The following paper is submitted to Oceanologica Acta for a special volume on the 8th Symposium of the Bay of Biscay (April 2002).  Similar and complementary results can be found in the presentation made during the Symposium (GIGON 2002)  and in a poster presented last February during the Micom workshop (LOM2002).
 

INTERNAL TIDES MODELLING IN THE BAY OF BISCAY. COMPARISONS WITH OBSERVATIONS

Pichon, a.1 Correard, s. m.2

1 Service Hydrographique et Océanographique de la Marine, Centre Militaire d?Océanographie, 13 rue le Chatellier B.P. 30316 29603 Brest Cedex France. e-mail pichon@shom.fr

2 Société HOCER, 5 rue Eugène Bourdon ZI de Kergaradec 29490 Guipavas, France. e-mail correard@shom.fr

Abstract

An Isopycnic Coordinate Ocean Model is used to represent the three-dimensional propagation of internal tides in the Bay of Biscay. The model is forced by the semi-diurnal tidal waves M2, S2, N2 and K2. A high resolution topography of French and Iberic continental slopes preserves the shape of the main canyons, which are areas of internal tides generation. Hydrological and velocity data collected during a French Naval experiment in 1994 are compared with the model results. Near the generation area, the vertical distribution of the internal tide amplitude, associated with a vertical shear of baroclinic tidal currents, is in agreement with the observations. Moreover, at most locations, the increase of the baroclinic current modelled near the bottom depth, matches the data. This increase is related to the distribution of the internal tide energy along characteristic rays. In most of the data/model comparisons, the vertical density variation in the deep layers shows a difference in phase in agreement with the rays theory. Over the abyssal plain, high horizontal shears of surface current are modelled at mid-Bay, i.e. in areas where the internal wave energy coming from the deep ocean encounters the seasonal thermocline. But, the location of these areas is very sensitive to the initial vertical density profile : the three-dimensional variation of the density has to be introduced in the initial conditions to improve the model results.

Résumé:

Un modèle en coordonnées isopycnales est utilisé pour représenter la propagation tri-dimensionnelle des ondes internes de marée dans le Golfe de gascogne. Le modèle est forcé par les quatre ondes semi-diurnes M2, S2, N2, K2. Une topographie haute résolution des talus continentaux Français et Espagnol préserve la forme des principaux canyons qui sont des zones de génération des marées internes. Des mesures de courantométrie et d'hydrologie, réalisées lors d'une campagne du Service Hydrographique et Océanographique de la Marine en 1994, sont comparées aux résultats de modèle. Près de la zone de génération, la répartition verticale de l'amplitude de l'onde interne associée à un cisaillement vertical de courants de marée baroclines est en accord avec les observations. De plus, l'augmentation de l?amplitude du courant barocline modélisée en certains points près du fond coïncide avec les données. Cette augmentation est reliée à la répartition de l'énergie des ondes internes le long de rayons caractéristiques. Dans la plupart des comparaisons modèle/mesures, l'évolution de la densité dans les couches de fond montre une différence de phase sur la verticale en accord avec la théorie des rayons. Au-dessus de la plaine abyssale, de forts cisaillements horizontaux des courants de surface sont modélisés au milieu du golfe de Gascogne, c'est à dire aux endroits où l'énergie de l'onde interne venant du fond de l'océan rencontre la thermocline saisonnière. Cependant la localisation de ces zones est très sensible aux conditions initiales en densité: pour améliorer les résultats du modèle, la variabilité tri-dimensionnelle de la densité dans la zone d'étude doit être prise en compte.

Introduction

In a stratified fluid, internal tides are generated by the passage of the astronomical tide above a steep bathymetry variation (e.g. the shelf break). The Bay of Biscay is an area where the internal tides are the most energetic (Baines,1982). Therefore, their effects in this region have an influence on the circulation over the continental shelf and over the abyssal plain, with an effect on the biological processes. In (Pingree et al., 1981, 1986) and in the ONDINE85 SHOM experiment, biological and physical observations shown that the biomass maximum (zooplankton and phytoplankton) is related to the cooling of the sea surface, where the internal tide amplitude is maximum. Following the theoretical model of (Mazé, 1987), a two-dimensional model of the Bay of Biscay with a two-layer seasonal thermocline (Serpette et al., 1989; Le Tareau et al., 1993) identifies the presence of cold water areas just above the shelf break as a result of interactions between large amplitude internal tides and mixing processes.

But the internal tide influence is not restricted to the near-surface layers over the continental shelf. (New, 1988) uses the linear model of (Prinsenberg and Rattray, 1975) along a realistic cross-section over the continental slope and the abyssal plain of the Bay of Biscay, to model the propagation of the internal tides in the vertical plane. From observations, (Pingree and New, 1989, 1991) show that the main part of the internal wave energy follows the characteristic rays slope, as theoretically shown by (Prinsenberg and Rattray, 1975) and (Baines, 1982). Other measurements (Pichon and Mazé, 1992) confirm the presence of large amplitude internal tides over the continental slope. Moreover, vertical velocity shears associated to the propagation of solitary internal waves are observed at mid-Bay (New and Pingree, 1990), and probably have an effect on the biological process through the mixing process. These previous studies show that there is an horizontal propagation of internal tides coming from many generation areas in the whole Bay. And even far away of the shelf break, the circulation is modified by the internal tides propagation on the vertical plane. Therefore, the three-dimensional effects of the topography and the spatial variation of the tidal forcing have to be taken into account to model the internal tide over the whole Bay of Biscay. Previous realistic studies of internal tides are developed in other regions, using cross-section models (Craig, 1988; Sherwin and Taylor, 1990; Holloway, 1996; Robertson 2001) and using fully three-dimensional models (Cummins and Oey 1997; Xing and Davies, 1998; Holloway, 2001). In this paper, the non linear three-dimensional propagation of internal tides in the Bay of Biscay is modelled with the Miami Isopycnic Coordinate Ocean Model, MICOM, developed by (Bleck et al., 1990). The model is forced by the semi-diurnal tidal waves with a realistic topography and stratification. The purpose is to model the effect of the internal tide propagation. Air-sea fluxes and the mixing due to internal tide are not introduced. The results are compared to data collected in the deep ocean during the MINT94 SHOM experiment.

The first part of the paper present the MINT94 experiment data and the model. In a second part, the modelled barotropic tide is validated and the three-dimensional evolution of the baroclinic tide is described, by focusing on the vertical sections where the data were collected. These comments support the comparisons between the modelled and the measured physical parameters, achieved in the third part.

2- Material and methods

2-1 The MINT94 experiment

The purpose of the MINT94 experiment was to achieve a description of the internal tides propagation over the abyssal plain. Measurements were collected along vertical sections perpendicular to the continental slope in order to observe a signature of these waves, mainly generated over the French shelf break. A second objective was to confirm that the Spanish continental slope was a generation area (this feature was modelled in a previous study where the domain of the (Le Tareau and Mazé, 1993) model was extended up to Ortegal Cape).

Velocity data was collected near the shelf break to evaluate the barotropic forcing term defining the internal tide amplitude in the generation area. In spring 1994, self-contained ADCP, moored on the bottom at 300m depth, were deployed at two locations: the DP94-1 and the DP94-2 moorings (figure 1). The measurements were recorded during one month, in weak stratification conditions. A data processing was performed to extract the depth-averaged velocity (Perenne and Pichon, 1999).

In Autumn 1994, density and velocity data were collected during the first days of September and October, i.e. around the Spring tide. At some locations, an ADCP was lowered from the ship with a CTD: hourly "yoyo" stations followed the evolution of the hydrological and velocity parameters over two tidal cycles (25 hours). At other locations, the density was measured by XCTD or XBT launched every half an hour. In order to include the deep ocean stratification in preserving a sampling frequency of one hour, profiles stations over the abyssal plain were only carried out down to 2500m depth. The French continental slope, the abyssal plain and the Iberic continental slope were sampled. The locations of the stations are plotted on figure 1. Details of the measurements (position, period, instrument) are summarized in table I.

2-2 The model

The MICOM equations (Bleck et al., 1990), describe rotating, stratified and viscous fluid motions in isopycnic coordinates: the momentum and continuity hydrostatic primitive equations are integrated over the thickness of each isopycnal layer. Previous studies using steep topography in a stratified fluid (Smith, 1992) confirmed the validity of the numerical results near the bottom slope. The model takes into account the sea-surface variations and gives the quickest barotropic mode and the lowest baroclinic mode with a time-splitting of the equations.The focus is on propagation tidal effects. Atmospheric momentum, heat fluxes and mixing processes are not considered.

The grid resolution of the model is chosen to well represent the canyons over the French continental slopes which are areas of the internal tides generation. An horizontal grid size of 1.8 km is used. Data processing from the SHOM data base leads to a smoothed bathymetry at the model resolution.

The domain is the Bay of Biscay, from 43N to 50N and from 15W to the isobath 80m over the continental shelves (figure 2).

The model is made with four open boundaries and is forced by the main semi-diurnal tidal harmonics (M2, S2, N2, K2) issued from the LEGI spectral model (Le Provost, 1996). A flow relaxation scheme (Martinsen and Engedahl, 1987) is used for the barotropic prognostic variables (depth-averaged velocities and sea surface elevation) over 13 grid points close to the boundaries (see figure 2). The internal tide is generated inside the domain and propagated towards boundaries. For the baroclinic mode, radiation conditions are applied to boundaries in order to allow waves propagation out of the computational domain. This radiation is performed by an implicit two dimensional Orlanski condition, applied to baroclinic prognostic variables (velocities and layer thickness), and is associated with a sponge layer over 13 grid points (see figure 2).

The barotropic and baroclinic time-step defined by the celerity of the surface tide and by the splitting method of the equations are respectively  and . The viscosity coefficient, u , is a Smagorinsky viscosity eddy coefficient (it is function of the absolute value of the total deformation of the velocity field) which is bounded by a lower limit ulow when the deformation of the velocity field is weak. u varies from  to  near the shelf break. The bottom friction coefficient is zero. As described in Xing and Davies (1996), the most important feature in the vertical current structure is the internal pressure gradient associated with the tide propagation ; the introduction of the bottom friction only reduces the intensity of the current in a near bed bottom layer of about 10 meters.

The model is initialized with a barotropic current field defined by the tidal forcing and with no baroclinic current. The density field is initially homogeneous in the horizontal plane. Vertically, a mean density is defined from two months, September and October. In the top 2500m, these profiles are monthly and spatially averaged from measurements collected during the MINT94 experiment. Below, an annual mean profile derived from the hydrological SHOM data base over the region is used. On figure 3, the mean Brünt-Vaisala frequency and the layered density profile are plotted for September case: thirty isopycnal levels represent the vertical density variations of the seasonal and permanent pycnoclines and of the deep ocean stratification. In the deep layers, i.e. between 2500m and 3600m, the Brünt-Vaisala frequency varies from 1.110-3 s-1 to 0.510-3 s-1: it is lower than the value defined previously by (New et al., 1988), but sufficient to allow the propagation of a semi-diurnal internal tide with a mean frequency of 1.410-4 s-1.

On figure 4, the October profiles are plotted in the upper 200m. In deeper waters, the mean vertical density profile is quite similar to September profile. In the seasonal thermocline, a cooling of the surface layers (i.e. an increase of the from 25.9 to 26.2) is observed between the two cases: this weak variation is a consequence of the measurements averaging. The wavelengths of the different baroclinic modes extracted from the vertical Brünt-Vaisala profiles are summarized in tables II and III to facilitate the interpretation of the model results.

3- Model results

3-1 Barotropic tide

The barotropic tide, calculated by MICOM, has to be validated over areas where strong topographic variations generate the internal tides. The barotropic tide is explored in a case with no stratification. The model is run during one month to extract each semidiurnal tidal components by harmonic analysis. At DP94-1 and DP94-2, the modelled barotropic tidal current is compared with the depth-averaged velocity calculated from ADCP observations (see table IV and figure 5). At DP94-1, for the M2 and S2 harmonics, the model overestimates the semi-major axis (bias of 5.3 cm s-1 for M2) and the semi-minor axis (bias of 2.3 cm s-1 for M2) of the tidal ellipses. At DP94-2, the semimajor axis is overestimated (bias of 6.2 cm s-1 for M2) while the seminor axis is underestimated (bias of 6.8 cm s-1 for M2). Locally the bathymetric gradient is north-south for both locations. The current ellipses is more cross shelf oriented in the model than in the data, with a difference of 15 to 25° at DP94-1 and 12 to 24° at DP94-2. The bias in the phase lag express a mean phase difference of 45 min and 2h45min at DP94-1 and DP94-2 respectively. At DP94-2, the M2 ellipses properties express a cross-isobath predicted current (37 cm s-1) slightly stronger than the observations (30 cm s-1), while the modelled along-isobath component (-15 cm s-1) is weaker than the observations (-21 cm s-1). These differences between model and data, particularly on the cross-shelf current and on the orientation of the ellipses, have an effect on the internal tides through the generation term (figure 5). But, the tidal velocity calculated by MICOM fit better to the observations than the tidal forcing used as initial conditions which is very weak at DP94-2 (for the M2 wave, the semi major and semi minor axis are of 15.0 cm s-1 and -7.4 cm s-1). These results show that the amplitude of the velocity is very sensitive to the local topography resolution. Therefore, even if there is still differences between model and data, the fine mesh of MICOM compared to the coarse grid of the spectral model (Le Provost et al. 1996) used to force the model at the boundaries and in initial conditions, improves the barotropic calculation. The discrepancies between model and observations, particularly on the phase of the tidal velocity, linked to the propagation of the surface tide, are probably due to the tidal forcing conditions.

3-2 Baroclinic tide

As it is described in (Serpette et al., 1989) , the baroclinic tide is generated by the spatial variations of the barotropic vertical velocity  near strong topographic accident such as the shelf break whereis the topographic gradient and  the barotropic horizontal tidal velocity. In the Bay of Biscay, two main generation areas are defined with a barotropic tidal forcing term greater than 10-5 s-1 and given by . These areas are located over the French shelf break (figure 6a) and the Spanish continental slope (figure 6b). They are characterized by strong bottom slope variations, such as canyon (figure 6a) or cape (figure 6b). The maximum barotropic forcing values ratio between the Iberic continental slope (1.4 10-5 s-1) and the French continental slope (8 10-5 s-1) is nearly 1/5. The internal tide generated in these two areas is characterized by vertical variations of isopycnals (with associated vertical and horizontal shears of currents) at tidal frequencies ; then, the internal waves take a few days to propagate inside the domain at different wave speeds defined by the baroclinic modes (tables II and III). The model is run over a period of 21 days, the initial baroclinic current being zero. The time needed by the baroclinic modes (see the wavelengths in tables I and II) to reach the limit of the domain corresponds to a transient state. The internal tide generation process is not the goal here, therefore we present the model results after this transient state.

Hereafter, the three-dimensional propagation of the internal tide over the abyssal plain is firstly described by horizontal variations of the surface baroclinic velocity. Then, the objective is to point out the correlation between these horizontal variations and the vertical internal tide propagation along a particular section S. This section is chosen to represent as well as possible the steep topography theoretical case (Baines, 1982).

The spatial variations of the East-West surface baroclinic current, after the Spring tide of September, is plotted on figure 7a. All baroclinic modes are propagated after 12 days of simulation: the model shows variations of surface baroclinic currents from -20cm s-1 to +20cm s-1 at the different baroclinic wavelengths of the internal tide. Indeed, successive positive and negative values are significative of the internal tide propagation. The most intense velocities correspond to the 45N/47N and 6W/8.5W region. They are due to the maximum values of the barotropic tidal forcing term between 6.5W and 7.5W near the French shelf break (figure 6a). The intense velocities observed in the South part of the model are the fact of the second generation area over the Iberic continental slope by 8.6W, 44.2N (figure 6b). The spatial repartition of the surface velocity and particularly the maximum negative values simulated around 7W-46.7N and 7.5W-45.6N are directly correlated to the propagation of the internal tide in the vertical plane. It can be explained by an example of the vertical distribution of the internal tide amplitude (figure 7b) and of the East-West baroclinic velocity (figure 7c) along S. The section S, perpendicular to the French continental slope, is chosen at the North-edge of the most energetic area (45N-47N, 9W-6W) in order to avoid the influence of the internal tides coming from the Iberic continental slope. The internal tide amplitude is defined by the ampitude of the interface elevation at the mean semi-diurnal frequency corresponding to the four tidal waves M2, S2, N2, K2, averaged over five tidal cycles around the Spring tide. On figure 7b, the maximum of internal tide amplitude follows the slope of the characteristic rays. The slope of the rays is defined as , where w is the tidal frequency, f the Coriolis parameter and N(z) the buoyancy frequency (New, 1988). Between 200m and 2000m, this slope is lower than the local bottom slope and the internal tide energy sweeps along the downward ray to be then reflected. Over the abyssal plain, the reflection on the bottom depth, H, occurs every 150km (the first downward ray is reflected at about 200km and the second one at 50km, figure 7b). This distance is close to the wavelength of the first baroclinic mode (table III). Indeed, the dispersion relation of the internal waves defined in the linear theory, with a constant Brünt-Vaisala frequency and a flat bottom, yields the ratio between the vertical mode  and the horizontal wavenumbers, kj, of the mode j: . For the first baroclinic mode, , , and l1 is proportional to the ray slope c(z).

On figure 7c, strong negative values of East-West baroclinic current in the upper layers (point A, B) are correlated to the resurgence of the internal tide coming from the deep ocean. The first and second maximum current areas located at 100km and 250km from the south end of the section S, correspond to the maximum negative values of figure 7a. The distance between these two maximum corresponds to the baroclinic first mode wavelength (points A and B of the section S on figure 7a).

In conclusion, over the abyssal plain, the spatial distribution of the East-West surface baroclinic velocity and particularly the horizontal shears within the most intensive area are induced by the propagation of the main baroclinic modes. These first results show that the propagation of the internal tide in the deep ocean has an influence on the distribution of the current in the upper layers.

The propagation of the internal tide over the French continental shelf has already been modelled (Serpette et al. 1989). We focus here on the values of the surface baroclinic currents in the North part of the French continental shelf, between 47N and 49N. In this realistic simulation, they reach more than 50cm s-1 at locations where waves interference are constructive (nodes and anti-nodes are the fact of the orientation of the bottom continental slope, different between 46.5N/47.5N and between 47.5N/48.2N, but are also due to canyons where are focused maximum values of forcing term (figure 6a). These high baroclinic velocities have probably an effect on the meso-scale circulation on the continental shelf.

In the following parts, we focus on the model results along sections where data were collected during the Mint94 experiment: the model outputs are presented along the two vertical sections S1 (PF01-PF05), S2 (PF06-PF10) for the September case and section S3 (PF11-PF15) for the October case (see figure 3). In this last case, the distribution of the horizontal tidal current is also briefly compared to the September case. On the sections, the internal tide amplitude has the same definition as on section S. The total across-slope current is the baroclinic velocity plus the depth-averaged velocity projected on the direction perpendicular to a bottom slope defined locally between isobath 200m and 1000m.

September stratification case

Section S1

On figure 8a, the vertical distribution of the maximum internal tide amplitude along the characteristic rays is not as clear as on section S (figure 7b). In addition to the shelf break topographic variations, strong bottom slope variations (at about the 80km position) are due to the Meriadzeck Terrace. These variations induce other generation areas at the two edges of this topographic feature, at a depth of about 2500m. Internal tide amplitude maximums are located between 2000m and 3000m around the Meriadzeck Terrace and vary from 50m to 70m in Spring tide. The PF04 position is also located in this area. Along S1, three waves are generated and interact. Two waves, generated near the shelf break and at the 75km position are in phase, whereas the third one, generated at 100km, is in opposition with the others. On figure 8b, the instantaneous interface elevations confirmed this difference in phase. The interface elevations are positive for the two first waves and negative for the third one. On figure 8c, the vertical distribution of the total across-slope velocity is correlated to the variations of the interface elevation. The maximum values, from 8cm.s-1 to 10cm.s-1, are confined above the Meriadzeck Terrace at about 2200m depth. Elsewhere on the section, the maximum horizontal velocity values are located between 0 and 2000m. This vertical velocity distribution (already observed on section S) is a consequence of the vertical density profile used in the model. Indeed, the buoyancy frequency N, greater than 1. 10-3 s-1 between 500m and 2500m (with a maximum value of 2.8 10-3 s-1 at 800m due to the Mediterraneen water) decreases from 1. 10-3 s-1 to 0.5 10-3 s-1 between 2500m depth and the bottom (figure3). These values, larger than the mean frequency of the tidal wave (1.4 10-4 s-1), allow a propagation of the internal tide in the whole water depth. But the maximum values of horizontal velocity are concentrated above 2500m depth where the vertical stratification and therefore the horizontal pressure gradients are important. Inversely, the maximum values of interface elevations (i.e. the vertical velocity) are concentrated in the bottom layers where the buoyancy frequency is weak. Along S1, the velocity is in phase opposition every 75km and in phase every 150km, as it is on section S (figure 7c). It confirms the main influence of the first baroclinic mode. On the vertical, this influence is characterized by a vertical shear of current which occurs at mid-depth at point PF02.

Section S2

On figure 9a, the internal tide amplitude plotted along section S2, exceeds 90m near the bottom depth at PF06 location. It is due to the characteristic ray slope which is very close to the bottom slope and therefore near the critical value (Baines 1982, Jezequel et al. 2002). The reflection of the characteristic ray occurs at the bottom depth (3000m). The maximum value of the internal tide amplitude decreases as the wave propagates over the abyssal plain. A part of this damping is due to the propagation of the baroclinic spring-neap tidal wave. The internal tide amplitude is an average of the interface elevation around the spring tide of the sea surface at the shelf break. Since the model is forced by the four main semi-diurnal waves, different tidal frequencies propagate at different wave speeds. Particularly, the baroclinic spring-neap tidal waves need several days to propagate from the generation area. Therefore, if the baroclinic spring tide is in phase with the spring tide of the sea surface near the shelf break, it is not the case at 180km (PF10) from the generation area. The damping of the amplitude is also due to the dissipation introduced in the model by the different viscous coefficients. On figure 9b, the instantaneous interface elevation, plotted after the spring tide, decreases by 40% at 70km (the maximum values decrease from 50m at 120km to 30m at 50km). On figure 9c, the total across-slope current is plotted at the same time than on figure 9b. The modelled maximum values are of 10cm s-1 to 15cm s-1 in the layers near the sea surface at about 75km, i.e. where the characteristic ray coming from the deep ocean encounters the sea surface. There is a transfer between the vertical velocity (which is zero in the top layers at 75km, see figure 9b) and the horizontal velocity.

October stratification case

The figure 10 shows the East-West surface baroclinic currents in the October case, which are weaker than in the September case (figure 7a). Within the main wave propagation area, the maximum current is of 15cm s-1 in the October case while it reaches 20cm s-1 in the September case. Indeed, the results of October and September are respectively shown before and after the spring tide. Nevertheless, the spatial distribution of the baroclinic current is the same in both cases (figure 7a and figure 10), considered at the same hour of the semi-diurnal tidal cycle. In fact, the difference between both buoyancy frequency profiles in the upper layers is not large enough to drastically modify the position of the horizontal current shears modelled at mid-Bay (see section 2.2 and figures 3a and 4a). Over the French continental shelf, the variations of the seasonal thermocline density gradient between September and October slightly modify the wavelength of the internal tide. Along section Sc (see figure 10), the internal tide wavelength extracted from the model output (not seen here) decreases from 33.5km in September to 30km in October. This variation is in good agreement with the calculation of the first baroclinic mode wavelengths with a bottom depth of 125m, i.e. over the continental shelf (see table II). Over the abyssal plain, the wavelength of the third baroclinic mode, defined by the seasonal thermocline density gradient decreases from 50 to 45km (see table III and figure 7 and 10).

On figure 11a, the internal tide amplitude before the Spring tide is plotted along section S3, where data was collected in October. The maximum internal tide amplitudes can reach more than 50m at mid-Bay, at 2000m depth. This high amplitude, compared to the other sections (S1, S2), is associated to the maximum forcing term area (see figure 6a). On figure 11b, the spatial distribution of the interface elevation plotted at a particular tidal time, is globally the same than on section S (figure 7b). But the maximum of the interface elevation does not follow exactly the slope of the characteristic rays. At mid-depth, there are successive maximums of the interface elevations, spaced of about 60km. They are due to a wave reflected on the Iberic continental slope. Indeed, at the same hour of the tidal cycle, the internal tide along the French continental slope is in phase opposition compared to the wave reflected on the Iberic continental slope. Therefore, the energy of the incident and reflected waves have the same distribution along the characteristic rays only if the distance between the two continental slopes is equal or close to  (where l1 is the first deep ocean baroclinic wavelength and n an integer). In our case where layers are defined from 0 to 4000m depth, the distance between the two continental bottom slopes is 350km. Then, with  (see table III), we are not exactly in a constructive interference case between the two continental slopes. On figure 11c, the spatial distribution of the total across-slope velocity shows particularly well the resurgence area where the top layers velocities are intensified by the internal wave coming from the deep ocean. In these stratification conditions, this area is situated at about 100km from the shelf break.

4- Data/Model comparisons

All data collected during the experiment are not presented here: we have chosen to focus on the measurements located on sections S1, S2 and S3 and well phased with the Spring tidal cycle, i.e. where the internal tide is well observed.

4-1 September stratification case

Section S1:

The section S1 includes velocity and density measurements available at PF02 and PF04. The North-South baroclinic velocity is used for the data/model comparison. Its orientation is closed to the across-slope component (near the shelf break, the orientation is 10° from North, while the mean orientation of the normal to the bottom continental slope is 30° ). The baroclinic velocity is similarly defined in the data and in the model output: it is the difference between the total current and the depth-averaged current.

On figure 12, the modelled and observed baroclinic component time evolution are displayed for PF02. This station over the French continental slope includes measurements down to 2300m depth (see table I). The temporal variation of the velocity, nearly in phase in the model (figure 12a) and in the data (figure 12b), follows the semi-diurnal tidal cycle. Maximum values of the baroclinic current reach 8cm s-1 on the model, and 12cm s-1 on the observations. These values validate the influence of the internal tide propagation on the velocity structure. Indeed, the barotropic tidal current (due to the surface tide) is only of 3cm s-1 for a water depth of 2400m (the data was collected 5 days before the Spring tide see table I). Nevertheless, the model result is weaker than the observed velocity: it is probably due to the viscosity of the model, slightly too high. The other main feature is the good agreement between the modelled and observed phase differences on the vertical: this vertical shear of baroclinic current above the continental slope is the result of the propagation of the internal tide in the vertical plane (see the model result of the across-slope current along the section S1, figure 8c). But, the depth of the vertical current shear is not exactly the same on the data (1400m) and on the model (1000m). The model water depth is directly correlated to the characteristic rays slope, which depends on the vertical stratification introduced as initial conditions. Therefore, an improvement of the model result could be achieved by introducing three-dimensional variations on the initial density field.

On figure 13, the time evolutions of the modelled and observed baroclinic component are displayed for PF04. This point, further offshore than PF02, is located at the South edge of the Merriadzeck Terrace (see figure 1 and figure8b). In both cases, the baroclinic velocity follows the semi-diurnal tidal cycle (figures 13a and 13b), but the data is much more noisy than the model result. The observed and modelled vertical shears of current are in nearly good agreement only between 20h and 24h. The main feature here is the increase of the velocity near the deepest level, at 2400m, in the model as well as in the data: maximum values can reach more than 20cm s-1 in the observations. In the model result along the section S1 (figure 8), this velocity increase near the deepest level is easily explained by the generation area located near the point PF04.

On figure 14, the time evolution of the isopycnal interfaces is plotted at the point PF04. In the data and in the model result, an increase of the internal tide amplitude at a water depth of 2000m is observed. The magnitude of the internal tide elevation modelled by MICOM can reach about 50m (see section S1, figure 8b); it is of the same order than in the data. This increase of the internal tide amplitude in the near-bed layers is probably due to an upward ray coming from the South edge of the Meriadzeck Terrace (see section 3.2). Unfortunately, the comparison is not so good in the time variations. There is a delay of about 4 hours between the model and the data which is not easily explainable. A poor definition of each forcing term (topography, surface tide, density) could be evoked. PF04 is close to strong topographic variations ; therefore, a bad definition of very fine topographic structures involving other generation locations could explain this difference rather than a bias on the initial density structure.

Along section S1, the vertical shear of current modelled at PF02 and the existence of several generation areas, particularly near the Meriadzeck Terrace (PF04), are confirmed.

Section S2:

Along the section S2, the main objective is to confirm by the observations the modelled vertical shear of current and the increase of the internal tide amplitude in the near-bed layers of the continental slope.

On figure 15, the time evolution of the North-South baroclinic velocity is plotted at PF06. This point is located over the French continental slope at a water depth of 1100m (see table I). As for PF02 and PF04, the time evolution of the velocity follows the semi-diurnal tidal cycle. The agreement between the model result ( figure 15a) and the data ( figure 15b) is nearly good with a phase difference of about two hours, probably due to the bias on the predicted barotropic current (see section 3.1). The vertical phase opposition, i.e. the vertical shear of current, is particularly well modelled between 50m and 1000m. Near the sea-surface, the data collected by the lowered ADCP are not available. The modelled vertical shear of current due to the seasonal thermocline can not be confirmed. In the near-bed layers, the predicted current (15cm s-1) is slightly weaker than the measured current (20cm s-1), which is an effect of the model viscosity.

The time evolution of the East-West baroclinic component plotted on figure 16 at the same location, PF06, confirms the previous result. In the data, there is an advance in phase of the velocity in the near-bed layers compared to the velocity in the near-surface layers. It is in agreement with the vertical distribution of the modelled current above the continental slope: the vertical shear of current is due to the propagation of the different baroclinic modes, mainly the first one, which generates a difference in phase across the ray characteristics (see figure 9c).

Hence, at the same location, the time evolution of isopycnal interfaces is plotted in the top layers (figure 17) and in the bottom layers (figure 18). This evolution follows the semi-diurnal tidal cycle and well represents the variations due to the internal tide. The vertical modulation of the internal tide amplitude is well-modelled even if underestimated in the layers of weak stratification (between 100m and 200m). As in the velocity evolution, the model results are nearly in phase with the data: by comparing model and data trough locations, the phase lag is 0.1 day (i.e. 2h). The amplitude of the internal tide between 400m and 1000m depth (100m crest to trough) is especially well modelled with a vertical variation of phase in good agreement with the data: the advance in phase of the internal tide in the near-bed layers compared with the near-surface layers is confirmed. On the section S2, the variations of the bottom slope near the shelf break are more regular than on section S1 and the resolution of the bathymetry is probably sufficient to well represent the internal tide.

The time evolution of the modelled and observed density is plotted on figure 19, for PF10. This point is located over the abyssal plain, at the limit of the section S2 (figure 9), i.e. at 180km off the shelf break. The model results and the data do not give a real information on the vertical distribution of the internal tide amplitude which is weak compared to PF06: it is probably due to the damping of the wave. But even if we are far away from the generation area, the modelled internal tide is nearly in phase with the data in the layers where the comparison is possible (i.e. between 200m and 1500m).

4-2 October stratification case

In October, density data was collected along the section S3. The main objective is to point out the differences or the similarities between the observed and modelled internal tide phases, at locations over the abyssal plain. The phase variations, in term of time evolution and vertical distribution, are compared far away from the generation area in order to estimate the validity of the three-dimensional waves distribution.

The observations at PF13 are collected three days after the surface spring tide, and therefore are two days after the baroclinic spring tide at PF13 (for the third baroclinic mode). The time evolution of the isopycnal interfaces inside the seasonal thermocline is displayed on figure 20. Despite the moment of the observation in the tidal cycle and the distance from the generation area (75km), the internal tide amplitude is high ( 40m from crest to trough, see the depths of isopycnal 27.0 and 27.1). Moreover the modelled amplitude is in good agreement with the observations. In the time evolution, the differences are similar to the other locations : the model is nearly in advance compared to the observations. This feature is found again in the time evolution of the deeper isopycnal interfaces plotted on figure 21. In the deep layers, the vertical variation of the internal tide phase may be estimated in following a particular trough on the different interfaces. Model result, plotted on figure 21a, show a delay of about 4 hours between the internal tide troughs at 1500m and 200m. This delay is also well observed on figure 21b. This numerical result firstly in agreement with the observations, also confirms the linear theory of the internal tide propagation with a flat bottom, which yields a vertical variation of the internal tide phase across the rays slopes (this one is at 1000m depth for PF13 see figure 11a). This vertical phase variation (delay modelled between the internal tide near the bottom and near the sea surface in agreement with data) is opposite in sign at PF13 located of an upward ray as PF13, compared to locations on an downward ray (PF06). Hence, the vertical distribution of the internal tide amplitude is not really well modelled particularly in the deep layers, i.e. 1500m and 2500m: the modelled amplitude is really too high compared to this of the observations. This "error" on the modelled amplitude, could be induced by the initial density conditions which are averaged on the horizontal plane. Indeed, as shown in figure 11a where the internal tide amplitude is plotted along the section S3, PF13 is at the edge of the first upward energetic ray. Therefore, a weak bias on the position of the ray, strongly dependent on the density structure, could explain the differences between the modelled and observed amplitude. This "error" is probably also a consequence of the too high barotropic velocity modelled at the top of the section S3 (see the data/model comparisons for DP94-2 in section 3.1).

The data-model comparison at PF14, located at 140km from the French shelf break is shown on figure 22 where the time evolution of the isopycnal levels in the deep layers is plotted. The observations were collected four days before the spring tide of the sea surface. PF14 is situated in time after the neap baroclinic tide if we consider the delay due to the propagation of the wave baroclinic group from the generation area. It explains why the internal tide amplitude is weak compared to PF13 location, in the model as well as in the data. On figure 22a, the modelled internal tide amplitude, represented by the vertical variation of the isopycnal levels, is maximum at 2000m depth. This increase of the internal tide amplitude at mid-depth, not modelled on the other sections, is probably an effect of the internal tide reflection on the Iberic continental slope (see figure 13 and section 3.2). In the data, figure 22b, the internal tide amplitude is larger at 1500m depth than at 500m. Below 1500m, if there are still strong vertical variations of isopycnal levels, the data (XCTD measurements) is very noisy. The observations are not sufficiently accurate to confirm the model result. The time evolution of the predicted internal tide is fairly good with a trough of the isopycnal levels at almost the same tidal hour (day 276,8) than in the data. The vertical variation of the internal tide phase occurs between 150m and 700m depths in the data (dashed lines on figure 22b), with a delay of the deep layers compared to the upper one. This is in agreement with the location of PF14 across the second modelled upward ray (see figure 11a). But the model result of figure 22b is plotted after the neap baroclinic tide, and the internal tide amplitude is too weak to confirm the observed vertical variations of phase.

In the October stratification case, the comparisons made far away from the generation area show that the model nearly well reproduce the three-dimensional propagation of the internal tide. But, there is a bias on the predicted internal tide amplitude. The strong across-slope barotropic velocity modelled at the shelf break on the section S3, i.e. in the generation area, and the use of an average vertical density profile in the initial conditions are probably the cause of the too high predicted amplitude.

Discussion

In this study, the three-dimensional distribution of the internal tides modelled in the Bay of Biscay by MICOM is compared with observations. All the internal tide process is strongly dependent on the barotropic forcing term, i.e. the tidal velocity in the generation area, mainly situated near the shelf break. Therefore, the barotropic tidal velocity modelled by MICOM in an homogeneous case, is compared with measured velocity at the top of the French continental slope. The amplitude of the barotropic current calculated by MICOM at DP94-2 is nearly in agreement with the observations. It is an essential result since DP94-2 is inside the main generation area of internal tides. The resolution of the model is sufficient to have a nearly good forcing term, which is strongly dependent on the local topography. But, the situation of the velocity ellipses are not really in phase with the observations. There is an advance in time from one to two hours between the modelled velocity and the data, which is found again in the modelled internal tide and associated baroclinic current. To have a better fit with the data, we have to improve the modelling of the current due to the surface tide, particularly in areas where topographic variations are important and modify the characteristics of the current ellipse.

The modelled results in the stratified cases are more or less similar in September and October: it is due to the using of an averaged density profile for each period. Therefore, differences in the internal tide distribution which could be induced by the horizontal density variations of the upper layers, are not represented.

Over the continental shelf and on the abyssal plain, the internal tides have an effect on the velocity structure. In the Celtic sea, internal tides coming from areas where the orientation of the bottom continental slope is different, produce waves interference: in particular locations, the baroclinic tidal current near the sea surface can reach +/- 40cm s-1 in spring tide which has to be added to the barotropic velocity. Therefore, the effect of the internal tide on the continental shelf circulation has to be investigated in the future. Over the bottom continental slope, the data/model comparisons at points PF02 and PF06 confirm the influence of the internal tide on the vertical shear of the across-slope velocity. At PF06 in deep layers, this one reaches +/-15cm s-1 on the data, a value three times larger than the barotropic tidal current. But, the modelled velocity is weaker than the observations; it is due to the scheme of the turbulent viscosity intensified by the horizontal shears of current and dependent on the spatial resolution. This numerical weakness acts directly on the velocity amplitude in the whole domain since the highest horizontal shears of current due to the internal tides occur in the generation area close to the shelf break. High internal tides are also modelled along a particular section (S3) defined by a line Ushant/La Coruna. These one generate horizontal shears of surface velocity, focused in areas defined by the direction of propagation of the internal tide energy on the vertical plane. Along this section, the modelled amplitude slightly too high compared with the observations is probably due to an overestimate of the barotropic forcing term on the across-slope component. The interest of a realistic modelling is well evidenced along the section S1. Model shows evidence of a generation area near the South edge of the Meriadzeck Terrace, where the horizontal tidal current and the internal tide amplitude are intensified near the bottom depth, i.e. by 2400m of water depth. This feature is confirmed by the observations. The variation of the topography due to the Meriadzeck Terrace also generates different internal tidal waves which produce interference processes. Hence, the vertical variations of the internal tide phase modelled and observed along sections S2 and S3 are nearly in agreement with the ray theory with a variation of phase is in opposition at PF06 (downward ray) compared to PF13, PF14 (upward ray).

Nevertheless, the existence and the location of areas at Mid-Bay of Biscay where the internal tide inside the seasonal thermocline is intensified has to be confirmed by future observations. More, these areas, strongly dependent on the rays slope are very sensitive to the stratification introduced as initial condition. Therefore, the aim of the future work is to run the model with an initial three-dimensional density, in order to introduce the spatial variations of the permanent and seasonal pycnoclines between the North and South part of the domain. A realistic density field is also necessary to well model the mixing processes induced by the internal tides.

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Figure 1: Map of the Bay of Biscay showing stations (PF01 to PF18) and moorings (DP94-1 and DP94-2) locations during the MINT94 experiment (see table 1 the experiment details). S1,S2 and S3 are model sections along measurements locations.

Figure 2: Numerical domain. Over the continental shelves, the domain is bounded by the isobath 80m. The relaxation zone and sponge layer are over 13 grid points (i.e. » 24 km).

Figure 3: Initial density profil in September. (a-b) Brünt-Vaisala frequency, N, from 0 to 150m depth (a) and from 150m to 3500m depth (b). The solid bold line is the mean Brünt-Vaisala profile and the others are the tidal-cycle-averaged N profiles from stations. Inside the seasonal thermocline, there is a large dispersion of the Brünt-Vaisala frequency around the mean maximum value.(c-d) Layered vertical density from 0 to 150m depth (c) and from 150m to 3500m depth (d). Below 2500m, the large layers (300m to 500m thickness) are defined by the weak stratification (N < 10-3s-1).

Figure 4: Initial density profil in October from 0 to 150m depth. Below 150m depth, the profile is the same as in September. (a) Brünt-Vaisala frequency, N. The solid bold line is the mean Brünt-Vaisala profile and the others are the tidal-cycle-averaged N profiles from stations. The mean profile is different from PF12 and PF15 profiles. (b) Layered density profile.

Figure 5: Barotropic tidal ellipses at DP94-1 and DP94-2, comparison between observation (dashed lines) model (solid lines) and forcing (dash-dotted lines).

Figure 6: Local topography and tidal forcing term,  where  is the barotropic tidal current for the M2 wave and  is the bottom depth. (a) Over the French continental shelf, isocontours are 3.10-5, 4.10-5, 6.10-5 , 8.10-5 s-1. The maximum values situated at depth of 300m, between 5.5W and 7.5W, defines the main generation areas. (b) Over the Iberic continental slope, isocontours are 1.10-5, 1,2.10-5, 1,4.10-5 s-1. The maximum values are situated at depth between 500m and 1000m at the North edge of the Ortegal Cape (44.2N and 8.5 W to 9W).

Figure 7: (a) Modelled East-West surface baroclinic velocity in September on 09/ 09 at 19h (after the spring tide). Over the abyssal plain, velocity varies from -20cm s-1 (red) to +20cm s-1 (yellow). Over the continental shelf, maximum values reach +/- 50 cm s-1 at different areas (around 7W/48N and 5.5W 47.25N); at 50km from the shelf break maximum values of the baroclinic current reach +/ -30cm s-1. (b) Distribution of the internal tide amplitude along the section S from 8.9W 45.0N to 6.9W 47.6N. The amplitude is the Fourier coefficient of the model result at the mean frequency of the four tidal waves, calculated over five tidal cycles. The bold dashed lines represent the paths of the characteristic rays. (c) Evolution of the total across-slope velocity along the section S, on 09/09 at 19h. The angle between the normal to the bottom slope and the North is 25° . Dotted lines are negative values, dashed lines are positive values.

Figure 8: (a) Distribution of the internal tide amplitude along the section S1 from 9.5W/46.9N (PF05) to 8.5W/48.10N (close to DP941), calculated as for section S (figure 7b). (b) Distribution of the interface elevations along S1 on 09/09 at 19h (same tidal hour as for figure 7). (c) Distribution of the total across-slope velocity along S1 on 09/09 at 19h. The angle between the normal to the bottom slope and the North is 30° . Dotted lines are negative values, dashed lines are positive values. The two bold shaded lines are the PF04 and PF02 locations.

Figure 9: (a) Distribution of the internal tide amplitude along the section S2 from 8.23W/46.25N (PF10) to 7.0W/47.6N, calculated as for section S (figure 7b). (b) Distribution of the interface elevations along S2 on 09/09 at 21h. (c) Distribution of the total across-slope velocity along S2 on 09/09 at 21h. The angle between the normal to the bottom slope and the North is 25° . Dotted lines are negative values, dashed lines are positive values. The bold shaded line is the PF06 location.

Figure 10: Modelled East-West surface baroclinic velocity in October on 06/10 at 6h (before the spring tide). Over the abyssal plain, velocity varies from -20cm s-1 (red) to +20cm s-1 (yellow). Over the continental shelf, maximum values reach +/-40 cm s-1 at different areas (around 7W/48N and 5.5W 47.25N); at 50km from the shelf break maximum values of the baroclinic current reach +/-25cm s-1.

Figure 11: (a) Distribution of the internal tide amplitude along the section S3 from 7.32W/ 45.66N (PF15) to 5.8W/47.4N (close to DP942), calculated as for section S (figure 7b). (b) Distribution of the interface elevations along S3 on 06/10 at 6h (same tidal hour as for figure 10). (c) Distribution of the total across-slope velocity along on 06/10 at 6h. The angle between the normal to the bottom slope and the North is 16o. Dotted lines are negative values, dashed lines are positive values.

Figure 12: Time series of North-South baroclinic velocity at PF02 location from the model (a) and from lowered ADCP measurements (b) during two semi-diurnal tidal cycles (25 hours).

Figure 13: Time series of North-South baroclinic velocity at PF04 location from the model (a) and from lowered ADCP measurements (b) during two semi-diurnal tidal cycles (25 hours).

Figure 14: Time evolution of isopycnal interfaces from the model (a) and of isopycnal depths from CTD stations between 0-2300 m depth (b), during two semi-diurnal tidal cycles at PF04 location.

Figure 15: Time series of North-South baroclinic velocity at PF06 location from the model (a) and from lowered ADCP measurements (b) during two semi-diurnal tidal cycles (25 hours).

Figure 16: Time series of East-West baroclinic velocity at PF06 location from the model (a) and from lowered ADCP measurements (b) during two semi-diurnal tidal cycles (25 hours).

Figure 17: Time evolution of isopycnal interfaces from the model (a) and of isopycnal depths from CTD stations between 0-150 m depth (b), during two semi-diurnal tidal cycles at PF06 location.

Figure 18: Time evolution of isopycnal interfaces from the model (a) and of isopycnal depths from CTD stations between 0-1100 m depth (b), during two semi-diurnal tidal cycles at PF06 location.

Figure 19: Time evolution of isopycnal interfaces from the model (a) and of isopycnal depths from XCTD stations between 0-2200 m depth (b), during two semi-diurnal tidal cycles at PF10 location.

Figure 20: Time evolution of isopycnal interfaces from the model (a) and of isopycnal depths from CTD stations between depths 0 to 150 m (b) , during two semi-diurnal tidal cycles at PF13 location.

Figure 21: Time evolution of isopycnal interfaces from the model (a) and of isopycnal depths from CTD stations over depths 0 to 2700 m (b), during two semi-diurnal tidal cycles at PF13 location.

Figure 22: Time evolution of isopycnal interfaces from the model (a) and of isopycnal depths from XCTD stations between depths 0 to 2300 m (b), during two semi-diurnal tidal cycles at PF14 location.

Table I: Summary of stations and ADCP moorings during MINT94 experiment.

Table II: Horizontal phase speed and wavelengths of the baroclinic modes 1 to 3 at the M2 tide frequency calculated with a bottom depth typical of the French continental shelf (125m) and with 10 layers (from 0 to 125m depth) .

Table III: Horizontal phase speed and wavelengths of the baroclinic modes 1 to 3 at the M2 tide frequency calculated with a bottom depth typical of the Abyssal plain (4500m) and with 33 layers.