synthesis - numerical modelling of the strait of gibraltar.pdf

8/10/2019 Synthesis - Numerical modelling of the Strait of Gibraltar.pdf

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SYNTHESIS REPORT

Master Thesis - Civil Engineering

Prof. Schleiss Anton, thesis supervisorMr. J. Franca Mario, thesis coordinator

Mr. Gustav R. Grob, external advisorMr. Zeimetz Fraenz, tutorMr. Smaoui Hassan, tutor

* Corresponding author.Tel.: +41 78 9121076

E-mail address: [email protected]

Numerical modelling of the Strait of Gibraltar for the purpose of a

project to stabilize the level of Mediterranean Sea from the globally

rising ocean levels

Ha-Phong Nguyena*

aLaboratory of Hydraulic Construction, EPFL, 1015 Lausanne, Switzerland

REPORT INFO

Article history:

Received 20 June 2014

Keywords:

Finite difference

Numerical model

Sea level increase

Strait of Gibraltar

Tidal barrage

Tidal simulation

ABSTRACT

In recent year, the threat of the rising ocean level due to global warming endangers coastal area. To solve

flooding problems in the Mediterranean shores, a dam project within the Strait of Gibraltar, called

MEDSHILD, is proposed in order to lower the sea level of the whole region. The objective of this study is

to simulate the water exchange through the Strait by considering the tidal forcing and to determine an

optimal closure that allows keeping the Mediterranean level constant by considering a climate change

scenario of 50 centimetres. A two dimensional general circulation model called MECCA (Model for

Estuarine and Coastal Circulation Assessment) is used. It is a sigma coordinates, time varying free

surface, primitive equation ocean model and uses the implicit finite difference techniques to solve the

hydrodynamic equations. The model works under the hydrostatic and Boussinesq approximations. The

domain incorporates actual bathymetry in very high resolution. Uniform horizontal and vertical grid

spacing of 500 metres is used. The model is forced along the open boundaries (Atlantic Ocean and

Alboran Sea) through the specification of the semidiurnal tidal heights. As first results, computed M 2and

S2amplitudes and phases are in good agreement with data in literature. Model results indicate, also, that a

closed area equal to 90% is sufficient to maintain the Mediterranean constant, coupled with a non-

negligible increase of the Atlantic level. The potential total annual tidal energy that can be extracted from

the barrage is assessed to range between 680 and 1364 GWh.

2014 EPFL. All rights reserved.

1.Introduction

Since decade, the Strait of Gibraltar is an area of great strategic

importance, given its geographical position between Africa and Europe.

Its position at a crossroad between the Atlantic and the Mediterranean

constitue a major corridor for maritime traffic. Over the years, many

projects, like the dam of German architect Srgel or the railway tunnel of

Lombardi Engineering Ltd, were developed in order to make the Western

Mediterranean area a key exchange passage between Africa and Europe.

Nowadays, bridging the gap between the two continents is still relevant,

but for others reasons than economic. Indeed, many surveys (Nicholls and

Hoozemans 1996; Gonella et al. 1998; Brochier and Ramieri 2001;

Nicholls 2002; Snoussi, Ouchani, and Niazi 2008; Vargas Ynez 2010;

Cronin 2012; Jevrejeva, Moore, and Grinsted 2012; Horton et al. 2014)

highlighted the threat of the constantly sea level rise on the coastal area of

the Mediterranean, Black and Red seas. Risk of flooding, erosion, salinity

intrusion, safety of foundations, to name but a few of the most serious

cases currently threatening the coastal population, deltas and islands.

More recently, according to the fifth assessment report on climate change

of the Intergovernmental Panel on Climate Change (Church, J.A. et al.

2013), scientists expect an increase of seal level of 26 cm to 98 cm by

2100 against 18 cm to 59 cm in the Fourth Assessment Report (Meehl,

G.A et al. 2007). As a result, the coastal populations and areas will be

subject to more frequent risk of flooding and erosion, two phenomena

aggravated by the massive urbanization of seashores.

It is in this context that the International Sustainable Energy Organisation


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4 SYNTHESISREPORT

!! !

!!

!!

!!"!

K is the turbulence energy; l the mixing length defined in Equation (16);

!!the Prandtl number; !! ! !!!!"#the coefficient of friction.

2.4.

Model Grid and Bathymetry

Area covered by the model contains the Strait of Gibraltar, and is limited

by the two sub-basins on both sides of the Straits; namely the Gulf of

Cadiz and the Alboran Sea. The model domain extends longitudinally

from 6.241 to 4.567 West and 35 to 36.666 North. Horizontal grid is

made by 306 x 330 grid points. It is characterized by a uniform spacing

and a high spatial resolution of 500 metres in both directions in order to

well resolve the dynamic within the Strait of Gibraltar Sannino (2004).

The model topography was generated by linear interpolation of the depth

data on to each grid point of the model grid. The depth data were obtained

from the EMODnet Bathymetry portal (available at http://www.emodnet-

bathymetry.eu). Model bathymetry is illustrated in Figure (1) with the

main topographic features (from left to right): Spartel sill, Tangier basin,

Camarinal sill, Tarifa narrow.

2.5.Boundary and initial conditions

As shown in Figure 1 the domain is composed of two open boundaries

located at the Eastern and Western end of the computation domain. At

these boundaries, values of surface elevation (!) or mean velocity (!! !)

should be specified. A lot of setting for open boundary conditions exists,

however, in this study, boundaries conditions used are the same as used

by Sannino, Bargagli, and Artale (2002) and Sannino (2004). Indeed, they

are proven to give the best model results for an application in the Strait of

Gibraltar. A description of these boundaries is set forth hereafter. For boundary conditions on either side of the computational domain, they

need to ensure that phenomena (e.g. waves) generated inside the domain

can freely leave it without being reflected at the boundaries and

accordingly contaminate the interior solution (Schot 1992; Blumberg and

Kantha 1985). For the purpose of minimizing the effects due to wave

reflection at the open boundaries, a force Orlansky radiation condition

(Orlanski 1976) is used for the sea surface elevation (!). According to

Bills and Noye (1987), this can be state as follow:

!!

!!!

!!

!!"

!!!

!! !!" !

!"!

!!

!!!

!! !"!

!!!

!

!! !"!

!!"!

Where!!

! is the surface elevation at the i grid point for the open

boundaries at time step n; !" ! !!! !!! the Courant number in x-

direction; !!"

!!!the tidal elevation at grid point i and time step n-1;!!" the

time independent mean sea elevation at grid point i (Bills and Noye 1987;

Sannino 2004).

As explained by Sannino (2004), Equation (20) incorporates a radiation

mechanism that allows the undesired transients to pass through the open

boundaries, going out of the model basin, without contaminating the

desired forced solution . In Equation (20), the sea elevation at the grid

points (!!

! ) situated on the open boundaries should be specified. To

achieve this, values from literature (Candela, Winant, and Ruiz 1990;

Padman and Erofeeva 2005) has been used. Moreover, as suggested bySannino (2004), sea elevation values must be augmented by the time

independent mean sea elevation, !!" , equal to 12 metre at the Western

open boundary and to 0 meter at the Eastern open boundary. These values

were obtained from the model of Sannino (2004) in the following manner:

The time independent mean elevation (!!") value used at the open

boundaries is obtained running the model in barotropic mode. This model,

as the baroclinic version (three dimensional), has at the eastern and

western ends of the computational domain two open boundaries where

values of barotropic velocity and surface elevation must be specified. For

the surface elevation an Orlansky radiation condition (Orlanski 1976) was

used at the western boundary while a clamped to zero condition was used

for the eastern end. For the barotropic velocity a zero gradient condition

was used at both ends. In this way the barotropic model was able to freelyadjust the western surface elevation, after 180 days of simulation, to about

12 cm .

Concerning the velocity, a zero gradient condition is used for the depth

integrated velocity (!!!).

As the most energetic system in the Strait of Gibraltar is the tidal

dynamics, the model is forced at the open boundaries with the tidal

forcing. The main tidal harmonics are shown in Table 1.

Table 1 The main tidal harmonic

Symbol Period [hour] Description

Semidiurnal components

M2 12.42 Main lunar constituent

S2 12.00 Main solar constituent

Diurnal componentsK1 23.93 Soli-lunar constituent

O1 25.82 Main lunar constituent

The semidiurnal tides arise from thegravitational forces of the moon (M2)

and sun (S2) while the diurnal components originates from the declination

in the moons orbit about the earth (O1) and the corresponding solar

declination (K1). In order to study the dynamic of the Strait of Gibraltar to

tidal forcing, the model is forced with the main semidiurnal (M2and S2)

components. M2wave has a period higher than 0.5 day because every day

the moon offset slightly (1/28th turn) whereas the period of S2 is worth

exactly 0.5 day. Consequently, the two waves will angle slightly towards

each another. Note also that the amplitude of M2 is larger than S2 (M2 %

Figure 1 Model bathymetry. The colour levels indicate the water depth in

meter.


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2.7 S2). Consequently, M2 imposes the period with a small perturbation

from S2. The choice to limit the simulation to the semidiurnal component

is justify because 90% of the total kinetic energy in the Strait of Gibraltar

stem from the semidiurnal components M2 and Ss (Kinder and Bryden

1987; Kinder and Bryden 1988; Candela, Winant, and Ruiz 1990).

Finally, the resulting two major semidiurnal surface tidal elevations

forcing at the open boundaries of the domain is defined as:

! !!! ! !! ! !"# !

!! ! !

! ! !!"!

!

!!!

Where!! ! and !

! ! are the surface elevation amplitude and phase of

the nthharmonic of the tidal signal; !!its frequency. The semidiurnal tidal

elevation amplitude (!! ! ) and phase (!

! ! ) are obtained from the

TPXO 7.1 global model of ocean tides (Padman and Erofeeva 2005). At

the Western and Eastern boundaries, four and three points are specified in

MECCA respectively (Table 2). Linear interpolation from these points is

made for the entire boundaries with satisfactory results as the variation in

regional amplitude and phase are relatively small.

Table 2 Semidiurnal tidal elevation amplitude and phase enter at

the Western and Eastern end of the computational domain for the

interpolation in MECCA.

Latitud

e [N]

Longitude

[W]

M2 S2

Amplitude

[m]

Phase

[]

Amplitude

[m]

Phase

[]

36.6667 -6.2410 1.0092 54.61 0.3653 79.15

36.5000 -6.2410 1.0104 54.46 0.3658 78.32

35.5000 -6.2410 0.9705 56.29 0.3529 82.2

35.0000 -6.2410 0.9992 54.97 0.3609 80.83

36.1467 -4.5670 0.2075 53.82 0.0777 81.9

35.9067 -4.5670 0.2099 55.96 0.0788 83.65

35.2800 -4.5670 0.2084 59.15 0.0791 86.48

For example, the tidal signal forced at the middle of the Western

computational domain is shown in Figure 2. The combination of M2and

S2, known as beating, has a fortnightly modulation with a period of 14.79

days.

Time step is fixed to 10 seconds according to the CourantFriedrichs

Lewy (CFL) condition.

2.6.Model experiments

The model is initially run separately for the M2and S2constituent forcing

over 123 hours and 131 hours respectively in order to compare the results

(amplitude and phase) with observed data (Candela, Winant, and Ruiz

1990; Tsimplis, Proctor, and Flather 1995; Sannino 2004). Once

validated, the model simulation is integrated for a fortnight period by

considering the combination of the semidiurnal component.

Three closures (70%, 85% and 95%) from both side of the Strait and two

(50% and 70%) starting from the Moroccan side representing the dam are

considered. The dam site is chosen according to previous geological study

from Lombardi Engineering Ltd. The five alternatives differ above all in

terms of the dam closure and site. The dam is 500 metres wide (this

choice is based on the grid resolution of 500 metres in each direction)

with a maximum length of 27 kilometres (Figure (3)). Total area

computed according to the so-called Rectangle Method equals 4025865

square meters. The model is run again for these configurations.

In this study, based on these forecast, a climate scenario of 50 centimetres

is considered. It is implemented in the model by adding a height of 50

centimetres to the semidiurnal tidal elevation forcing applied at the

Western open boundary (Atlantic). The simulations were extended for this

climate scenario by considering the different closures defined previously.

Figure 2 Semidiurnal tidal elevation forcing applied at the middle of the

Western end.

27km

0.5 km

Figure 3 (top) Dam site with the main characteristics. (bottom) Cross section

(b) corresponding to the dam site showing the bottom topography.

Area = 4025865 m2


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6 SYNTHESISREPORT

3.Model validation

A harmonic analysis is made for the tidal elevations and currents in order

to compare the obtained results with measured data (Candela, Winant, and

Ruiz 1990; Tsimplis, Proctor, and Flather 1995; Sannino 2004).

3.1.Tidal elevation

Compilation from these data of the two semidiurnal components for the

observed amplitudes and phases are summarized in Table 3 and 4. Also,

the simulated amplitudes and phases of the semidiurnal tide computed by

the model are given in order to compare them with the observed values at

some relevant points (Figure 4) in the Strait of Gibraltar.

Table 3 Comparison between observed and computed amplitudes

(A) and phases (P) of M2 tidal elevation.

Table 4 Comparison between observed and computed amplitudes

(A) and phases (P) of S2 tidal elevation.

As it can be observed, a general good agreement between observed and

Figure 4 Chart of the computational domain showing the geographic

features referred to in the text. Blue points are the relevant points used forthe comparison between observed and predicted values (exception at

Tangier and Sebta). Shaded red line represents the dam site.


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computed values of amplitudes and phases for the semidiurnal component

is found. Indeed, the maximum difference do not exceed 8.6 centimetres

in amplitude and 8.24 in phase for M2constituent and 4.6 centimetres in

amplitude and 8.47 in phase for S2constituent. The maximum differences

(in relative units) are concentrated in coastal regions (e.g. Tarifa, SN, SS)

since the model grid is not coastal-fitted Sannino (2004).

Figures (5) and (6) show the computed amplitude and phase contours of

the simulated M2and S2tidal waves respectively. For the M2chart (Figure

5.2), it is in good qualitative and quantitative agreement with those

presented in literature (Candela, Winant, and Ruiz 1990; Tejedor et al.

1999; Tsimplis 2000). However, the cotidal lines (lines of constant phase)

of M2differ slightly at the Camarinal sill area causing a deviation toward

North. This deformation can be explained by the irregularities of the

topography in this area.

From Figure (5) two information can be highlighted: (i) the unchangeable

of the amplitude in the cross-Strait direction except the Eastern part of the

Tarifa narrow and (ii) a decline of more than two-fold in the M2amplitude

in the along-Strait direction. Concerning the M2phase, it is characterized

by a southwestward propagation. For the S2 tidal wave (Figure (6)), the

same features are observed. The amplitude and phase ratios differences

between M2 and S2 constituents remain constant throughout the Strait of

Gibraltar as predicted by Candela, Winant, and Ruiz (1990). The

amplitude and phase ratios range from 2.5 to 2.8 and from 23.8 to 27.5

respectively.

Figure 5 Amplitude (left), in meters, and Phase (right), in degrees, contours of the M 2tidal wave

Figure 6 Amplitude (left), in meters, and Phase (right), in degrees, contours of the S 2tidal wave.


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8 SYNTHESISREPORT

3.2.Tidal currents

In order to describe the motion of fluids within the Strait of Gibraltar, the

depth integrated velocity (!!!) is computed for the M2and S2constituent

as well as for the semidiurnal M2S2constituents. Appendix G (refer to the

report) shows the direction of the velocity field during an entire M 2period

(12.42 hours) simulation with the module in background for the high

water at Gibraltar harbour. As expected, the direction of the velocity

reverses periodically. The velocity is the highest in the area of Camarinal

sill section. Figure (7) shows a semidiurnal tidal cycle during spring tide

at Gibraltar (top) and Pt5 (bottom).

Tidal currents value during the spring tide ranges from 0.06 m s-1 at

Gibraltar to 1.85 m s-1at the cross section of Camarinal sill. For the neap

tide (Figure (8)), the currents range from 0.02 m s-1at Gibraltar to 1.02 m

s-1 at the cross section of Camarinal sill. These values are in quite good

agreement with Sannino (2004). The fact that the Camarinal sill exhibits

the highest current was an expected result. Consequently, at the Camarinal

sill, due to the interaction of the strong tidal flow with the complex

bathymetry, the currents are not always reverse which means that the

water column can flow in the same direction twice per day. This result

should be confirmed with a three dimensional model (Sannino 2004) in

order to highlight outflow and inflow currents at the Camarinal sill.

4.Results

4.1.Basic scenario

The sea elevation for the semidiurnal tidal cycle during spring tide for a

closure of 70% (Figure 9) compared to the normal case (without closure)at some relevant point is computed. Only results for spring tide are

presented as it is the regime with the higher surface elevation. The major

sea elevation change is at Pt5 with a decrease of 12.6 centimetres

compared to the normal case. The maximum increase in sea level is at Pt4,

with an increase of 9.4 centimetres. These points are located to the right

(Mediterranean) and left (Atlantic) side of the dam respectively. The

change in sea elevation at other location is: Tanger (+2.8 cm), Sebta (-0.6

cm), Gibraltar (-1cm), Tarifa (-2.9 cm), Pt1 (-0.3 cm), Pt2 (-1.5 cm), Pt3

(+1.5 cm).

Figure 7 Semidirunal (M2S2) tidal cycle during spring tide at Gibraltar(top) and Pt5 (bottom) (see location in Figure 4). Blue line indicates the

tidal height, green line the corresponding velocity in absolute value.

Figure 8 Semidirunal (M2S2) tidal cycle during neap tide at Gibraltar (top)

and Pt5 (bottom) (see location in Figure 4). Blue line indicates the tidal

height, green line the corresponding velocity in absolute value.


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For a closure of 85% (Figure (10)), the change in sea elevation at the

locations is: Tanger (+5.9 cm), Sebta (-1.3 cm), Gibraltar (-2.2cm), Tarifa

(-6.5 cm), Pt1 (-0.5 cm), Pt2 (-2.1 cm), Pt3 (+2.7 cm), Pt4 (+12.1 cm), Pt5

(-17.2 cm). The same trend is observed with an amplification of the

increase or decrease in sea level at each location.


locations is: Tanger (+21.5 cm), Sebta (-4.2 cm), Gibraltar (-8.2cm),

Tarifa (-22.5 cm), Pt1 (-1.8 cm), Pt2 (+1.1 cm), Pt3 (+8.2 cm), Pt4 (+24.9

cm), Pt5 (-34.2 cm). It can be seen that the sea surface variation follow the

same trend than the two previous cases except for Pt2 who undergoes an

increase of sea level instead of a decrease as previously observed. This is

certainly caused by the high degree of obstruction or numerical noise in

the computation of surface elevation at this point.

For the closure of 95%, the phase shift is most pronounced with the higher

closure. Indeed, the signal is perturbed and distorted. This effect is more

pronounced at Tarifa (Figure 12), Pt3, 4 and 5. This can be explained by

plotting the stream function corresponding to this closure (Figure (13)).

The disturbance stems from the fact that eddies and recirculation zones

appear on both sides of the closure. As the latter points are in this area,

their signals are deformed. Indeed, water coming from the Atlantic (and

respectively the Mediterranean) through the closure will form an eddy just

behind it creating a stagnant region. The streamlines (tangent curve to the

velocity vector field) form an arc just after passing through the opening.

At this location, the water is stagnant with small tides. As Tarifa is veryclose, the signal at Tarifa is completely disturbed.

Total Area = 4025865 m2

Close Area = 1229670 m2

Open Area = 2796195 m2

9.5 km 9.5 km8 km

Figure 9 Cross section corresponding to the dam site showing the bottom

topography where shaded blue represents the area closes by the dam. In

this case, 30% area closed.




4 km11.5 km 11.5 km

Figure 10 Cross section corresponding to the dam site showing the

ottom topography where shaded blue represents the area closes by the

dam. In this case, 60% area closed.


ottom topography where shaded blue represents the area closes by thedam. In this case, 90% area closed.




12.5 km12.5 km

1 km

Figure 12 Semidirunal (M2S2) tidal cycle during spring tide at Tarifa. Blue

line indicates the sea elevation for the normal case, green line the sea

elevation for a closure of 95% of the Strait.


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Figure (14) shows surface elevation difference (maximum absolute sea

elevation for normal situation minus maximum absolute sea elevation for

closure situation) for the closure of 70%, 85% and 95% at different

locations for a semidiurnal (M2S2) tidal cycle during spring tide. The

closure is expressed in term of percentage closed area (closed area divided

by total area), which corresponds to 30%, 60% and 90% respectively

(markers in Figure (14)). Positive values indicate an increase in surface

elevation and negative value a decrease of sea level. As expected, a

correlation between the closed area and the increase or decrease of sea

level difference is established. When the surface elevation increases (at

Tanger, Pt3 and Pt4), the larger the closed area, the greater the increase.

Same pattern is observed when the surface elevation decreases (at

Gibraltar, Sebta, Tarifa, Pt1 and Pt5); the larger the closed area, thegreater the decrease. Sea elevation of points situated to the left of the dam

tend to increase while it decrease for the points located to the right side.

Moreover, the closer to the dam the points, the higher the increase (Pt4) or

decrease (Pt5).

In order to confirm these results, two others simulations with a closure

from the Moroccan side is made. Results are presented in the following.

Figure (15) shows the sea elevation for the semidiurnal tidal cycle during

spring tide for a closure of 95% compared to the normal case at some

relevant point. The change in sea elevation at the locations is: Tanger

(+6.8 cm), Sebta (-1.3 cm), Gibraltar (-2.2cm), Tarifa (-5.7 cm), Pt1 (-0.5

cm), Pt2 (+3.0 cm), Pt3 (+2.0 cm), Pt4 (+0.3 cm), Pt5 (-18.5 cm). These

results are in good agreement with the closure of 85% from both sides,

except at Pt4 where the difference in sea level does not change much

because of the opening on the Spanish side (contrary to the closure of

85% on both sides).


locations is: Tanger (+30.2 cm), Sebta (-7.4 cm), Gibraltar (-12cm), Tarifa

(-34.5 cm), Pt1 (-2.8 cm), Pt2 (+14.1 cm), Pt3 (+15.5 cm), Pt4 (+10.3

cm), Pt5 (-50.5 cm). Same pattern are observed with the important

deformation of the tidal signal and can be explained as before by plotting

the streamlines (Figure (17)).

Figure 13 Stream function for the M2constituent for a closure of 95%.

Figure 14 Difference in sea elevation of the closures compared to the

normal case at different location for a semidiurnal tidal cycle (M 2S2)

during spring tide. Positive value means an increase sea level compared to

the normal case, negative value a decrease in seal level. X-axis shows the

closed area (30%, 60%, 90%) corresponding to the closure 70%, 85% and

95% respectively.




13.5 km 13.5 km

Figure 15 Cross section corresponding to the dam site showing the bottom

topography where shaded blue represents the area closes by the dam. In

this case, 50% area closed on Moroccan side.


ottom topography where shaded blue represents the area closes by the

dam. In this case, 95% area closed on Moroccan side.




8 km 19 km


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Finally, the trend of Figure (14) is confirmed by Figure (18). The higher

area closed, the higher the increase or decrease in surface elevation

compared to the normal case. The dam site (closure on both sides or on

Moroccan side) does not affect the trend for points located far from the

dam (Sebta, Gibraltar, Tarifa, Pt1, Pt3). This means that for a constant

closed area, the result is the same no matter where the dam is positioned

(same longitude but different latitude). Concerning points situated near

the dam (Pt4, Pt5), different behaviours are observed. For Pt4, when the

closure is only on the Moroccan side, there is almost no increase in sea

elevation which is logical since it is an open area. For Pt5, the fact to close

only the Moroccan side seems to accentuate the decrease of sea level

compared to the closure on both side. This suggests that the dam site has

an area of influence on the flow regardless of area closed. From these

results, it can be seen that a closure of the Strait of Gibraltar can reducethe sea level on the Mediterranean side. However, with counterpart an

increase of the surface elevation on the Atlantic side.

4.2.Climate scenario

Results of simulations by modifying the signal at the Western open

boundaries (+50 centimetres) and with different closures are presented.

The increase in sea level is taken into account by increasing the signal at

the Western end of the computational domain. Figure (19) shows how the

signal is modified. The rise is not exactly equal to 50 centimetres as linear

interpolation from four points is made for the Western boundary.

Figure 19 Semidiurnal (M2S2) tidal cycle during spring tide applied at the

middle of the Western computational domain.

The increase in sea level introduced at the Western boundary did not

spread everywhere throughout the domain in the similar manner. Thesignal decrease as moving away from the Western boundary. For example,

at Tanger, the climate scenario is still strong (+46 centimetres). But at

Gibraltar, as the signal passes through rugged bathymetry, friction and

other phenomena, it decreases in intensity (+8 centimetres).

The goal with the closure is to ensure that the sea level in the

Mediterranean stay constant, meaning that the difference between the sea

level in the normal case (without climate and closure) and the climate

scenario with closure must be as close as possible to zero for points

located in the Mediterranean side. If this difference is greater than zero,

this means that the closure is too much. On the contrary, if the difference

is below zero, this means that the closure is not enough to keep the level

constant (equal to the normal case). For example, Figure (20) shows thesurface elevation at Tarifa. If the difference (in term of maximum absolute

value) between the normal case (in blue in Figure (20)) and the climate

with closure is positive, this means that the corresponding closure (95%

and 70% Moroccan side in this case) is enough to ensure the sea level to

stay constant (in purple and black in Figure (20)). If the difference is

negative, the closure is not enough (70%, 85% and 50% Moroccan side in

this case).

Figure 17 Stream function for the M2constituent for a closure of 70% on

the Moroccan side.

Figure 18 Difference in sea elevation of the closures compared to the

normal case at different location for a semidiurnal tidal cycle (M 2S2)

during spring tide. Positive value means an increase sea level compared to

the normal case, negative value a decrease in seal level. X-axis shows the

closed area (30%, 60%, 90%, 50%, 95%) corresponding to the closure

70%, 85%, 95% on both side and 50%, 70% on the Moroccan side

respectively. Pt 2 is not presented for the closure 50% (50% area closed)and 70% (95% are closed) on Moroccan side.


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12 SYNTHESISREPORT

Figure 20 Semidirunal (M2S2) sea elevation during spring tide at Tarifa for

different configuration.

In Figure (21), the difference between the sea level in normal case and the

climate scenario with different closure is shown for point located in the

Mediterranean side. A closed area equal to 90% allows maintaining the

sea level constant at these locations and even reduces the surface elevation

compared to the actual situation.

Figure 21 Difference in sea elevation of the closures with climate change

compared to the normal case at Mediterranean points for a semidiurnal

tidal cycle (M2S2) during spring tide. Positive value means a decrease in

sea level compared to the normal case, negative value an increase in sea

level. X-axis shows the closed area (30%, 60%, 90%, 50%, 95%)

corresponding to the closure 70%, 85%, 95% on both side and 50%, 70%

on the Moroccan side respectively.

Taking a look at the other side of the dam is necessary. Figure (22) shows

the difference between the sea level in normal case and the climate

scenario with different closure is shown for point located in the Atlantic

side. As expected, the more the closure, the more the increase of surface

elevation at the Atlantic. This important counterpart cannot be neglected.

Indeed, Moroccan and Spanish coastal area would be flooded due to the

important increase of surface elevation.

Figure 22 Difference in sea elevation of the closures with climate change

compared to the normal case at Atlantic points for a semidiurnal tidal

cycle (M2S2) during spring tide. Positive value means a decrease in sea

level compared to the normal case, negative value an increase in sea level.

X-axis shows the closed area (30%, 60%, 90%, 50%, 95%) corresponding

to the closure 70%, 85%, 95% on both side and 50%, 70% on the

Moroccan side respectively.

4.3.Estimation of annual energy output

In order to estimate the annual energy that can be extracted from a dam

exploiting the tidal power through the Strait of Gibraltar, a method based

on the principle of tidal hydrodynamic is used (Xia et al. 2012). The

principle is to block the entry and exit tides to create a water level

differential. As suggested by Charlier and Finkl (2009), the most efficient

way to operate for tidal barrage is to generate power during ebb tide asshown in Figure (23).

Figure 23 Sketch of ebb generation mode. Image from Xia et al. (2012).

The principle described by Xia et al. (2012) is as follows: First, the basin

(upstream) is filled through the sluice of the barrage until it achieves the

high tide level. From there, the sluices are closed (filling C-D in Figure

(23)). The turbines and sluices stay closed until the sea level downstream

decreases sufficiently to create a water level differential (called starting

head) across the dam (holding D-A in Figure (23)). Therefore, the turbines

gate are spun to create electricity (generating A-B in Figure (23)) until the


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14 SYNTHESISREPORT

estimated annual tidal energy of 1364 GWh is found by using an

operating efficiency of 0.4.

5.Summary and Conclusions

The aim of this project has been the developing of a numerical model able

to reproduce the circulation through the Strait of Gibraltar by considering

the tidal forcing. Then, the paper is devoted to determine the size of the

closure needed to ensure a constant level of the Mediterranean to solve

flooding problems due to global warming.

The GCM used in this study is the two dimensional vertically integrated

tidal model MECCA initially developed by Hess (1986) to study costal,

estuarine and open ocean circulation. The version used has already been

successfully implemented for the Strait of Gibraltar by Smaoui andOuahsine (2006). Study domain extends longitudinally from 6.241 to

4.567 West and 35 to 36.666 North. The model grid has a uniform

horizontal and vertical spacing of 500 metres. A significant aspect of this

model is that it solves a prognostic equation for the turbulent kinetic

energy and uses a semi-empirical expression for the mixing length(Davies, Luyten, and Deleersnijder 1995). At the two open boundaries, the

model is forced with the semidiurnal M2 and S2 surface elevation. The

model is run for a complete fortnightly period and a harmonic analysis is

performed to compare results with observed data. Computed amplitudes

and phases for the two semidiurnal constituent are in good agreement with

observed values. Also, results show that the model is able to reproduce

some major features of the tidal flow in this region: a decline of more than

two-fold in the M2 amplitude in the along-Strait direction, a general

invariability of the amplitude in the cross-Strait direction, a

southwestward propagation of the phases, and a constant amplitude and

phase ratios differences between M2 and S2 constituents throughout the

Strait of Gibraltar. However, the two dimensional model has proved its

limitations concerning the simulation of tidal current and cannot substitutea global modelling of the water circulation in this area (a three

dimensional model is needed). Since the flow within the Strait is done at

least in two layers, it is evident that a two dimensional model is not able

to describe all the exchange and hydraulics circulation aspect due to the

complex physics present in one of the most complicated region of the

world.

Once the model validated, simulations are performed for three closures

(70%, 85%, 95% corresponding to 30%, 60%, 90% are closed

respectively) starting both sides of the Strait and two closures (50%, 70%

corresponding to 50%, 95% area closed respectively) starting from the

Moroccan side supposed to represent the dam. The location of the latter it

determined by previous geological reconnaissance. The dam is 500 metres

wide with a maximum length of 27 kilometres. As a first step, simulationsare made for the basic scenario, i.e. with the actual surface elevation

specified at the two open boundaries. Sea elevations at some relevant

points are compared in order to assess the impact of the closure on tidal

height. For the basic scenario, results show a clear correlation between the

percentage area closed and the increase or decrease of sea level compare

to the normal case (without dam): the larger the closed area, the greater

the increase for points situated to the left of the dam, the greater the

decrease for points situated to the right side. Also, for points located

sufficiently far away from either side of the barrage, the dam

configuration (closure on both side or on Moroccan side only) does not

affect the increase/decrease trend. Consequently, a closure of the Strait of

Gibraltar can reduce the sea level on the Mediterranean side. However,

with counterpart an increase of the surface elevation on the Atlantic side.

The second step consisted to add 50 centimetres to the semidiurnal tidal

elevation signal at the Western open boundary supposed to reproduce the

sea level increase due to global warming. As expected, due to the rugged

bathymetry and friction, the signal did not spread everywhere throughout

the domain in the similar manner. By considering the sea level increase of

50 centimetres, it was found that a closed area equal to 90% allows

maintaining the sea level constant at points located on the Mediterranean

side. However, with such closure, the sea level on the Atlantic side

dramatically increased.

In the final part of this paper, a first assessment of the annual energy

output from a barrage within the Strait of Gibraltar is done using a

theoretical estimation method (Xia et al. 2012). The result indicates that

the magnitude of the annual energy output from the barrage would range

between 680 and 1364 GWh depending on the power conversion

efficiency considered. These values are relative with regard to the surface

area being considered. Moreover, as these predictions are based on

simplifying assumptions, a more accurate estimation of the annual energy

output should be conducted with more detailed information on the dam,

sluices, turbines and tidal ranges.

The objective of this study is reached, since its principal aim is the

understanding of tidal flow in the Strait of Gibraltar for a dam project. In

the future, a three dimensional version of MECCA model should be

develop in order to be able to simulate others major features of the flow in

the Strait, especially to estimate water transports along the whole Strait

and to provide an estimation of the impact of the barrage on these

quantities. The simulations have brought to light an important issue

(increase surface elevation on the Atlantic part) of a closure in the Strait

of Gibraltar. But it also showed that a barrage with an adapted closing can

keep the Mediterranean Sea level constant. Two improvement of this

study can be done in the future: (i) extend the area covered by the model

to cover the whole Mediterranean Sea in order to avoid forcing the

Eastern boundary with surface elevation values. As the Mediterranean isan enclosed sea, it will be able to freely adjust to the forcing of the

Atlantic. From there, one can specify a constant sea level in the

Mediterranean and optimize the corresponding closure of the Strait; (ii)

the global mean sea level increase introduced in the model assumes a

sudden rise of 50 centimetres applied uniformly on the Atlantic. In reality,

this increase takes place in the long term and is highly nonuniformly

distributed over the ocean. A solution could be to make a simulation of

several years with a different sea level increase every year for each

location.

Acknowledgements

I would like to thank my external advisor, Hassan Smaoui (UTC-CETMEF), for his vital guidance during this project. He kindly provided

his numerical model for the purpose of my work. His deep knowledge in

oceanography modelling allowed insightful discussions and constructive

critique of my simulations. I would also like to thank the members of

FlowScience, Frieder Semler, Dr. Matthias Todte and John Wendelbo for

their warm welcome in Rottenburg and for their support. I am also

extremely grateful to Gustav R. Grob (ICEC) for his constant

encouragement and financial support for my trip to Germany.

This project was supervised by Prof. Dr. Anton Schleiss, Mario Franca

and Fraenz Zeimetz from the department of Hydraulic Constructions,

EPFL. I wish to thank them for their willingness to help and advise

throughout the duration of the project.


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15

Finally, a special thanks to my dear family and friends, for their patience

and for never being short of a few words of encouragement when they

were needed.

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