Alfacs Bay is defined as a bar-built estuary (Pritchard 1952) formed by the interaction of Ebro River sediment and Mediterranean coastal currents (Fig. 1). The bay is around 16 km long and 4 km wide, with an average depth of ~4 m. Its connection with the Mediterranean Sea is 2.5 km wide, with a central channel with a maximum depth of 6.5 m and shallow shoals of around 1-2 m on both sides. The bay is surrounded by rice fields to the north and a sand spit closing it on the east side. The rice fields contribute around 10 m³ s^–1 of nutrient-laden freshwater into the bay from April to December. Alfacs Bay has been defined as a salt wedge estuary for almost all of the year (Camp and Delgado 1987), with a noticeable influence of freshwater fluxes (Llebot et al. 2011, Solé et al. 2009) and heat fluxes during the spring and summer (Cerralbo et al. 2015b). Surface heating and freshwater inputs stratify the bay, promoting the two-layered structure in the water column.

The synoptic winds on the Catalan coast are affected by orographic constraints, such as the blocking winds of the Pyrenees that promote tramontane (N) and mistral (NW) winds over the Ebro Delta area, and the wind channelling due to river valleys (Grifoll et al. 2016). Northerly winds in the region are produced by high pressures over the Azores and lows over the British Isles and Italy (Martín Vide 2005). Winds in the bay have been characterized as having a northwestern and southwestern predominance, with the strongest ones coming from the NW (Cerralbo et al. 2015a).

The bulk of the observational data came from two field campaigns: from July to mid-September 2013 and from February to April 2014. The data set consisted of water currents from two 2-MHz acoustic Doppler current profilers (ADCPs) moored at the mouth (A1) and the inner bay (A2). Instruments recorded ten-minute averaged data from ten pings per minute and with 25-cm vertical cells. Both devices were equipped with pressure and temperature sensors, and were mounted on the seabed at 6.5 m depth. Water level data were obtained from the Catalan Meteo-Oceanographic Observational Network (described in detail in Bolaños et al. 2009) in Sant Carles de la Ràpita harbour (M-SC in Fig. 1), and bottom pressure data were from the ADCPs. Atmospheric data (wind, atmospheric pressure, solar radiation and humidity) were obtained from a fixed land station, Alcanar (M-A), and from M-SC. From 2012 to 2014, more than 100 CTD profiles were collected during five intensive daily campaigns. More details on the CTD data are available in Cerralbo et al. (2015b).

In order to analyse the dynamics at low frequencies, both currents and wind observations were filtered using a 30-h low-pass filter (Lanczos filter) (Emery and Thomson 2004). The vertical structure of the water column was investigated using empirical orthogonal functions (EOF) (Emery and Thomson 2004). The EOF analysis was performed considering both along- and cross-shore components at both stations, so that the EOF would explain the combined spatial variability at A1 and A2.

The three-dimensional hydrodynamic model used in this study is the Regional Ocean Modelling System (ROMS). Numeric aspects are described in detail in Shchepetkin and McWilliams (2005), and a complete description of the model, with documentation and code, is available at the ROMS website: http://myroms.org. The implementation of the model consisted of a regular grid of 186×101 points with a spatial resolution of 100 m (in both the x and y directions) and 12 sigma levels in the vertical dimension. More details about the configuration and validation of the model are described in Cerralbo et al. (2016).

Spectral analysis (Fig. 2A) of wind data from 1996 to 2013 at M-SC (see location in Fig. 1) revealed prominent variance peaks at 24-h and 12-h periods. Both periodicities correspond to sea breezes with strong asymmetry between daily influences (onshore winds) and nightly influences (weaker offshore winds). Lower frequencies contain energy over a broad band. This low-frequency energy is usually associated with the synoptic passage of low-pressure systems, which in the Catalan Sea has periods of 3-12 days (Font et al. 1990).

During the summer, unfiltered data from M-A show a mean wind speed of 3.1 m s^–1, with a standard deviation of 1.7 m s^–1 and maximum hourly winds of 13.4 m s^–1. The sea breeze pattern (diurnal cycle) is clearly observable during the entire summer (Fig. 2B) in unfiltered data, with the exception of two periods of seaward winds. These events occurred on 8 and 25 August and lasted for a few hours (orange box in Fig. 2B, C). In winter, the mean wind speeds rose to 4.2 m s^–1, with a standard deviation of 3 m s^–1 and a maximum of 14.2 m s^–1. On the other hand, the 30-h filtered wind data in summer (winter) showed a maximum of around 6 m s^–1 (12 m s^–1). Moreover, in March 2014 more than four events were observed with winds >10 m s^–1 (Fig. 2D in orange).

The filtered depth-averaged current speeds at A1 and A2 (see locations in Fig. 1) are plotted in Figure 2C and 2E for the summer and winter seasons, respectively. The standard deviations are also higher at A1 than at A2 (2.2 and 1.6 m s^–1 against 1.8 and 1.2 m s^–1 for summer and winter, respectively). In order to qualitatively compare the wind and current intensities, the filtered wind speeds were scaled by a factor of 0.03. This value corresponds to the theoretical surface layer velocity (u_w) due to the wind speed (W), assuming that the relationship follows the quadratic stress law u_w=(ρ_a/ρ_w)^1/2W (Large and Pond 1981, deCastro et al. 2003), where ρ_a and ρ_w are the air and water densities, respectively. From 7 to 20 July the depth-averaged water speed response (in both A1 and A2) followed the main pattern described by the winds, but for the rest of summer period the graphical comparison in Figure 2C does not reveal a clear relationship between wind and depth-averaged currents. Correlation coefficients between depth-averaged current speeds and winds were close to 0, while in winter their values increased to 0.2 and 0.4 at A1 and A2, respectively. In summer, the maximum current speeds were observed on 4 August, as well as in late August and early September (and with considerable differences between A1 and A2). In both cases, water currents have been related to co-oscillating waves ("seiches”) instead of winds or other forcings with hourly time scales (Cerralbo et al. 2014, 2015b). In this case, because the filter is applied on the water speed, the high-frequency signal is not completely filtered and some energy remains in the low-frequency band.

Current rose plots for the filtered currents in the surface and bottom layers (1-m averaged) are shown in Figure 3. In summer, different patterns were observed at each mooring. Seaward flows dominated in the surface layers at A1, and opposite flows in the bottom layers. Meanwhile, at A2 (not shown), inflows dominated in the surface layers. The events with highest current speeds in summer corresponded to NW and NE winds (8 and 25 August, respectively). In winter, the filtered data were more scattered at A1, showing two predominant directions in the surface layers (NE and S-SE), while at A2 (not shown) the surface layers were similar to those observed in summer, although more dispersed from the main axis. The maximum surface velocities at A1 coincided with periods of NW winds (2 to 5 March and 25 March).

Correlations between the surface and bottom layers for both A1 and A2 in both periods are shown in Table 1. At both locations and during all periods, correlations between the bottom and surface layers were negative, indicating the presence of two differentiated layers. In contrast, in winter, the correlation coefficient between the surface and bottom layers was ~0 at A1 for the northward component.

Low-frequency current observations show that the maximum variability of the water currents at A1 (Fig. 3) and A2 is associated mostly with one axis aligned with the coastline (following the central axis of the bay). This axis was obtained by adjusting a line (linear regression) between both components (northward and eastward) and obtaining the angle with the east-west axis. Therefore, the explained variability shown in Figure 4A and C expresses the variance of each axis with respect to the total variance. These results are consistent with previous contributions that used unfiltered velocities in Alfacs Bay (e.g. Camp 1994, Cerralbo et al. 2015b). Velocities corresponding to the rotated axis are defined as u′_{a_b} and v′_{a_b}, with a representing A1 or A2 observations, and b as s or w indicating the summer or winter periods, respectively. The u′ axis corresponds to the along-bay (alongshore) circulation and the v′ axis to the cross-bay (cross-shore) circulation. Alongshore positive values indicate velocities toward the head of the bay. New axes for the filtered data are rotated 20° anticlockwise for A2 for both seasons because the summer and winter observations reveal similar values (19° to 21°). On the other hand, for A1, the axis is 43° anticlockwise in summer. However, winter observations do not reveal a major axis of variability because there are two clearly dominant components (Fig. 3B). For this reason, the rotation for the A1 observations in winter is carried out using the same axis as for the summer observations. In order to compare winds and currents, the wind is also rotated according to the corresponding location.

The variability explained by the new axis for each vertical layer is shown in Figure 4. Alongshore currents accounted for more than 75% of the total variability at A2 in both seasons and at A1 in summer. In winter, the surface layers exhibited a higher variability at A1, indicated by the cross-shore component, as shown by the current rose (Fig. 3B).

The linear correlations between the rotated currents and winds are plotted in Figure 4B and D (considering all water layer depths). There is only a modest correlation of the surface alongshore layer with the corresponding alongshore wind component in summer (R=0.4). In winter, surface currents and winds showed a weak correlation (i.e. ≈0.2), and in all cases this correlation decreased quickly with depth, the sign of the correlation coefficients changing to negative values, with the maximum correlation in the bottom layers (e.g. maximum R=–0.7 in winter at A2).

Considering the limitations of linear correlation coefficients, alongshore and cross-shore currents (both surface and bottom layers) are graphically compared with the corresponding wind components (rotated to the same axis as the currents) for the summer and winter periods in Figure 5. In summer, the results show the maximum wind variability in the alongshore axis. Two energetic events are observed on 8 and 25 August (in green in Fig. 2B). For the currents, the maximum variability is observed in the alongshore direction, with higher speeds in the surface layers. The u′_{A1_S} shows that 59% of the total speeds are higher than 3 cm s^–1, while for u′_{A2_S} only 23% of the total current speeds exceed this threshold. In the cross-shore direction, only 16% and 3% of the observations show values higher than 3 cm s^–1, respectively. Current velocity in the bottom layers at A2 does not exceed 3 cm s^–1, and only 14% of the bottom velocities at A1 alongshore exceed this value. Qualitatively, alongshore currents at both A1 and A2 show a clear two-layered structure. In general, at A1 the surface layers show negative values (seaward), reproducing the oscillations observed for the winds, while at A2, the surface currents oscillate between positive and negative values following the main oscillations of the winds. Thus, a relevant surface response to the wind forcing is observed qualitatively on alongshore currents in summer.

In winter, two northerly wind events were observed on 3 to 5 March and 23-28 March (in orange in Fig. 2D). Also, two events of E-NE winds occurred on 13 and 30 March. In general, both the surface and the bottom currents showed the highest alongshore velocities. In early March, there was a direct surface response to two events of SW winds in the alongshore velocities. Between 15 and 17 March, light winds from the SW (aligned with the main axis of the bay) were correlated with surface currents. The most energetic events (northerly winds) did not induce a clear water response at low frequencies in the alongshore velocities. Between 23 and 27 March, both the surface and bottom layers showed a direct response to the wind in their cross-shore components (orange shaded area in Fig. 5B). Using a threshold of 3 cm s^–1 (as for the summer observations) the measurements at A2 exceeded this velocity 20% and 23% of the time at the surface and the bottom, respectively. On the other hand, at A1, surface layer velocities exceeded 3 cm s^–1 44% and 28% of the time. This speed threshold is similar to the observed standard deviation. Comparisons between currents at A1 and A2 only reveal correlations higher than 0.40 for alongshore components in the surface layers (0.47 and 0.46 in summer and winter, respectively). The maximum correlation was observed in winter in the alongshore component of the bottom layers (0.60).

Along-axis EOF analysis shows differences along both moorings and periods: the first EOF explains 42% in both periods, and reveals a clear two-layered structure (i.e. Fig. 6A-C, F-H), excluding cross-shore at A2 (Fig. 6D, I) with a barotropic response. The second and third EOFs explain ~20 and ~10% of the variability, respectively. In this case, the two-layered structure is only observed in A1 alongshore currents (Fig. 6A, F). The time evolution of the coefficients (PC1, PC2 and PC3) correlates with the alongshore winds (rotated with the same angle as currents at A1). The highest correlation is observed between PC1 and alongshore winds, with values of ~0.66 and ~0.59 in summer and winter, respectively (see Fig. 6E, J). In summer, correlations between the rest of the components (PC2 and PC3) and winds (along- or cross-shore) are not significant. On the other hand, correlation around ~0.5 is observed between PC2 and PC3 with cross-shore winds in winter. Finally, correlations of the first component with currents show maximum values at the bottom layers.

Since gravitational circulation typically occurs over long time scales (weekly and higher), it is instructive to examine the deployment-long mean currents at the moorings (Wong and Valle-Levinson 2002). Averaged circulation for both A1 and A2 was obtained by time-averaging the observations corresponding to the filtered u and v velocities for all measurements in both time periods (summer and winter). The results are summarized in Figure 7. A typical gravitational circulation is observed at A1 during both periods, with outflow at the surface and inflow at depth (Pritchard and Kent 1956). In summer, water currents show southwestward velocities in the surface layers around 4-5 cm s^–1, and northeastward flows of 2 cm s^–1 at 2-3 m above the seabed. In winter, the currents are almost in the same direction but at lower speeds. At A2 the situation is completely different. In summer, the surface velocities are very small (close to 0), but in the E-NE direction, while in the lower layers the flow is directed westward at around 1 cm s^–1. In winter a nearly depth-independent flow is observed at A2, toward the E-NE. The corresponding standard deviations for each averaged current are shown in grey. In general, the variability is higher than the mean value, and only during the summer at A1 do the surface currents show mean values higher than the standard deviation.

Low-pass filtered velocities revealed a clear two-layered structure, which for 60% to 80% of the time featured opposite directions in the surface and bottom layers. Previous investigations (Cerralbo et al. 2014, 2015b) with unfiltered data showed a one-layered structure for ≈70 % of the time, mostly related to barotropic seiches. In consequence, the removal of these high-frequency oscillations resulted in the predominance of a two-layer vertical structure. Moreover, some additional data analysis using low-pass filters of 6 h and 12 h (not shown) revealed similar percentages to those observed using 30-h cut-off filters. This low-frequency characterization is in agreement with previous studies by Llebot et al. (2013), who observed the predominance of a two-layered structure in averaged circulation.

At A2, the main axis of the bay coincided with the axis of greatest variability in currents in both seasons and was almost equal at all depths (the percentage of variability explained by the first—alongshore—axis was more than 80% for the entire water column). However, A1 showed greater variability in the cross-shore component in winter (mostly in the surface layers), which is related to wind influence. In fact, A1 is 1.5 km from the coast, while A2 is at 600 m. As observed by Noble (1996), close to the shoreline laterally sheared boundary layer currents are expected to flow parallel to the coast. Thus, a transference from cross-shore winds in both locations to the alongshore currents seems clear, as they are higher at A2. A similar example of the strong influence of coastline on water circulation is described in Grifoll et al. (2012).

In contrast to a previous EOF analysis with unfiltered flow (Cerralbo et al. 2015b), the current low-frequency EOF analysis showed an evident baroclinic behaviour in alongshore currents at both locations. The first mode (with two-layer structure) explained ~42% of the variability in all cases. These results are similar to those of Llebot (2010), though in their study they suggest that the first baroclinic mode (obtained using weekly time-scale analysis) was related exclusively to gravitational circulation rather than wind forcing. The analysis of the time evolution of each mode is useful to determine possible relationships between physical forcing and the variability described by the EOFs (Salas-Monreal and Valle-Levinson 2008, Schaeffer et al. 2011), even if sometimes the results of EOF analysis may have no physical meaning (Huang et al. 1998; https://climatedataguide.ucar.edu). In our case, the PC1 correlates positively with wind in all periods and locations, linking the main mode to winds (correlations of 0.66 and 0.59 in summer and winter, respectively). On the other hand, cross-shore currents and winds only show relevant correlation or modes 2 and 3 (which explain ~20% and ~10% of variability) in winter, with correlations of around 0.59 and 0.47, respectively. This could be explained by the high winter prevalence of winds aligned with the cross-shore direction.

Similar relevant correlations are observed when filtered winds and surface currents in the along-axis are compared at both locations in summer. However, in winter, the effects of winds in along-axis surface currents are relatively weak, and the only noteworthy hydrodynamic response is observed in the cross-shore component of A1 during the most intense northwesterly wind. The low-frequency response shows the strongest correlations between winds and bottom currents. Different factors could be responsible for this hydrodynamic response. For example, stratification of the bay modifies the response to wind forcing in the water column. Surface layers are directly affected by wind, while bottom layers respond to the pressure gradient established along the bay due to the wind set-up, as observed in a shallow stratified system by Noble (1996). So, even if the origin is the same (i.e. wind forcing), the current-driving mechanism is different. Surface current observations are restricted to the 1-m layer below the free-surface. Therefore, the oscillations on the pycnocline (close to the surface) may induce a high degree of variability in the water response related to surface winds and the depth of the surface mixed layer. Conversely, bottom layers are farther from the effects of pycnocline oscillation, implying a more stable and consistent hydrodynamic response. Furthermore, the short distances of the observational points from the coast suggest a strong coastline influence (higher at A2), which in turn implies some energy transfer from cross-shore winds to alongshore surface currents.

Another possibility is related to the effects of remote forcing. Winds can induce low-frequency variability in estuaries through a combination of remote and local effects. Considering the remote effect, winds on the continental shelf adjacent to an estuary can produce sea level fluctuations at the estuary mouth (Wong and Valle-Levinson 2002). For instance, variations in the coastal sea level due to the effects of winds (and atmospheric pressure variations) will induce incoming and outgoing flows in the bay. To investigate this phenomenon, we compared the alongshore velocities to the sea level variations and the results shows correlations of 0.6 at the bottom layers and lower correlations (–0.23 to –0.43) at the surface in winter. No correlation was found in summer. These results indicate the possible influence of shelf dynamics in the low-frequency response of the bay, as observed in other environments (Gačić et al. 2004, Murphy and Valle-Levinson 2008, Valle-Levinson et al. 2001). However, more observations on the shelf and numerical experiments covering the Ebro Delta shelf would be necessary to confirm the hypothesis.

At the monthly time scale, the average circulation shows considerable differences from A1 to A2 (Fig. 7). The theoretical gravitational circulation due to freshwater influences (Hansen and Rattray 1965, Pritchard 1952) on the bay would be represented by surface velocities to the west at A2 and to the southwest at A1. Only observations at A1 coincided with the expected gravitational circulation. Moreover, considering some basic statistics such as the standard deviation (Fig. 7), only at A1 and in summer (and especially at the surface) were the averaged currents higher than the standard deviation.

Depth-averaged density fields observed on 7 May 2014 (I-5 campaign) are shown in Figure 7. Two density distribution patterns are observable: 1) in the alongshore direction, from saltier water in the open sea to the freshest water in the inner bay (1027 to 1022 kg m^–3); and 2) a cross-shore gradient in the inner bay, with the freshest water at the northern margin. Moreover, the freshest water in the north is concentrated around A2, close to the main drainage channels. This density field is representative for the open channel season and similar to that observed in summer 2012 and summer 2013, and to the scenarios described in Camp (1994) and Llebot et al. (2013). Consequently, it seems reasonable to conclude that the average circulation at A1 is explained by the density distributions and differences between inside and outside the bay (considering all freshwater sources in the inner bay), as well as the narrow shape of the bay mouth.

Another factor to consider is the wind stress influence on the gravitational circulation. Several reversals of surface flows have been observed in previous studies (Llebot et al. 2013, Cerralbo et al. 2015b). On those occasions, the wind stress overwhelmed the gravitational circulation. The competition between wind stress and density gradients to produce subtidal flows is characterized with the Wedderburn number W (e.g. Monismith 1986, Valle-Levinson and Blanco 2004):

$$\text{W}=\frac{{\tau }_{\text{s}}\text{L}}{\text{g}\Delta \rho {\text{h}}^2}$$

with L being the basin length (around 16 km), g the gravity acceleration (9.81 m s^–2), Δρ the density difference between two points, h the depth, and τ_s the surface wind stress. The wind stress τ_s is computed following Large and Pond (1981) as τ_s=C_dρ_airU², where C_d=1.3 10^–3, ρ_air=1.22 kg m^–3, and U is the wind speed. Using W~1, we can obtain the theoretical threshold for overcoming the gravitational influences by wind stress. The only unknown value is the corresponding density gradient. Considering the depth-averaged density fields shown in Figure 7, density differences between the inner bay and the open sea in summer are around 3-5 kg m³. These values suggest that winds of between 4 and 5 m s^–1 would be able to overcome the gravitational circulation. This analysis therefore gave us a general picture of the bay behaviour, but no specific description of responses at A1 and A2.

A2 is located in the middle of the bay and close to drainage channels. Thus, if the bay is divided into two areas from a cross-sectional axis at A2, freshwater inputs are distributed on both sides, diminishing (even cancelling) the possible gravitational circulation along the main axis of A2. This means that the average circulation in the along-axis direction at this point is likely to be more influenced by other factors, but mainly wind forcing.

The spatial variability of the mean circulation in the bay is illustrated with the results from a numerical model (Figs 8-9). Modelled average salinity and temperature fields (Fig. 8) revealed similar structures to those described by observations. For example, the modelled surface 2D salinity fields are very similar to the density structures observed in May 2014 (Fig. 7G). Moreover, the modelled salinity during the closed channels season (Fig. 8) shows a similar structure to that observed and described in Figure 7H, and previously described by Camp (1994), with density gradients along the bay and a well-mixed water column (not shown). Averaged surface currents in summer (Fig. 9A) show maximum velocities located close to the bay mouth. On the other hand, modelled velocities at A2 are much weaker than at A1, agreeing with observational data, with the directions also showing same vertical variability. As stated above, A2 is more sensitive to the freshwater inputs and the influence of winds, which influence the density-driven circulation.

Moreover, numerical results show how the near-surface average circulation exhibits two different behaviours inside the bay. The inner area (from A2 to the head of the bay) describes a near-surface anticyclonic circulation that follows isobaths. This behaviour was more evident in winter and related to spatial variability of northwesterly winds and bathymetry (Cerralbo et al. 2016). On the other hand, from A2 to the bay entrance, the main surface currents are seaward, consistent with the classical gravitational circulation. Also, in winter (Fig. 9D-F) relatively lower velocities appeared throughout the bay, and the maximum averaged velocities occurred at the margins (in the shallower areas). Moreover, two different structures are visible: the clearest being an anticyclonic gyre in the inner bay (close to the head), which clearly separates the average circulation from the region close to the bay mouth. These patterns suggest weak connectivity between the two bay volumes, and this disconnection would imply differences in residence times in the bay.

In summer, flows perpendicular to the cross sections (Fig. 9B, C) reveal two-layer exchange with the interface at a depth of 3-4 m. The maximum outflows in the bay mouth are at the centre of the section (3 cm s^–1) and the maximum inflows are at the bottom. However, the inner bay flows also display horizontal shears over the shallower area close to the channels (also shown by the observations in Fig. 7C). This zone is located between the main freshwater discharge points and the surface anticyclonic circulation. During the winter, there is also a two-layered circulation in both sections. However, in winter the maximum outflows (1 cm s^–1) are located over the margins, while outflows are almost null in the centre of the bay.

The summer results revealed that during that season the average behaviour of the bay seems to predominate over the variability at this time scale (low frequency, with a cut-off time of 30 h). This dominance is clearer at the bay mouth, and probably directly correlated with the gravitational circulation. In winter, the average circulation is not as evident as in summer, and the variability dominates over the mean behaviour in the shallower areas.