Morphodynamics of intermittent coastal lagoons in Southern Spain: Zahara de los Atunes

Geomorphology 121 (2010) 305–316

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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h

Morphodynamics of intermittent coastal lagoons in Southern Spain: Zahara de los Atunes Isabel María Moreno ⁎, Alberto Ávila, Miguel Ángel Losada Environmental Fluid Dynamics Group, Andalusian Centre for Environmental Studies (CEAMA), Avda. del Mediterráneo s/n, 18006, Granada, Spain

a r t i c l e

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Article history: Received 3 September 2009 Received in revised form 19 April 2010 Accepted 26 April 2010 Available online 6 May 2010 Keywords: Coastal lagoon Intermittence Inlet stability 1-D model Coastal zone management

a b s t r a c t Coastal lagoons are valuable water bodies since they are of great ecological and economic interest throughout the world. Their existence is controlled by variations in sea level and the geological substrate of their location. Their morphology is linked to local topography, alternation of high and low pressure, the presence of a river, as well as tidal regime. All these factors influence lagoons along the coastline in the south of Spain. The main morphological characteristics of such lagoons are the following: intermittence, onedimensional morphology, small size, shallow waters, high area/depth ratio, no flood- or ebb tide deltas, overwash of their low barriers during storms, high evaporation rates and feeding by rivers. Effective management of these systems requires the evaluation not only of their hydrodynamics and opening and closure rate, but also the prediction of possible future scenarios as a response to meteorological events. This paper describes the behavior of a coastal lagoon in Zahara de los Atunes (Cádiz) by means of a numerical model implemented with the objective of serving as a tool for optimizing the coastal zone management. Although the coastal lagoon at Zahara de los Atunes is closed most of the year, it is artificially opened at the beginning of the summer. The results of our study showed that during this period, the lagoon is flooddominated with a pumping-mode response. It naturally tends to close since it is a trap for littoral drift sediments. The precise date of closure depends on the events that take place during the autumn, which determine whether the sediments deposited in the inlet by the littoral drift are flushed out by the river flow or flushed in by the waves. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Coastal lagoons are transitional water bodies located in coastal areas, which are isolated from the sea by a barrier but connected to it by an inlet. Along with other critical transition zones they play an important role in the maintenance of the biogeochemical fluxes on the planet by allowing interchanges of mass (e.g. water, sediments, nutrients and pollutants), momentum, and energy between the sea, land and atmosphere. Lagoons are highly dynamic systems with productivity typically 10 to 15 times greater than continental shelves (Valiela, 1995). However, they are characterized by extreme fluctuations in salinity, temperature, water level, and dissolved oxygen, which restrict the number of species in these environments (Levin et al., 2001). Coastal lagoons also contribute significantly to human welfare. They provide services to the population, such as shoreline stabilization, fishing, shelter for navigation, educational and recreational activities, and even aesthetic enjoyment. The potential economical value of transitional coastal zones has been estimated at over ⁎ Corresponding author. Tel.: +34 958241000x31163; fax: +34 958 132479. E-mail addresses: [email protected] (I.M. Moreno), [email protected] (A. Ávila), [email protected] (M.Á. Losada). 0169-555X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2010.04.028

$22,000 ha− 1 y− 1 (Costanza et al., 1997). A thorough understanding of natural flushing rates through exchange processes in a coastal lagoon is fundamental for the maintenance of its ecological health and economic value (Smith, 2001). Some coastal lagoons are intermittent, and thus not permanently connected to the sea. They are often connected to a river with seasonal variations in its flow. The inlet becomes shallow or even sealed in dry seasons when river outflow is weak. It reopens, widens and deepens when the wet season brings greater volumes of water outflow from the lagoon (Bird, 1994). This outflow removes the sediments accumulated in the inlet. The dimensions of the inlet and the duration of the opening determine the tidal prism entering the lagoon and, in conjunction with the freshwater inflow, condition the physical and chemical regime of the lagoon (turbidity, salinity, temperature, pH, concentration of the nutrients) and therefore its biology and ecology. Detailed studies have been conducted in South Africa and Australia to evaluate the influence of breaching on different levels of the trophic chain. Wooldridge (1991) focused on the consequences for decapod larvae after changes in the pattern of management of intermittent inlets. Whitfield and Kok (1992), Harrison and Whitfield (2006) and Chuwen et al. (2009) reported changes in the ichthyofaunal composition or abundance depending on the relative duration of the open/closed period. Froneman (2002) found that the Kasouga

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intermittent estuary changes from an oligotrophic state during the overwash phase to a eutrophic one during the flooding stage. This leads to a dramatic increase in the size structure and phytoplankton production that contributed to elevated zooplankton stocks during the flood phase. However, Whitfield et al. (2008) stated that river flooding of the intermittent East Kleinemonde estuary can result in major declines in zooplankton, zoobenthos, hyperbenthos and fish populations during this phase. On the other hand, the opening of the system is important because it facilitates the recruitment of larvae and post-larvae of certain marine invertebrate and fish species. For these fauna and even for some vegetation, the alternation of open and closed periods is essential. Therefore, the ecological functions that the system develops are different in every stage, each of which is of great importance for the maintenance of the biodiversity. Currently, there is much debate regarding the best management options for coastal lagoons both now and in a context of global climate change (Zedler, 1996; Griffiths, 1999; Haines, 2008; Anthony et al., 2009) and the advantages and disadvantages of human intervention which affects their geomorphology, ecology, and water quality (e.g. Schallenberg et al., 2010). One of the questions to be answered for intermittent coastal lagoons is whether it is better to allow them to evolve under the sole influence of natural forces or to manage them to control their functions and prevent them from eutrophication, hypersalinization or disappearance. Coastal lagoons with an economic or social interest are generally subject to human intervention, which implies changes in the ecology of the system. Certain engineering techniques have long been used to avoid inlet closure, such as periodic dredging or jetty building, sometimes complemented with sand bypassing (Dean and Dalrymple, 2002). In southern Spain, intermittent coastal lagoons can be found all along the c.1000 km Andalusian coastline, where more than 200

coastal wetlands have been identified (Moreno, 2005). However, there is still very little hydro-morphological information available regarding these coastal lagoons. According to Gale et al. (2006), similar systems can be found in South Africa (Largier et al., 1990), the east coast of South America (Suzuki et al., 1998), and the southwest and southeast coast of Australia (Ranasinghe and Pattiaratchi, 1999; Dye and Barros, 2005). The accurate description of their behavior is a complex task. It not only depends on multi-year processes that occur because of the random sequence of storm events and subsequent calm periods, but also, for long term evolution, on processes related to sealevel rise and fall, and their effect on sediment supply. Generally speaking, the reason for the intermittence of coastal wetlands in Andalusia lies in the fact that the dry season coincides with maritime conditions of low energy, and the wet season coincides with high energy waves. Coastal lagoons located between the towns of Conil and Tarifa in the province of Cadiz are of particular interest (Fig. 1). The topography of this region is relatively smooth, with rounded hills near the coast, which have an altitude of around 500 m. There are short rivers here, which flow into coastal wetlands. The almost flat coastal areas have marshes, such as those found in Barbate. In contrast, those areas with a more irregular topography tend to have coastal lagoons. The climate in this region is typically Mediterranean, with more than 2800 hours of sunshine per year and an annual rainfall between 550 and 800 mm. The Strait of Gibraltar influences the maritime climate. The wind blows mainly from the west or the east, while the wave climate is characterized by prevailing west-northwesterly waves (Fig. 2). The tide is semidiurnal meso-tidal, with a maximum tidal range of 2.6 m on spring tides and 0.8 m on neap tides. This means that intermittent coastal lagoons are present not only on micro-tidal coasts (Gale et al., 2006), but also on meso-tidal coasts, like the coast described in this article.

Fig. 1. Coastal lagoons of Cádiz province located between Barbate and Tarifa villages.

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Fig. 2. Wave chart and wind chart for the SIMAR node 1056044 (close to Barbate).

The main characteristic of coastal lagoons in the area of our study is their one-dimensional morphology stemming from their long, narrow shape and shallow waters. The bays can be up to 2000 m long and 300 m wide, with maximum depths of around 2 m. Keulegan's coefficient (Keulegan, 1967) has values greater than 0.8. Inlets commonly have a width less than 50 m and a depth of up to 1.5 m. The development of flood- and ebb tidal deltas is infrequent because inlets are closed most of the year. This situation is the source of environmental problems, mainly related to water quality. Water renewal is somewhat limited, whereas nutrients from the uplands are transported to the lagoon by the rivers. A good example of eutrophication can be found in the coastal lagoon at Zahara de los Atunes (ALATEC-PROES, 2002). The main objective of our study was to diagnose the general hydrodynamic and morphological behavior of a representative intermittent coastal lagoon in the province of Cádiz in order to gain enough knowledge to manage it accordingly with the principles of sustainability. Given the scarcity of studies about small temporarily open lagoons, O (1 km2), it is also an aim to contribute approaches that are adapted to this scale. Coastal lagoons in the region have been notably altered by human effects, some of them compensated with expensive periodical actions (such as dredging); tools developed in this study must therefore be useful to optimize management actions and their results. 2. Field site description The coastal lagoon of our study is located west of the town of Zahara de los Atunes (36° 08′ N, 5° 51′ W, WGS84). The bay is approximately 1300 m long and 50 m wide (Fig. 3). The inlet, when open, has a mean width of 16 m and a length of 160 m. From a geomorphologic point of view, this lagoon has some of the main characteristics of a perched coastal lagoon (Cooper, 2001), but as it is situated on a mesotidal coast, it also shares some peculiarities with non-perched estuaries. The coastal lagoon is enclosed behind a dissipative beach and its upper inner part constitutes a barrier for the lagoon. The elevation of the barrier is still higher than the spring high tide level but not far from it (Fig. 4). Therefore, high wave energy is necessary to produce overwash. The inlet location can be inferred from the differences in the saturation of the sand of the beach and from the development of ripples on top of the crest sand bar surface. According to its grain size distribution, the coastal lagoon can be divided into two main stretches: the first stretch is near the beach, and is composed of well-sorted sands, which presumably come from the overwash (D50 = 0.20 mm and D90 = 0.35 mm). The second stretch is located in the inner lagoon, the bottom of which is covered by a layer of sediment from the river. The exact thickness of the deposit is not known, but it is at least 18 m, which is the depth of the foundations of the bridge that crosses the lagoon (ALATEC-PROES, 2002). Submerged

macrophites and algae grow in this stretch. The shallowness of this lagoon (approximately 0.60 m), along with frequent winds, guarantees a complete mixing of its water column throughout the year. The coastal lagoon at Zahara de los Atunes is fed by the Cachón River, an intermittent river, which is 10 km long. Its basin has an area of 39.5 km2, and its highest point has an altitude of 458 m. The mean slope of the river is 0.78%. No discharge records are available. Previous studies (ALATEC-PROES, 2002) propose 48 m3/s for a ten-year return period and 126 m3/s for a return period of fifty years. Zahara de los Atunes has mild temperatures throughout the year. They range from 15 °C in the winter to 23 °C in the summer. The mean annual rainfall (1992–2006) is 590 mm. Rain falls mainly in the winter, autumn, and spring, which is when the low pressures coming from the Atlantic Ocean arrive at the Iberian Peninsula. These precipitation events generally last three or four days. However, some storms cause intense daily rain; the maximum of the cited series is above 90 mm (Fig. 5). During these episodes of high freshwater discharge, or when low pressures cause high wave energy, the barrier may be breached and an inlet develops. If the inlet is still open when the extreme conditions are over, depending on the range of the tide, the system may be recharged with saline water (spring tides) or may be drained (neap or medium tides). The drainage of the system once the barrier is breached is a typical feature of perched estuaries and its duration is usually hours (Cooper, 2001). However, as the tide is mesotidal, an alternation of periods of recharge and drainage are observed in this lagoon when the inlet is naturally or artificially open. Although the lagoon diminishes its volume over the time, the drainage of the basin is not as fast as that observed in the perched lagoons of South Africa. Over the 20th century, the lagoon surface has experienced a reduction in size (Losada et al., 2010, Fig. 3). At the beginning of the century, the main income source of the inhabitants of Zahara de los Atunes came from activities related to fishing and agriculture. These activities have been complemented or even substituted by developments related to the tourist industry. The main tourist attraction of Zahara is its straight dissipative beach, which is long, wide, and sandy with a smooth slope. Although the population of the town is around 2000 people during the winter months, it soars to 20 000 in the summer time. These changes have caused environmental problems over the years even though authorities have done their best to minimize them. For example, ten years ago, wastewater was discharged into the lagoon. As a result, the lagoon waters acquired a very unpleasant odour, and swarms of insects proliferated throughout the area. When Zahara wastewater was finally collected and piped into the Barbate waste treatment plant, the problem was solved. Still another problem was the heavy rain that caused the lagoon water to flood the town. The last flood occurred in December 2000. To solve this problem, the lateral slopes of the lagoon were reinforced with a rubble mound. As a

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Fig. 3. Aerial photograph of the coastal lagoon at Zahara de los Atunes in 1956 (top) and 2007 (bottom).

solution for water quality problems, an inlet is artificially opened at the beginning of the summer every year. Although the inlet current interrupts the continuity of the beach in the high tourist season, this is preferable to the eutrophication that would otherwise ensue.

The inlet of Zahara de los Atunes is the only one that is annually maintained in this region. Those lagoons located in Bolonia and Valdevaqueros beaches are the smallest ones in the study area and although it is not frequent, they may become almost dry during some summers (dry season) due to evaporation. The coastal lagoons of Conilete and Los Lances are even bigger than Zahara de los Atunes; their surface is reduced during the summer but they rarely dry out completely. The coastal lagoon at Zahara de los Atunes faces more environmental problems than the others and for this reason it has been selected for study. 3. Methods

Fig. 4. Longitudinal profile of the coastal lagoon at Zahara de los Atunes from the ocean to the river. Water levels in the ocean during high spring tide (HST) and low spring tide (LST) are also shown.

The complex dynamics of coastal lagoons requires an approach that takes into account natural forces, such as river flow, waves, and tides. The approach should also be able to quantify their influence on the hydrodynamics of the lagoon as well as on the opening and closure processes during any meteorological year. Forces stemming from waves, storm surge and river flow normally appear during the

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Fig. 5. Daily rainfall in Zahara de los Atunes from 1992 to 2001.

passage of low pressure fronts. These forces operate simultaneously or separately to favor inlet breaching due to overwash, river floods or sustained high discharge of the river, depending on the duration of the storms. The tide is a deterministic variable, but depending on its range during an extreme event, it can either act in synergy with the other forces or can reduce their effects. Inequalities in longshore drift rates may also cause inlet breaching although this process is not taken into account in this study. The evolution of the water level when the lagoon is closed is basically determined by the interaction between evaporation, rainfall, groundwater fluxes, seepage, overwash and river flow. 3.1. Numerical model To better understand the hydrodynamics of the lagoon in our study, we implemented and calibrated a numerical model. Although a three-dimensional approach to hydrodynamics is always desirable, the geometry of most of the Andalusian coastal lagoons makes a 1-D approach sufficiently accurate. Consequently, we selected SaintVenant equations, non-linear hyperbolic equations with no analytical solution for the conditions to be analyzed. Keulegan (1967) and DiLorenzo (1988), among others, made assumptions and solved this type of problem for regular cross-sections and simplified tides analytically. The numerical implementations of Saint-Venant equations have certain advantages over analytical solutions when dealing with irregular geometries, and when it is necessary to include other sources of mass and momentum apart from the tide, as is the case of coastal lagoons fed by rivers in semi-arid environments, where the influence of evaporation is not negligible if the lagoon is closed for long periods of time. The model provides a complete vision of the system in which accuracy and computational speed should be harmonized. To solve these equations, the MacCormack-TVD scheme, a high-order non-oscillatory numerical scheme, was used (GarcíaNavarro et al., 1992). This finite-volume scheme was implemented by following Ávila (2007). However, in our study, it was modified to include a dry and wet technique to simulate intermittence, and to better fit the distinctive characteristics of the coastal lagoon. The Courant–Friedrichs–Lévy condition (Courant et al., 1967) was used as a stability criterion. The evaporation was modeled using the combination method described by Chow et al. (1994) while measured data had to be used to include rainfall. The interchange of mass with the ground could also be included in the model through the source terms of Saint-Venant equations, although it has not been implemented for this study. State variables in this problem were the flow and cross-sectional area. For sub-critical flows, this scheme required

at least one boundary condition for every boundary, since the other one could be calculated by the model. The cross-sectional area was imposed at the sea boundary according to sea level (tide, storm surge and waves), whereas flow was that at the river boundary, both as a Dirichlet condition. The assumed initial condition was usually still water level, although a previously computed stage was also possible. 3.2. Verification and calibration The model was verified by using Ippen and Harleman's (1966) analytical solutions and certain cases typically used for this purpose in hydraulics: Goutal and Maurel's (1997) channel, Tseng's channel and flow over a bump (Tseng, 2003). Two field surveys were conducted in order to calibrate the model. The first one was performed in May 2008 for the purpose of taking morphometric measurements. The equipment used to measure width and length was a DGPS device with a horizontal resolution of 0.01 m. For the elevation, a leveled stick was used. These measurements created a DEM with GIS tools, based on a DEM of 10 m × 10 m resolution of the study area (Consejería de Obras Públicas y Transportes et al., 2005). The bathymetry of the sea region was obtained from the Spanish coastal authorities (Demarcación de Costas de Andalucía-Atlántico). The second field survey was carried out in July 2008, when the inlet was dredged. Pressure and water velocities were recorded for flood and ebb tides while the water level was high enough to provide reliable measurements. Tidal amplitude was 1.16 m, and the high tide was reached at 17:15 (local time). Two acoustic Doppler velocimeters (Vector 1 and Vector 2) placed at the inlet and inner bay (Fig. 6) measured the three components of the water current at heights of 0.22 m and 0.27 m above the bed, respectively. They were set in a vertical position near the bed in order to avoid wind influence, and to be able to take as many measurements as possible. These instruments also included a pressure gauge. Both sensors sampled at 4 Hz. To validate the water column pressure record, depth was also measured with a leveled stick. To complete the measurements, an acoustic Doppler current profiler was set horizontally parallel to the bottom to obtain a cross-sectional velocity profile. Cells were 0.5 m wide. The velocity was surveyed for 40 min/h, and one datum was recorded per minute. Pressure was surveyed at a sampling rate of 17 min/h. A meteorological station with a Gill 2D sonic anemometer and a Setra CS100 barometer was also used to sample wind velocity and direction as well as pressure. During the data analysis, it was found that the wind was so light that its effect was negligible. The river flow was null during the measurement period while the wave influence was being filtered. There were no available data about groundwater fluxes and seepage

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Fig. 6. Location of the equipment used in the monitoring of the coastal lagoon at Zahara de los Atunes during the second field survey.

and they were dismissed in this study. Therefore, the astronomical tide was the only agent present in the calibration process. The Manning roughness coefficient (Chow, 1959) was used as the calibration parameter. Water elevation data were contrasted and calibrated with direct manual measurements. The calibration results (Fig. 7) determined that the Manning roughness coefficient that best fitted the data was 0.05 s/m1/3. This value, which was relatively high for sand channels, was in accordance with the values offered by Fisher and Dawson (2003) for channels with vegetated bottoms, such as the coastal lagoon at Zahara de los Atunes.

induced by different water levels both inside and outside the lagoon. Since there is little or no rainfall, the river does not supply water. Storms are infrequent, and the waves have little effect. Therefore, the main agent controlling the system's hydrodynamics is the tide. The sediment contributions to the inlet by the wind and littoral drift cause the inlet to close in the autumn. The precise date of closure depends on the magnitude of the events that take place during this season, which determines whether the sediments deposited in the inlet can be flushed out by the river flow or flushed in by the waves. 4.1. Hydrodynamic characterization

4. Results and discussion During the dry season, when the coastal lagoon is artificially opened, water interchange between the Atlantic Ocean and the coastal lagoon is the main consequence of ebb and flood currents

The first parameter used to characterize the hydrodynamics of the study site was an astronomical tide with only one constituent, M2. Table 1 shows the principal constituents of the astronomical tide in the area, obtained from a seven-month record (one datum every

Fig. 7. Model calibration with the data collected during the second field survey for a Manning roughness coefficient of 0.05. Left graphs show water surface elevation while the right ones correspond to velocities. From top to down, vector 1, ADCP and vector 2 results are plotted. The grey dashed line represents the results for an irregular geometry, the black dashed line a regular geometry and the solid line the measured data.

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Table 1 Principal harmonic constituents of the astronomical tide in Zahara de los Atunes. Harmonic

Amplitude

Phase

M2 S2 N2 K2 SSA NU2 K1

0.7288 0.266 0.1543 0.0759 0.0744 0.0295 0.0281

106.78 133.1 89.96 131.53 26.44 96.67 103.79

5 min) by a tide gauge (Valeport model 740) located at the port of Barbate. The harmonic analysis of the water level time series was performed with T-tide software (Pawlowicz et al., 2002). Since Barbate is only 9 km from Zahara de los Atunes, the astronomical tide was assumed to be similar in both places. After the reconstruction of the tide series, it was observed that the spring tide was around 1.25 m of amplitude, and the neap tide was around 0.40 m (Fig. 8). The introduction of an M2 spring tide in the model gave the following information: 1) the bay tide had a lower amplitude than the ocean tide; 2) the bay tide was asymmetrical, and was characterized by a longer ebb tide and a shorter, more intense flood tide (Fig. 9). These two facts led us to the conclusion that the lagoon in Zahara de los Atunes was flood-dominated. The non-linearities caused by the advection term, such as the half-period overtide (M4), and to a lesser extent, the friction and shoaling of the tidal wave were responsible for the tidal wave shape inside the lagoon. Its principal effects were the lowering of the velocities and a wave delay between different parts of the bay. The tide inside the lagoon was found to be out of phase with the ocean tide. The delay was small, and was roughly 5 min in relation to the inlet and twenty minutes in relation to the lagoon stretch close to the river. The inlet bottom elevation reached by dredging was above mean sea level, thus the lagoon was open during only part of the tidal cycle. Slack water inside the lagoon coincided with the high tide but not with the low tide in the ocean because the change from null velocities to landwards movement took place only after the tidal level rose over the inlet bottom (Fig. 9). This partial rising tide made the falling tide even longer. For this reason, the tidal asymmetries (duration and velocity) observed inside the bay caused the water particles to have a net motion (tidal cycle averaged) towards the ocean (Fig. 11). Moreover, tidal asymmetries have long been recognized as important factors in controlling the direction and magnitude of net sediment transport (Postma, 1967). For the lagoon in Zahara de los Atunes, the trend is to introduce sediments into the lagoon during the flood tide. These sediments remain inside the lagoon since ebb velocities are unable to move the coarse fraction. Thus, an inlet closure is to be expected. The deposition of sediment coming from the

Fig. 8. Astronomical tide in Barbate coast during the year 2008.

Fig. 9. Water surface elevation (top) and velocity temporal evolution (bottom) due to a M2 tide of 1.25 m amplitude for several stretches of Zahara de los Atunes coastal lagoon.

river and the sea favors the silting and the shallowness of this coastal lagoon. Water surface elevation within the basin showed a spatially uniform oscillation. Consequently, a pumping mode or Helmholtz response was assigned to this coastal lagoon. The velocities, however, were found to be different from one stretch of the bay to another. The current intensity was higher in the inlet and other narrow stretches, while in the wider stretches, the velocities were near zero. During the neap tide, the bay tide became more asymmetric, highly damped, and with a smaller current erosion capacity. The results provided by the model when the forcing agent was a reconstructed tide series (from a neap tide of 0.35 m to a spring tide of 1.33 m) were similar to those previously explained for the M2 tide (Fig. 10). 4.2. Water renewal The tidal prism can be defined as the water volume entering the lagoon every tidal cycle. This variable reaches 27 930 m3 for a M2 tide of 1.25 m of amplitude, while the maximum coastal lagoon volume is 36 417 m3. Therefore, the tidal prism renews around 75% of the bay water every spring tidal cycle. Although this is a high renewal rate, it is not entirely true for the inner part of the lagoon. Particle motion is almost non-existent in this stretch, and thus, the residence time of water is high (Fig. 11). Furthermore, spring tides are not so frequent during the opening period of the lagoon, which is around three months per year. During neap tides, the residence time of the water increases because the velocities are lower, and the distance travelled by particles is even shorter. Consequently, the eutrophication of the inner area of the lagoon is highly probable during long closure periods, and in fact it has already occurred. The river flow or the rainfall can relieve these symptoms of bad ecosystem health by supplying fresh water. The benefits will be higher if the continental flow is highly turbulent, thus facilitating the mixture and renewal of the water.

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Fig. 10. Water surface elevation (top) and velocity temporal evolution (bottom) due to a real tide for several stretches of Zahara de los Atunes coastal lagoon.

4.3. Inlet stability 4.3.1. Tide One of the approximations often used to evaluate the stability of coastal lagoons is the Escoffier (1940) curve. In this test, the irregular real

cross-sectional geometry, mentioned earlier, was not implemented, but rather a rectangular-equivalent geometry to facilitate comparison with the analytical solutions. Two different case studies were performed. In both, the agent forcing the system was an M2 spring tide, but the geometry of the inlet was varied. The first case study corresponded to a

Fig. 11. Lagrangian transport of water particles: net movement of a particle (top) and total length travelled by the same particle during a M2 spring tidal cycle (bottom).

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bay in which the cross-sectional area was increased by keeping the width constant and uniformly deepening the inlet and bay. The selected inlet width was 16 m, which corresponded to the width given to the artificially opened inlet. In the second case study, the inlet depth was 0.75 m, whereas the inlet width was varied from 5 to 40 m. The bay width remained constant. The results of these tests are shown in Fig. 12. One of the principal differences between both cases is the velocity value when the cross-sectional area approaches zero. In the first case, the inlet always had the same width, independently of its depth. Therefore, the numerical model calculated the inlet velocities when the peak tidal elevation was higher than the maximum height of the barrier, thanks to the implementation of the dry and wet technique. This explained why there was no null velocity in the Escoffier curve for a null mean cross-sectional area. In the second case, when the width approached zero, the inlet became smaller, and the friction higher. As a result, the velocities tended to zero. The position of the current geometry in the Escoffier curve was the same for both cases. Most inlet stability criteria have been proposed for large permanently open coastal lagoons (O`Brien, 1969, 1931; Dean, 1971; Jarrett, 1976), where the measured equilibrium velocity was around 1 m/s. However, Byrne et al. (1980) found velocities around 0.35 m/s for inlets with cross-sectional areas smaller than 100 m2. This average velocity is in accordance with the Shields diagram for sediment particles with D90 = 0.35 m/s. The coastal lagoon at Zahara de los Atunes has a cross-sectional area of around 15 m2, and thus, this criterion was selected to evaluate inlet stability. The position of the artificially open inlet in the closure curve was very close to the maximum in the diagram, and therefore, the inlet should evolve to reach the equilibrium flow area, which is 30 m2. However, even when the inlet is in a region of equilibrium, it closes every year by the end of the summer. The asymmetry of the inlet currents along with sediment deposition, due to the wind and the littoral drift, reduce the inlet's efficiency to flush the sediments out to sea. As previously mentioned, spring tides are not so frequent during the opening period, which favors sediment deposition in the inlet. The combination of all these factors results in a decrease of the minimum cross-sectional area until it reaches the region of instability, and therefore, closure. 4.3.2. Other agents: littoral drift and river flow Although the tide is the main agent controlling the hydrodynamics of the lagoon, waves, currents, and river flow determine the

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geomorphologic evolution of the barrier. For this reason, these agents should also be taken into account in the evaluation of inlet stability. Another widely used stability criterion is the one introduced by Bruun and Gerritsen (1960), which relates the spring tidal prism (Ω) and the total annual littoral drift quantity (Mtot). Bruun (1991) quantified the magnitude of this ratio for different navigation conditions based on inlets located on semi-diurnal mesotidal coasts, such as the coastal lagoon at Zahara de los Atunes. The tidal prism entering the lagoon, as calculated by the numerical model, was around 28 000 m3 for spring tide. The annual littoral drift was evaluated under the assumption that the grain size of the marine sands was similar to that of the inlet sands. The threshold between calm and storm conditions for the wave climate (SIMAR-44 data, node 1056044) was set at 2.5 m for the spectral significant wave height (Hm0). Representative values of Hm0 were obtained for both conditions (50%, 90% and 95%). The peak periods (Tp) were selected as the mode of the peak periods related to the wave heights obtained. The wave climate for one year was assumed to be composed of only one sea state, represented by Hm0 and Tp, arriving at the region of the coastal lagoon from the west. The CERC formula for deep water variables (according to Ashton and Murray, 2006) was applied to calculate the annual longitudinal sediment transport rate. This transport ranges from 106 to 107 for calm conditions to 108 for storm conditions (Table 2). Fig. 13 shows the values obtained for the ratio Ω/Mtot, all of which are significantly less than 20. These results are in accordance with the previous ones, and show the tendency of the open inlet to closure, even if conditions are calm in the area all year round. The ability of the tidal current to flush the marine sediments deposited in the inlet was also assessed. As shown in Fig. 9, the maximum velocity of the current in the narrower cross-section of the inlet during an M2 spring tidal cycle was 0.26 m/s for a water level of around 0.85 m. The critical current velocity was estimated by using Van Rijn's (1984a,b) experimental formulas for current sediment transport. The value obtained was 0.32 m/s. Therefore, the current flushing ability of the lagoon to remove sediments from the inlet is almost non-existent during the calm conditions prevalent in summertime, when the inlet must be artificially opened. However, after a heavy rain, the river flow and its related velocities increase considerably. The river flow was estimated from the rainfall by applying the WiM-Med model, a physically-based distributed hydrological model that evaluates the flow of a river from the rainfall of the basin (Herrero et al., 2009). A representative hydrograph of the area was selected with a peak flow of 21 m3/s and a duration of 60 h. For this hydrograph, we used the Van Rijn formulation to calculate the maximum velocity and its associated sediment transport in the inlet. It was also assumed that these velocities remained the same in the river during the whole year. We then compared the inlet transport due to the littoral drift with the inlet transport due to river flow. Fig. 13 shows that the annual sediment load eroded by the river could be greater than the sediment load deposited by waves with Hm0 = 0.8 m, only if the water velocity in the inlet was greater than 1.8 m/s. Therefore, if the first storms of the wet season are sufficiently strong, the river flow will help to flush the inlet and keep it open, otherwise the inlet will close.

Table 2 Longitudinal sediment transport in the coastal lagoon region assumed that the wave conditions are the same during the whole year. Calms

Fig. 12. Escoffier curves for the study site. In the top figure, width is held constant and depth varies while in the bottom figure depth is held constant while width varies. The Byrne et al. (1980) stability criterion is also presented in both graphs.

Hm0 (m) T (s) Qs (m3 s− 1) Qs (×108 m3 year− 1)

0.8 5.8 0.0582 0.01

Storms 1.45 6.3 0.24 0.07

1.8 7.1 0.42 0.13

3.05 8.6 1.56 0.49

4.5 11 4.17 1.31

5.05 11.1 5.51 1.74

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Fig. 13. Velocities reached in the coastal lagoon inlet due to a river hydrograph of 21 m3/s peak flow (left). Sediment flow in the inlet assuming constant inlet velocities and wave climate conditions along a year (right).

In order to obtain an integrated approximation to the inlet opening and closure, a joint implementation with a one-line coastal evolution model is currently being developed, according to the methodology elaborated by Baquerizo and Losada (2008). Ávila (2007) and Payo et al. (2008) show how this methodology can be effectively used for management purposes at medium time scale (decades). Geomorphologic and management-oriented variables, such as the number of openings/closures of the inlet or dredge volumes can thus be studied, and conservation strategies evaluated in terms of their statistical effectiveness. 5. Conclusions A deeper knowledge of coastal lagoon systems can only be acquired by a qualitative and quantitative characterization of the agents acting on these lagoons as well as the system's response to these agents on various scales. Such data are necessary for sustainable management and provide a sound basis for decisions that take into account all the possible risks involved. The intermittence of Andalusian coastal lagoons determines their behavior and functions. The study described in this article analyzed the influence of hydrodynamics in relation to inlet morphology of the intermittent coastal lagoon at Zahara de los Atunes where an artificial inlet is opened during the dry season. The tool used for this purpose was a numerical model that solves Saint-Venant equations. The conclusions reached were the following: i) The coastal lagoon at Zahara de los Atunes was found to show a pumping-mode response and a damped asymmetrical oscillation inside the bay when the inlet is open. The lagoon is flooddominated which means that it is a sink for marine sediments. ii) The dimensions of the artificially open inlet do not allow the total renewal of the water of the inner coastal lagoon and, therefore, it has a long residence time. This leads to water quality degradation, which is currently one of the main environmental problems of this lagoon. iii) The stability of the open inlet was evaluated with the Escoffier curve offered by the model and the stability criterion of Byrne et al. (1980). Our results showed that the position of the inlet in the curve was not far from the unstable root, which means that the inlet will probably close. The littoral drift of this region is high enough to transport and deposit sediments in the inlet that cannot be removed by the tidal current. Nevertheless, the river flow after heavy rain (peak flow ∼20 m3/s) can help to flush sediments from the inlet by temporarily opening it. iv) A good management practice when opening the inlet would be to widen or deepen it until it reaches the equilibrium flow area.

In this way, the inlet would not close so easily, and would remain open until the arrival of storm conditions and high river flows that would help to remove the sediments deposited. The new cross-sectional area would have additional benefits, such as the increase of the water interchanged between the ocean and the lagoon, which would improve water quality. However, because of the lagoon shape, this measure would not be sufficient in itself to solve all the water quality problems during the summer. Other measures that should be considered are the opening of the inlet at the beginning of the spring as well as an annual maintenance program so that the inlet could be dredged as many times as necessary to keep it open. Acknowledgements This study was funded by the Spanish Ministry of the Environment and the Andalusian Regional Government (Consejería de Innovación, Ciencia y Empresa). We thank the two anonymous reviewers for their comments which helped improve this manuscript. We are also grateful to Puertos del Estado for providing the wind and wave climate data. Appendix A. Mathematical formulation of the problem In the literature, the most typical analytical equations for characterizing coastal lagoons are: b∂η = ∂t + ∂Q = ∂x = 0

ðA1Þ

2

∂Q = ∂t + ∂ðQ = Ac Þ = ∂x = −gAc ∂η = ∂x−bτbx = ρ

ðA2Þ

where b is the width of the cross-sectional area Ac; η is the water surface; Q is the flow; t the time; x the longitudinal axis of the coastal lagoon; ρ the water density; and τbx the bottom shear stress. DiLorenzo's (1988) version of the momentum equation uses the Darcy–Weisbach expression for the bottom shear stress: 2

2

∂Q = ∂t + ∂ðQ = Ac Þ = ∂x = −gAc ∂η = ∂x−fPmQ j Q j = Ac

ðA3Þ

The Saint-Venant equations solved numerically are: ∂Ac = ∂t + ∂Q = ∂x = qf 2

∂Q = ∂t + ∂ðQ = Ac Þ = ∂x + gI1 = gAc ðS0 + Sf Þ + gI2

ðA4Þ ðA5Þ

where the variables I1 and I2, respectively, account for the hydrostatic pressure force and the forces exerted by changes in the cross-sectional geometry, S0 for the bottom slope, and Sf for the slope friction. Some

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advantages of the numerical model over the analytical solutions are that it can deal with real geometries, various agents (not only tide), and several mass or momentum sources or sinks (such as evaporation). Further advantages are that the model requires a small number of input data, and that the computational cost for simple regular geometries is low (which makes it possible to compute long periods of time). Some of the variables of interest that can be computed with the model, and those which are relevant to lagoon management are the closure tendency of an inlet, its stability, the tidal prism, the symmetry of the current, and whether the lagoon acts as a source or sink for sediments. Disadvantages of the model include its high computational cost for irregular cross-sections, as well as difficulties in evaluating derived variables, such as the energy balance and the transport of a conservative substance because of the appearance of small instabilities in the flow which suffer from amplification. The main differences between the formulation of the analytical solution and the numerical solution appear in the comparison of the momentum equations of both solutions. The assumption of a pumping-mode response by DiLorenzo cancels out I1 while I2 is not considered by this author. The friction term is also treated in a different way. By comparing the friction terms and by rearranging them, we obtained the equivalence between the friction coefficients of these two terms:   2 4=3 Ab ken + kex + gn = Rh = LAc = Ab = 2LAc ðken + kex + fd L = 4hÞ ðA6Þ fsv = 4RhðLfd = 4h−ken −kex Þ = L

ðA7Þ

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