In this section, we investigate the impact of tidal forcing on the Bay of Biscay by comparing the results of the two model simulations (TON and TOFF). We consider the differences in the thermohaline properties, the circulation patterns and the evolution of the stratification in different areas of the domain. Finally, we perform spectral analysis of the SSH evolution, in order to identify the impact of tides on the energy distribution at different time and spatial scales.
As an illustration of the tidal forcing applied in the TON simulation (and excluded from the TOFF simulation), we present in
Figure 2 the amplitude and phase of M2 and M4 tidal constituents. M2 is the major tidal constituent in the Northeast Atlantic Ocean with amplitudes exceeding 3 m in the domain (
Figure 2a). M4 is a principal quarter-diurnal compound tide generated from the interaction of M2 with itself. The M4 amplitude is more significant over the continental shelf than the abyssal plain, with maximum amplitudes localised in the Armorican shelf and the English Channel (
Figure 2b). The tidal map of M4 shows two amphidromic points (zero amplitude) located in the English Channel as described by [
46].
3.1. Distribution of Thermohaline Properties
Figure 3,
Figure 4 and
Figure 5 present the observational data OSTIA [
47] and the modelled Sea Surface Temperature (SST) and Salinity (SSS), respectively. The data and model results are illustrated for two representative days at the end of summer (upper panels) and in mid-winter (lower panels). In
Figure 4 and
Figure 5, the left panels correspond to the TON simulation, the middle panels to the TOFF simulation and the right panels to their difference “TON minus TOFF”. In summer, both simulations reproduce the characteristic “warm pool” in the southeastern corner of the Bay of Biscay (
Figure 4a,b), with SST values exceeding 20
C verified also by the OSTIA-SST satellite observations (
Figure 3a). During the same period and over the Celtic and Armorican shelves, we observe the Ushant tidal front at the entrance of the English Channel (
N,
W) in the OSTIA-SST dataset and only in the realistic TON simulation; we observe cold waters at about
C in the vicinity near the coasts and warmer waters outside the front (
Figure 3a and
Figure 4a). During winter, there is a marked spatial variability in hydrography with warmer and generally saltier waters in the open ocean compared with the shelves (i.e., by approximately 12–13
C and 35.6–35.8;
Figure 3b,
Figure 4d and
Figure 5d). A thermal front observed in the OSTIA-SST and in both simulations during winter, separates the coastal cold waters (i.e., values do not exceed 10
C) of the Armorican shelf influenced by the river plumes, with the open ocean warm waters. The same period, in the abyssal plain, we observe the presence of coherent eddies and filaments in both simulations, leaving a clear imprint of the circulation pattern on the SST and SSS fields (
Figure 4d,e and
Figure 5d,e) in contrast with the smoothed OSTIA fields (
Figure 3b). When we validate the model with in situ observations at the Channel Lightship station (
N
W;
https://marine.copernicus.eu;
Figure S1), we find that the TON simulation has smaller Mean Absolute Error (MAE) at about
C over the simulation period, as opposed to the TOFF experiment with MAE
C.
Differences in SST between TON and TOFF simulations suggest that the addition of tidal forcing produces high spatial changes of SST locally exceeding 1
C (
Figure 4c,f). The tidal forcing contribution to the SST fields is different in the two periods. For example, during summer, the SST is colder when tides are activated, while the opposite is true during the winter period (
Figure 4c,f). In summer, the SST is colder in TON compared with the TOFF simulation in the English Channel, the shelves (near the continental shelf break at approximately
N) and in the Spanish continental slope at approximately
N (
Figure 4c). The largest temperature differences are locally observed in the position of the Ushant front, which is formed only in the TON simulation (
Figure 4a–c). The latter result is of substantial importance as oceanic fronts play a key role in the circulation of shelf seas which are regions of intense biological activity. Another finding is that the northern coast of the English Channel has warmer SSTs than the rest of the Channel when tides are activated, which can affect the ocean model’s skill to represent the SST compared to satellite observations (cf. [
48]).
Examining the differences in winter, the SST is warmer when tides are activated, notably in the English Channel and in the largest part of the abyssal plain (
Figure 4f). In the Armorican shelf, we observe small-scale contrasting positive–negative SST fields for the difference “TON minus TOFF” (i.e., differences up to 1
C), attributed on the frontal displacement of the river plumes. The latter is also in agreement with the coastal SSS fields modulated by the river plumes (
Figure 5f). In the same area, along the continental slope at about
W to
W, the SST appears to be colder in the simulation with tides than without tides. This SST cooling is less intense compared with values observed during summer (
Figure 4c). This cooling is most likely associated with internal tides breaking in the continental slope and subsequently enhancing mixing in the shelves, bringing cold bottom waters on the surface (cf. also [
21]).
In
Figure 5c,f, we present the differences in SSS between the two simulations and the two periods. The greatest differences are observed in the English Channel (i.e., greater than 0.6), most notably in the entrance of the Channel (near
N,
W). This is possibly explained by the fact that the Ushant front acts as a barrier to the intrusion of low salinity waters (i.e., values < 35.2; cf. [
49]), originated from the Loire and Gironde rivers. We note that the SSS increases (in both periods) in the English Channel when tides are activated, in contrast to SST which only increases in the TON simulation and only during the winter. The rivers freshwater transport from the shelves to the open ocean is constrained when tides are activated in the model simulation, probably due to changes in stratification and mixing (discussed in
Section 3.3). This pattern is observed during summer, when occurring high salinity differences (i.e., values up to 0.6) in the transition area of the Landes Plateau at approximately
N,
W (
Figure 5c).
Figure 6a,b shows the temperature difference between the surface and bottom waters during summer for the TON and TOFF simulations. As shown in
Figure 6a, the English Channel is an area characterised by intense tidal mixing, illustrated by
with values lower than
C. The location of the Ushant front can be identified by the
isotherm of
C (
Figure 6a; black line) and the area spanned by the 2.7 and 3.0 contours of the Simpson–Hunter parameter (
Figure 6a; magenta lines). In the simulation without tides,
has greater values than the
C threshold (e.g., up to 7
C) confirming the absence of fronts in the area (
Figure 6b).
Figure 6c presents the longitudinal cross section of the water column temperature near the entrance of the English Channel. The cross section was selected in the area where the
isotherm of
C and the SH contours are collocated, denoting the presence of the Ushant tidal front (
Figure 6a). We observe a homogenisation of the water column east of
W (
Figure 6c). On the contrary, in the simulation without tides, we observe a well-formed seasonal thermocline at approximately 40 m depth (
Figure 6d).
3.2. Relative Vorticity and Divergence
In this section, we investigate the relative vorticity and surface divergence fields to assess the dynamical impact of tides on the Bay of Biscay mesoscale activity. In
Figure 7, we depict the relative vorticity, with and without tides, for the same dates as in the SST and SSS fields. As expected, during winter, we observe in both simulations more intense circulation patterns in the abyssal plain compared with the summer circulation, attributed to coherent and more energetic eddies and vortices constrained in the abyssal plain by the continental slope.
Near the shelf break and only during summer in the TON simulation, there is a crest-through signal of internal tides propagation in the Armorican and Celtic shelves at approximately
–
N
–
W (
Figure 7a). During winter, when tides are activated, the relative vorticity fields present small-scale structures, especially in the Armorican shelf near the coasts and the Loire and Gironde river discharges (
Figure 7c).
During summer, when tides are included in the simulation, there is a marked increase in relative vorticity over the Armorican and Celtic shelves at approximately
–
N and
–
W, compared with the TOFF simulation (
Figure 7b). On the other hand, during the same period, the relative vorticity is decreased in the northern part of the English Channel in the presence of tidal forcing (
Figure 7a,b). During winter, there are evidences of small-scale vortices over the Armorican shelf in
Figure 7d (TOFF simulation), confirmed also previously by the winter temperature and salinity fields (cf.
Figure 4e and
Figure 5e). In the same period over the abyssal plain, we observe an increase of mesoscale activity southern to the shelf break in the TON simulation, i.e.,
N,
W, near the generation area of internal tides (
Figure 7c,d). Overall, when tides are included, small-scale and mesoscale activity weakens on the shelves during both periods and increases in the open-ocean, notably southern to the shelf break and during summer when stratification is strong.
In this study, we depict also the summer divergence of the surface circulation for the TON experiment, as a means to investigate the dynamics of internal tides in our model domain (
Figure 8). There are evidences of spatial patterns with positive/negative values of divergence flow, denoting the vertical variations in the water column as a result of internal tides. We note that, in the TOFF experiment, this divergence pattern is totally absent (i.e., lower values at about two orders of magnitude compared with the TON simulation; not shown). In more detail, we observe high values of divergence flow along the continental shelf slope, most notably at
–
N,
–
W and in agreement with the literature, characterised as a hot spot area of internal tides generation, due to the interaction of barotropic tides with the steep slope [
20,
21,
22,
23]. In addition, we observe a crest-through signal of divergence flow (more apparent compared with vorticity) gradually reducing its signal as we move away from the continental slope. The signal over the Armorican shelf dissipates near the coastal regions and in the English Channel near the location of the Ushant front.
3.3. Vertical Stratification
We calculate the Brunt-Väisälä frequency
(Equation (
1)), using the daily modelled profiles of potential temperature and salinity at selected stations depicted in
Figure 1, to quantify the impact of tides on the vertical stratification.
Figure 9 shows Hovmöller plots of the Brunt-Väisälä frequency for the Armorican shelf and the English Channel stations, respectively. The impact of tides on the vertical stratification of the abyssal plain is negligible (except locally near the continental shelf break) and therefore, not shown here for the two simulations.
During winter we observe near-zero values for the Brunt-Väisälä frequency in both simulations, indicating strong mixing due to surface heat loss over the shelves and nearly homogenous conditions in the water column structure (
Figure 9; white areas between December and March). The most prominent differences in the Brunt-Väisälä frequency between the two simulations are observed in summer and during transition periods (i.e., spring/fall), when there is a strong stratification due to the thermocline shoaling. The changes brought by tides in the water column are visible in the Armorican shelf at depths below the seasonal thermocline and down to the seabed, and in the English Channel over the whole water column.
The stratification in the Armorican shelf below the seasonal thermocline, i.e., from 20 to 50 m depth, shows high variations and appears to be weaker when tidal forcing is activated, compared with the smoother vertical profiles and the stronger stratification when tides are excluded (
Figure 9a,b). An interesting remark, is that when tides are activated in the model, the vertical stratification in the English Channel vanishes (almost) completely during the transition periods and in summer, as opposed to the simulation without tides (cf. lack of dark blue colour in
Figure 9c against
Figure 9d).
The mechanism controlling the changes in the vertical stratification over the shelves is associated with the bottom Ekman flow pattern. In the presence of tides, the bottom stress (and its coefficient) is increased, leading to an increase in the vertical velocity shear and mixing in the shelf areas of the English Channel dominated by strong tidal currents. In order to quantify this impact, we calculated the bottom stress when tides were activated and we found an increase by about one order of magnitude larger in the Armorican shelf (i.e., values up to 0.1 N/m) and two orders of magnitude larger in the English Channel (i.e., values up to 1 N/m).
3.4. Spectral Signatures of Tides
In this section, we quantify the impact of high-frequency spatiotemporal tidal signals by means of frequency and wavenumber energy spectra, using the hourly NEMO model output and examining different regions in the Bay of Biscay.
Figure 10a,b shows the hourly modelled SSH variations of the TON and TOFF simulations at three locations presented in
Figure 1. When tides are included, the SSH variations exhibit fortnightly spring-neap consecutive tidal cycles (
Figure 10a). This is observed in all three areas, with SSH variations being higher in the macrotidal area of the English Channel, followed by the Armorican shelf and the abyssal plain where the smallest variations are observed. When tidal forcing is included in the simulation, the SSH variations increase by about one order of magnitude in all three locations (
Figure 10b). We also note that the SSH variations of the TOFF simulation are different from the SSH detided variations in the TON simulation (
Figure 10c). This is due to the strong interaction between barotropic tides and dynamical processes controlled by mesoscale and small-scale activity, leaving a residual signal in SSH.
The power spectral density of the SSH hourly variations (
Figure 10a,b) in the frequency domain is shown in
Figure 11, for both simulations and seasons and the three locations discussed above. The energy spectra for both seasons present many similarities (
Figure 11a,b), with slightly more energy during winter for the low and semidiurnal frequency bands. Both simulations, with and without tides, have similar energy spectra values at low frequencies (i.e., frequencies smaller than 0.4 cpd—cycles per day). The most important differences between the two simulations, are observed for higher frequencies than 0.4 cpd, where energy spectra are significantly decreased, showing a steeper spectral slope, when tides are not modelled. The energy spectra of the TON simulation (solid lines in
Figure 11a,b) exhibit large peaks at diurnal and semidiurnal frequency bands, at about 1 and 2 cpd, respectively, as a result of the tidal constituents modelled in this simulation. The semidiurnal peaks at 2 cpd appear to have more energy spectra than the diurnal peaks at 1 cpd, in all three locations. This is because the M2 is the main tidal constituent in the Northeastern Atlantic, with large tidal amplitudes (cf.
Figure 2). In the high-frequency range (i.e., frequencies larger than 3 cpd), smaller peaks are observed including also the M4 tidal constituent at frequencies near the 4 cpd. As expected, in most cases the English Channel (black line in
Figure 11) appears to be the more energetic area compared with the other two areas. For the higher frequencies, the Armorican shelf (orange line in
Figure 11) appears also to be tidal energetic, especially in periods with strong stratification (
Figure 11a).
In addition, we investigate the dynamical impact of tides at different spatial scales, performing wavenumber spectral analysis in the abyssal plain (red box area in
Figure 1).
Figure 12 shows the wavenumber power spectral density computed from hourly SSH and relative vorticity fields, averaged over the summer and winter periods.
When tides are included, the SSH spectra slope appears to be steeper during winter compared with summer, i.e., higher energy values at large-scale and lower energy values at the mesoscale and small-scale (
Figure 12a; solid red/black lines). This is because, during summer when stratification is strong, the tidal forcing appears to contribute energetically on a wider range of spatial scales, from the large to mesoscale and small-scale. When tides are not considered in the simulation, the most prominent spectra differences between the two seasons are observed at the mesoscale and small-scale, by about two orders of magnitudes, with the summer values being the smallest ones (
Figure 12a; dashed red/black lines). The spectral slope during winter when stratification is weak and is not affected by the presence (or not) of tides at the mesoscale and small-scale (
Figure 12a; black solid/dashed lines).
During winter, the relative vorticity spectra appear almost always with more energy compared with its summer values, remaining unchanged by the simulation (or not) of tides (
Figure 12b; red/black lines). The latter remark was also verified by the vorticity maps shown in
Figure 7 and discussed in
Section 3.2. On the other hand, during summer and including tides, there is a marked increase in energy spectra at the mesoscale, with a peak at a range of approximately 70–80 km wavelengths (
Figure 12b; solid red line). This finding is explained by the M2 tidal constituent triggering the generation of internal tides and their baroclinic effect on mesoscale activity in the abyssal plain (cf. also [
23]).