Numerical modeling of the semidiurnal tidal exchange through the Strait of Gibraltar
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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, C05011, doi:10.1029/2003JC002057, 2004 Numerical modeling of the semidiurnal tidal exchange through the Strait of Gibraltar G. Sannino, A. Bargagli, and V. Artale Ocean Modeling Unit, Special Project Global Climate, ENEA C. R. Casaccia, Ente per le Nuove Technologie, l’Energia e l’Ambiente, Rome, Italy Received 21 July 2003; revised 22 February 2004; accepted 5 March 2004; published 7 May 2004. [1] A three-dimensional sigma coordinate free surface model is used to investigate the semidiurnal tidal exchange through the Strait of Gibraltar. The model makes use of a coastal-following, curvilinear orthogonal grid that includes the Gulf of Cadiz and the Alboran Sea, with very high resolution in the strait (
C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 1. Chart of the Strait of Gibraltar showing the principal geographic features referred to in the
text. Locations of current meter moorings deployed during the Gibraltar Experiment (October 1985 –
1986) and during the Canary Islands Azores Gibraltar Observations (CANIGO) observations (October
1995 –April 1996) are also shown with red and blue solid circles, respectively.
Lafuente et al., 2002], semidiurnal variations due to strong during a tidal cycle, which is precisely the situation that
tides and finally, on very short timescales, modifications occurs in the Strait of Gibraltar. Both theories assert that the
due to internal bores (internal wave reaching amplitudes of exchanged flows increase with the strength of the barotropic
up to 150 m [Richez, 1994]). tidal forcing, but the quasi-steady theory always predicts
[7] The tidal forcing in the strait has been extensively more flow than the time-dependent theory.
studied and analyzed in the past. On the basis of data [9] The purpose of this work is to implement a three-
collected during the Gibraltar Experiment during 1985 – dimensional (3-D) high-resolution, primitive equation, free-
1986 [Bryden and Kinder, 1988]. Candela et al. [1990] surface numerical model, of the circulation in the strait
(hereinafter referred to as CA90) and Bryden et al. [1994] region and to use it to: (1) reproduce the semidiurnal tides
described the structure of the barotropic M2 tide and of the within the Strait of Gibraltar, (2) estimate the water trans-
tidal transport through the strait, respectively, Bruno et al. ports through the strait and (3) evaluate the effect of tidal
[2000] have described the vertical structure of the semidiur- forcing on the mean exchanges and entrainment.
nal tidal current at Camarinal Sill, while Wang [1993] used a [10] The paper is organized as follows. Section 2 con-
numerical model to study tidal flows, internal tide as well as tains a description of the model used to simulate the tide
fortnightly modulation. Recently, others studies have been in the strait. In section 3, model results are compared with
carried out, based on direct observations collected during the available data of surface elevation, currents and internal
Canary Islands Azores Gibraltar Observations (CANIGO) bores measurements. Section 4 is devoted to the study of
project (1995 – 1996) [Parrilla et al., 2002]: Tsimplis [2000] the tidal effect on water transports and entrainment
has described the vertical structure of tidal currents at through the strait, while summary and conclusions com-
Camarinal Sill, Tsimplis and Bryden [2000] (hereinafter plete the paper.
referred to as TB00) have estimated the water transports
through the strait, Garcı́a Lafuente et al. [2000] have
analyzed in detail the tide at the eastern section of the strait, 2. Model Description
and Baschek et al. [2001] (hereinafter referred to as BA01) [11] The numerical model used for this study was imple-
have estimated the transport with a tidal inverse model. mented in SBA02, where it was used to investigate the
[8] To estimate the effect of tidal forcing on mean flow, mean exchange through the Strait of Gibraltar. The model
Farmer and Armi [1986] included tides into their hydraulic was only forced by the density contrast between the
theory by using a quasi-steady approximation in which the Alboran Sea and the Gulf of Cadiz, without any other
steady solution is verified at each time of a tidal cycle. forcing, such as tides, wind or atmospheric pressure. The
However, Helfrich [1995] showed that this approach is not main differences introduced in the present model regard the
valid for dynamically long straits, i.e., straits having a treatment of open boundary conditions, forcing and vertical
length greater than the distance traveled by an internal wave resolution. In the following we only focus on the principal
2 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
model characteristics and on the main differences with forcing tide elevation at the grid point i and time step n 1,
respect to the model implemented in SBA02. and zMi is the time-independent mean elevation at the grid
point i, which is set to about 12 cm at the western open
2.1. Model Grid and Bathymetry boundary and to 0 cm at the eastern open boundary.
[12] The region covered by our model includes the Condition equation (1) incorporates a radiation mechanism
Strait of Gibraltar and the two adjacent subbasins that allows the undesired transients to pass through the open
connected to it: the Gulf of Cadiz and the Alboran Sea. boundaries, going out of the model basin, without
The horizontal model domain is discretized by a curvi- contaminating the desired forced solution [Arnold, 1987].
linear orthogonal grid made by 306 53 grid points (see A zero gradient condition is used for the depth-integrated
Figure 2 in SBA02). The resolution in the strait is much velocity.
higher (500 m) than in the eastern (8 – 15 km) and [14] The time-independent mean elevation values used at
western ends (10 – 20 km), so that the dynamics in the the open boundaries (zM) are obtained running the model in
strait will be well resolved. The vertical grid is made of barotropic mode. This model, as the baroclinic version, has
32 sigma levels, logarithmically distributed at the surface at the eastern and western ends of the computational domain
and at the bottom, and uniformally distributed in the rest two open boundaries where values of barotropic velocity
of the water column. The model topography has been and surface elevation must be specified. For the surface
obtained by merging the high-resolution ( 0.2, as suggested by Mellor the normal velocities are set to zero along coastal
et al. [1994]. In order to estimate the residual pressure boundaries, at the bottom, adiabatic boundary conditions
gradient error, we have integrated the model for one year are applied to temperature and salinity and a quadratic
without initial horizontal density gradient, i.e., with sa- bottom friction, with a prescribed drag coefficient, is
linity and temperature fields only varying with depth, applied to the momentum flux. This is calculated by
with no open boundary applied, i.e., closed domain, and combining the velocity profile with the logarithmic law
without any other external forcing. In this integration the of the wall:
maximum intensity of erroneous currents introduced by
the sigma coordinates is of about 2 cm s1. Since the
CD ¼ max 2:5 103 ; k 2 lnðDzb =z0 Þ ; ð2Þ
expected baroclinic velocities are up to 1 m s1 this error
seems to be tolerable. The resulting model topography in where k is the Von Karman constant, z0 is the roughness
the region of the strait, with the minimum depth of the length, set to 1 cm, and Dzb is the distance from the bottom
shelf set to 25 m, is shown in Figure 2. The dominant of the deepest velocity grid point.
topographic features of the strait (from west to east) are [16] For the initial condition we have used the same
clearly recognizable: Spartel Sill (Sp), Tangier basin, lock-exchange condition as in SBA02, i.e., we have filled
Camarinal Sill (Cm) with a minimum depth of 284 m the model with two water masses, horizontally uniform
and Tarifa Narrows. and vertically stratified, separated by an imaginary dam in
2.2. Boundary, Initial, and Forcing Conditions the middle of the strait (longitude 5420W) that is removed
[13] Near the eastern and western ends of the computa- at the initial time. Initial temperature and salinity fields for
tional domain two open boundaries are defined, where the Alboran basin have been obtained from a horizontal
values of velocity, temperature, and salinity must be average of the spring MODB data (available at http://
specified. In order to minimize the contamination of the modb.oce.ulg.ac.be/modb), while the spring Levitus [1982]
interior model solution due to wave reflection at the data set has been used to set initial values over the Gulf of
boundaries, an Orlanski radiation condition [Orlanski, Cadiz (see Figure 5 in SBA02). As in SBA02 and
1976] is used for the depth-dependent velocity at both Napolitano et al. [2003], we have used the Smolarkiewicz
boundaries. A forced Orlanski radiation condition [Bills upstream-corrected advection scheme [Smolarkiewicz,
and Noye, 1987] is used for the surface elevation at the 1984, 1990], in order to simulate correctly the free flow
western and eastern boundaries: adjustment to the density gradient within the strait after the
1 dam is removed.
n n1
nþ12
zTi 2 þ zMi ðCr=2Þzi 2 þ Crzni1 [17] The model is forced at the open boundaries
zi ¼ ; ð1Þ through the specification of the surface tidal elevation.
1 þ Cr=2
Candela et al. [1990] and more recently Tsimplis [2000]
where zni represents the surface elevation at the i grid point have found that 75% of the current variability in the strait
of the open boundary at time step n, Cr = cDt/(2Dx) is a is due to the semidiurnal tide, so we have limited our
Courant number defined in the x direction, zn1 Ti is the modeling study to the semidiurnal component, forcing the
3 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 2. (top) Model bathymetry, computational grid, and transects for the presentation of model
results within the Strait of Gibraltar. The gray levels indicate the water depths. The points Cm and Sp
mark the points where Spartel Sill and Camarinal Sill are located, respectively. (bottom) Bathymetry
along the longitudinal section E.
model with only the M2 tide, with period of 12.42 hours, boundary (ywm) during the neap tide ranges from 48 to
and the S2 tide, with period of 12.00 hours: +75 cm, while during the spring tide ranges from 128 to
+140 cm. Owing to the strong velocities generated by the
X
2 tidal forcing short external and internal time steps of 0.1 and
zT ð y; t Þ ¼ An ð yÞ cosðsn t jn ð yÞÞ; ð3Þ 6 s need be used in the simulation.
n¼1
where An (y) and jn (y) are the prescribed surface elevation 3. Model Results
amplitude and phase of the nth tidal constituent and sn is its [18] The model was run for 360 days without tidal forcing
frequency. The M2 and S2 surface tidal elevation amplitudes (zT ( y, t) = 0) in order to achieve a steady two-layer
and phases have been obtained from the global tidal model exchange system. The steady exchange obtained is charac-
of Kantha [1995] and Kantha et al. [1995]. The resulting zT terized by an inflow (toward the Mediterranean) and an
(ywm, t) applied at the middle point of the western open outflow (toward the Atlantic Ocean) of 0.62 and 0.51 Sv
4 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Table 1. Comparison Between Observed and Predicted Amplitudes A and Phases P of M2 Tidal Elevationa
Observed M2 Predicted M2 Difference (Pre Obs)
Location Latitude North Longitude West A, cm P, deg A, cm P, deg A, cm A, % P, deg
Tsimplis et al. [1995]
Gibraltar 36080 05210 29.8 46.0 29.7 46.0 0.1 0.3 +0.0b
Garcı́a Lafuente [1986]c
Pta. Gracia 3605.40 0548.60 64.9 ± 0.2 49.0 ± 0.5 64.9 51.0 +0.0 0.0 +1.5
Tarifa 3600.20 0536.40 41.5 ± 0.2 57.0 ± 0.5 40.5 46.3 0.8 1.9 +10.2
Pta. Cires 3554.70 0528.80 36.4 ± 0.2 46.5 ± 0.5 33.6 50.1 2.6 7.1 +3.1
Pta. Carnero 3604.30 0525.70 31.1 ± 0.2 47.5 ± 0.5 29.1 43.8 1.8 5.8 3.2
Candela et al. [1990]
DN 35580 05460 60.1 51.8 56.2 53.9 3.9 6.4 +2.1
DS 35540 05440 54.0 61.8 51.4 61.6 2.6 4.8 0.2
SN 36030 05430 52.3 47.6 50.1 48.2 2.2 4.2 +0.6
SS 35500 05430 57.1 66.8 58.0 65.3 +0.9 1.5 1.5
DW 35530 05580 78.5 56.1 73.3 58.4 5.2 6.6 +2.3
TA 36010 05360 41.2 41.2 41.0 47.3 0.2 0.4 +6.1
AL 36080 05260 31.0 48.0 28.6 46.0 2.4 7.7 2.0
CE 35530 05180 29.7 50.3 27.5 47.3 2.2 7.4 3.0
DP5 36000 05340 44.4 47.6 38.2 43.9 6.2 13.9 3.8
a
Station locations are shown in Figure 1.
b
Calibration.
c
± indicates standard errors.
at the Camarinal Sill section, and of 0.69 and 0.58 Sv at SBA02. This difference mainly depends on the value of
the Gibraltar-Ceuta section (1 Sv = 106 m3/s1). mean elevation (zM) used in the open boundary condition
[19] Transports were computed integrating the along- equation (1) and on the better vertical resolution imple-
strait velocity vertically from the bottom up to the depth mented in this present work.
where the along-strait reverts its direction for the outflow, [20] In order to achieve a stable time-periodic solution, the
and from this depth up to the surface for the inflow, and then model was run for further 29 days, forced only by the two
meridionally, across the Camarinal Sill and Gibraltar-Ceuta principal semidiurnal tidal components. Finally, after reach-
sections (sections C and D in Figure 2): ing the stable time-periodic regime, the model was run for a
Z Z further fortnightly period and the least squares harmonic
North 0
INð xÞ ¼ uð x; y; zÞdzdy analysis was applied to the surface elevation and currents.
South hð x;yÞ
Z North Z hð x;yÞ
ð4Þ 3.1. Tidal Elevation
OUTð xÞ ¼ uð x; y; zÞdzdy; [21] In Tables 1 and 2 the observed [Tsimplis et al., 1995;
South bottom
Garcı́a Lafuente, 1986; Candela et al., 1990] and simulated
where u is the along-strait velocity, h is the depth of the amplitudes (A) and phases (P) are compared, for the M2 and
interface, and x is the longitude. The computed transports S2 tidal elevation, respectively. A good agreement between
are about 15% less than the estimation carried out in observed and predicted values is found; the maximum
Table 2. Comparison Between Observed and Predicted Amplitudes A and Phases P of S2 Tidal Elevationa
Observed S2 Predicted S2 Difference (Pre Obs)
Location Latitude North Longitude West A, cm P, deg A, cm P, deg A, cm A, % P, deg
Tsimplis et al. [1995]
Gibraltar 36080 05210 10.7 72 10.5 72.0 !0.2 1.8 +0.0
b
Garcı́a Lafuente [1986]
Pta. Gracia 3605.40 0548.60 22.3 ± 0.2 74.0 ± 1.0 20.3 77.9 1.8 8.1 +2.9
Tarifa 3600.20 0536.40 14.2 ± 0.2 85.0 ± 1.5 14.7 69.8 0.3 2.0 13.7
Pta. Cires 3554.70 0528.80 14.1 ± 0.2 74.0 ± 1.0 13.1 76.7 0.8 5.7 +1.7
Pta. Carnero 3604.30 0525.70 11.5 ± 0.2 71.0 ± 1.0 10.6 68.6 0.7 6.9 1.4
Candela et al. [1990]
DN 35580 05460 22.5 73.8 20.3 77.9 2.2 9.7 +4.1
DS 35540 05440 21.1 83.3 18.3 87.3 2.8 13.2 +4.0
SN 36030 05430 18.5 73.4 18.1 74.2 0.4 2.1 +0.8
SS 35500 05430 20.6 92.3 21.0 90.0 +0.4 1.9 2.3
DW 35530 05580 29.0 82.2 26.6 81.8 2.4 8.2 0.4
TA 36010 05360 14.7 67.9 15.1 70.7 +0.4 2.7 +2.8
AL 36080 05260 11.1 73.9 10.2 71.2 0.9 8.1 2.7
CE 35530 05180 11.4 75.6 9.6 74.8 1.8 15.7 0.8
DP5 36000 05340 16.1 73.9 14.0 69.1 2.1 13.0 4.8
a
Station locations are shown in Figure 1.
b
± indicates standard errors.
5 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 3. Cotidal charts of the (a) M2 and (b) S2 surface tides. Solid lines are phase contours in degrees;
dashed lines are amplitude contours in cm.
differences do not exceed 6.2 cm in amplitude (with a propagation, more evident east of Camarinal Sill as far as
maximum error of about 15%) and 13 in phase. The the eastern entrance of the strait. The same features are also
maximum differences are confined to coastal points as present on the S2 cotidal chart even if the cotidal lines
Ceuta (CE), Algesiras (AL), Tarifa and Pta. Cires, since exhibit a greater deviation toward North over the Camarinal
our model grid is not coastal fitted. Sill. In agreement with CA90, the ratios and phase differ-
[22] In Figure 3 are also shown the computed cotidal ences between the M2 and S2 components remain quite
charts for the strait region, for the simulated M2 and S2 constant throughout the strait; the amplitude ratio is con-
surface tidal waves. The M2 chart is in good qualitative fined between 2.6 and 2.8 and the phase difference
agreement with the empirical cotidal chart presented by decreases from west to east of only 2 degrees between
CA90. The only difference is in the Camarinal Sill area, 24 to 26.
where the cotidal lines (lines of constant phase) undergo a
deviation toward North. The principal features to be noted 3.2. Tidal Currents
on this chart are the reduction (more than 50%) of the [23] A direct comparison between the predicted fields of
amplitude in the along-strait direction, the invariability of major and minor axes of tidal ellipse and data are difficult
the amplitude in the cross-strait direction (except for the because of the lack of data in most part of the strait, with the
eastern part of Tarifa narrow), and the southwestward phase exception of Camarinal Sill (see CA90) and of the eastern
6 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 4. Comparison between observed and simulated semimajor axis components of tidal ellipses.
Observed data M1, M2, M3, M7, M8, M9, and F3 are from Candela et al. [1990], and N, C, and S are
from Garcı́a Lafuente et al. [2000].
entrance [see Garcı́a Lafuente et al., 2000]. Thus in order to [24] Figures 5 and 6 show a complete semidiurnal tidal
quantitatively compare the model results with observed data, cycle simulated by the model during spring tide at the
a linear regression between predicted and observed semi- Gibraltar-Ceuta and Camarinal Sill sections, respectively. It
major axis, in only ten different locations, was performed is apparent from Figure 5 that the lower-layer flow, at the
(Figure 4). The mean errors and the root mean square errors eastern section D, is periodically reversed by tidal currents
are shown in Table 3. The errors are limited to 4.0 cm s1 and toward the Mediterranean Sea (also during neap tide, not
7.5 cm s1 for the S2 and 5.9 cm s1 and 7.9 cm s1 for the showed). The typical currents range from 60 to 30 cm s1
M2, except for the stations M3 and F3 where the mean error during spring tide and from 40 to 30 cm s1 during neap
reaches the value of 24.7 cm s1 and the root mean square tide. On the contrary, the upper layer is always directed
reaches 31.9 cm s1. These differences are mainly due to an toward the Mediterranean Sea, indicating a clear weakness of
overestimation of the simulated lower-layer currents. the tidal amplitude in comparison with the mean upper layer
7 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Table 3. Mean and Root-Mean-Square Error of the Simulated is only a difference of 20, i.e., a difference of 40 min
Semimajor Axis between the appearing of the maximum velocity in the
M2 S2 upper layer and the appearing of the maximum velocity in
Station Mean Error RMS Error Mean Error RMS Error
the lower layer. This difference goes up to 60(2h) at the
eastern entrance (Figure 7b), where the phase decreases
Candela et al. [1990]
M1 3.4 3.9 0.8 3.3 from about 210 in the upper layer to 150 in the lower
M2 0.9 5.5 4.0 7.5 layer.
M3 24.7 29.8 3.5 7.2 [27] The S2 tidal current amplitude also decreases of more
M7 0.8 1.9 0.1 0.3 than 70% from Camarinal Sill to the eastern entrance
M8 1.0 1.0 3.3 3.3
M9 5.9 5.9 2.3 2.6
(Figures 10a and 9a, respectively). At the eastern entrance
F3 24.5 31.9 0.4 0.8 the amplitude increases with depth, from the surface to about
250 m, of only 2 cm s1, remaining constant at 11 cm s1 as
Garcı́a Lafuente [1986] far as the bottom on the southern side. S2 tidal current phase
N 2.7 7.9 0.9 1.7 (Figure 9b) decreases from 170 to 130 in the first 200 m
C 3.9 7.9 0.9 1.5
S 0.1 1.1 0.5 0.8 and increasing up to 150 at about 350 m, remaining
constant below 350 m to the bottom. At Camarinal Sill the
S2 tidal current amplitude increases from surface to 90 m of
flow, that is too strong to be reversed. Here the upper layer, about 14 cm s1, with an increment that is not uniform along
the currents range from 80 to 140 cm s1 during spring tide the cross section (maximum values of about 42 cm s1 are
and from 60 to 110 cm s1 during neap tide. These results are concentrated on the south and north sides), while below 150
in good agreement with BA01, who showed very similar m the amplitude decreases going toward the bottom. Phase
results for the M2 component, computed with an inverse (Figure 10b) is constant (150) from the surface to the
model at the eastern entrance of the strait. bottom for nearly the whole section.
[25] At Camarinal Sill, the tidal signal is so strong to
always reverse the currents, both in the upper and lower 3.3. Internal Bore
layers, for a part of each semidiurnal tidal cycle, except for [28] One of the most important features of the dynamics in
the neap tide where the Mediterranean layer is not reversed the strait is the presence of internal bores which are generated
completely (for the spring tidal cycle see Figure 6). To over Camarinal Sill and propagate both eastward and west-
discriminate between upper and lower-layer velocities we ward [Armi and Farmer, 1988; Farmer and Armi, 1988]. In
superimposed to the velocity contours the depth of the Figure 11 we present six sequential snapshots of longitudinal
37.25 isohaline, that, as suggested by SBA02, can be salinity sections which cover the overall spring tidal period.
considered as an interface between the two layers. Using Here one can see that, in good agreement with the two-
this method, it is possible to see that velocity in the upper dimensional, two-layer, hydrostatic model of Izquierdo et al.
layer ranges from 130 to 200 cm s1 during spring tide and [2001], the generation of the eastward propagating internal
from 100 to 130 cm s1 during neap tide. For the lower bore begins with the formation of an interfacial depression
layer, velocity ranges from 230 to 150 cm s1 during over the western edge of Camarinal Sill, approximately
spring tide and from 190 to 70 cm s1 during neap tide. 1.5 hours before high tide at Tarifa, i.e., as soon as the
[26] Figures 7 – 10 show the simulated M2 and S2 tidal westward barotropic forcing over Camarinal Sill starts
amplitude and phase of the along-strait velocity at Camari- weakening and the interface located upstream of Camarinal
nal Sill and Gibraltar-Ceuta cross-strait sections. Looking at Sill is not sustained any more. Subsequently, about 30 min
Figures 7a and 8a it is clear that there is a drastic decrease in before high tide at Tarifa, the internal bore is released from
the M2 amplitude (more then 70%) going from Camarinal Camarinal Sill and starts to travel eastward. The bore is
Sill to the eastern entrance of the strait. At Camarinal Sill released when the upper layer starts to move toward east
the amplitude constantly increases from 100 cm s1 at the while the lower layer continues to move westward. Its initial
surface up to 140 cm s1 at a depth of about 220 m and then length scale, in the along-strait direction, is about 3 km and
decreases in the vicinity of the bottom due to the influence its travel times from Camarinal Sill to Tarifa, Pta. Cires and
of friction. On the other hand, in good agreement with Gibraltar sections are 2, 4 and 6 hours, respectively. It
BA01, at the eastern entrance of the strait the amplitude follows that, always in agreement with the two dimensional
increases from 8 cm s1 at the surface to 42 cm s1 in the model of Izquierdo et al. [2001], the speed of the bore is
lower layer. The main increase is in the upper layer: about 1.7 m s1 between Camarinal Sill and Tarifa sections,
amplitude reaches the value of 34 cm s1 in the first 2.5 m s1 between Tarifa and Pta. Cires sections, and
200 m, and remains rather constant in the rest of the water 1.5 m s1 between Pta. Cires and Gibraltar sections.
column. It is also evident a meridional variation of the [29] In agreement with Armi and Farmer [1988], a much
amplitude from the southern part (40 cm s1) to the weaker westward propagating internal bore is also released
northern part (18 cm s1) of the strait. Another point to from Camarinal Sill, just 30 min before the eastward prop-
highlight is that the phase at Camarinal Sill (Figure 8b) is agating bore reaches Gibraltar-Ceuta section, i.e., 40 min
quite constant from the upper layer to the lower layer; there before the low tide at Tarifa. The amplitude of the eastward
Figure 5. (a – f ) Simulated sections of the along-strait current (cm s1) showing several phases of a semidiurnal (M2 + S2)
tidal cycle during spring tide at the Gibraltar-Ceuta section. The time difference between the single sections is 2 hours.
(g) Time moments referred to the surface elevation at Tarifa. The contour interval is 10 cm s1. Red and blue shadows
highlight outflow and inflow currents, respectively. Yellow lines represents the depth of the 38.1 isohaline.
8 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 5
9 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 6. Same as Figure 5, but for the Camarinal Sill section. Yellow lines represent the depth of the
37.25 isohaline.
10 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 7. M2 tidal constituent of the along-strait velocity at the eastern section D. (a) Amplitude in
cm s1; the contour interval is 2.0 cm s1. (b) Phase relative to the Moon transit at Greenwich in degrees;
the contour interval is 10.
propagating bore diminishes progressively from about 100 m TB00. They considered two methods of estimating the mean
on the western edge of Camarinal Sill to about 50 m at the transport across the sill: in the first one they used the time-
Gibraltar section. Initially the bore is characterized by two averaged along-strait velocities, fixing the interface depth at
large and steep internal waves that during the eastward 147 m, while in the second method they produced 30 min
propagation seem to be subject to an amplitude dispersion. time series of transport by finding the depth of the interface
What happen actually is that the bore, during its eastward for each measurement. In the first case the inflow transport
propagation, disintegrates into a train of internal solitary was estimated to be 0.46 Sv, while in the second case the
waves [Artale and Levi, 1990; Artale et al., 1990; Brandt et average over the time series gave an estimated transport of
al., 1996]. The model is not able to reproduce these internal 0.78 Sv.
solitary waves since nonhydrostatic effects are neglected and [31] At the eastern entrance of the strait other direct
the horizontal model resolution is lower in the eastern part of measurements have been carried out by BA01. They report
the domain; however the final effect is the same, since the an inflow of 0.81 Sv, estimated by using an inverse model to
bore is in any case dispersed. The model shows also that the predict every instant the interface displacement and the
bores are always released from Camarinal Sill in the course along-strait velocities, while using an interface at constant
of the fortnight period, even during neap tides. mean depth they estimated a transport higher than 7%
respect to the nonstationary interface case.
[32] As initially argued by Bryden at al. [1994] and more
4. Transport recently by TB00 the contribution of the fluctuating terms in
4.1. Effect of Tidal Forcing on Transport and Mean velocity and interface depth represents the main difference
Quantities between the two methods of computation. To better explore
[30] Recent estimates of transport based on direct mea- the effect of these fluctuating terms on the mean flow along
surements over Camarinal Sill have been carried out by the strait, we analyze numerical results of both experiment
Figure 8. M2 tidal constituent of the along-strait velocity at the Camarinal Sill section B. (a) Amplitude
in cm s1; the contour interval is 10.0 cm s1. (b) Phase relative to the Moon transit at Greenwich in
degrees; the contour interval is 10.
11 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 9. S2 tidal constituent of the along-strait velocity at the eastern section D. (a) Amplitude in cm
s1; the contour interval is 2.0 cm s1. (b) Phase relative to the Moon transit at Greenwich in degrees; the
contour interval is 10.
(with and without tidal forcing (hereinafter TE and NTE)), S2) and plus a residual component that also includes the
in a two-dimensional two-layer formulation; in particular internal bore:
we have integrated the model results in the cross-strait
direction choosing, as in SBA02, the 37.25 psu as interface cð x; t Þ ¼ c ~ M2 ð xÞ cos wM2 t þ jcM2 ð xÞ þ c
ð xÞ þ c ~ S2
isohaline between the two layers. In this case the momen- h i
c
ð xÞ cos wS2 t þ jS2 ð xÞ þ c^ ð x; t Þ; ð7Þ
tum and continuity equations for the upper layer can be
written as
where c represents the mean component, c ~ M2, c
~ S2 are the
amplitudes of the semidiurnal components, wM2, wS2 and
@u @ u2 r @ ðh he Þ
þ þ 0g ¼0 ð5Þ jMc , jSc are the frequencies and phases of the semidiurnal
@t @x 2 r1 @x 2 2
components, respectively, and c ^ represents the residual
component, which includes the internal bore. Time-aver-
aging the continuity equation (6), we obtain the following
@h @ ðhuÞ
þ ¼ 0; ð6Þ transport equation for the upper layer:
@t @x
@ uM ~
~ hM ~
uS ~
hS
where u is the velocity, h is the thickness of the layer, h is
u h þ 2 2 cos juM2 jhM2 þ 2 2
the surface elevation, he is the equilibrium potential, r0 is the @x 2 2
density of surface water, and r1 is the mean density of the !
layer. Moreover we decompose each model variable (c) in a cos ju jh þ ^ ^ ¼ 0:
uh ð8Þ
S2 S2
mean term, plus the two semidiurnal components (M2 and
Figure 10. S2 tidal constituent of the along-strait velocity at the Camarinal Sill section B. (a) Amplitude
in cm s1; the contour interval is 10.0 cm s1. (b) Phase relative to the Moon transit at Greenwich in
degrees; the contour interval is 10.
12 of 23C05011
13 of 23
SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE
Figure 11. Evolution of salinity perturbations during a tidal period. Contours are shown with an interval of 0.5 psu. The
snapshots are plotted at an interval of 2 hours. The time moments are referred to the surface elevation at Tarifa (insets).
C05011C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 12. Along-strait total upper layer transport in the case with (A) and without (B) tidal forcing,
and single component of upper layer transport in the case of tidal forcing: mean component (C), M2 and
S2 components (D, E), and residual component (F).
In Figure 12 all terms of equation (8) are plotted: the mean the current (B) shows a local maximum in the same region.
transport (C), the transport due to the M2 and S2 Residual (E) and S2 (D) terms appear negligible.
components (D, E) and the residual transport (F). Also [34] Always from Figure 13 one can note that in most part
plotted are the total upper layer transport (A) and the of the strait, and in particular in the eastern part, the mean
transport computed for NTE (B). This figure reveals that current is higher for TE (A) respect to NTE (B). Most of tidal
the contribution of the semidiurnal tidal component M2 energy is dissipated toward smaller scales, but we suppose
((~uM2 ~hM2 cos(juM2 jhM2 ))/2) is relevant over Camarinal that part of this energy can be transferred also to the mean
Sill whereas it is negligible at the eastern end of the strait. flow. This supposition is based on the fact that the only
In practice, while in the eastern region of the strait the difference between the two experiments is the tidal forcing,
mean current nearly determines the whole transport, it only and so the difference between the mean currents can only be
contributes about 60% of the total transport near caused by this forcing. It is plausible that everywhere within
Camarinal Sill, in agreement with the results of TB00 and the strait, with exception at Camarinal Sill and surroundings,
BA01. Contributions of the S2 component and of the bore are tidal fluxes interact with mean motion enhancing it. At
less than 4%, but, whereas the S2 component has its Camarinal Sill, dissipation processes (bottom friction, mix-
maximum effect near Camarinal Sill, the bore is more ing) and energy transfer to internal bore generation drop
effective in the eastern region. Deviations from the energy probably from both tidal and mean motion.
conservation relation equation (8) are mainly due to the [35] The effects of tide on the interface depth are shown
large entrainment of Mediterranean water near the hydraulic in Figure 14. Plotted are the mean depth of interface (A),
jump, just west of Camarinal Sill, whereas in the eastern part its range of variation due to the M2 component (Bmin,
diffusion of salinity moves the interface toward 38.1 psu Bmax), its range of variation due to the residual term
(see BA01, see also section 4.2 of this paper), implying an (Cmin, Cmax), and the interface depth for NTE (D). The
underestimation of transport in this zone when the upper variation due to the residual term is mainly due to the bore
layer is limited to 37.25 psu. and it is of the same order of that associated with the M2
[33] In order to investigate the effect of the tidal forcing component. In the presence of tidal forcing the mean depth
on the mean currents of the layers we have plotted in of the interface rises of about 20 m just west of Camarinal
Figure 13 (for the upper layer only) the mean currents u Sill up to about 40 m over the sill respect to the depth of
(A), half of the M2 current amplitude (1/2 ~uM2) (C), half of interface of NTE. The minimum difference of about 13 m
pffiffiffiffiffi amplitude (1/2 ~
the S2 current uS2) (D), the mean quadratic is limited at Tarifa Narrow. This interface rising is probably
residual ( ^u2 ) (E), and the current for NTE (B). It is evident related to the increased mixing between upper and lower
that the mean current (A) shows a local minimum in the layer introduced by tidal forcing. However, in spite of this
region where the amplitude of the M2 current (C) has its reduction of the upper layer thickness the transport
maximum value, whereas in the case without tidal forcing increases for TE, indicating that the effect of a stronger
14 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 13. Along-strait current amplitudes for the mean component u (A), the Mp
2 component
ffiffiffiffiffi (1/2 ~
uM2)
(C), the S2 component (1/2 ~ uS2) (D), the mean quadratic residual component ( ^ u2 ) (E), and for the
experiment without tidal forcing (B).
mean current, together with that of tidal transport prevail four layers framework. This was accomplished integrating
on the effect of depth reduction. model results in the across-strait direction and then choosing
[36] Mean surface elevation is another quantity that shows the following three separating isohalines: 36.8, 37.5 and 38.2
an unexpected change due to tidal forcing. It is well known psu. Figure 16 shows the thickness of the four layers and the
that there is a gradient of elevation between Atlantic Ocean depth of the three interface isohalines for NTE and TE; here
and Mediterranean Sea that compensates for the different the layers are numbered, starting from the upper one, from 1
densities of the two seas. In the presence of tide, there is a to 4 (hereinafter L1, L2, L3 and L4), while arrows represent
strong gradient of elevation just west of Camarinal Sill with volume fluxes between adjacent layers, i.e., entrainment and
an extra 1.9 cm of gradient between the two seas. The equa- detrainment.
tion for the mean elevation is analogous to equation (8); [39] Including to volume and salt conservation equations
in the presence of tide there are terms like 1/2UA fM h ~ terms representing intrusion of volume flux from one layer
2 M2
h
cos(jUAM2 jM2 ) (where UA represents the barotropic cur- into an adjacent one, it is possible to calculate entrainment
rent), that act to modify the mean elevation with respect to the and detrainment fluxes:
case without tide. This quantity has its maximum value near
Camarinal Sill, in coincidence with the maximum value of the @ ðBk hk Þ
fM . Dx þ rH ðBk hk uk Þ ¼ Fupkþ1 Fdwk Fupk þ Fdwk1
tidal amplitude of the barotropic current UA 2 @t
[37] The mean salinity field within the strait is also ð9Þ
modified by tidal forcing. This appears particularly clear
in Figure 15, where are shown the along-strait (section E)
difference between the salinity field obtained for NTE and a @ ðBk hk Sk Þ
fortnightly average of the tidally forced salinity field. This Dx þ rH ðBk hk uk Sk Þ ¼ Skþ1 Fupkþ1 Sk Fdwk
@t
figure shows strong differences in the mean profiles of Sk Fupk þ Sk1 Fdwk1 ;
salinity: the yellow spot (+0.6 psu) east of Camarinal Sill is
an evidence of the increased entrainment of Mediterranean ð10Þ
water in the upper layer due to the effect of tide; while the
long blue patch (0.3 psu) is due to an increment of where k indicates the number of the layer, hk and Bk are the
entrainment of the Atlantic water in the denser layer. The thickness and the width of the kth layer, Dx is the
hydraulic jump is characterized by strong mixing also in the longitudinal distance between two adjacent grid point
case without tidal forcing, and for this reason in the region, (600 m), and Fupk and Fdwk represent upward and
west of Camarinal Sill, the effect of tide is less evident. downward volume flux of the kth layer through the BkDx
surface, respectively.
4.2. Effect of Tidal Forcing on Entrainment [40] The resulting time averaged (on a fortnight period)
[38] In order to estimate entrainment and detrainment upward and downward fluxes, for NTE and TE, are
fluxes, we have analyzed model results in a two-dimensional shown in Figure 17. For NTE entrainment increases just
15 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 14. Along-strait mean depth of interface (37.25 psu) (A), its range of variation due to the M2
(Bmin, Bmax), its range of variation due to the residual term (Cmin, Cmax), and interface depth for the case
without tidal forcing (D).
west of Camarinal Sill (Figure 17a), i.e., in the same water flows from L2 to L3. Weaker entrainment is also
location of the stationary hydraulic jump. Here water evident at the western entrance of Tarifa Narrow. Here,
mass is exchanged prevalently between L3 and L4: water mass is exchanged prevalently between L1 and L2:
0.06 Sv of L4 water intrudes into L3, while 0.04 Sv of 0.013 Sv of L1 water intrudes into L2, while 0.01 Sv of
Figure 15. Along-strait (section E) salinity difference between the field obtained in the case without
tidal forcing and the field obtained by averaging the tidally forced salinity field on 15 days.
16 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 16
17 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
show a behavior similar to NTE. West of Camarinal Sill the
most active layers are the second, third and fourth: 0.075 Sv
of L4 water are entrained into L3 and 0.08 Sv of L3 water into
L2, while 0.07 Sv of L2 water are detrained downward L3
(see peaks number 1 in Figure 17b). East of Camarinal Sill
the most active layers are the first and second: 0.12 Sv are
exchanged from L1 to L2 and a slightly more is exchanged
from L2 to L1 (peaks n. 2), while 0.08 are exchanged from L3
to L2. Entrainment between layers decreases from Camarinal
Sill as far as Tarifa, from here to the eastern entrance of the
strait entrainment increments again showing two relative
maximum (peaks n. 4 and n. 5). Within Tarifa Narrow the
most active layers are the first, second and third: in the
western maximum, 0.08 Sv of water are exchanged between
L1 and L2 in both direction, 0.05 Sv of water flows from L3
to L2, 0.025 Sv are exchanged from L2 to L3, while only
0.01 Sv flows from L4 to L3. The second maximum shows a
behavior similar to the first one, except for the amplitudes
that are reduced of about 25% for layers 1, 2 and 3.
[42] Results shown for TE are representative of a complete
fortnight period, however for a complete understanding of the
tidal entrainment along the strait it is necessary to investigate
also the single ebb (toward Gulf of Cadiz) and flood (toward
Alboran Sea) tidal periods both for spring and neap tide.
[43] During ebb tide (not showed) only peaks n. 1 are
present, that is entrainment is located only west of Camari-
nal Sill where 0.18 Sv of water is exchanged from L4 to L3
and from L3 to L2 for spring tide and 0.12 Sv for neap tide,
while 0.15 Sv are exchanged between L3 and L4 for spring
tide and 0.09 for neap tide.
[44] During flood tide (not showed) peaks n. 1 are not
present and entrainment is located only at east of Camarinal
Sill and within Tarifa Narrow. East of Camarinal Sill, during
spring tide, the water exchanges principally from L1 to L2
and from L2 to L1 at a rate of 0.4 Sv, and from L3 to L2 and
from L2 to L3 at a rate of 0.21 Sv and 0.11 Sv, respectively.
During neap tide the active layers are always L1, L2 and L3
with weaker values for peaks n. 3, 4, and 5 while peaks n. 2
are totally absent. The only possible cause of a such behavior
is that the dynamical mechanisms generating peaks n. 2 are
Figure 17. Along-strait time-averaged (on a fortnight
activated only when intensity of tidal currents exceed a
period) entrained and detrained volume fluxes between
threshold value. Observing that at Camarinal Sill only during
layers (the same as Figure 16) for the case (a) without and
neap tide the entire water column it is not reversed com-
(b) with tidal forcing. Positive values (solid lines) indicate
pletely, we can assume that peaks n. 2 appear only when both
upward volume flux, while negative value (dashed lines)
the upper Atlantic layer and the lower Mediterranean layer
represent downward volume fluxes. Positive red, blue, and
flow simultaneously in the same direction.
green lines represent entrainment from L2 to L1, from L3 to
L2, and from L4 to L3, respectively. Negative red, blue, and 4.3. Transport Estimates
green lines represent entrainment from L1 to L2, from L2 to [45] The simple and intuitive method of computation of
L3, and from L3 to L4, respectively. inflow and outflow volume transport introduced in section 3
is strictly related to the existence of an internal surface of
water flows from L2 to L1. 0.01 Sv of water are also zero along-strait velocity, used as an interface between
exchanged from L2 to L3. Atlantic and Mediterranean water. However, this method
[41] TE shows an increased entrainment along whole the cannot be used to determine the volume transport when tidal
strait respect to NTE (Figure 17b). Strong exchange between forcing is included, since, as described in section 3.2, the
the first and second layer as well as the second and third layer semidiurnal tidal signal is so strong to reverse the inflow or
are located at Camarinal Sill and within whole Tarifa Narrow, the outflow during part of each tidal cycle, obscuring the
while exchange between the fourth and third layer seems to two-layer character of the mean flow. Another way of
Figure 16. Along-strait time-averaged (on a fortnight period) thickness of four layers (L1, L2, L3, and L4) separated by
three isohalines (36.8, 37.5, and 38.2 psu) for the experiment (a) without and (b) with tidal forcing. Arrows represent
volume fluxes (Fup and Fdw) between adjacent layers, i.e., entrainment and detrainment.
18 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 18. Internal surface salinity interface between the upper Atlantic layer and lower Mediterranean
layer.
defining the interface between upper and lower layer is by Camarinal Sill (section B) (Figure 19a), at Tarifa (section C)
using an isohaline. For example, Bryden et al. [1994] and (Figure 19b), and at the east entrance of the strait (section D)
Candela et al. [1989] used the 37.0 and 37.5 isohalines, (Figure 19c). In agreement with CA90 the largest amplitude
respectively, to define the exchange interface over Camarinal of the instantaneous transport occurs in the upper layer at the
Sill, while BA01 used the 38.1 isohaline at the eastern sill, and in the lower layer at the eastern section. The behavior
entrance of the strait. The choice of different values for the of tidal currents noted in 3.2 is apparent in the transports: it is
separating isohaline has to be ascribed, as argued in the clear that the upper currents have decreasing amplitudes
previous section, to the strong entrainment developing along going eastward and reverse their directions only as far as
the strait: in particular, along Tarifa Narrow the inflowing Tarifa, while the lower currents increase eastward and reverse
Atlantic water entrains denser water and west of Camarinal their direction everywhere in the strait.
Sill the outflowing Mediterranean water entrains part of the [47] Red lines in Figure 20 show the mean along-strait
inflowing Atlantic water [Bray et al., 1995; SBA02]. transports, obtained averaging over the fortnight period the
[46] Thus it emerges that it is incorrect to use a single ULT and LLT. From west to east the upper layer transport
isohaline as an interface for the whole strait. For this reason, ranges from 0.68 Sv to 0.9 Sv, while lower-layer transport
an alternative definition is used in this paper. We define as ranges between 0.5 Sv to 0.75 Sv. At Camarinal Sill the
interface the fortnightly averaged internal salinity surface transports are 0.85 Sv and 0.70 Sv for the upper and lower
associated with the internal surface where fortnightly aver- layer, respectively, while at the east entrance they are 0.9 Sv
aged along-strait velocity zero occurs. The internal salinity and 0.75 Sv.
surface obtained is shown in Figure 18; here it is possible to [48] At Camarinal Sill the most accurate estimates of
note that the salinity contrast between upper- and lower-layer transports from direct measurements are the ones given by
changes from 37.25 psu at Camarinal Sill up to 38.1 at the Bryden et al. [1994] and, more recently, by TB00. In their
east entrance of the strait. This salinity surface is then used to computation they considered the vertical movement of the
find the time-dependent depth of the internal surface interface interface and determined the transport of the upper layer to
between the two layers. Now we are able to calculate the be 0.72 ± 0.16 Sv and 0.78 Sv, respectively, and the
instantaneous upper (ULT) and lower-layer transport (LLT) transport of the lower layer to be 0.68 ± 0.15 Sv and
in the whole strait by using the following equations: 0.67 Sv, respectively. At the eastern entrance of the strait
Z Z the last most accurate estimates of transports are from
north 0
ULTð x; t Þ ¼ uð x; y; z; t Þdzdy BA01. They calculated the transports using an inverse
south hð x;y;t Þ model to predict for every instant the depth of the isohaline
Z Z ð11Þ
north hð x;y;t Þ 38.1 obtaining an upper layer transport of 0.81 ± 0.07 Sv
LLTð x; t Þ ¼ uð x; y; z; t Þdzdy; and a lower-layer transport of 0.76 ± 0.07 Sv. The results
south bottom
of the present study are in reasonable agreement with all
where u is the along-strait velocity and h is the time- these transport estimates since they lie within the error bars.
dependent depth of the interface. In Figure 19, the computed [49] Also plotted in Figure 20 (blue lines) are the tran-
upper and lower-layer transports are shown for a complete sports computed for the experiment without tidal forcing
fortnight cycle at three different cross-strait section over (equation (4)). Comparison with the results with tidal forcing
19 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 19. Sixteen days of computed upper (blue) and lower (red) layer transport at three different
cross-strait sections: (a) over Camarinal sill, (b) at Tarifa, and (c) at the east entrance of the strait.
shows that the tidal forcing increases transport, both in the with and without tidal forcing, are showed. It is evident that
upper and in the lower layer. It is also interesting to note that tidal forcing increases the particle fluxes in both directions.
the increment is different between upper and lower layer; in However a quantitative estimate of the effect of tidal forcing
particular, at Camarinal Sill is 37% for the upper layer and on particles flux is better deduced looking at ratios of
34% for the lower layer, while at the eastern entrance the particles arrived with and without tide; taking into account
increment is 28% and 29% for the upper and lower layer, also other intermediate sections at the longitudes 5150,
respectively. 5200, 5250. After 15 days, these ratios indicate that the
[50] With the purpose of verifying our transport estima- inflow transport increment is in the range 40%/65%, where-
tion, a comparative experiment using particle tracking has as the outflow increment is in between 15%/35%.
been carried out. A particle was released every 60 min from
each grid point of two cross-strait sections located at the
western (l ’ 5500) and eastern (l ’ 5180) end of 5. Summary and Conclusions
the strait, both with and without tidal forcing. In Figure 21 [51] In this paper we have presented a 3-D numerical
the total number of particles arrived at the west (east) model that is capable to reproduce reasonably well the main
section starting from the east (west) section, in the cases aspects of the semidiurnal tidal cycle in the Strait of
20 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
Figure 20. Variation of the eastward (positive values) and westward (negative values) transports along
the strait computed for the cases without tidal forcing (blue) and with tidal forcing (red). Dashed lines
represent net water flow.
Gibraltar and, also, to provide new water transport 1989; Hibiya, 1990; Longo et al., 1992; Brandt et al., 1996;
estimates. Izquierdo et al., 2001; Morozov et al., 2002], another 2-D
[52] Differently from previous modeling works, which model was instead developed to investigate the semidiurnal
have concentrated on specific aspects of the phenomenology surface tides in the strait [Tejedor et al., 1999], and two 3-D
related to tidal forcing, this numerical experiment tried to models were developed, in the last 14 years, to study tidal
reproduce all the principal effects of the tide. For example flows, internal tide as well as fortnightly modulation [Wang,
many 2-D models were developed to study the generation 1989, 1993]. However, none of these models, except partly
and propagation of internal waves within the strait [Pierini, Brandt et al. [1996], was able to estimate water transports
Figure 21. Total number of particles that arrived at (a) the west section starting from the east section
and at (b) the east section starting from the west section. Solid lines represent the experiment with tidal
forcing, while dashed lines represent the experiment without tidal forcing.
21 of 23C05011 SANNINO ET AL.: STRAIT OF GIBRALTAR SEMIDIURNAL TIDAL EXCHANGE C05011
along the whole strait and, at the same time, to provide an transport reduction (20%) assumed by Helfrich [1995], their
estimation of the impact of tidal forcing on the mean flow estimated transport increment reduces from 1.6 to 1.3, i.e., a
exchange. value very similar to that simulated by our model.
[53] The 3-D model described in this work can be [56] Experiments with particles seem to show an incre-
considered as a natural improvement of Wang’s models. ment for the upper layer tidal transport (1.4/1.65) greater
It is based on the model developed by SBA02: it makes than the ones calculated in the Eulerian way. However, this
use of a curvilinear grid and terrain-following vertical result must be evaluated with care, observing that the
grid, with mean horizontal resolution, within the strait, of particle count does not depend on the arriving depth of
500 m, it is forced at the open boundaries through the particles. For example, Atlantic particles are counted also if
specification of the M2 and S2 surface elevation. The they arrive at the Mediterranean section at a depth charac-
validity of our numerical model has been tested by terized by salinity greater than 38.1 psu, that is inside the
applying it to the description of tidal elevation, tidal part of upper layer that entrains the lower layer. In order to
currents and internal bores. It has been shown that results evaluate the increased entrainment due to tidal forcing, we
of our model are in good agreement with the observed have compared the number of Atlantic particles arrived at
tidal elevation amplitudes and phases. The model repro- the Mediterranean section, below the upper layer, for the
duces all of the known features of the spatial structure of case with and without tidal forcing. What we have observed
the M2 and S2 tidal waves: a decrease of more than 50% is that for the case without tide only 2% of Atlantic particles
in amplitudes and slight variations in phases along the arrived below 150 m, while for the case with tide this value
strait, a prevailing propagation of phases southwestward, increased up to 9%, so that the increased entrainment of
and nearly constant amplitude ratios and phase differences Atlantic water in the lower layer can be estimated as 7%.
between the M2 and S2 tidal elevations throughout the Applying this value of increased entrainment to reduce the
strait. At the same time the model has revealed a upper layer tidal transport computed with the particle
distribution of amplitude and phase in the region of tracking method, we obtained an increment in transport
Camarinal Sill (both for the M2 and S2) that is different limited between 1.30 and 1.53, values that are closer to
from the empirical cotidal chart presented by CA90. The those resulting from our direct Eulerian calculation. More-
predicted semimajor axis as well as amplitude and phase over, if we reduce the upper layer tidal transport computed
of the along-strait velocities are quantitatively and quali- by Farmer and Armi [1986] and Helfrich [1995] of the
tatively in good agreement with all available observed same factor (7%.), their tidal transport increase of 1.49 and
data. The simulated eastward and westward internal bores 1.12, respectively, positioning our result in between of
are also in agreement with available data as well as the them.
internal bore speeds in different sections of the strait [ 57 ] The study of calculated entrainment fluxes
coincide with those estimated by Izquierdo et al. [2001], (section 4.2) reveals that this phenomenon is effective
who used a completely different model. only at precise positions along the strait, in particular at
[54] However, the principal aim of this work was to Camarinal Sill and within Tarifa Narrow, i.e., the two zones
quantify the effects of tidal forcing on transport of where the flow has higher probability to become critical.
Atlantic and Mediterranean water along the strait. To this However a more theoretical treatment is needed to justify
end, initial conditions were produced by the stationary that higher values of entrainment fluxes will be associated
experiment, where about 12 cm of mean sea level with critical transition of the flow.
difference was set between west and east boundaries.
With this setting the stationary experiment simulated an [58] Acknowledgments. We thank many colleagues, particularly
inflow of 0.62 and 0.69 Sv at Camarinal Sill and Roberto Iacono, Adriana Carillo, and Paolo Ruti, for discussion and
Emanuele Lombardi and Antonio Iaccarino for informatic support. The
Gibraltar-Ceuta sections, respectively, whereas the outflow reviewers made helpful and knowledgeable suggestions. This work was
at the same locations was 0.51 and 0.58 Sv, with a done using climatological data supplied by S. Levitus and the MODB
mean net flow toward the Mediterranean sea of about project partners. This work was supported by the National project Ambiente
0.1 Sv. In presence of the semidiurnal tidal forcing (M2 + Mediterraneo – SINAPSI.
S2), the Atlantic inflow is of 0.85 and 0.90 Sv at the
same locations, whereas the Mediterranean outflow is of References
0.70 and 0.75 Sv. This implies a mean increment Armi, L., and D. M. Farmer (1985), The internal hydraulics of the Strait of
of 1.32 and 1.31 for the inflow and the outflow, respec- Gibraltar and associated sill and narrows, Oceanol. Acta, 8, 37 – 46.
tively, with respect to the stationary experiment. Armi, L., and D. M. Farmer (1988), The flow of Mediterranean water
through the Strait of Gibraltar, Prog. Oceanogr., 21, 1 – 105.
[55] Helfrich [1995] studied exchange flows through a Arnold, R. J. (1987), An improved open boundary condition for a tidal
two-dimensional variable geometry strait forced by a peri- model of Bass Strait, in Numerical Modelling: Application to Marine
odic barotropic (tidal) flow. He showed that the exchange Systems, edited by J. Noye, pp. 159 – 194, Elsevier Sci., New York.
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