Thèse de Doctorat en Océanographie Physique

Présentée par Pierrick Penven

Composition du Jury:

- Alain Colin de Verdière, Directeur de thèse
- Bernard Barnier, Rapporteur
- Geoff Brundrit, Rapporteur
- Xavier Carton, Examinateur
- Philippe Gros, Examinateur
- Robert Mazé, Examinateur
- Claude Roy, Examinateur

- Introduction
- 1 The Benguela
- 1 Geographical settings
- 2 Large scale
- 3 Atmospheric forcing
- 4 Along the West Coast
- 5 The spawning area: the Agulhas Bank
- 6 Variability
- 7 Summary

- 2 Recirculation and retention on the shelf in St. Helena
Bay
- 1 Interactions between coastal currents and capes
- 2 Model description
- 3 Analytical expectations
- 4 The reference experiment
- 5 Diagnostic analysis
- 6 Sensitivity tests
- 7 An upwelling plume ?
- 8 Standing coastal trapped waves in the lee of Cape Columbine
- 9 Retention induced by the attached barotropic eddy
- 10 Summary

- 3 A regional model of the South African West coast
- 1 Previous modeling work conducted in the Benguela
- 2 Model description
- 3 Configuration
- 4 Results for the low resolution model
- 5 Results for the high resolution model
- 1 Time averaged variables
- 2 Comparison with temperature and salinity data
- 3 Variability
- 4 Along the West Coast
- 5 Generation of cyclonic eddies by the Agulhas Current in the lee of the Agulhas Bank
- 6 Shear edge eddies of the southern Agulhas Current
- 7 Transport patterns from the Agulhas Bank to the South African West Coast

- 6 Summary

- Conclusion
- Bibliography
- About this document ...

The Benguela ecosystem, along the South-west coast of Africa is, with the California
Current, the Peru-Chile and the North African upwelling systems, one of the world's 4
major ecosystems driven by an upwelling along the eastern margin of the Oceans. Their
combined total area accounts only for 0.1 % of the total surface of the world oceans,
but they provide almost 30 % of the world's total fish catch [*Durand et al.,* 1998].
Furthermore, their yearly fluctuations explain most of the inter-annual variability of the
total marine fish catch. These fluctuations, showing years of high abundance and
dramatic collapses, result from the variability of the recruitment (which is the number
of young fish produced each year). The vulnerability of the fish larvae during the first
weeks of their lives when their displacement capabilities are limited, leaving them at
the mercy of the ocean for food accessibility or transportation, explains this large
variability in recruitment. This critical period implies that the number in a year
class is determined at a very early stage [*Hjort,* 1914,*Hjort,* 1926]. During this period, the
environment has a major impact on the survival rate of larvae. Bakun [1993] has
identified 3 classes of environmental processes that combine together to create a
favorable environment for recruitment:

- The processes of enrichment which supply the beginning of the food chain with nutrients. They involve upwelling and vertical mixing.
- The processes of concentration, that aggregate food, eggs and larvae together. These can occur in convergence areas such as fronts or when vertical stratification inhibits vertical movement.
- The processes of retention that keep eggs, larvae and juveniles in a favorable area for their survival.

In upwelling areas, the existence
of multi-variable and non-linear relationships between recruitment and
upwelling intensity is a recurrent pattern resulting from the interaction
between several environmental process [*Cury and Roy,* 1989,*Cury et al.,* 1995,*Durand et al.,* 1998].
The competition between
these different processes (enrichment, mixing, dispersion...)
leads to an "Optimal Environmental Window" that gives a
maximum for pelagic fish recruitment success in upwelling areas for a limited
averaged wind range ( 5-7 m.s) [*Cury and Roy,* 1989].

The Benguela upwelling system is a highly dispersive environment, where a strong
equatorward wind along the coast induces an offshore displacement of the surface
waters. Although important for the enrichment of the ecosystem in nutrients, this
divergence can have a detrimental effect on the recruitment: eggs and larvae are then
carried offshore, away from their coastal habitat. In the Southern Benguela, sardines
and anchovies, the most abundant pelagic species, have adapted their reproductive
strategies to the environmental constraints. They migrate to spawn on the western
Agulhas Bank, upstream of the food sources. Eggs and larvae are advected by the currents
towards the productive areas of the West Coast of South Africa. St Helena Bay, in the
North of Cape Columbine, is recognized as the most important nursery ground of the West
Coast of South Africa [*Hutchings,* 1992]. This area shelters the biggest fishing industry of
the country. The loss of biological material during transport from the Agulhas Bank
to the West Coast and the retention inside the nursery ground of St Helena Bay are
supposed to be the principal factors affecting the recruitment of sardines and
anchovies [*Hutchings et al.,* 1998].

The work presented in this manuscript is part of the VIBES (Viability of exploited pelagic fish resources in the Benguela Ecosystems and Stocks in relation with the environment) project. VIBES is a pluridisciplinary research project involving IRD (Institut de Recherche pour le Développement, France), UCT (University of Cape Town, South Africa), MCM (Marine and Coastal Management, South Africa) and LPO (Laboratoire de Physique des Océans, France). One of the scientific goals of VIBES is to improve our understanding of the spatial dynamics of the pelagic marine resources, the fisheries and the environment through modeling. The present work concentrates on the modeling and the understanding of the physical oceanic processes affecting pelagic fish recruitment in the Southern Benguela upwelling system.

To carry out this study, we use numerical tools in order to simulate the complex physical patterns observed in the Southern Benguela. We follow a step by step approach. We start by setting up idealized experiments in order to provide an understanding of the peculiarities of the circulation in St Helena Bay. At a later stage, a 3-dimensional realistic model is implemented to reproduce the dynamics of the ocean around the South western corner of Africa. The key processes of the dynamics of the Southern Benguela will be identified from idealized and realistic experiments. An analysis of these processes and a quantification of their impact on the transport, retention and dispersion of the biological material are performed in order to obtain the characteristic patterns affecting recruitment. The South western corner of Africa has been much studied because of the global climate implication of the inter-ocean exchanges that occur in this area. A high resolution model of this region might also give new insights on the physical processes involved in the South Atlantic-Indian Ocean exchange of properties.

The first part of the thesis concentrates on the description of the characteristic
elements of the Benguela dynamics. Numerous articles related to surveys conducted in
the Benguela upwelling system have been published during the last 30 years.
Several reviews [*Nelson and Hutchings,* 1983,*Shannon,* 1985,*Shannon and Nelson,* 1996,*Shillington,* 1998] provide a broad outline of the
observed dynamics of the Benguela. The bibliographic study conducted in this first part
of the manuscript provides a general description of the actual understanding of the
system and leads to the identification of key questions relevant to the thesis.

The second chapter presents the idealized experiments conducted to analyze the
peculiarities of the shelf circulation in St Helena Bay. The bay is situated North of
Cape Columbine, a step like variation of 100 km in the coastline. Associated with the
cape, the shelf broadens from 50 to 150 km. These topographic variations should
considerably alter the shelf dynamics. Two hypothesis are used to simplify the
problem. Firstly, the gentle slope of the shelf should allow the neglect of
processes related to stratification in the simulation of the shelf dynamics
[*Clark and Brink,* 1985]. Secondly, spatial and temporal wind variations are assumed to be of
secondary importance in comparison to the processes related to topography. Hence,
barotropic experiments are conducted, forced by a constant wind. These experiments are
conducted to test if a topographically induced process can balance the dispersion
caused by the wind forced coastal currents. Diagnostic tools are designed to help in the
understanding of the simulated process and a sensitivity analysis will explore the
shelf dynamics response to a range of wind forcing, bottom friction parameter and size
of the cape. An analytical solution in the form of standing shelf waves, illuminates this
important behavior of the shelf dynamics. A tracer of water age is integrated into
the model to quantify retention.

For the third chapter, a realistic regional model is implemented in order to produce a high resolution portrayal of the ocean dynamics surrounding the South-western corner of Africa and to explore the physical processes involved in the different biological stages leading to recruitment, from eggs to larvae and juveniles. A meeting organized at the beginning of the project and discussions with the different partners of the project allowed the selection of model requirements:

- The numerical model must be able to resolve the mesoscale features that develop over the coastal domain (like filaments, plumes, eddies, or coastal jets...).
- The model domain must include the main pelagic fish spawning and nursery grounds.
- It must be large enough to allow the relevant physical processes to fully develop, but small enough to obtain sufficient fine spatial resolution at a reasonable computational cost.

The Benguela upwelling system is unique in a way that the
African continent ends at around 34 S. This induces the highly energetic poleward
termination of the western boundary current of the Indian Ocean, the Agulhas Current,
to flow along the Agulhas Bank and somehow to interact with the Benguela upwelling
system. It retroflects South of the Agulhas Bank to flow back into the Indian Ocean. One
should note that the anticyclonic eddies shed at the retroflection area, the Agulhas
rings, are the biggest coherent structures observed in the Ocean. The handling of these
highly energetic structures and currents by a regional oceanic model of finite dimension
is a challenge that require specific treatments. Recently, long term simulations (of more
than 10 years) have been conducted using a regional oceanic model for the California
Current System [*Marchesiello et al.,* 2000]. The model employed is ROMS, the Regional Ocean Modeling
System. It uses a generalized nonlinear terrain-following coordinate, high order schemes
and new parameterizations that have been especially implemented to resolve with a high
level of accuracy the primitive equation of momentum along the shelf and the slope on a
regional scale. Though there is no equivalent of the Agulhas Current along the West
Coast of the United States, we expect to obtain long-term meaningful results using the
same tool for the Benguela upwelling system. The validation of the model results will be
done through comparison with data. The study of the variability of the system and of
typical mesoscale processes will give insights for the understanding of the Benguela
dynamics. Special attention is given to the model solution on the shelves along the
South and West coasts, and comparison is also made with the results of the idealized
experiments. If the realistic model solution is satisfactory, it will be possible to use
the model to explore transport mechanisms from the Agulhas Bank to West Coast and
retention processes in the coastal domain. This is done by introducing a passive
tracer that simulates eggs and larvae transport behavior.

Following this approach, we expect to provide a better understanding of the dynamics of the Southern Benguela as well as necessary tools for the ongoing study of the dynamics of the recruitment.

1 The Benguela

The fisheries of the South African West Coast being of large economical importance, an important effort has been directed by South African marine research institutes to analyze the ecosystem. Thus, numerous studies have been undertaken in the last 30 years, involving for the physical part: hydrological samplings, current meters deployments, aerial atmospheric and sea surface temperature measurements, ADCP current measurements, drifters deployments, satellite data analysis and theoretical studies. As a result, a thorough description of the system is available and the understanding of many important processes has significantly progressed. These results have been summarized in several reviews [

Les pêcheries le long de la Côte Ouest de l'Afrique du Sud étant d'une importance économique majeure, un effort considérable a été réalisé par les instituts de recherches marines Sud-africains pour analyser l'écosystême du Benguela. Ainsi, de nombreuses études ont été conduites durant les 30 dernières années, comprenant pour la partie physique: des échantillonages hydrologiques, le déploiement de mouillages courantométriques, des mesures aériennes des composantes atmosphériques et de la température de surface de l'eau, des mesures courantométriques par ADCP, le larguage de flotteurs dérivants, l'analyse d'images satellitales, et des études théoriques. Il en découle une descrition détaillée du système; et des progrès significatifs ont été obtenus dans la compréhension des principaux processus. Ces résultats ont été résumés dans différentes revues d'articles [

1 Geographical settings

[

2 Large scale

3 Atmospheric forcing

4 Along the West Coast

2 Circulation

[

[

[

4 The nursery ground of the West Coast: St Helena Bay

- What is specific in the dynamics of St Helena Bay that make it a successful nursery ground ?
- How does the transport work from the Agulhas Bank to the upwelling centers ?
- What is the impact of mesoscale activity on the transport patterns?

2 Recirculation and retention on the shelf in St. Helena Bay

In this chapter, we will concentrate on the first question listed in the summary of the first chapter: "Why is St. Helena Bay such a successful nursery ground ?". The shelf being large in St. Helena Bay, idealised barotropic numerical experiments are conducted in order to explore the interactions between an equatorward, upwelling favorable, wind forced current and the topogaphy of the Bay. Diagnostic analysis and analytical calculations bring to light the dynamics involved in the simulations. The impact of the circulation on the retention of biological material in the Bay is explored through a tracer marking the age of the water masses.

Dans ce chapitre, nous nous concentrerons sur la première question énoncée dans le résumé du chapitre pr'ecédent: "Quelle est la cause du succès de la nourricerie de la Baie de Ste Hélène ?". La Baie de Ste Hélène présentant un large plateau, des expériences idéalisées barotropes sont mises en place afin d'explorer les interactions entre un courant vers l'équateur, forcé par un vent favorable a l'upwelling, et la topographie de la baie. Des analyses diagnostiques, et des calculs analytiques éclairent la dynamique impliquée durant les simulations. L'impact de la circulation sur la rétention des composantes biologiques est quantifiée à l'aide d'un traceur représentant l'age des masses d'eau. The upwelling of the West Coast of South Africa provides the necessary enrichment for the recruitment. But the driving mechanism of coastal upwelling, the offshore Ekman transport, at the same time, advects the larvae away from the productive area. Hence, the success of recruitment requires the presence of a retention process that keeps the larvae in the favorable area [

- Small S: flow fully attached, no eddy generated;
- Medium S: generation of an attached anticyclonic eddy;
- Larger S: shedding of anticyclonic eddies.

- Small S: generation of an attached cyclonic eddy (quickly formed but subsequently spins down);
- Larger S: shedding of cyclonic eddies.

2 Model description

Where is the operator:

The continuity equation takes the from:

Where:

- x is the along shore coordinate (positive towards the equator).
- y is the cross-shore coordinate (positive towards the open ocean).
- and are the vertically averaged flow velocity respectively in each coordinate direction.
- is the free surface elevation.
- is the total water column depth, , where is the ocean depth.
- is the Coriolis parameter, , where is the Earth angular velocity and is the latitude. In our case, because the time scale O(10 days) and the length scales O(100 km) are small enough, we can assume a constant Coriolis parameter as explained by Kundu [1990]. s at Cape Columbine.
- is the Earth gravity acceleration, m.s.
- is the lateral biharmonic constant mixing coefficient (m.s).
- is the linear bottom drag coefficient (m.s).
- and are the kinematic surface momentum fluxes (wind stress) respectively in each coordinate direction (m.s).

The along shore velocities are forced by the along shore wind and the free surface remains in geostrophic equilibrium with the along shore velocities. In order to satisfy equation (2.7) and the fact that there is no cross-shore flow at the coastal boundary, the cross-shelf transport has to vanish everywhere [

If the maximum depth is 500 m, the solution is nearly stationary after 40 days with along shore velocities:

This result shows that bottom friction allows us to expect for the numerical experiments a steady solution after nearly 50 days with along shore velocities of the order of magnitude: , resulting from a balance between the wind stress and the bottom friction. For example if the wind stress value equal 0.1 N.m, after 50 days the mean along shore velocities should be m.s.

4 The reference experiment

- the Rossby number,

- Because of the use of a biharmonic operator, the Reynolds number takes
the form:

- The Reynolds number associated with bottom friction,

which is equivalent to the 'island wake parameter' P introduced by Wolanski et al. [1984]. A scaling analysis shows that it is equivalent to the parameter defined by Becker [1991] (The same analysis shows that the lateral boundary layer thickness defined by Becker [1991] is in our case: ). - The Ekman number,

- U is a characteristic velocity, m.s.
- f is the Coriolis parameter, .
- L is a characteristic length scale, for example the size of the cape: km.
- is the viscosity parameter, .
- is a characteristic depth, m on the shelf.
- is the bottom friction parameter, .

- Attached cyclonic eddy: before day 10, the flow detaches from Cape Columbine and generates an attached cyclonic eddy (figure 2.2-a, x=50 km y=100 km). The size of the eddy is approximately 60 km at day 10 and expands to a size of 110 km by day 50 (figures 2.2-b and 2.2-c). The presence of this stationary attached-cyclonic-eddy is in agreement with the in-situ measurements of Holden [1985] and the recent averaged ADCP data of Boyd and Oberlholster [1994]. It can be compared with the schematic representation of the currents in St Helena Bay (figure 1.13) made by Shannon [1985]. This is also in agreement with the experimental results of Boyer and Tao [1987a] for the cape on the left (Northern Hemisphere), the smallest Burger number and . Further, the presence of the cyclone and the strength of the velocities match the results of the 3D model of Oey [1996, see figure 12 and figure 13]. In the Santa Barbara Channel model, which includes baroclinic processes, Oey [1996] applied an equatorward wind stress similar to the forcing of the reference experiment. The bottom fiction is quadratic ( ) and the grid resolution is 5/3 km. The equatorward flow associated with a pronounced coastal upwelling is comparable with the barotropic velocities obtained here, and forms a stationary cyclonic eddy in the lee of Point Conception. The size of this eddy is approximately half the size of our barotropic eddy. This discrepancy might be due to the depth of the shelf (300 m versus 150 m in our experiment), the width of the shelf (50 km versus 150 km in our experiment) or the presence of the Santa Barbara islands that might block the cyclone extension.
- Influence of the shelf break: the steep shelf edge offshore (figure 2-b, y=150 km) apply a strong topographic constraint on the flow, prohibiting cross-topographic currents. Thus, mass conservation implies that the velocities between Cape Columbine and the shelf break (figures 3-a, 3-b and 3-c, for x=0 km and y=0 to 150 km) are stronger than in the other parts of the shelf. This can affect the detachment process. An experiment with no shelf break (figure 2.2-d) shows that at day 50, the size of the cyclonic eddy is approximately 60 the size of the eddy in the reference experiment. The value of the along shore velocities near the tip of the cape is 80 the value of the velocities in the reference experiment. Further, vortex squashing produces an anticyclonic bend on the shelf edge (figure 2.2-c, x=180 km, y=150 km) and a divide in the currents (figure 2.2-c, x=110 km, y=150 km). Its location corresponds approximately to the location of the Columbine divide described by Shannon [1985a], and it can be an explanation of this phenomenon.
- Upstream blocking: the artificial cape on the right seems to have no influence on the detachment processes, but it produces weak near shore velocities on the right of the shelf (figure not shown). This effect can be felt up to 300 km [O(external Rossby radius of deformation)] upstream of the cape. Because we use a large domain (900 km along shore), this phenomenon does not affect our area of interest. This has been tested using a smaller domain (600 km along shore) and the similarities between the solutions validate the use of the periodic channel.

Where is the vertically averaged flow velocity, is the wind stress and is a vertical unit vector. Because and , the terms of equation (2.14) are respectively equivalent to the terms of the vertically averaged momentum equation:

- Viscous terms are of an order of magnitude lower than the other ones. They have some relative importance near the tip of the cape (figure 2.3-b, x=40 km, y=100 km). As explained by Becker [1991], viscosity has to be small for detachment to occur.
- Around the external part of the eddy (figure 2.3-b, x=50 to 130 km, y=70 to 130 km), there is a competition between advection and ageostrophic pressure gradient. It appears that around the eddy (figure 2.3-b, x=140 km, y=100 km), the radius of curvature of the flow is approximately km and the tangential velocities are about m.s. Then the normal acceleration is m.s, which is close to the value of the advective acceleration ( m.s). This shows a cyclo-geostrophic equilibrium around the eddy. This advective acceleration, forcing the water particles away from the cape, seems to be responsible for the detachment.
- Away from perturbations (figure 2.3-b, for example y220 km), the wind forcing and bottom friction relative equilibrium controls the along shore velocities as in the analytical solution.
- Another equilibrium occurs where the velocities are weak: inside the eddy (figure 2.3-b, x=75 km, y=70 km) and in the upstream blocking area (x=650 to 850 km, y=0 to 60 km, figure not shown). In those places, the Coriolis acceleration is weak and a static wind stress-pressure gradient balance prevails.

2 Vorticity balance

- is the advection of vorticity added to the vortex stretching associated with relative vorticity.
- is the vortex stretching associated with planetary vorticity. Because the Rossby number is small, this term is much larger (10 to 100 times) than the vortex stretching associated to relative vorticity.
- As explained by Signell and Geyer [1991], the first term of is the vorticity dissipation by bottom friction, and the second one is the 'slope torque' which acts as a source of vorticity when there is a component of velocity normal to a depth gradient. These two terms are in the same order of magnitude. Because , the curl of bottom friction should be the same order of magnitude as the advection of vorticity.
- The first term of
is the Ekman pumping associated with the wind stress curl and
the second term is, by analogy with the 'friction slope torque', a 'wind stress
slope torque' which can be a source of vorticity when the wind is normal to
a depth gradient. In our case, for and ,
the order of magnitude of the ratio between 'wind stress slope torque' and
advection of vorticity is:

This term can not be neglected. Its effects can be illustrated by traking the curl of the analytical solution for the velocities (equation 2.8). During the spin-up, because is a function of y, is also a function of y. Thus the vorticity is:

In this case, the vorticity produced continually from the beginning of the experiment by the 'wind stress slope torque', is progressively dissipated by bottom friction and 'friction slope torque'. Thus, after 50 days, the stationary solution is irrotational. In the same manner as the 'friction slope torque', the 'wind stress slope torque' appears because surface and bottom stresses have a stronger effect in shallow waters than in deep waters.

- The balance between advection of vorticity and vortex stretching occurs almost everywhere where the slopes are strong: on the shelf break (figures 2.4-a and 2.4-c, y=150 to 200 km) and in the bay (figures 2.4-a and 2.4-c, y=0 to 60 km)
- Around the external part of the eddy, where the shelf is relatively flat and the dynamics are cyclo-geostrophic (see previous section), the curl of bottom friction balances the advection of vorticity (figures 2.4-a and 2.4-b, x=50 to 130 km, y=70 to 130 km). This balance seems to follow the contour of the eddy, and might control its extension.
- As pointed out in the previous section, the lateral viscosity has some importance near the tip of Cape Columbine. In figure 2.4-d, the viscous boundary layer is clearly seen for x=0 to 50 km and y=100 to 110 km. Past the cape, there is a detachment of this boundary layer (figure 2.4-d, x=50 to 80 km, y=115 km).
- In shallow waters, the friction and wind stress slope torques start to have a strong influence and seem to be in balance for x80 km and y=0 to 10 km (figures 2.4-b and 2.4-e).

This length scale can be seen as a frictional e-folding distance and is equivalent to the eddy length scale described by Pattiaratchi et al. [1986] and Wolanski et al. [1984]. It is also equivalent to the frictional length scale tested by Signell and Geyer [1991]. Taking the analytical result (equation 2.9) for the characteristic velocities, the equation (2.20) becomes:

That gives us a characteristic eddy length scale which is a function of the wind stress and of the linear bottom friction parameter. This length scale can be compared to the size of the eddy. In this example, = 150 m, m.s, and m.s so that km (the difference with the model outputs can be seen in figure 2.2).

- to
- to
- to
- as in the reference experiment.

- to
- to
- to
- to
- to .

3 Influence of the size of the cape

- In the bay, the drag induced by the presence of the cape produces an averaged weaker current as the size of the cape increases. This averaged velocity ranges from 32 cm.s for a cape of 25 km to 22 cm.s for a cape of 50 km (for a wind stress of 0.1 N.m).
- The shelf break acting as an offshore barrier, mass conservation implies a stronger current at the tip of the cape for a larger cape than for smaller ones. The velocities at the tip of the cape range from 56 cm.s for a cape of 25 km to 80 cm.s for a cape of 150 km (for a wind stress of 0.1 N.m).
- These large differences in velocity, imply that a scaling of the eddy length only dependent on the wind stress is no longer valid: large variations in the size of the eddy depends on the size of the cape (see figure 2.10 and figure 2.11).

To avoid the generation of numerical noise, biharmonic viscosity has been added. At the model initialization, the value of the tracer is 20 everywhere, except on a narrow band of 10 km at the tip of the Cape (x 30 km, y =110 km) where it has a value of 10, accounting for the coastal upwelling. During all the simulation, the tracer is nudged towards 10 in this band. Although the offshore Ekman drift is not taken into account, this experiment is performed to simulate the characteristic sea surface temperature pattern observed in St Helena Bay.

8 Standing coastal trapped waves in the lee of Cape Columbine

2 Wave lengths selected by a mean along shore current

For an observer moving with the cape, in the absence of wind stress, the vertically averaged momentum equation (2.15) and the continuity equation (2.4) take the form (removing the subscripts for the coordinates):

With the variables made dimensionless by the characteristic values defined in section (2.4) ( is a characteristic time scale, days), equations (2.24) leads to:

where and are the Rossby and the vertical Ekman numbers defined in section (2.4), is the horizontal Ekman number associated to the biharmonic operator, and is the external Rossby radius of deformation. In the regime of parameters of the reference experiment (section 2.4), , , and are small compared to 1. 400 km is greater than the characteristic length scale (100 km) of our problem, allowing the use of the rigid lid approximation. Although no constraint is given on the value of in comparison to , equations (2.25) are linearized keeping the term of advection of momentum by . Hence the dimensional remaining equations of motion are:

Equations (2.26) show that we are looking for a standing process looking from the point of view of a moving cape. The resulting vorticity equation takes the form:

where the vortex stretching balances the advection of vorticity due to the displacement of the frame. Because bottom topography is defined in the fixed referential, it does not make sense that variations of bottom topography move from the cape point of view. Hence, H must not be variable in the along shore direction. Equation (2.27) becomes:

The continuity equation in (2.26) is not divergent for the transport and allows us to define a transport stream function of the form:

Introducing the transport stream function into the vorticity equation (2.28) yields to:

The vorticity equation (2.31) can be linearized as done by Wilkin and Chapman [1987] by using a bathymetry that follows an exponential function:

Where is the position of the offshore boundary. This gives:

Equation (2.33) accepts solutions in the form of standing shelf waves:

Introducing the wave solution (2.34) into (2.33) gives for :

As in section (2.2) an the analysis of Wilkin and Chapman [1987], we will suppose that the offshore boundary is closed by a wall at . It has been demonstrated that the presence of a wall at the shelf edge does not affect dramatically the shelf wave structure and dispersion relation [

Introducing the solution (2.36) into equation (2.35) selects an along shore wavenumber for each mode in the form:

The full solution of the vorticity equation (2.33) can be write in the form of a sum of standing waves:

In the Southern Hemisphere, the Coriolis parameter f is negative. Thus, equation (2.37) implies that lee shelf waves can form only for positive , accounting for an equatorward eastern boundary current. A more general condition for the presence of a lee shelf wave of mode n is:

If the relation (2.39) is not satisfied, is imaginary and the wave is evanescent. For only evanescent waves can be generated. Following Lighthill [1966], lee waves produced by a moving perturbation have to propagate at a phase velocity equal to the speed of the perturbation. Taking the propagating wave solution of Wilkin and Chapman [1987], we obtain , which is identical to equation (2.37). The condition (2.39) says that standing lee shelf wave can only exist if is opposite to the shelf wave propagation and smaller than the fastest shelf wave phase celerity. Following the same approach of the section (2.5.2) , the wind forced characteristic velocity defined by equation (2.9) can give a reasonable value for in equation (2.37). We obtain a standing shelf wave length for each mode as a function of the wind stress:

To compare this result to the outputs from the previous experiments, the topographic parameters have been chosen: , km and m, so that the exponential topography is relatively close to the bathymetry of the numerical model in St. Helena Bay (2.2) (figure 2.14).

Giving as a function of :

The velocity () offshore of the cape and the presence of the cape at x=0 imply that the along shore velocity, solution of the vorticity equation (2.27), must have equal values at x=0 (in the frame moving with the cape):

This implies a wave solution in the same order of magnitude of . Hence, the term has the same importance as the term in the addimentional momentum equation (2.25). Solving the linear vorticity equation (2.27), applying the boundary condition (2.43) for x=0, is equivalent asking if a set of linear propagating waves can account for the flow generated just at the back of a moving cape. The frictional boundary layer is no longer necessary to explain the redistribution of the flow behind the cape; this can be done by a set of linear standing waves. The boundary condition at x=0 for the transport stream function accounting for the lee shelf waves is:

One can note that is continuous and that , in agreement with the properties of the standing waves. For the following we will define and . For x=0, pressure and transport should be both continuous. In this case, although pressure can be obtained from the along shore momentum equation, there is no information for the pressure for . This information could be obtained by deriving also a wave solution upstream of the Cape (where the mean current is ). To stay simple, we will keep only local conservation of the transport for the matching conditions at x=0. This gives:

Because , we obtain:

Introducing the value of :

With,

To confirm the validity of the assumptions made previously, a numerical experiment using SCRUM has been conducted. The configuration is the same as the reference experiment described in the section (2.4), except for the bottom topography and the value of the wind forcing. In this experiment, the bottom topography follows the equation (2.32) with m and (see figure 2.14). The value of the constant wind stress is fixed at 0.05 N.m. The solution is stationary after 50 days, thus a transport stream function can be extracted from the model outputs. The transport stream function and the barotropic velocities in the lee of the cape, for the model at day 100, are shown on figure (2.17-a). Using this topography, no recirculation is visible, the current follows the lee side of the cape to fill the bay. Nevertheless, large standing waves remain in the lee of the cape. They exhibit wave lengths ranging from roughly 50 km in the bay up to 100 km for the small oscillations visible near the offshore boundary. The averaged value of the along shore velocities is 0.1 m.s, which is 40 % less than the wind forced velocities expected if there was no coastline variations (equation 2.9). This accounts for the drag induced by the cape on the wind forced circulation. The wave pattern is rapidly damped with increasing x, and oscillations are hardly visible after 3 wave lengths. The total transport is about 3.5 Sv. The transport isocontour closest to the coast is moving slightly offshore with increasing x, due to the presence of the downstream cape associated to the periodic channel.

Where is the mean value of the bottom topography and r is the linear bottom friction parameter defined in section (2.2). This gives an e-folding length of 50 km. The new solution is shown on figure (2.17-c). It coincides relatively closely to the numerical solution (figure 2.17-a). This result confirms the assumptions made in deriving the standing waves equation and emphasizes the importance of bottom friction. Another discrepancy is the difference between the numerical and standing wave solutions for the incoming current at x=0. A remedy should be to resolve the standing wave dynamics upstream of the cape and to add a boundary condition on the free surface at x=0 as explained previously.

accounting for a flat shelf rising at the coast. Ball [1967], derived the linear barotropic equations of motion over this topography for along shore propagating waves with no offshore limit. He found solutions in the form of edge waves. The same approach is applied in the case of standing waves. Therefore, as in section (2.8.2), we look for solutions in the standing wave form , where is a function of y only. Introducing this form for each variable in the linear equations of motion (2.26), we obtain the system:

Where all the variables are now only y-dependent. The solution of the system (2.51) for (the linear vorticity equation) is:

with finite at the coast and zero at infinity. Introducing the value of H and applying the variable transformation:

We obtain:

Following Ball [1967], this equation accepts solutions in the form:

where

and

In order to keep finite for , we must have . The ratio (2.57) shows that the series (2.55) is divergent unless it terminates. To terminates the series, an integer n must exist such that:

Thus, selecting the wavelengths of the standing edge waves:

The number 1 on the right of equation (2.60) is the time forcing term. To be consistent with the numerical SCRUM model, the equation (2.60) has been rewritten in the flux form and for the sake of numerical stability, biharmonic viscosity has been included.

has been kept as small as possible, and because in all experiments is of the order of , viscosity should not perturb the solution. T is kept at zero at the upwind boundary. Away from the boundary, T increments continuously. To test this, T has been introduced in an experiment with a rectilinear coastline and a flat bottom. Using the former analytical results, at day 50, when the solution is stationary (equation 2.9), the time since a water particle has left the upwind boundary is only x-dependent:

The rectilinear coastline numerical experiment is in agreement with this solution (figure not shown).

3 A regional model of the South African West coast

Setting up a high resolution numerical model of the ocean circulation in the surroundings of the South and West coasts of southern Africa was the direction chosen by the VIBES project to explore the physical processes affecting fish, eggs, larvae and juveniles during the recruitment cycle. This chapter provides a description of the main characteristics of the numerical tools that were set up. A detailed analysis of the numerical model output is provided and is aimed at evaluating the validity of the modeling experiments. An illustration of the potential use of such numerical tools in fisheries oceanography is provided by a set of experiments designed to investigate the effect of transport on the fish spawning products using a passive tracer.

Afin d'explorer les processus physiques affectant poissons, ufs, larves et juvéniles durant le cycle de reproduction, la direction choisit par le projet VIBES consistait en la mise au point d'un modèle numérique à haute résolution de la circulation océanique autour des côtes Sud et Ouest de l'Afrique australe. Ce chapître apporte la description des caractéristiques principales des outils numériques développés. Une analyse détaillée des sorties du modèle numérique est conduite et est employée afin d'évaluer la validité des solutions. Une illustration de l'utilisation potentielle de ces outils numériques en Océanographie des pêches est fournie par une suite d'expériences utilisant un traceur passif, développées pour étudier les effets du transport sur les produits de la ponte des poissons.

With the vertical boundary conditions prescribed as follows:

Where,

- x, y, z are the coordinates in the Cartesian frame (z being the vertical, increasing towards the top)
- u, v, w are components of the velocity vectors in this frame
- f is the Coriolis parameter
- is the dynamic pressure
- , , , are the forcing terms
- , , , are the dissipation terms
- T is the potential temperature of the Ocean
- S is the salinity of the Ocean
- P is the total pressure
- is the total in-situ density
- g is the acceleration of gravity
- is the free surface elevation
- , , are the vertical turbulent mixing coefficients, defined by a vertical turbulent closure scheme
- , are the surface wind stress components
- is the surface heat flux
- is the evaporation minus the precipitation
- , are the bottom stress components, the bottom
stress is parameterized in a sum of linear and quadratic terms:

- H is the resting thickness of the water column

(82) |

As an extension to standard terrain-following transformations, a nonlinear stretching of the vertical coordinate is applied that depends on local water depth [

(83) |

(84) |

(85) |

(86) |

(87) | |||

(88) |

Here, and are the scale factors which relate the differential distances to the physical arc lengths (figure 3.1). Coastal boundaries can also be specified as a finite-discretized grid via land/sea masking.

4 The pressure gradient scheme

The first term of the right involves the variation of pressure along a constant -surface and the second is the hydrostatic correction. Near steep topography, these 2 terms are large, comparable in magnitude and tend to cancel each other. A small error in computing either term can result to a relatively large error in the resulting horizontal pressure gradient [

- Reducing the truncation error in the derivation of equation (3.27) by subtracting an horizontally homogeneous averaged density to the density field. This trick has an efficiency only for small domains, where the horizontal variations in density are limited.
- Interpolating density back to z levels before computing the pressure gradient. Problems can arise with the lowest and highest levels that could require extrapolations over steep topography.
- Using higher-order numerical schemes.
- Retaining integral properties. The best pressure gradient formulation should minimize truncation errors while retaining integral properties such as mass, energy and vorticity.

Hence, vertical variations in the horizontal pressure gradient are given by an integral of the Jacobian:

Song [1998] defined the standard Jacobian formulation as the second order central difference discretization of equation (3.29). He proposed another scheme, the weighted Jacobian, centered in z space rather than in s space, as for the standard Jacobian. In an idealized case, Song [1998] shows that whereas the standard Jacobian outperforms the weighted Jacobian when the hydrostatic consistency condition is satisfied, the weighted Jacobian gives superior results if the condition is violated (which is often the case in realistic configurations). The conservation of momentum and energy and the accurate representation of the bottom pressure torque has been validated [

3 Configuration

1 The grids

- the domain must be large enough so that the most important dynamic features for the transport of eggs and larvae have enough space to develop. This includes the upwelling filaments that extend several hundred of km offshore, the Agulhas retroflection, etc...
- the domain must be small enough so that we can keep a high resolution at a reasonable computational cost.
- the open
boundaries should cross the current at right angles. They should be placed where
there is a minimum in current velocities and in variability, they should also be
placed where the topographic gradient perpendicular to the boundary is as small as
possible to avoid along-boundary currents [
*Penduff,*1998].

- a low resolution one where the resolution is linearly ranging from 18 km at the coast to 31 km offshore.
- a high resolution one where the resolution is linearly ranging from 9 km at the coast to 16 km offshore.

Empirical studies have shown that robust results are obtained if r does not significantly exceed a value of 0.2 [

2 Surface fluxes

The term is computed as from the different contributions for the heat fluxes: infrared, sensible heat, and latent heat [Siefridt, 1994]:

Where is the constant of Stefan, is the specific heat of the atmosphere, is the sensible heat transfer coefficient, is the wind speed, is the latent heat transfer coefficient, is the latent heat of vaporization, and is the sea level specific humidity. The term is portrayed on figure 3.12. For a mixed layer depth of 50 m it corresponds to a nudging coefficient toward the climatology ranging from about 50 days in the South to a maximum 90 days in the West Coast. Figure (3.13) shows the sea surface temperature used for the correction of the surface heat flux, obtained from the COADS dataset. In this dataset, the Agulhas Current and the upwelling system are poorly represented.

This method has been chosen for our configuration, using a nudging coefficient, corresponding to 75 days, the same order of magnitude as the averaged value of the heat flux correction term. Unfortunately, a bug has crept into the model and the salinity flux remained equal to zero during all the simulations. Nevertheless, the cold water doesn't evaporate dramatically in an upwelling system and the precipitation in the Benguela is low (figure 3.14). This induces low values for the E-P field of the West Coast. The salinity fluxes coming from the lateral boundaries should overwhelm the surface flux. Hence, we expect the solution to not drift excessively from the climatology values.

3 Initial and boundary conditions

If the propagation is towards the open ocean, the features produced inside the model are evacuated following the wave equation:

If the propagation is towards the interior, the value at the boundary is nudged towards data:

The tangential and normal propagations are discretized in ROMS in an upstream biased fashion, where the normal component is treated implicitly. Hence, this scheme allows large time steps without loss of stability. At the corners the averaged value of the two adjacent boundary points is taken. Mass conservation is enforced around the model domain [

- The solution is weakly relaxed towards data in outflow conditions [right term of equation (3.36)].
- The solution is weakly nudged towards data in nudging bands close to the boundaries. The nudging coefficient is linearly decreasing in the 6 points near the boundaries (figure 3.15).
- Whereas no explicit mixing is mandatory
in the model domain, a sponge layer with linearly increasing lateral mixing
coefficient (figure 3.16) filters out the possible numerical noise or
reflections produced by the open boundaries. Recent simulations of the US West
Coast ocean model [
*Marchesiello et al.,*2000] have shown that with the active boundary condition schemes, the sponge layers were no longer necessary.

- days for all the variables
- days for the velocities
- days for the tracers

The sign in equation (3.41) depends on the position of the boundary. For the phase velocity, we assumes that the waves approaching the open boundary are mostly non dispersive surface gravity waves. Hence, c in equation (3.41) is fixed at (g being the gravity acceleration and H the water column depth). Equation (3.41) becomes;

This open boundary scheme can be seen as a one way nesting scheme that conserves mass. The differences between the specified values ( and ), and those calculated by the model ( and ) are forced to radiate at the speed of the external gravity waves [

- The solution was dependent of the arbitrary choice of the no-motion reference level.
- Extrapolation was necessary to obtain data on the shelf and gave spurious recirculation.
- The Agulhas Current was badly represented (see figure 3.13).

4 Results for the low resolution model

1 Spin-up

2 Time average

5 Results for the high resolution model

1 Time averaged variables

Hence, the time averaged transport is non-divergent and a time averaged transport function can be extracted from the time averaged barotropic velocities. The resulting time averaged transport function for the high resolution experiment is portrayed on figure (3.36). It shows that the averaged transport associated with the Agulhas Current is around 65 Sv, and that the averaged transport of the simulated part of the Benguela ranges from 10 Sv to 20 Sv. These values can be compared to the measured transport of 75 Sv for the Agulhas Current and of 15 Sv for the a similar part of the Benguela current (figure 1.5) [

2 Comparison with temperature and salinity data

3 Variability

where is the variance along the major axis and is given by

and is the variance along the minor axis given by

Note that the eddy kinetic energy () is connected to the velocity variance by

The subsurface variances ellipses are represented for the high resolution model for z = -50 m (figure 3.43-top). They show a high degree of similitude with the variances ellipses derived from Geosat satellite altimer data (figure 3.43-bottom). The remarks made for the eddy kinetic energy are also valid for the variances ellipses: good comparison along the west coast, whilst the ellipses are smaller for the model outputs in the Agulhas retroflection area. The incoming variability pattern of the Agulhas Current is illustrated by the two elongated ellipses on the Eastern part of the Agulhas Bank for the satellite analysis (figure 3.43-bottom). This shows important cross isobath variations (characteristic of the meanders and natal pulses) in the Agulhas Current around 23 E. As explained previously, this variability generated upstream of the area is not resolved by the model. As a consequence, the simulated variability in the Agulhas retroflection area is two times smaller than the observations. Both the model results and the observations show an important anisotropy in the variability, mostly near strong topographic gradients. This anisotropy is important along the southern tip of the Agulhas Bank. The variability appears to be more isotropic on the south west of the Agulhas Bank (where the Agulhas rings are shed) for the observations. This behavior is not noticeable in the model solution, the Agulhas rings being quasi-immediately in contact with the offshore open boundary. Along the West Coast, where altimeter data are available, the model and satellite variances ellipses compare fairly well. This is especially true near the Cape Peninsula, where the presence of the cape induces a strong anisotropy in the subsurface current variability. Animations of the model output reveals that cyclonic eddies are mostly generated from Cape Columbine, Cape Peninsula and the Southern tip of the Agulhas Bank. These areas of eddy generation coincides with areas of strong anisotropy of the current variability. Another interesting feature is the anisotropy of the variability close to the open boundaries. It happens that the open boundary inhibits the cross boundary velocity variance. This can be an effect of the Flather open boundary scheme that constrains the cross boundary barotropic velocities to remain close to smooth climatology data values. One can conclude from this section that though the strong variations in the Agulhas Current coming from the Indian Ocean are not taken into account in the model solution, and disregarding the Agulhas ring behavior when they have a size comparable to the model width, the variability developed in the model in the form of eddies, plumes,... compares remarkably well to observations. This is particularly true along the South African West Coast.

4 Along the West Coast

- A small cyclonic eddy, characterized by core of colder water located at 17.2 E and 33.6 S, has detached from the Cape Peninsula upwelling center and is advected in a north-westward direction.
- A large upwelling plume, showing the characteristic inverted s shape described by Shannon [1985], extends from Cape Columbine.
- Upwelling filaments extend from a well defined Namaqualand upwelling center at 30.5 S.

- A reverse flow of about 10 cm.s is visible on the 200 m isobath on the Eastern Agulhas Bank.
- A sluggish circulation is present on the Agulhas Bank.
- A shelf edge jet of about 25 cm.s flows from the Southern tip of the Agulhas Bank towards Cape Peninsula and Cape Columbine.
- A convergent flow occurs on the western margin of the Agulhas Bank to fill the Cape of Good Hope jet.
- The flow North of Cape Columbine follows the 200 m isobath that curves inshore at 31.5 S and moves offshore at 30 S with characteristic velocities of 20 cm.s.

5 Generation of cyclonic eddies by the Agulhas Current in the lee of the Agulhas Bank

6 Shear edge eddies of the southern Agulhas Current

- The grid is regular and isotropic ( km). The length of the domain is 700 km in the x direction and the width is 300 km in the y direction.
- For the sake of simplicity, the model domain consists of a periodic channel along the x direction.
- The bottom topography is defined analytically and is periodic to satisfy mass conservation in the periodic channel. Figure (3.60-a) represents the bottom topography employed. It consists of a large shelf ending on a slope. A perturbation of the slope in the middle of the domain account for the Agulhas Bight.
- In the vertical, 20 s-levels are evenly distributed.
- The equation of state takes a linear form depending solely on temperature: T.
- All the surface fluxes are set to zero (no wind stress, no heat flux)
- No bottom flux for temperature and linear parameterization for the bottom momentum flux: m.s.
- The vertical mixing coefficient for momentum and temperature are constant: m.s, m.s.
- Figure (3.60-b) shows the cross section of the analytical function employed for the temperature initial condition. It reproduces a typical cross section across the Agulhas Current. The velocity and free surface elevation are set to zero at the model start.
- The temperature is relaxed towards its initial value with a nudging time of 5 days during all the simulation.
- The Coriolis parameter f is constant equal . The related processes are not taken into account.

7 Transport patterns from the Agulhas Bank to the South African West Coast

- Feeding of the adults during the spawning on the Agulhas Bank.
- Feeding of the larvae.
- Transport of the eggs and larvae from the Agulhas Bank to the Benguela upwelling system.
- Migration and retention of the larvae in the Coastal productive area.
- Feeding of young recruits.

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- Cyclonic eddies that are shed from the southern tip of the Agulhas bank, where the Agulhas Current detaches from the topographic control.
- Shear edge eddies that are formed on the eastern Agulhas Bank, where the Agulhas Current overshoots the concave part of the shelf break.

- to study the dynamics of mesoscale processes related to retention within the St Helena Bay nursery ground
- to develop a high resolution regional model to simulate the shelf circulation along the South and West coasts of South Africa.

The barotropic study reveals that a wind driven equatorward current can generate a standing process in the lee of a cape. In the case of St Helena Bay, the numerical study shows that this process should take the form of a standing cyclonic eddy, controlled by a balance between advection and bottom friction. A length scale derived from this balance, which can be considered as an e-folding length scale, can then predict the size of the eddy as a function of the wind stress and the bottom friction parameter. Sensitivity tests reveal some discrepancies between this length scale and the size of the eddy, especially for smaller capes where the slope in the bay has gained importance. In the presence of bottom slope, standing shelf waves are more likely to develop. An analytical study shows that standing shelf waves can be excited by a mean current past a cape. The tracer, representing the age of the water, has been introduced in the model. It exhibits the retention induced by the standing recirculation process. Upwelling favorable winds can generate currents responsible for eggs and larvae dispersion. But, at the same time, these currents can induce recirculation in the lee of capes like Cape Columbine that can trap eggs and larvae in a favorable environment.

The particularity of the Benguela system, with the Agulhas Current retroflecting just South of the area of interest did not facilitate the implementation of a realist 3-D model of the region. Tests have been conducted using a low resolution configuration to set-up the open boundary conditions. The treatment of the bottom topography for this simulation gave an incorrect representation of the shelf circulation and the detachment of the Agulhas Current. For the high resolution experiment the solution is more satisfactory, and compares with observations for most of the processes. They include:

- The localized upwelling centers of Cape Peninsula, Cape Columbine, Namaqualand and Lüderitz.
- The upwelling eddies that are shed from the Cape Peninsula and Cape Columbine
- The upwelling plume that extend from Cape Columbine
- The filaments that extends from the upwelling front
- The equatorward baroclinic jet associated with the upwelling front
- The Columbine divide
- The poleward subsurface counter-current and the poleward undercurrent along the shelf break
- The poleward deep motion along the slope
- The weak circulation on the Agulhas Bank
- The convergent currents on the western margin of the Agulhas Bank that feed the Good Hope jet
- The cyclonic eddies shed from the Agulhas Current in the lee of the Agulhas Bank
- The shear edge eddies along the eastern and southern part of the Agulhas Bank
- The Agulhas retroflection

- The time-averaged modelized sea surface temperature along a coastal
narrow band North of Cape Columbine is 2 to 3 C smaller than the
temperature observed from satellite imagery. It has been observed that the intensity of
upwelling favorable wind stress is smaller along the coast North of Cape
Columbine [
*Jury,*1988], but this pattern is not present in the dataset used to force the model. This can explain the difference between the model and the observations. - The subsurface eddy kinetic energy is 2 times smaller than the eddy
kinetic energy derived from altimeter data in the Agulhas retroflection area.
There is 2 possible causes for this difference. Firstly, the Agulhas Current
shows important variations that are generated upstream of the model domain and
propagate with the flow, like the Natal pulses [
*De Ruijter et al.,*1999a,*Lutjeharms and Roberts,*1988]. The seasonal time-averaged data set employed to force the Agulhas Current at the eastern open boundary does not inject this non-local variability into the model. Secondly, the western open boundary is close to the retroflection area and mights affect the Agulhas rings generation process. - The cyclonic weak motion observed in St Helena Bay and analyzed in the
second chapter is not present in the realistic model outputs. The treatment of
bottom topography for this level of resolution enhanced the slope of the shelf,
inhibiting the possible generation of this standing process.

A tracer, representing the probability of presence of an egg spawned on the western Agulhas Bank has been introduced to simulate the transport patterns between the Agulhas Bank and the West Coast of South Africa. It shows the negative effect of the upwelling favorable wind for the transfer from the Agulhas Bank to the West Coast and the positive effect of the mesoscale eddies and jet on the retention of the biological materials in the favorable areas. This is in agreement with the last result of the second chapter.

**Prospects**

- The realistic 3D model has been developed in order to produce an accurate
portrayal of the dynamics of the Southern Benguela to study the impact of the
environment on the recruitment of small pelagics. An individual based model (IBM)
has been developed by the VIBES group. This model allows the simulation of the path
of fish eggs, larvae and juveniles when they are released in the model domain. The
coupling of the IBM with the results of the physical model allows the simulation and
analysis of transport processes affecting the recruitment of sardines and anchovies in
the Southern Benguela. Specific scenarios (like strong upwelling or weak upwelling)
can be undertaken to understand the impact of the variability of the environment on
the living resources. The coupling of a coastal ocean model to an IBM constitutes
a powerful tool for the understanding of ecosystem dynamics. This technique has
been successfully applied to quantify the effects of advection on pollock larvae in
Alaska [
*Hermann et al.,*1996] and on cod and haddock larvae on George Bank [*Werner et al.,*1993]. - In the second chapter, we have shown the generation of a standing process in
the barotropic case. Is it still valid when stratification is taken into account ?
The comparison of the results with the observed circulation in St Helena Bay seems
to maintain this hypothesis, but the advection by a mean current is not clear in
the baroclinic case.
- The realistic model provides a large amount of information and specific
processes that can been studied from the model outputs. The forcing of the poleward
undercurrent and counter-current can be diagnosed by computing the different terms
of the momentum and vorticity equations from the model outputs.
Special attention can be given to the de-stabilization processes of the upwelling
front along the West Coast of South Africa. The quantification of energy
transformation mechanisms can lead to the indication of the type of instability
process that is responsible of the de-stabilization of the front.
- Simplified models and analytical analysis, inspired by the work of Gill and
Schumann [1979], of the shear edge eddies obtained on the Agulhas Bight could
explain the reason for these recurrent features. This process should be also present
on the coastal side of the other western boundary currents.
- The analysis of the results of the high resolution experiment allows us to
identify directions to follow in the future, in order to improve the quality of the
realistic simulation:
- The topography on the shelf near Cape Peninsula and in St Helena Bay
has been significantly altered during the smoothing process. The 100 m
isobath passes through the Cape Peninsula and the exaggerated slope of the shelf in St
Helena Bay can inhibit the generation of the cyclonic process, important for the
retention of biological material in the coastal area. The algorithm of topography
smoothing can be corrected in order to respect the general shape of the shelves.
Simulation with higher spatial resolution can allow the use of a more realistic
bottom topography, but at a larger numerical cost. A new pressure gradient scheme
is still in development at UCLA [
*Shchepetkin and McWilliams,*in preparation]. If this formulation gives the results expected, it could be possible to employ a more accurate bottom topography at the actual level of resolution. - The shedding of the Agulhas rings seems to have been constricted by
the vicinity of the eastern open boundary. This boundary should be placed at a few
hundred of kilometers offshore in order to allow a greater degree of freedom for the
detachment of the Agulhas rings.
- The level of eddy kinetic energy in the Agulhas area is 2 times
smaller for the model than for the observations. Although an important source of
variability for the Agulhas Current has been recognized to be the Mozambique
channel [
*Biastoch and Krauß,*1999], thousands of km upstream of our domain, the displacement of the western boundary around 28 E, where the Agulhas Current appears to be more stable, should enhance the simulation of the variability in the retroflection area. Another possibility could be the utilization of the direct outputs of AGAPE instead of using a seasonal climatology. In this case, the larger amount of data that should have to be treated to fit to the regional model grid dramatically increases the numerical cost of the preprocessing chain. We will rapidly reach the paradox that more cpu time should be necessary to prepare the experiments than to actually run them. In this case, in order to obtain a meaningful solution, it should be also necessary to enforce the compatibility of the surface forcing between the regional model and the AGAPE basin scale model. - A finer climatological dataset can be derived for the surface wind
forcing to obtain a sea surface temperature closer to the observations along the
west coast.

- The topography on the shelf near Cape Peninsula and in St Helena Bay
has been significantly altered during the smoothing process. The 100 m
isobath passes through the Cape Peninsula and the exaggerated slope of the shelf in St
Helena Bay can inhibit the generation of the cyclonic process, important for the
retention of biological material in the coastal area. The algorithm of topography
smoothing can be corrected in order to respect the general shape of the shelves.
Simulation with higher spatial resolution can allow the use of a more realistic
bottom topography, but at a larger numerical cost. A new pressure gradient scheme
is still in development at UCLA [
- Test experiments with low wind forcing, high wind forcing, warm water
intrusion from the North, or using a more variable wind stress can allow the
quantification of the response of the Benguela upwelling system on the interannual
variability of the external forcing. This response can dramatically affect the
recruitment.
- The use of realistic surface forcing and the comparison with the simulation
obtained in the present work can give a quantification of the direct impact of the
surface
forcing on the variability of the Benguela system.
- The use of embedded grids, in one way and in two ways, can resolve one of the
most important problem of coastal dynamics: the need for a high resolution solution
in the coastal domain in opposition to the need for a proper representation of the
effects induced by the large scale circulation. This method can be useful for the
inclusion of processes such as the variability produced by eddies generated as far
as the Mozambique Channel. Using these methods, it will also be possible to have
fine scale high resolution subgrids for the areas of interest such as bays like St.
Helena Bay, Saldanha Bay, or False Bay. It opens a wide field of non-academic
applications of the model solution for coastal management, harbor and industrial
installations, or pollutant dispersion studies.

Many other improvements can be added to the actual model to produce a better
representation of the Benguela ecosystem, such as the assimilation of data, the
introduction of tides, the modeling of the river outflows, or the modeling
of the primary production... Each increase of the complexity of the modelized
system, will result in an increase of the complexity of the solution. New tools
should then be designed to help the understanding of the key processes that are
structuring these solutions. Recently, an important effort has been conducted to
understand the dynamics of coastal ecosystems, an example is the work conducted for
the West Coast of the United States [*Miller et al.,* 1999]. The experience gained and the
tools designed for the study of the Benguela ecosystem could be applied to other
coastal domains of the world. Important fundamental insight could
be obtained by comparing the dynamics of the different domains.

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*Deep-Sea Res.*,*14*, 79-88, 1967. *Barnier et al.,*1998-
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