular grid and for several time resolutions [Zhang et al., 2006]. Wind speeds are converted to (u, v) components using the NCEP Reanalysis 2 (NRA-2). In this work, the wind stress data has a temporal resolution of 12 h.
 The mean zonal and meridional components of the wind stress are shown in Figures 2a–2d for austral summer (DJF) and winter (JJA). These charts capture the main spatial structure of the observed means, in agreement with the published literature [Trenberth et al., 1990; Harrison, 1989; Castelão and Barth, 2006]. During austral summer, the zonal wind is negative (easterlies) over nearly the entire domain, while positive (northward) meridional wind stress is restricted to equatorial latitudes in the western part of the South Atlantic Ocean and negative (southward) for almost the entire western South Atlantic (Figures 2a and 2b). The zonal components of the wind stress are strongest in June, July and August. Northward meridional wind stress is observed in the South Atlantic during JJA, expanding equatorward and reaching 20°S in the western basin (Figures 2c and 2d). Negative (southward) meridional wind stress is found between 20° and 30°S, and positive (northward) to the south of it.
3.1. Current Structure at 11°S
 The current meter time series were smoothed using a 40-h lowpass filter to eliminate tidal and inertial effects. Current vectors were divided into alongshore and cross-shore components by rotating clockwise by 36°, i.e., parallel to the coastline.Figure 3 shows the mean section of alongshore velocities at 11°S for the entire deployment length (2000–2004); instrument locations for moorings K1–K4 are marked by black dots. The strongest contribution to the NBUC transports occurs near 250 m depth at moorings K1 and K2 [Schott et al., 2002; Stramma et al., 2003; Schott et al., 2005], indicated by the strong subsurface core in the upper left corner of Figure 3. Below the NBUC, we find the colder water masses of the DWBC, with the core centered at 1500–3500 m depth along mooring K3 (dark blue colors). Mooring K4 is located outside the equatorward boundary current, with a weak mean southward flow between 500 and 3500 m depth.
 Fluctuations about these means are shown as anomalies of the 100 m current vectors (i.e., demeaned), as at this level the measurements are available for all moorings K1–K4 (Figure 4). The dominant intraseasonal signals have periodicities of 2–3 weeks and 2–3 months (see also Figure 5). The highest amplitudes at periods of 2–3 weeks are found in the coastal boundary region at moorings K1 and K2, gradually decreasing away from the NBUC core. Figure 5shows the spectral distribution of currents between 50 and 300 m depth for moorings K1 to K4. High-frequency fluctuations (10–30 days) are more prominent near the coast, at mooring K1. Farther offshore, at moorings K2 to K4, these fluctuations have the highest energy in the upper layers and scale down with increasing distance from the NBUC current core. Note that the variance levels at mooring K2 are nearly identical between 150 and 300 m.
3.2. Cross-Correlation Between Wind Stress and Currents
 We used cross-correlation analysis between the meridional wind stress and alongshore currents to spatially localize the remote forcing across the entire ocean basin. Previous work indicates that the meridional component of wind stress is the prime generator of such coastal-trapped waves [Brink, 1991; Csanady, 1997], and the periods involved correspond to those of the weather systems. The meridional wind stress components are cross-correlated with alongshore currents at 100 m depth at 11°S for moorings K1–K4 (Figure 6) as this depth level is available for all moorings (see Figure 5).
 For mooring K1, two separate intervals are shown, caused by a gap in the available current measurements. Since we are interested in the intraseasonal components of the signal in the 10–30 day band, we applied a 10–30 day band-pass filter to both the atmospheric and oceanic data. The correlation of the meridional wind stress for each grid point with the K1 alongshore current at 100 m depth is mapped for the entire ocean basin (Figure 6a), and the lag between the two signals is shown in the maps of the right panels. Identical procedures were used for the other moorings, displayed in Figures 6b–6e. Clearly, the lag between the wind stress of a given grid point and the 11°S currents decreases with decreasing distance to the moorings, showing a systematic propagation along the shore. For the first interval of available data at mooring K1, the maximum cross-correlation between meridional wind and alongshore current is found between 22° and 36°S, which is approximately 1500–2000 km from the 11°S moorings (Figure 6a). The corresponding lag is 6.5 days. For the 2003–2004 period of mooring K1 (Figure 6b), there are weaker cross-correlations, with alongshore currents lagging the wind stress by 10 days. Subsequently, we find a lag of 9 days at mooring K2 (Figure 6c), a lag of 7 days at mooring K3 (Figure 6d), and a lag of 9.5 days for mooring K4. Here is also where we find the highest cross-correlation values between meridional wind stress and the alongshore current at about 36°S (Figure 6e).
Table 2summarizes the cross-correlation results ofFigure 6between the meridional wind stress and alongshore current at 11°S. The coordinates of cross-correlation maxima, the distances to the mooring sites, and the lag period clearly indicate a strong connection between the alongshore current signal at 11°S and its remote atmospheric forcing located at about 22°S to 36°S (box area inFigure 6).
Table 2. Coordinates of Maximum Cross-Correlation Between Meridional Wind Stress and Alongshore Currents, Corresponding Distances and Lag Periodsa
Lag Period (days)
The 95% confidence limits are shown in parentheses.
 To further investigate this connection, we spatially averaged the meridional wind stress components across the area defined by the highest cross-correlations shown inFigure 6. The resulting time series were cross-correlated with the corresponding time series of meridional currents at 11°S (moorings K1–K4) at different depths, 50 to 1000 m (Figure 7). The highest correlations are found in the near-surface layers of the NBUC core, gradually weakening downward and outward toward the open ocean. The right panel shows the corresponding lags, where currents lag the wind-forcing by 8 to 10 days (Figure 7, right).
3.3. Time-Frequency Common Power Between Wind Stress and Currents
 Most traditional mathematical methods to examine periodicities in frequency space, such as the Fourier analysis, implicitly assume that the underlying processes are stationary in time. However, wavelet transforms can be used to analyze a non-stationary time series at many different frequencies and scales by expanding the time series into time-frequency space in order to find localized intermittent periodicities. The wavelet transform is based on a practical guide to wavelet analysis ofTorrence and Compo . One of the problems with the resulting “global wavelet spectra” is a distortion of the energy distribution [Liu et al., 2007; Veleda et al., 2012], with high-frequency peaks shown lower than their low-frequency counterparts. In this work, we construct rectified Cross Wavelet Transform (XWT) by normalizing the wavelet transform by the square root of the scale, based onVeleda et al. .
 An XWT analysis was applied to meridional wind stress and alongshore currents at 100 m depth (moorings K1–K4). The XWT identifies the regions in time-frequency space with a large common power between two time series. The individual cross-wavelet spectra, from 2002 to 2004, are averaged to form a seasonal ensemble cross-wavelet spectrum, for austral winter (June to November) and austral summer (December to May), respectively. In this case, we used the wind stress data restricted to the region where the highest cross-correlations between the wind stress and alongshore currents were found (seeFigure 6).
 The seasonal ensemble averages of the XWT between the meridional wind stress averaged over the high cross-correlation area [22°–36°S] and the corresponding alongshore currents within the matching time interval are shown inFigure 8, with the blocked out “white” margins indicating the “Cone of Influence” (COI), where edge artifacts become important [Grinsted et al., 2004]. The color scale for Figure 8 shows maxima in dark red and minima in dark blue.
Figure 8clearly indicates that the XWT between currents and wind stress is strongest for the 16-day period during the month of September, linking this periodicity band of the NBUC, at 11°S for mooring K1 (winter) at 100 m depth, to the wind stress forcing at 22°–36°S close to the Brazilian coast. The ensemble average XWT for the winter season shows a stronger or more prominent response of the 16-day period of the alongshore currents to the wind stress.
 An identical analysis was done for moorings K2, K3 and K4 (Figure 8). The result shows that during austral winter, the 16-day periodicity of the 100 m currents at moorings K1–K4, along the western and eastern flank of the NBUC at 11°S, is linked to the wind-forcing at 22°–36°S along the coast of Brazil. At mooring K1, the highest energy spans the period from July through October, except for August. For mooring K2, the highest energy is centered in July and weaker in September and November. For moorings K3 and K4, the highest energy extents from July through October.
 Previous studies in other regions have confirmed the presence of CTWs with typical periods of 5–20 days. Brink associated these waves with remote wind-forcing, whileBattisti and Hickey determined that the pressure and alongshore velocity fields in the Northwest Pacific may be a response of the wind-forced CTW. The variance in sea surface pressure off Oregon and Washington was found to be generated by wind forcing between San Francisco and Cape Mendocino, California. The signal propagates 900 to 1300 km northward to Washington-Oregon, arriving there 3 to 4 days later.Brink  also pointed out the agreement between CTW theory and observations off Peru in 1977, indicating free wave phase speeds of about 200 km day−1, as well as sea level and alongshore velocity fluctuations in the 5–10 day period band. Spillane et al.  found oscillations with intraseasonal periods of 36–73 days close to the coast of Peru, with poleward phase propagation of 150–200 km day−1. Enfield  established that the intraseasonal sea level variations pointed out by Spillane et al.  are forced in the western equatorial Pacific by atmospheric oscillations, consistent with previous studies with propagation speeds of 216–259 km day−1.
Smith  found a persistent poleward propagation of fluctuations in currents and sea level along the Peruvian coast between 10° and 15°S, with a wave speed of about 200 km day−1. Enfield and Allen  also estimated the wave phase speed as the ratio of alongshore station separation to the corresponding lag. Along the Peruvian coast, Camayo and Campos  used wavelet analysis to study the intraseasonal current oscillations, suggesting remotely forced baroclinic Kelvin waves with periods between 10 and 20 days, with velocities of approx. 200 km day−1.
 In this work, we establish the propagation of Coastal Trapped Waves along the Brazilian coast as a suitable mechanism for explaining the strong correlation between the meridional wind stress at latitudes of 22°S–36°S and the alongshore currents at 11°S. Kelvin waves are low-frequency gravity waves which occur where the deflection caused by the Coriolis force is either constrained by coastlines or goes to zero at the equator. These waves have typical amplitudes of several tens of meters in the thermocline region, and lengths are thousands of kilometers.
 Spectral analysis of the current velocities identified high-frequency components present near the surface and gradually decreasing with depth. A fluctuation at 10–30 day periodicity is observed in the four moorings at the jointly available 100 m depth level. At 11°S, the thermocline is located at about 65 m depth [Schott et al., 2005; von Schuckmann, 2006], so that the core of the NBUC is located just below these strong density and temperature gradients, making this flow regime potentially favorable for internal Kelvin wave propagation.
 Internal coastal-trapped Kelvin waves may be generated by an abrupt change in the winds and depend on the existence of a coast against which they can lean. Our work showed maximum cross-correlations for the nearshore wind data located between 22°S and 36°S, a region along the Brazilian coast usually referred to in the literature as the Southeast Brazil Bight (SBB) [Castro Filho, 1985; Stech and Lorenzzetti, 1992; Campos et al., 1995; Cirano and Campos, 1996]. The northern boundary of this area corresponds to a relatively narrow shelf close to Cabo Frio (22°S), where an abrupt change in coastline orientation exists. Furthermore, the SBB is also under the influence of synoptic and mesoscale frontal low pressure systems which interact with the western reaches of the South Atlantic High (or “St. Helena High”). Strong meridional winds from the northeast (NE) occur before the passage of a low pressure system, then rapidly changing to southwesterly winds (SW).These frontal systems have frequencies of 3 to 4 per month [Rodrigues et al., 2004], with average speeds of 500 km day−1, thereby crossing the SBB region in about 2 days [Stech and Lorenzzetti, 1992]. As a result, these atmospheric anomalies induce drastic changes in wind direction and cause significant disturbances in the ocean, such as mean sea level changes, generation of surface waves and currents [Castro Filho, 1985; Campos et al., 1995]. We argue that the combination of local wind stress variability and the abrupt change in coastline direction reveals the SBB as a preferred locus for CTW generation along the Brazilian shore. The distance between the currents at 11°S and the area where high cross-correlations were found is about 1600–2700 km. In addition, the ratio between these distances and their corresponding lag periods yields an equatorward propagation speed of 285 ± 63 km day−1along the Brazilian shore. Coastal trapped waves certainly have major effects on sea level and currents locally, but their far-reaching consequences may not yet be fully explored: As the waves approach the equator, they continue eastward as equatorial Kelvin waves, only to be dispersed again as coastal Kelvin waves along the eastern boundary (off Africa) and also reflected westward as equatorial Rossby waves. The conclusions regarding our observations may have significant effects on the entire equatorial waveguide system.
 The western boundary regime of the tropical South Atlantic is well known for its complex dynamics and multiple scales of variability, with the North Brazil Undercurrent (NBUC) playing an important role in the Atlantic Subtropical Cell (STC) and in the coupled ocean-atmosphere system.
 Previous studies of these moorings (K1–K4) at 11°S section have shown that the NBUC core, about 50 km offshore, has a dominant fluctuation with a periodicity of two months [Schott et al., 2005; von Schuckmann, 2006]. In this work we investigate the forcing mechanism behind additional intraseasonal periodicities of the near-surface alongshore current measurements at 2 to 3 weeks. Cross-correlation analysis between currents and meridional wind stress points to the wind field located between 22° and 36°S close to Brazilian coast as the driving mechanism.
 The distances between the wind-forcing area and the mooring locations, as well as the corresponding lags, indicate an equatorward propagation speed of 285 ± 63 km day−1 along the Brazilian coast. Such distances and travel times suggest Coastal Trapped Waves (CTWs) as the prime candidates for accomplishing this task. Therefore, two of the main ingredients for the existence of CTW are readily available, namely wind stress variability and abrupt change in coastline direction.
 We investigated the relationship between the NBUC, wind stress and CTWs by using several statistical and mathematical tools. High-frequency variability is the dominant mode along the western flank of the NBUC. Spectral analysis of the current velocities for K1 (the mooring closest to the coast) shows a spectral peak at 14 and 30 days at 100 m depth. This peak decreases as we move farther offshore. Cross-correlation analysis of currents and wind stress along the entire Brazilian coast reveals the precise origin of these fluctuations. In addition, the Cross-Correlation Wavelet Transform accurately identifies the main structures in the frequency-time space where the atmospheric and oceanic time series both had their largest common power.
 The correlations between meridional wind stress, from 22° to 36°S near the Brazilian coast, and alongshore currents at 11°S are strongest during austral winter and spring. As shown in Enfield and Allen , these signals propagate equatorward with the coast to the left (in the southern hemisphere) and have alongshore speeds consistent with wave propagation processes. Furthermore, the area of origin for the forcing of intraseasonal current signals is dominated by the first baroclinic mode over the continental slope. It has also been shown that this area has stronger density stratification during austral winter than austral summer [Campos et al., 2000], making it more favorable for the propagation of internal Kelvin waves.
 The authors would like to thank the scientific team of the German Climate Variability and Predictability (CLIVAR) program and, in particular, our colleagues from GEOMAR for providing full access to the K1–K4 mooring data. We also thank the editor and the two anonymous reviewers for their valuable suggestions and comments. The first author thanks Peter Brandt and Lothar Stramma for their assistance during her one-year stay at GEOMAR in Kiel. She also wishes to thank CAPES/DAAD (Coordination for the Improvement of Higher Education Staff/Deutscher Akademischer Austauschdienst) for scholarship support. R.M. acknowledges financial support from the Pernambuco State Agency FACEPE (APQ-0871-1.05/08).This work was carried out under the National Institute on Science and Technology in Tropical Marine Environments - INCT-AmbTropic (CNPq process 565054/2010-4), and under the project BIO-NE (CNPq process 558143/2009-1.