The main driving forces that affect the dynamics of an estuarine front are winds, tides, the Earth’s rotation and river discharges [2]. The Atrato River generates a river discharge estimated between 2500 m³/s during the dry season and 5000 m³/s during the rainy season [23]. The wind pattern in the region is affected by the position of an inter tropical convergence zone, and there are two well defined seasons, a dry season from December to March with north and northwesterly winds, and a rainy season from May to November with winds blowing south and southwest. Tides exhibit a semidiurnal pattern with amplitudes of less than 40 cm [25] and with five dominant astronomical constituents (Mf, O1, K1, M2 and others with low frequency) identified using surface level registers of a tide gauge in San Cristobal, Panama (located at 9º 21' N and 79º 54' W).

Figure 1 Source: The authors.

Two types of measuring campaigns were conducted for this study. They were general campaigns that included the entire Gulf, and local campaigns that included only the southern zone of the Gulf, Colombia Bay. Three intensive measuring campaigns were carried out in the entire Gulf collecting data from 117 stations using a mini Sea-Bird conductivity temperature depth (CTD) profiler. Three local campaigns were conducted taking salinity and temperature profiles using an IQ net system 2020 XT probe. These campaigns exhibited different wind, tide and river discharge conditions (as shown in Table 1). The locations of the measurement stations are shown in Fig. 1.

Field data revealed that four zones can be identified in the Gulf of Uraba according to stratification patterns: 1) an oceanic zone, 2) a far field plume zone, 3) a near field plume, and 4) Colombia Bay zone (with a variable pattern according to wind direction). Plume thickness ranges from 2 to 4 m (in the far plume, the near field plume and Colombia Bay), and it shows a defined pattern of a highly stratified estuarine front with salinity differences ranging from 7 to 35 in the central zone and from 20 to 35 in the northeastern zone. Also, field data showed that salinity in the plume can vary considerably in time from 15 to 30 in some stations near the plume front. Furthermore, the data showed that the freshwater the river discharged formed a river plume that was maintained near the surface flowing northeast leaving the Gulf parallel to the eastern coast near Punta Arenas in the north-eastern end of the gulf. The surface layer has most of the salinity and the most temperature variations, while the deep layer is homogeneous.

Field campaign data were used to calibrate and validate the hydrodynamic Estuary, Lake, and Coastal Ocean model (ELCOM), which simulates free-surface flows in lakes and estuaries. ELCOM was developed by the Centre for Water Research (CWR) of the University of Western Australia. It uses hydrodynamic and thermodynamic equations to simulate spatial and temporal variations of velocity, water levels, temperatures, salinity and water density, especially, for stratified bodies of water subjected to environmental forces. ELCOM solves the Reynolds-averaged Navier- Stokes and transport equations using Boussinesq and hydrostatic approximations using an eddy viscosity approximation for horizontal turbulence and a one-dimensional mixed-layer model for vertical Reynolds stress terms [26]. Free surface levels are computed using the vertical integration of the mass conservation equation. To numerically solve these equations, the model uses a semi-implicit method with quadratic Euler-Lagrange discretization of the momentum advection terms [27], the ULTIMATE QUICKEST scheme for scalar transport [28].

Table 1

Source: The authors.

A set of numerical experiments with different grid size and time step were used to compare the performance of the model to numerical parameters allowing the identification of grid size and time step [23]. A horizontal grid of 500 m × 500 m and a non-uniform 33-layer vertical distribution was used. ELCOM is unconditionally stable for pure barotropic flows, but presents stability restrictions associated with the baroclinic term, and discretization appears in stratified flows [26] limiting the time step. Therefore, a time step of 112.5 s was used. The simulation time used was 1 month for all of the simulations where only the last days (between 3 and 7, see Table 1) were used for the analysis. The first days were used to allow the plume to develop and the adjustment of initial conditions.

Data from the first campaign were used for calibration, and the data from the other campaigns were used for validation. Several parameters were adjusted one by one comparing the results of a set of numerical experiments with field data at measuring stations. These parameters were adjusted within physical ranges reported by other authors, and the values of the parameter that offers the best adjustment to the measurements were chosen (for mayor details see [23]). The coefficients and variables chosen for calibration were a mixing model, a diffusion coefficient, percentages of distribution of the discharges by each mouth of the Atrato River and a light extinction coefficient (for more details see [23]). To adjust the model to initial conditions, approximated meteorological data were used such as solar radiation, cloud cover and air temperature obtained from NCEP/NCAR Reanalysis Project data [29]. The wind field was measured in a meteorological station located near the shore in city of Turbo. Small river discharges were estimated using hydrologic balance models [30]. Other values used to represent boundary conditions or physical parameters were a 100 m²/s diffusion coefficient of and a light extinction coefficient of 3.

For all the simulations, a salinity of 35 and a temperature of 30 °C was imposed at the open boundary of the Caribbean Sea, and a salinity of 10 and a temperature of 27 °C was imposed at river boundaries. The initial condition was obtained by interpolation of measured profiles.

4.1.1. Comparison of field data and model results

During the calibration process, measured and simulated salinity and temperature profiles for the first campaign were compared finding good adjustment with a global root mean square value of 1.29 for the error in salinity and 0.27 °C for the error in temperature, and a correlation coefficient of 0.92 for an adjustment between measured and simulated profiles. These profiles exhibited a good fit, particularly below 4 m of depth with salinity close to 36 and with the major differences found near the surface layers. Greater differences appeared in stations located in the south of Colombia bay. Stations located in the central region of the Gulf and to the north exhibited an adequate fit with differences in the halocline position of less than 40 cm. Temperature profiles exhibited a good fit between simulated and measured profiles, with the larger differences near the surface, and a simulated temperature that was higher than that measured at some stations. It was possibly because of an inaccurate estimate of the light extinction coefficient for these zones, and the deep layers (under 4 m) exhibited a good fit in the entire Gulf.

A comparison of simulated and measured profiles for campaign 1 is presented in Fig. 2, and similar results were found for other campaigns. Generally, good agreement between field measurements and model simulations was found despite some differences. This was so, especially, near the surface in the region near the Atrato river mouth where the model over predicted the measured values. The main differences were found in salinity profiles in the stations located in Colombia Bay. However, a very good fit was found at stations located in the northeast where there is a strong influence of Atrato River plume.

Measurements and field data revealed the river’s influence near the surface. During the validation, the RMS of salinity differences ranged from 5.5 to 1.43, and the RMS for temperature differences ranged from 1.62 °C to 0.47 °C.

A systematic analysis was performed to study the response of a system to different driving forces and the relative importance of each driving force. Various forcing factors were successively introduced (see results in Fig. 3) into the model to simulate their influence upon the plume. First, simulations were considered with and without Coriolis force. Second, variations in the freshwater discharges were considered, and third, tides and their periodical effect were studied. Finally, the effects of the winds were introduced considering main direction changes which were the main characteristics of the climatic seasons.

4.2.1. Effect of the earth's rotation

At high and mid latitudes, the Coriolis force produces important effects on plume dynamics and distribution that can be detected from the direction of plume propagation. The plume turns right (in the northern hemisphere) in the absence of other strong forcing factors. The studied zone is located between 7.9° N and 9.4°N latitude; therefore, a moderate Coriolis force effect was expected. Small differences were found comparing results with and without Coriolis acceleration (Figs. 3a, and 3 )b. However, despite the low value of the Coriolis parameter, its effect must be considered along with the other factors. A simulation considering the Coriolis force (Fig. 3a) produces a plume that leans more towards the northeast coast and with a wider plume slightly lower than simulations without the Coriolis force (Fig. 3b).

Figure 2 Source: The authors.

4.2.2. Freshwater discharge effect

River discharges affect local plume circulation patterns [2,31], especially, in the near field, where the river’s discharge generates an important advection force. A comparison of the simulations for rainy and dry season discharges was conducted (Figs. 4a and 4b), and the results showed that the extension of the plume increases during the rainy season (Fig. 4a) when discharges are higher.

4.2.3. Tidal forcing

Tides play an important role in the mixing process in river plumes. Several authors [19] highlight tide effects on a plume’s characteristics analyzing Amazon river plume and reporting the variation in the stratification pattern during tidal cycles while observing periodical movements of a freshwater plume front during the ebb or the flood tide. To introduce tide effects in the simulations, a set of numerical experiments were conducted with different tide forcing with tide forcing estimated using 5 of the principal harmonics (Fig. 3a) and with no tide at all (Fig. 5).

Figure 3 Source: The authors.

4.2.4. Wind effects

Different authors pointed out that the wind plays an important role in the circulation of an estuarine plume [3], and reported different plume responses according to wind direction [2]. There are variations in the thickness, width, and propagation speed of a plume in response to wind stress changes [34]. Wind forcing has a strong influence on the characteristics of a buoyant plume because the momentum added by wind stress is trapped in a relatively thin layer which has a low level interchange with the oceanic layer because of density differences [34]. Winds induce a shear stress on the surface layer that can act in favor of or against the buoyant plume motion, promoting or hindering plume dispersion. Lentz and Lagnier [34] show three situations of buoyant plume response to different along-shelf wind forcing: (a) upwelling wind promoting plume spread causing plume to become thin and wide, (b) moderate downwelling wind, inhibiting plume development and causing a thicker narrower plume with a steep front, and (c) strong downwelling winds causing vertical mixing. Simple models had been used to try to explain the response to upwelling winds [4]. However, there is no general model that provides quantitative estimates of the dependence of plume characteristics on wind stress.

Figure 4 Source: The authors.

Figure 5 Source: The authors.

Figs. 6a and 6b show the results of two simulation cases with different wind patterns. The shape and direction of the plume was particularly sensitive to wind direction. Northerly winds (Fig. 6b) direct the plume South increasing plume surface mixing. On the other hand, southerly winds (Fig. 3a), direct the plume northwards forcing the plume to leave the gulf by the northeast coast generating a surface plume. No-wind conditions, (see Fig. 6a) allow mixing near the surface by the tidal effect. All the simulation cases show that wind effects were limited to the surface layer. A comparison of the vertical structure of water for different wind scenarios showed that waters deeper than 4 m are practically the same. Two distinct circulation plume patterns were found. One had a southwest-northeast direction induced by southwest winds, and a second pattern induced by northeast winds which guided the plume southwards. Wind direction affects plume direction and imposes a direction that can be intensified or decreased by other factors such as tides or river discharges [23].

Figure 6 Source: The authors.

Surface circulation is strongly influenced by Atrato River plume. To analyze surface currents in the Gulf of Urabá, Figs. 7a and 7b show velocity and surface salinity (on June 18, 2006 at 6:00 a.m. (a) and 6:00 p.m. (b). They were obtained with simulations of the climatic conditions during campaign 3 at ebb and flood tides (Fig. 7g) with southeast winds (uniform over the whole domain, with the magnitude and direction shown in Figs. 7e and 7f). The vertical structure of salinity in the plume is presented for previous conditions in Figs. 7c and 7d along section A-A (see location in Fig. 1). A comparison of surface salinity contours (Figs. 7a and 7b) shows tide-related variations throughout the day, especially, near the river mouth.

Figure 7 Source: The authors.

The plume spreads from the river mouth and heads east driven by river advection. When the plume reaches the east coast, it turns left heading north forming a coastal current leaving the gulf via the northeast coast, and finally, it turns east as a coastal current outside the gulf. This behavior was found with different intensities in all the campaigns. A general analysis of the simulated characteristics showed four horizontal zones in the Gulf which were: (1) an oceanic influenced zone in the northwest with homogenous salinity and temperature profiles (salinity from 30 to 36 and temperatures from 28 to 30 ºC), (2) a region of freshwater influence characterized by a strong stratification around 2 m (salinity from 7 to 36) with a surface layer occupying the central and northeast portions of the Gulf, which could be divided as near field and far field, (3) a region to the south in Colombia Bay with salinity variations ranging from 15 to 36 and high spatial variability in the stratification, and (4) an oceanic water mass that occupies the deepest layer (under 4 m of depth) covering the entire gulf.

Fig. 8 shows a detail of section B-B near the river mouth at different times of June 6 and 7, 2005. The zonal velocity along section B-B is greater near the surface layer, and particularly, near the river mouth as a result of the strong advection induced by river discharges. A seaward current in the plume and a net landward current at lower layers reveal a typical estuarine circulation.

Figure 8 Source: The authors.

Simulation results of other campaigns (not shown) reveal a similar behavior. In section B-B, the maximum velocity is located near the river mouth with approximate values of 0.6 m/s. High values of the zonal velocity were found at the first 2 m of plume depth (Fig. 8) indicating that the plume has a velocity which is greater than the deepest oceanic layer.

The plume exhibits significant velocity reductions below the halocline, and it was not notably affected by wind action. Most of the time, the velocity at surface layer flows out of the gulf, whereas the oceanic layer changes the direction of the velocity throughout the day. During the flood tide (Figs. 8a and 8c), the velocity enters the gulf, and during the ebb tide (Fig. 8d) the velocity leaves the gulf. Typical current speeds are 0.3 m/s in the surface layer and 0.05 m/s in the oceanic layer. At deeper layers, currents (below 2 m) change magnitude and direction during the day. Simulations exhibit plume movement during the day as a result of tidal forcing changing the location of the plume. During the ebb tide, the plume reaches its maximum extension in the Gulf, and during the flood tide, freshwater flow shrinks the plume back.

Regarding mass flux, simulations reveal (Fig. 9) that there was a permanent flow leaving the Gulf (positive discharges) via surface layers and an oscillatory flow below the halocline (below 4 m deep) but with a net flow entering the gulf to compensate the effects of surface flow. Surface flow presents low salinity and relatively strong velocities, and deep flow presents high salinity, low velocity, and changes in direction according to ebb tides and flood tides. The total mass crossing section D-D follows tide oscillation as seen in Fig. 9b although a face lag of roughly 4 hours is also clear.

The wind field modifies the position of the salinity front, which is subject to periodical horizontal migration under tide forcing. For example, Fig. 10 shows surface salinity and a vertical cross section A-A during campaign 2. The Northeast winds (Figs. 10a and 10b) have an important effect on plume extension, deflecting and spreading it towards the northwest. From south to north, Fig. 10b shows the salinity along section A-A, and it is clear that the plume remains near the surface in the region near the river mouth (coordinate 900 km in Fig. 10a). As one moves north, salinity increases towards oceanic values indicating that plume influence is no longer active in this region: it has moved to a northwesterly direction.

Figure 9 Source: The authors.

Figure 10 Source: The authors.

Studies of Rhone river plume [15,31], Ebro river plume [32], Columbia river plume [17], and Río de la Plata river plume [2] revealed that the Coriolis force is fundamental in plume motion, particularly its deflection along the coast. However, studies of river plumes near the Equator, like Amazon River plume [19] show that coastal currents have a fundamental role in plume dynamics. When a river discharge occurs in semi-enclosed zones like a bay or a gulf, residual baroclinic flows can appear [8, 9] as a response to topographic forcing. Near the Equator, plume dynamics are controlled by winds, tides, and river discharges and, less importantly, by the Coriolis force. In the Gulf of Uraba, we found that wind direction rules surface circulation and that tides play a role on plume motion by enhancing it during ebb tides, and constraining its spread during flood tides. The currents below the halocline are governed completely by the tidal force.

Atrato River plume has the characteristic properties of a low-latitude plume generated by a high river discharge. According to Garvine’s [12] classification of dynamics, Atrato River plume with a Kelvin number of 0.56 should be classified as a “small-scale” discharge. Its low Kelvin number value appears because of the effect of its low latitude where the Rosby radius is long. This means that near the Equator, plumes have an important contribution from all momentum terms as advection, pressure gradient, wind stress and basal current stress [19]. According to Yankovsky and Chapman [33], Atrato River plume would be classified as intermediate in behavior. However, its structure reveals a surface-advected plume behavior. It is also necessary to bear in mind the topographic restriction imposed on the plume for the Gulf of Uraba coastline making it turn north.

For a better understanding of these plume dynamics, they can be described in terms of water masses. Near the river mouth, strong non-linear dynamics can be observed. A strong advection dominates plume motion, and plume behavior is a jet-like outflow dominated by the momentum of the river (close to the mouth). In the far field, far away from the river mouth, plume distribution changes according to wind direction in such a way that even low wind magnitudes can affect plume dynamics. The intensity of the mixing processes in this plume zone is modified by tides, winds and river discharges. Baroclinic flow was evident from the persistent flow that leaves the gulf via the northeast coast caused by a pronounced salinity gradient. This baroclinic flow appears only in the surface layer, but the entrainment induced a mixing process in the plume, and an opposite flow was required in the deeper layers to compensate for the flow entrainment in the plume. Barotropic tide-induced movements are detected for the region below the plume, specifically, below 2 m deep. A tidal current generates basal stress, and during the ebb tide the current goes out of the gulf and propitiates plume movement. While during flood tide, the current enters the gulf making it more difficult for the plume to spread.

Finally, as in other studies [5,2], numerical models and field observations have shown that wind forcing has a strong influence on the plume’s characteristics. Atrato River plume simulations show that under different wind forcing conditions, wind stress is an important factor of plume structure. According to wind direction, wind stress makes it either difficult or easy for a plume to move. A wind-induced momentum flux is trapped in a relatively thin plume and strong stratification hinders wind momentum transference to the deepest layers. An important relationship between wind direction and shape and plume extension were found in the Gulf of Uraba. Southeast winds and currents during ebb tide facilitated plume movement while northeast winds directed the plume south and brought about plume mixing. Thus, we can conclude that both of these forcing factors affect the plume, and they can have a common effect when the plume heads Northeast.