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Impact of vertical structure on water mass circulation in a tropical lagoon (Ebrié, Ivory Coast)
Journal of African Earth Sciences 55 (2009) 47–51
Contents lists available at ScienceDirect
Journal of African Earth Sciences journal homepage: www.elsevier.com/locate/jafrearsci
Impact of vertical structure on water mass circulation in a tropical lagoon (Ebrié, Ivory Coast) Isabelle Brenon *, Olivier Audouin, Nicolas Pouvreau, Jean-Christophe Maurin Littoral, Environnement et Sociétés UMR 6250, Université de La Rochelle, 2 rue Olympe de Gouges 17000 La Rochelle, France
a r t i c l e
i n f o
Article history: Received 20 July 2006 Accepted 11 December 2008 Available online 9 April 2009 Keywords: Water mass circulation Lagoon Channel Vertical structure Modelling
a b s t r a c t A one-dimensional vertical model has been developed to simulate the water mass circulation along the vertical structure in all deep coastal areas. The model has hydrodynamic and transport components solved using finite difference scheme. The one-dimensional vertical model results are coupled to the vertically averaged two-dimensional model results at each point of a horizontal grid. A theoretical salinity profile is introduced for each vertically integrated value obtained from the 2DH model results. A viscosity profile, simulating a viscosity value close to zero at the surface and with large viscosity gradients, is applied along the water column. The model is applied to the Vridi channel, connecting the Ebrié lagoon to the sea (Ivory Coast). The response of the Ebrié lagoon is studied in terms of inflow and outflow of water in the system through the Vridi channel. Due to the abrupt variation of the surface slope, vertical velocities along the water column show an anticlockwise spiral from bottom to surface during a tidal cycle. Due to the bottom friction and to the vertical viscosity profile, velocities decrease from surface to bottom. However, the freshwater inflow slows down the tidal propagation during the flood and causes the surface velocity to be smaller than the bottom velocity at mid-tide. Close to the bottom, velocities follow an anticlockwise movement due to the tidal propagation. At the water surface, velocities follow only an alternative movement of either ebb or flood, along the channel direction. No cross shore velocities can develop at the surface in the channel. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Coastal lagoons and estuaries are typically centres of population, commerce, industry and recreation. Consequently they are also sites for disposal of industrial and municipal wastes (Cheng et al., 1993). The Ebrié lagoon (Fig. 1) is no exception. Important questions concerning its uses and potential changes to the lagoon are left unanswered without a good understanding of the hydrodynamic processes occurring in the lagoon. All over the world, these tropical lagoons are studied by measurements and modelling. Two-dimensional vertically averaged models are generally used to study the hydrodynamic patterns in these lagoons (Nameche and Vasel, 1998; Fernandes and Niencheski, 2000; Lopes et al., 2001; Baléo et al., 2001), in which it is assumed that the vertical structure could be neglected. It seems to be necessary to check this important assumption especially in deeper areas. Tastet (1987) carried out in situ experiments including bathymetry, water level, currents, salinity and temperature at some points of the Ebrié lagoon. Some recent measurements of the hydrodynamic parameters have been made (Pouvreau et al., submitted * Corresponding author. E-mail address: [email protected] (I. Brenon). 1464-343X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jafrearsci.2008.12.005
for publication). Assuming the Ebrié lagoon is well mixed, a twodimensional depth-averaged model for tide propagation was used to determine the respective impact of hydrodynamical effects (wind, river flows and tides) on the water mass circulation in the Ebrié lagoon (Brenon et al., 2004). However, due to the tidal and river flow effects, a vertical hydrodynamic structure is present in deep areas close to the sea, especially in the access channel (Vridi channel) and the Abidjan harbour. Our purpose here is to determine the impact of this vertical structure on the water mass circulation in the lagoon: can it be neglected or not? A one-dimensional vertical model is developed and coupled to the vertically averaged two-dimensional model results at each point of the horizontal grid in order to evaluate the impact of vertical gradients in the Vridi channel (Fig. 1). 2. Geographical and physical characteristics of Ebrié lagoon Stretched along the Ivory seacoast, the Ebrié lagoon (Fig. 1) is one of the largest lagoons in West Africa (4 km by 132 km), classified as an estuarine semi-closed lagoon. It connects to the Atlantic through the Vridi channel, which was opened in 1951, for the economic development of the Abidjan harbour. It remains quite shallow (average depth: 4.8 m) with a few deep areas, especially
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I. Brenon et al. / Journal of African Earth Sciences 55 (2009) 47–51
Fig. 1. The Ebrié lagoon system and location (after Tastet, 1974) and location of Optical Back Scattering apparatus.
Fig. 2. Salinity vertical profile introduced in the 1DV model according to vertically averaged salinity simulated using the 2Dh model.
around Abidjan (27 m deep in the South of Boulay island). These deep areas (Vridi channel and Abidjan harbour) are under large economical constraints. The Comoé River, which is the main river that flow into the lagoon, has a typical tropical flow pattern: large discharges during the rainy season (August to November) followed by low to very low (January to May) river inflow throughout the rest of the year. According to climate variations, the discharge shows large year-toyear variation. The mean annual freshwater contribution of the Comoé River is 300 m3 s1 with a river discharge peak of 1150 m3 s1 associated with the tropical monsoon. A major part of the freshwater input is expulsed through the Vridi channel, as evaporation remains very low. During monsoon (Durand and Guiral, 1994), the Abidjan area is under the influence of both ocean and river inputs while during the rest of the year, it is mainly under a tidal influence (Brenon et al., 2004). The differences in salinity and temperature between surface and bottom waters are small (5‰ for salinity and 4° for temperature, Tastet, 1974), except in areas under the influence of tides where a tidal prism can be very large during dry season. The tide is semi-diurnal with a diurnal pattern (Brenon et al., 2004; Pouvreau et al., submitted for publication). Close to the Vridi channel, it shows an average amplitude of 0.8 m during spring tides, down to 0.2 m during neap tides. However, the amplitude of the tidal range quickly decreases further to the East or to the
West due to locally broken geometry and bathymetry of this otherwise shallow lagoon (Fig. 1). The velocity of the tidal current is clearly dependent on water depth and lagoon geometry. Its value is about 0.9 and 0.3 m s1 near in the Vridi channel but decreases to 0.1 m s1 close to the Comoé mouth. 3. One-dimensional numerical model 3.1. Used equations The one-dimensional vertical model developed has hydrodynamic and transport components. The model can simulate water mass transport processes due to tidal and freshwater forcing. Hydrostatic pressure distribution, i.e. the weight of the fluid balances the pressure, and the Boussinesq approximation, i.e. the way density variations enter into the equations of motion (Kowalik and Murty, 1995) are used as simplifying approximations in the model. The transport model component calculates the spatial and temporal distributions of water temperature and density. The variations in the water temperature and density influence the water density and in turn the velocity field. The governing equations in the one-dimensional vertical model are obtained by subtracting the shallow-water equations from the 3D Navier Stokes equations and are as follows:
I. Brenon et al. / Journal of African Earth Sciences 55 (2009) 47–51
49
Fig. 3. (a) Viscosity profiles along the vertical structure and (b) velocity vertical structure in the Vridi channel at low water.
~ ~ @u @ @u f v~ ¼ Ax þ Gx þ T x þ Nxz @t @z @z @ v~ @ @ v~ ~ ¼ Ay þ Gy þ T y þ Nyz þf u @z @t @z with Ai spatial inertia terms such as:
~ ~ @u @u @u @u @u ~þu Þ i ðv~ þ v Þ i u ~ i v~ i w i Ai ¼ ðu @x @y @x @y @z Z 1 Z 1 1 @ 1 @ ~i u ~ dz þ ~ i v~ dz u u þ H @x d H @y d
h R R 1 1 with Gi density terms such as: Gi ¼ qg H1 d @x@ i z qdz dz 0 R f @ qdzwith Ti friction terms close to bottom and surface: @xi z T i ¼ ssi Hsbi where x, y are horizontal coordinates, z is vertical coor; v vertically averaged velocity components in x, y dinate, t is time, u ~; v ~ ; w vertical component directions at any grid locations in space, u of velocity x, y, z directions at any grid locations in space, f is Coriolis coefficient, Nij: vertical diffusion coefficients in x, y directions, q is in situ water density, q0 is density after Boussinesq approximation, g is gravitational acceleration, z is reference level, H is water level, d is bottom level, 1 is free surface level, ssi is surface shear stress in any directions x and y, sbi is bottom shear stress in any directions x and y. 3.2. Numerical parameters Fig. 4. Vertical velocity profile during tidal cycle (HW = high water, LW = low water).
As the Ebrié lagoon is very close to the equator (4°N), the Coriolis force is neglected. Advection terms mainly express the bathymetry variations. As Vridi channel bathymetry can be consid-
ered as homogeneous in any direction x and y, the advection terms have been neglected in this study.
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I. Brenon et al. / Journal of African Earth Sciences 55 (2009) 47–51
The variation of temperature between sea water and lagoon water are small in this area (Pouvreau et al., submitted for publication). This causes the density of sea water to be a function of salinity S alone such as: q ¼ q0 ð1 þ aSÞ where a is a coefficient equal to 0.0008. The surface boundary conditions are supposed to be independent of the wind shear at the free surface, as the wind is very low in this area (Pouvreau et al., submitted for publication). The surface shear stress at the free surface is expressed as: s~s ¼ 1:8 106 ððu þ u~f ÞÞ. At the sea bed, the bottom shear stress b ¼ Cg2 juju where C is determined by the Chézy equation such as: s~ 1/2 1 is the Chézy coefficient, calibrated as 65 m s using the 2DH model. At the sea bottom, the gradients of temperature and salinity are taken to zero, indicating that there are no advective and diffusive fluxes across the sea bed. 3.3. Numerical scheme To study the vertical hydrodynamic structure, vertically averaged model results (vertically averaged velocity components in x, y directions at any grid locations in space, water level, free surface level and salinity) are introduced into these 1DV equations at each node of the 2DH grid. A finite difference approximation is applied to the 1DV governing equations. As it is numerically more stable, an implicit–explicit numerical scheme has been used to allow a higher time step equal to three minutes at low water and two minutes at high water. Water depths are divided into the same number of layers following the bottom topography. Ten layers have been simulated along the water column in this study. Higher resolution could be achieved by increasing the number of layers. 3.4. Salinity profile From the 2DH model results (Brenon et al., 2004), only a vertically integrated value of salinity can be obtained. To simulate the vertical hydrodynamic structure a salinity profile is necessary. Only a few measurements (Varlet, 1978) of the vertical salinity structure are available. As these results were obtained before the Vridi channel was opened, they cannot be used for this study. A theoretical salinity profile is introduced for each vertically averaged salinity value (Fig. 2). A vertical gradient is reproduced where the marine (therefore dense) water is close to the bottom. The
higher the vertically averaged salinity is, the deeper the marine water is close to the bottom. 4. Results The study area is only the Vridi channel, which connects the lagoon to the sea. In this channel, large vertical gradients for salinity and thus density occur due to the marine water inflow to the lagoon and the lagoon water outflow through the channel. An important advantage of this model is that it is very economic in CPU time. This allows using it for any large area. 4.1. Viscosity profile Four different viscosity profiles (Fig. 3a) are implemented to simulate the vertical velocity structure in the Vridi channel (Fig. 3b). The higher the viscosity can increase (for example the n(1 – 0.5n) line), the steeper the velocity profiles are. Therefore, the higher the viscosity is, the more homogeneous the flow is along the water column. According to measurements (Varlet, 1978), the vertical velocity gradient is high close to the water surface with large viscosity differences between surface and bottom. Therefore, the viscosity profile n(1 n)2, simulating a viscosity value close to zero at the surface and large viscosity gradients along the water column, is chosen. 4.2. Validation of velocity results The numerical velocity results are validated at the surface by comparison to a three-month continuous measurement (Brenon et al, 2004) by Optical Back Scattering (apparatus located in Abidjan harbour, close to the studied area and under tidal influence at 4°010 0100 W–5°180 1600 N; Fig. 1). The statistical studies give a correlation coefficient R equal to 0.93, which indicates that the agreement between data and numerical results is good. 4.3. Vertical velocity profile In the middle of the channel, during a tidal cycle, the vertical velocities along the water column show an anticlockwise spiral from bottom to surface (Fig. 4). This seems to be a consequence of the quick variation of the surface slope, which induces a uniform
Fig. 5. Velocity hodograph at surface and bottom (HW = high water, LW = low water).
I. Brenon et al. / Journal of African Earth Sciences 55 (2009) 47–51
acceleration of the vertical velocities from bottom to surface. As bottom velocities are smaller, this effect appears more quickly close to the bottom especially during the ebb and the flood (Fig. 4). Due to the bottom friction and the vertical viscosity profile, velocities (Fig. 4c) decrease from surface to bottom (from 0.85 to 0.32 m s1 at low water). However, during the flood, at mid-tide (Fig. 4d), the surface velocity (0.46 m s1) is smaller than the bottom velocity (0.75 m s1) This result is not in agreement with the theoretical viscosity profile introduced in the model. Due to freshwater input, the water surface in the lagoon is higher than at the sea. This causes the lagoon freshwater to flow out at the surface of the channel and slow down the tidal propagation during the flood. 4.4. Velocity hodograph The differences between water circulation at bottom and surface can be study using a velocity hodograph (Fig. 5). Close to the bottom, velocities follow an anticlockwise movement due to the tidal propagation, identifying marine water. At the water surface, freshwater input flows out the lagoon in the whole channel as it has small dimensions. This causes velocities to follow an alternative movement only, either ebb or flood, along the channel direction. No cross shore velocities can develop at the surface in the channel. 5. Discussion and conclusion A one-dimensional vertical model has been developed to simulate the water mass circulation along the vertical structure in the Vridi channel, which connects the Ebrié lagoon (Ivory Coast) to the sea under different tidal conditions. Comparison of the model results with field measurements are purchased in order to check the model’s ability in reproducing hydrodynamic and salinity measurements. Then, an attempt was made to disclosure some of the channel’s features, such as residual circulation, cross-sectional vertical structure of the channel and tidal evolution of salinity. The numerical model is shown to be capable of predicting the vertical water mass circulation and of taking into account the inflow of marine water at the sea bed (due to tides) and the outflow of lagoon water at the surface (due to freshwater input) in this type of channel connecting the sea to a coastal lagoon. The vertical velocities along the water column show an anticlockwise spiral from bottom to surface during a tidal cycle. Velocities decrease from surface to bottom except during the flood due to the freshwater inflow that slows down the tidal propagation. This characteristic within the domain reveals an ebb-dominated channel. This feature will impact the outflow of any particles from the lagoon to the sea. It plays an important role for the horizontal transport of any particle and could induce large ecological consequences: a particle, such as water, but also any pollutant (such as chemicals), has a greater chance to flow out the lagoon if it is at the surface than if it is at the bottom. This could be relevant to all petro-chemical industries along the Vridi channel and could have large consequence in the lagoon water quality. The model is
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part of an ongoing research programme on pollutant transport in lagoon area. Since the water is rather deeper in the channel than in the rest of the lagoon, tidal mixing cannot reach the whole water column. Therefore vertical stratifications remain notable and density gradients are much larger in the vertical axis than in the horizontal axis. No cross shore velocities can develop at the surface in the channel. The flow pattern in the Vridi channel is mainly driven by the large vertical stratification due to the increased water level between the lagoon and the channel. This could also have large consequence in the lagoon water quality. After studying the impact of different tidal range, it would be necessary to study the impact of the freshwater inflow, which is very variable between dry and rainy season in this equatorial area. New vertical salinity profile measurements will also allow to calculate the ration between freshwater and sea water. To confirm the model, it would be interesting to implement it in others types of coastal areas. These studies could help to evaluate the impact of dryness in West Africa and more over the impact of present climatic variations. Acknowledgements This work was funded by the CAMPUS research program of the French Ministry of Foreign Affairs. The authors wish to thank Sylvain MONDE (University of Cocody, Abidjan, Côte d’Ivoire). References Baléo, J.N., Humeau, P., Le Cloirec, P., 2001. Numerical and experimental hydrodynamic studies of a lagoon pilot. Water Research 35 (9), 2268–2276. Brenon, I., Pouvreau, N., Mondé, S., Maurin, J.C., 2004. Modelling hydrodynamics in the Ebrié lagoon (Côte d’Ivoire). Journal of African Earth Science 39 (3-5), 535– 540. Cheng, R.T., Casulli, V., Gartner, J.W., 1993. Tidal, residual, intertidal mudflat (TRIM) model and its application to San Francisco Bay, California. Estuarine, Coastal and Shelf Sciences 36, 235–280. Durand, J.R., Guiral, D., 1994. Hydroclimat et hydrochimie. In: Durand, J.-R., Dufour, P., Guiral, D., Zabi, S.G.F. (Eds.), Environnement et ressources aquatiques de Côte d’Ivoire Tome II, Les milieux lagunaires, éditions de l’ORSTOM. Fernandes, E., Dyer, K.R., Niencheski, L.F.H., 2000. Calibration and validation of the TELEMAC 2D model of the Patos lagoon (Brazil). Journal of Coastal Research 34, 470–488. Lopes, J.F., Dias, J.M., Dekeyser, I., 2001. Influence of tides and river inputs on suspended sediment transport in the Ria de Aveiro lagoon, Portugal. Physics and Chemistry of Earth 26 (9), 729–734. Kowalik, Z., Murty, T.S., 1995. Numerical Modelling of Ocean Dynamics. Advanced Series on Ocean Engineering. World Scientific Publishing, London, vol. 5, pp. 1– 6. Nameche, T.H., Vasel, J.L., 1998. Hydrodynamic studies and modelization for aerated lagoons and waste stabilization ponds. Water Research 32 (10), 3039–3045. Pouvreau, N., Brenon, I., Mondé, S., Maurin, J.C., submitted for publication. El Niño impact on water mass circulation during the tropical monsoon in a tropical lagoon (Ebrié, Ivory Coast). Geo-Marine Letters. Tastet, J.P., 1974. L’environnement physique du système lagunaire Ebrié. Rapport de l’Université Abidjan, série documentation. Departement des Sciences de la Terre, vol. 11, 28p. Tastet, J.P., 1987. Effets de l’ouverture d’un canal d’accès portuaire sur l’évolution naturelle du littoral d’Abidjan (Afrique de l’Ouest). Bulletin de l’Institut de Géologie du Bassin d’Aquitaine, Bordeaux 41, 177–190. Varlet, F., 1978. Régime de l’Atlantique près d’Abidjan, Etudes Eburnéennes, cahier de l’ORSTOM, série Océanographie, VII.
Contents lists available at ScienceDirect
Journal of African Earth Sciences journal homepage: www.elsevier.com/locate/jafrearsci
Impact of vertical structure on water mass circulation in a tropical lagoon (Ebrié, Ivory Coast) Isabelle Brenon *, Olivier Audouin, Nicolas Pouvreau, Jean-Christophe Maurin Littoral, Environnement et Sociétés UMR 6250, Université de La Rochelle, 2 rue Olympe de Gouges 17000 La Rochelle, France
a r t i c l e
i n f o
Article history: Received 20 July 2006 Accepted 11 December 2008 Available online 9 April 2009 Keywords: Water mass circulation Lagoon Channel Vertical structure Modelling
a b s t r a c t A one-dimensional vertical model has been developed to simulate the water mass circulation along the vertical structure in all deep coastal areas. The model has hydrodynamic and transport components solved using finite difference scheme. The one-dimensional vertical model results are coupled to the vertically averaged two-dimensional model results at each point of a horizontal grid. A theoretical salinity profile is introduced for each vertically integrated value obtained from the 2DH model results. A viscosity profile, simulating a viscosity value close to zero at the surface and with large viscosity gradients, is applied along the water column. The model is applied to the Vridi channel, connecting the Ebrié lagoon to the sea (Ivory Coast). The response of the Ebrié lagoon is studied in terms of inflow and outflow of water in the system through the Vridi channel. Due to the abrupt variation of the surface slope, vertical velocities along the water column show an anticlockwise spiral from bottom to surface during a tidal cycle. Due to the bottom friction and to the vertical viscosity profile, velocities decrease from surface to bottom. However, the freshwater inflow slows down the tidal propagation during the flood and causes the surface velocity to be smaller than the bottom velocity at mid-tide. Close to the bottom, velocities follow an anticlockwise movement due to the tidal propagation. At the water surface, velocities follow only an alternative movement of either ebb or flood, along the channel direction. No cross shore velocities can develop at the surface in the channel. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Coastal lagoons and estuaries are typically centres of population, commerce, industry and recreation. Consequently they are also sites for disposal of industrial and municipal wastes (Cheng et al., 1993). The Ebrié lagoon (Fig. 1) is no exception. Important questions concerning its uses and potential changes to the lagoon are left unanswered without a good understanding of the hydrodynamic processes occurring in the lagoon. All over the world, these tropical lagoons are studied by measurements and modelling. Two-dimensional vertically averaged models are generally used to study the hydrodynamic patterns in these lagoons (Nameche and Vasel, 1998; Fernandes and Niencheski, 2000; Lopes et al., 2001; Baléo et al., 2001), in which it is assumed that the vertical structure could be neglected. It seems to be necessary to check this important assumption especially in deeper areas. Tastet (1987) carried out in situ experiments including bathymetry, water level, currents, salinity and temperature at some points of the Ebrié lagoon. Some recent measurements of the hydrodynamic parameters have been made (Pouvreau et al., submitted * Corresponding author. E-mail address: [email protected] (I. Brenon). 1464-343X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jafrearsci.2008.12.005
for publication). Assuming the Ebrié lagoon is well mixed, a twodimensional depth-averaged model for tide propagation was used to determine the respective impact of hydrodynamical effects (wind, river flows and tides) on the water mass circulation in the Ebrié lagoon (Brenon et al., 2004). However, due to the tidal and river flow effects, a vertical hydrodynamic structure is present in deep areas close to the sea, especially in the access channel (Vridi channel) and the Abidjan harbour. Our purpose here is to determine the impact of this vertical structure on the water mass circulation in the lagoon: can it be neglected or not? A one-dimensional vertical model is developed and coupled to the vertically averaged two-dimensional model results at each point of the horizontal grid in order to evaluate the impact of vertical gradients in the Vridi channel (Fig. 1). 2. Geographical and physical characteristics of Ebrié lagoon Stretched along the Ivory seacoast, the Ebrié lagoon (Fig. 1) is one of the largest lagoons in West Africa (4 km by 132 km), classified as an estuarine semi-closed lagoon. It connects to the Atlantic through the Vridi channel, which was opened in 1951, for the economic development of the Abidjan harbour. It remains quite shallow (average depth: 4.8 m) with a few deep areas, especially
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I. Brenon et al. / Journal of African Earth Sciences 55 (2009) 47–51
Fig. 1. The Ebrié lagoon system and location (after Tastet, 1974) and location of Optical Back Scattering apparatus.
Fig. 2. Salinity vertical profile introduced in the 1DV model according to vertically averaged salinity simulated using the 2Dh model.
around Abidjan (27 m deep in the South of Boulay island). These deep areas (Vridi channel and Abidjan harbour) are under large economical constraints. The Comoé River, which is the main river that flow into the lagoon, has a typical tropical flow pattern: large discharges during the rainy season (August to November) followed by low to very low (January to May) river inflow throughout the rest of the year. According to climate variations, the discharge shows large year-toyear variation. The mean annual freshwater contribution of the Comoé River is 300 m3 s1 with a river discharge peak of 1150 m3 s1 associated with the tropical monsoon. A major part of the freshwater input is expulsed through the Vridi channel, as evaporation remains very low. During monsoon (Durand and Guiral, 1994), the Abidjan area is under the influence of both ocean and river inputs while during the rest of the year, it is mainly under a tidal influence (Brenon et al., 2004). The differences in salinity and temperature between surface and bottom waters are small (5‰ for salinity and 4° for temperature, Tastet, 1974), except in areas under the influence of tides where a tidal prism can be very large during dry season. The tide is semi-diurnal with a diurnal pattern (Brenon et al., 2004; Pouvreau et al., submitted for publication). Close to the Vridi channel, it shows an average amplitude of 0.8 m during spring tides, down to 0.2 m during neap tides. However, the amplitude of the tidal range quickly decreases further to the East or to the
West due to locally broken geometry and bathymetry of this otherwise shallow lagoon (Fig. 1). The velocity of the tidal current is clearly dependent on water depth and lagoon geometry. Its value is about 0.9 and 0.3 m s1 near in the Vridi channel but decreases to 0.1 m s1 close to the Comoé mouth. 3. One-dimensional numerical model 3.1. Used equations The one-dimensional vertical model developed has hydrodynamic and transport components. The model can simulate water mass transport processes due to tidal and freshwater forcing. Hydrostatic pressure distribution, i.e. the weight of the fluid balances the pressure, and the Boussinesq approximation, i.e. the way density variations enter into the equations of motion (Kowalik and Murty, 1995) are used as simplifying approximations in the model. The transport model component calculates the spatial and temporal distributions of water temperature and density. The variations in the water temperature and density influence the water density and in turn the velocity field. The governing equations in the one-dimensional vertical model are obtained by subtracting the shallow-water equations from the 3D Navier Stokes equations and are as follows:
I. Brenon et al. / Journal of African Earth Sciences 55 (2009) 47–51
49
Fig. 3. (a) Viscosity profiles along the vertical structure and (b) velocity vertical structure in the Vridi channel at low water.
~ ~ @u @ @u f v~ ¼ Ax þ Gx þ T x þ Nxz @t @z @z @ v~ @ @ v~ ~ ¼ Ay þ Gy þ T y þ Nyz þf u @z @t @z with Ai spatial inertia terms such as:
~ ~ @u @u @u @u @u ~þu Þ i ðv~ þ v Þ i u ~ i v~ i w i Ai ¼ ðu @x @y @x @y @z Z 1 Z 1 1 @ 1 @ ~i u ~ dz þ ~ i v~ dz u u þ H @x d H @y d
h R R 1 1 with Gi density terms such as: Gi ¼ qg H1 d @x@ i z qdz dz 0 R f @ qdzwith Ti friction terms close to bottom and surface: @xi z T i ¼ ssi Hsbi where x, y are horizontal coordinates, z is vertical coor; v vertically averaged velocity components in x, y dinate, t is time, u ~; v ~ ; w vertical component directions at any grid locations in space, u of velocity x, y, z directions at any grid locations in space, f is Coriolis coefficient, Nij: vertical diffusion coefficients in x, y directions, q is in situ water density, q0 is density after Boussinesq approximation, g is gravitational acceleration, z is reference level, H is water level, d is bottom level, 1 is free surface level, ssi is surface shear stress in any directions x and y, sbi is bottom shear stress in any directions x and y. 3.2. Numerical parameters Fig. 4. Vertical velocity profile during tidal cycle (HW = high water, LW = low water).
As the Ebrié lagoon is very close to the equator (4°N), the Coriolis force is neglected. Advection terms mainly express the bathymetry variations. As Vridi channel bathymetry can be consid-
ered as homogeneous in any direction x and y, the advection terms have been neglected in this study.
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The variation of temperature between sea water and lagoon water are small in this area (Pouvreau et al., submitted for publication). This causes the density of sea water to be a function of salinity S alone such as: q ¼ q0 ð1 þ aSÞ where a is a coefficient equal to 0.0008. The surface boundary conditions are supposed to be independent of the wind shear at the free surface, as the wind is very low in this area (Pouvreau et al., submitted for publication). The surface shear stress at the free surface is expressed as: s~s ¼ 1:8 106 ððu þ u~f ÞÞ. At the sea bed, the bottom shear stress b ¼ Cg2 juju where C is determined by the Chézy equation such as: s~ 1/2 1 is the Chézy coefficient, calibrated as 65 m s using the 2DH model. At the sea bottom, the gradients of temperature and salinity are taken to zero, indicating that there are no advective and diffusive fluxes across the sea bed. 3.3. Numerical scheme To study the vertical hydrodynamic structure, vertically averaged model results (vertically averaged velocity components in x, y directions at any grid locations in space, water level, free surface level and salinity) are introduced into these 1DV equations at each node of the 2DH grid. A finite difference approximation is applied to the 1DV governing equations. As it is numerically more stable, an implicit–explicit numerical scheme has been used to allow a higher time step equal to three minutes at low water and two minutes at high water. Water depths are divided into the same number of layers following the bottom topography. Ten layers have been simulated along the water column in this study. Higher resolution could be achieved by increasing the number of layers. 3.4. Salinity profile From the 2DH model results (Brenon et al., 2004), only a vertically integrated value of salinity can be obtained. To simulate the vertical hydrodynamic structure a salinity profile is necessary. Only a few measurements (Varlet, 1978) of the vertical salinity structure are available. As these results were obtained before the Vridi channel was opened, they cannot be used for this study. A theoretical salinity profile is introduced for each vertically averaged salinity value (Fig. 2). A vertical gradient is reproduced where the marine (therefore dense) water is close to the bottom. The
higher the vertically averaged salinity is, the deeper the marine water is close to the bottom. 4. Results The study area is only the Vridi channel, which connects the lagoon to the sea. In this channel, large vertical gradients for salinity and thus density occur due to the marine water inflow to the lagoon and the lagoon water outflow through the channel. An important advantage of this model is that it is very economic in CPU time. This allows using it for any large area. 4.1. Viscosity profile Four different viscosity profiles (Fig. 3a) are implemented to simulate the vertical velocity structure in the Vridi channel (Fig. 3b). The higher the viscosity can increase (for example the n(1 – 0.5n) line), the steeper the velocity profiles are. Therefore, the higher the viscosity is, the more homogeneous the flow is along the water column. According to measurements (Varlet, 1978), the vertical velocity gradient is high close to the water surface with large viscosity differences between surface and bottom. Therefore, the viscosity profile n(1 n)2, simulating a viscosity value close to zero at the surface and large viscosity gradients along the water column, is chosen. 4.2. Validation of velocity results The numerical velocity results are validated at the surface by comparison to a three-month continuous measurement (Brenon et al, 2004) by Optical Back Scattering (apparatus located in Abidjan harbour, close to the studied area and under tidal influence at 4°010 0100 W–5°180 1600 N; Fig. 1). The statistical studies give a correlation coefficient R equal to 0.93, which indicates that the agreement between data and numerical results is good. 4.3. Vertical velocity profile In the middle of the channel, during a tidal cycle, the vertical velocities along the water column show an anticlockwise spiral from bottom to surface (Fig. 4). This seems to be a consequence of the quick variation of the surface slope, which induces a uniform
Fig. 5. Velocity hodograph at surface and bottom (HW = high water, LW = low water).
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acceleration of the vertical velocities from bottom to surface. As bottom velocities are smaller, this effect appears more quickly close to the bottom especially during the ebb and the flood (Fig. 4). Due to the bottom friction and the vertical viscosity profile, velocities (Fig. 4c) decrease from surface to bottom (from 0.85 to 0.32 m s1 at low water). However, during the flood, at mid-tide (Fig. 4d), the surface velocity (0.46 m s1) is smaller than the bottom velocity (0.75 m s1) This result is not in agreement with the theoretical viscosity profile introduced in the model. Due to freshwater input, the water surface in the lagoon is higher than at the sea. This causes the lagoon freshwater to flow out at the surface of the channel and slow down the tidal propagation during the flood. 4.4. Velocity hodograph The differences between water circulation at bottom and surface can be study using a velocity hodograph (Fig. 5). Close to the bottom, velocities follow an anticlockwise movement due to the tidal propagation, identifying marine water. At the water surface, freshwater input flows out the lagoon in the whole channel as it has small dimensions. This causes velocities to follow an alternative movement only, either ebb or flood, along the channel direction. No cross shore velocities can develop at the surface in the channel. 5. Discussion and conclusion A one-dimensional vertical model has been developed to simulate the water mass circulation along the vertical structure in the Vridi channel, which connects the Ebrié lagoon (Ivory Coast) to the sea under different tidal conditions. Comparison of the model results with field measurements are purchased in order to check the model’s ability in reproducing hydrodynamic and salinity measurements. Then, an attempt was made to disclosure some of the channel’s features, such as residual circulation, cross-sectional vertical structure of the channel and tidal evolution of salinity. The numerical model is shown to be capable of predicting the vertical water mass circulation and of taking into account the inflow of marine water at the sea bed (due to tides) and the outflow of lagoon water at the surface (due to freshwater input) in this type of channel connecting the sea to a coastal lagoon. The vertical velocities along the water column show an anticlockwise spiral from bottom to surface during a tidal cycle. Velocities decrease from surface to bottom except during the flood due to the freshwater inflow that slows down the tidal propagation. This characteristic within the domain reveals an ebb-dominated channel. This feature will impact the outflow of any particles from the lagoon to the sea. It plays an important role for the horizontal transport of any particle and could induce large ecological consequences: a particle, such as water, but also any pollutant (such as chemicals), has a greater chance to flow out the lagoon if it is at the surface than if it is at the bottom. This could be relevant to all petro-chemical industries along the Vridi channel and could have large consequence in the lagoon water quality. The model is
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part of an ongoing research programme on pollutant transport in lagoon area. Since the water is rather deeper in the channel than in the rest of the lagoon, tidal mixing cannot reach the whole water column. Therefore vertical stratifications remain notable and density gradients are much larger in the vertical axis than in the horizontal axis. No cross shore velocities can develop at the surface in the channel. The flow pattern in the Vridi channel is mainly driven by the large vertical stratification due to the increased water level between the lagoon and the channel. This could also have large consequence in the lagoon water quality. After studying the impact of different tidal range, it would be necessary to study the impact of the freshwater inflow, which is very variable between dry and rainy season in this equatorial area. New vertical salinity profile measurements will also allow to calculate the ration between freshwater and sea water. To confirm the model, it would be interesting to implement it in others types of coastal areas. These studies could help to evaluate the impact of dryness in West Africa and more over the impact of present climatic variations. Acknowledgements This work was funded by the CAMPUS research program of the French Ministry of Foreign Affairs. The authors wish to thank Sylvain MONDE (University of Cocody, Abidjan, Côte d’Ivoire). References Baléo, J.N., Humeau, P., Le Cloirec, P., 2001. Numerical and experimental hydrodynamic studies of a lagoon pilot. Water Research 35 (9), 2268–2276. Brenon, I., Pouvreau, N., Mondé, S., Maurin, J.C., 2004. Modelling hydrodynamics in the Ebrié lagoon (Côte d’Ivoire). Journal of African Earth Science 39 (3-5), 535– 540. Cheng, R.T., Casulli, V., Gartner, J.W., 1993. Tidal, residual, intertidal mudflat (TRIM) model and its application to San Francisco Bay, California. Estuarine, Coastal and Shelf Sciences 36, 235–280. Durand, J.R., Guiral, D., 1994. Hydroclimat et hydrochimie. In: Durand, J.-R., Dufour, P., Guiral, D., Zabi, S.G.F. (Eds.), Environnement et ressources aquatiques de Côte d’Ivoire Tome II, Les milieux lagunaires, éditions de l’ORSTOM. Fernandes, E., Dyer, K.R., Niencheski, L.F.H., 2000. Calibration and validation of the TELEMAC 2D model of the Patos lagoon (Brazil). Journal of Coastal Research 34, 470–488. Lopes, J.F., Dias, J.M., Dekeyser, I., 2001. Influence of tides and river inputs on suspended sediment transport in the Ria de Aveiro lagoon, Portugal. Physics and Chemistry of Earth 26 (9), 729–734. Kowalik, Z., Murty, T.S., 1995. Numerical Modelling of Ocean Dynamics. Advanced Series on Ocean Engineering. World Scientific Publishing, London, vol. 5, pp. 1– 6. Nameche, T.H., Vasel, J.L., 1998. Hydrodynamic studies and modelization for aerated lagoons and waste stabilization ponds. Water Research 32 (10), 3039–3045. Pouvreau, N., Brenon, I., Mondé, S., Maurin, J.C., submitted for publication. El Niño impact on water mass circulation during the tropical monsoon in a tropical lagoon (Ebrié, Ivory Coast). Geo-Marine Letters. Tastet, J.P., 1974. L’environnement physique du système lagunaire Ebrié. Rapport de l’Université Abidjan, série documentation. Departement des Sciences de la Terre, vol. 11, 28p. Tastet, J.P., 1987. Effets de l’ouverture d’un canal d’accès portuaire sur l’évolution naturelle du littoral d’Abidjan (Afrique de l’Ouest). Bulletin de l’Institut de Géologie du Bassin d’Aquitaine, Bordeaux 41, 177–190. Varlet, F., 1978. Régime de l’Atlantique près d’Abidjan, Etudes Eburnéennes, cahier de l’ORSTOM, série Océanographie, VII.