OSOcean ScienceOSOcean Sci.1812-0792Copernicus PublicationsGöttingen, Germany10.5194/os-13-777-2017Interannual evolution of (sub)mesoscale dynamics in the Bay of BiscayCharriaGuillaumeguillaume.charria@ifremer.frhttps://orcid.org/0000-0001-5204-1654TheettenSébastienVandermeirschFrédéricYelekçiÖzgeAudiffrenNicoleIfremer, Univ. Brest, CNRS, IRD, Laboratoire d'Océanographie
Physique et Spatiale (LOPS), IUEM, 29280 Brest, FranceCINES, 34090 Montpellier, FranceGuillaume Charria (guillaume.charria@ifremer.fr)25September201713577779729November201626January20176August20178August2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://os.copernicus.org/articles/13/777/2017/os-13-777-2017.htmlThe full text article is available as a PDF file from https://os.copernicus.org/articles/13/777/2017/os-13-777-2017.pdf
In the north-east Atlantic Ocean, the Bay of
Biscay is an intersection between a coastal constrained dynamics (wide
continental shelf and shelf break regions) and an eastern boundary
circulation system. In this framework, the eddy kinetic energy is 1 order
of magnitude lower than in western boundary systems. To explore this coastal
complex system, a high-resolution (1 km, 100 vertical sigma layers) model
experiment including tidal dynamics over a period of 10 years (2001–2010)
has been implemented. The ability of the numerical environment to reproduce
main patterns over interannual scales is demonstrated. Based on this
experiment, the features of the (sub)mesoscale processes are described in the
deep part of the region (i.e. abyssal plain and continental slope). A system
with the development of mixed layer instabilities at the end of winter is
highlighted. Beyond confirming an observed behaviour of seasonal
(sub)mesoscale activity in other regions, the simulated period allows
exploring the interannual variability of these structures. A relationship
between the winter maximum of mixed layer depth and the intensity of
(sub)mesoscale related activity (vertical velocity, relative vorticity) is
revealed and can be explained by large-scale atmospheric forcings (e.g. the
cold winter in 2005). The first submesoscale-permitting exploration of this
3-D coastal system shows the importance of (sub)mesoscale activity in this
region with its evolution implying a potentially significant impact on
vertical and horizontal mixing.
Introduction
As a semi-enclosed region, the Bay of Biscay (Fig. 1) can be divided in three
dynamical regimes: the circulation over the continental shelf, the transition
region above the shelf break and the open ocean part. Our understanding of
the general associated circulation in the Bay of Biscay has been
progressively refined following the available observations and the
improvement of numerical models. The first review by Koutsikopoulos and Le
Cann (1996) introduced the general circulation patterns with a poleward
circulation over the continental shelf, a poleward slope current and a
general anticyclonic circulation in the open ocean. This general scheme has
been detailed with new datasets from drifters in van Aken (2002), Charria et
al. (2013) and Porter et al. (2016); from acoustic
Doppler current profiler (ADCP) moorings in Batifoulier et
al. (2012), Le Boyer et al. (2013) and Kersalé et al. (2015); and from
satellite altimetry in Herbert et al. (2011) and Le Henaff et al. (2011).
Finally, the most intense circulation patterns are today explained by
intermittent coastal density-driven jets disturbed by tidal dynamics over the
continental shelf, a slope current with seasonal and interannual reversals
meandering to generate eddies and an open ocean region with a weak average
circulation but several eddies propagating. From this statement, the next
questions to be addressed to fulfil the scheme explaining the evolution of
this coastal system concerns the mesoscale and submesoscale dynamics.
Bathymetry of the modelled region (a). Red points
correspond to the mooring sites used for model validation. A zoomed-in
area around 48∘ N is represented in panel (b).
The underlying mechanisms of the mesoscale and submesoscale activity in the
ocean have been widely described and discussed during the past years (e.g.
McWilliams, 1985; Capet et al., 2008a, b, c; Klein et al., 2008; Ferrari,
2011; Scherbina et al., 2013; Sasaki et al., 2014; Callies et al., 2015;
Molemaker et al., 2015). This dynamics is particularly active (in terms of
eddy kinetic energy) in western boundary currents.
In the present study, we aim at contributing to the description and the
understanding of small-scale features in eastern boundary regions where the
average level of kinetic energy remains low (Caballero et al., 2008;
Dussurget et al., 2011) and of the mesoscale and submesoscale activity
impact on long-term fluctuations related to evolution in atmospheric
conditions.
The considered definition for the studied scales, depending on the depth of
the water column and the stratification, has to be recalled as we progress in
a coastal environment. In this framework, the mesoscale is defined by scales
around the internal Rossby radius of deformation (∼ 20–50 km in the
midlatitudes; Chelton et al., 1998) where the flow is adjusted under the
effect of the rotation. Over the continental shelf, this internal Rossby
radius of deformation decreases to values around 3–8 km (M. Valdivieso Da
Costa et al., personal communication, 2006), for example, in the Bay of
Biscay. The submesoscale, as introduced by McWilliams (1985), refers to
scales lower than the internal Rossby radius of deformation where the
influence of the Earth's rotation tends to decrease in order to reach a
non-rotating regime of three-dimensional turbulence (Kolmogorov, 1941).
Submesoscale is then ranging from O(100) m to O(10) km over the continental
shelf and in the open ocean (Capet et al., 2008b; Thomas et al., 2008). In the
present work, we refer to (sub)mesoscale (i.e. mesoscale and submesoscale
features) for processes with a length scale lower than 40 km.
In the Bay of Biscay abyssal plain, coherent mesoscale structures have been
identified like the long-lived anticyclonic Slope Water Oceanic eDDIES
(SWODDIES) described by Pingree and Le Cann (1992a, b) generated by slope current
instabilities or quasi-stationary eddies in the south-eastern Bay of Biscay
(Caballero et al., 2013, 2016). Following satellite altimetry-based studies
in the region (Caballero et al., 2008; Dussurget et al., 2011), observations
of mesoscale variability have been described with higher eddy kinetic energy
from December to May. However, the spatiotemporal resolution and coverage
from altimetry does not allow exploring underlying processes and interannual
variability at submesoscale.
In this context, after controlling the efficiency and accuracy of a coastal
model with a 1 km spatial resolution to reproduce the observed processes in
the Bay of Biscay, the (sub)mesoscale variability at annual and interannual
scales is explored as a first step to define the role of related vertical
motions at small scales on long-term evolution and associated biogeochemical
production.
Numerical frameworkModel description
Numerical simulations are based on the MARS3D model
http://wwz.ifremer.fr/mars3d
. MARS3D (Duhaut et al., 2008; Lazure and
Dumas, 2008) is a primitive equation model with a free surface to represent
the gravity waves in the coastal area. In this finite-difference code, the
primitive equations are discretized on an Arakawa C-grid centred at tracer
points (Mesinger and Arakawa, 1976). The sigma coordinates are used on the
vertical dimension to resolve simultaneously the shallow and deep waters. A
specificity of MARS3D model is that the barotropic mode and baroclinic mode
are using the same time step and the barotropic mode is resolved by an
alternating direction implicit method (Lazure and Dumas, 2008). Detailed
equations are given in Appendix A.
The new numerical MARS code can run without explicit viscosity (Duhaut et
al., 2008). The k-ϵ turbulent closure scheme is used to model
vertical mixing (Rodi, 1993).
Numerical experiments
The MARS3D model has already been used to investigate the Bay of Biscay and
its extension to the western English Channel and focused on the validation of
hydrology on the French continental shelf with a 4 km horizontal resolution
and 30 vertical levels (Lazure et al., 2009). In this new configuration (Theetten et al., 2017),
the model domain extends from the Bay of Biscay to the English Channel from
41 to 52.5∘ N and 14.3∘ W to 4.5∘ E, with a 1 km
spatial horizontal resolution with a time step of Δt= 60 s.
This configuration (called BACH1000_100lev) has 1449 × 1282 grid
points and uses 100 vertical sigma levels. The vertical discretization is a
generalized vertical, terrain-following coordinate system (with
hc=20 m; θ=6 and b=0; hc is the shallower
depth above which we wish to have more resolution, θ and b are
surface and bottom control parameters; Appendix A). The bathymetry is a
composite of several IFREMER digital terrain models (DTMs) with 100 m
resolution along the coast covering the French part of continental shelf
completed by a 1 km resolution DTM covering the bay of Biscay and finally
completed by a 1 nautical mile resolution from the North West Shelf
Operational Oceanographic System (http://noos.bsh.de). Both digital
terrain models and mean sea level are interpolated on the grid and merged
(Fig. 1). Some hand editing has been performed in few key areas specially
to correct spurious interpolation near the coastline. The maximum depth in
the model is 5310 m. The interpolated topographies are smoothed by
selectively applying a local filter to reduce the r factor to below 0.25
(r=Δh/2h, where h is the depth of the water column; Haidvogel and
Beckmann, 1999). River runoffs are provided from 95 chronological records
(daily measurements and climatology for the past years when no observations are
available) located on the Spanish, French, Dutch, British and Irish
coasts.
Comparison between observed (SEVIRI satellite SST) and modelled
(BACH1000_100lev simulation) sea surface temperature (SST).
(a) Mean bias between model and observations for the year 2010. (b) Temporal
evolution of the spatial mean SST bias during 2010. The shading around the
curves represents the spatial standard deviation (i.e. the standard deviation
over the domain computed for each time step).
Initial conditions for temperature, salinity, sea surface height, baroclinic
and barotropic velocities (calculated from baroclinic components) are derived
from a DRAKKAR global configuration named ORCA12_L46-MJM88 (Molines et al.,
2014). At the open ocean boundaries, the same variables as initial conditions are
used with adaptive boundary conditions in a sponge layer on the north, south and
west boundaries (Marchesiello et al., 2001). The sponge layer width is 20 km
and the maximum horizontal viscosity/diffusivity values are
100 m2 s-1 and 0 outside the open boundary layers. The tide
with 14 harmonic constituents is imposed along the boundaries using the
FES2004 ocean tide atlas (Lyard et al., 2006).
The atmospheric forcing, which drives the simulation presented here, is
provided by ERA-Interim, produced by the European Centre for Medium-Range
Weather Forecasts (ECMWF; Berrisford et al., 2011). Using the 2 m air
temperature, atmospherical pressure, relative humidity, rain and cloud cover
from ERA-Interim data, indirect calculation of the different components of the
air–sea heat exchange are computed by several bulk formulae (from Lazure et
al., 2009).
The simulation starts from 1 January 2001 and covers a 10-year period until
31 December 2010. A spin-up of 2 years is taken into account to set up an
established seasonal cycle in the circulation even in the open ocean
constrained by a large-scale solution forced in open boundary conditions. The
analysed period is then run from 2003 to 2010. The BACH1000_100lev
configuration is implemented on the Tier-1 supercomputer machine OCCIGEN
provided by GENCI and hosted at CINES
http://www.cines.fr, Centre Informatique National de l'Enseignement Supérieur (CINES)
. The supercomputer OCCIGEN with a performance peak of 2.1 Pflops
encompasses 2106 dual-socket nodes on an Intel Xeon Haswell cadenced at 2.6 GHz.
A total of 12 cores are present on each socket. This numerical experiment was part
of the “Big Challenges program” conducted during the VRS period from
December 2014 to January 2015. Using a domain decomposition technique, the
computational domain is split into 558 subdomains leading to the same number
of MPI tasks with 12 OpenMP threads each. This hybrid MPI/OpenMP application
runs on 6696 cores and produces daily averaged outputs using the input/output
server XIOS
http://forge.ipsl.jussieu.fr/ioserver
specially
implemented in MARS3D for this configuration.
Example of modelled (BACH1000_100lev configuration)
sea surface temperature (a, b) and salinity (c, d) in summer (a, c – 28 July 2003) and winter (b, d – 27 February 2010).
Sea surface salinity (28 July 2009) during an event of
freshwater export in the open ocean as described by Reverdin et al. (2013). Panel (a) represents the full model domain and (b) is focused on
the south-eastern part of the Bay of Biscay to highlight the freshwater
export around 44∘ N and 3.5∘ W.
Normalized distribution of the misfit (modelled–observed) in
temperature (a, b, c) and salinity (d, e, f) from RECOPESCA and Argo in situ
profiles (only for profiles deeper than 100 m) for three vertical
layers: 0–20 m depth (a, d), 20–40 m depth (b, e) and 40–100 m depth
(c, f). The integral of the histogram sums up to 1.
Bay of Biscay features from a spatial high-resolution simulation
Before exploring (sub)mesoscale features in the Bay of Biscay, the ability
of the numerical experiment to reproduce known processes in the region needs
to be evaluated. Following a general view of the modelled fields, a few key
diagnostics on the hydrology and the circulation are presented.
Sea surface temperature and salinity
The numerical experiment is validated using remotely sensed sea surface
temperature (SST). Based on SEVIRI SST remotely sensed
data (METEOSAT SST provided by OSI-SAF belonging to EUMETSAT with ∼ 2 km
spatial resolution), modelled fields are evaluated. In Fig. 2a, the mean bias
between observed and modelled SST over 2010 is computed:
〈SSTbias〉long,lat,t=1(NiNjNt)∑i=1,j=1,t=1Ni,Nj,NtSSTi,j,tmodel-1(NiNjNt)∑i=1,j=1,t=1Ni,Nj,NtSSTi,j,tobservations,
where NiNjNt is the number of grid points in space and time.
At the end of the experiment, this bias shows an averaged underestimation of
the temperature by the model (-0.24 ± 0.28 ∘C over the
domain). These biases do not exceed 1.75 ∘C. Such large values are
obtained in two regions. First, in the Ushant front region (around
47.5–49∘ N and 5–6∘ W; Le Boyer et al., 2009), the
model underestimates the SST. This bias can be explained by the variability
of the Ushant front, developed during stratified seasons, which remains
complex to reproduce (Renaudie et al., 2011; Pasquet et al., 2012). The
second main bias exceeding 1.5 ∘C is located along the western
Spanish coast. The shape of the bias is typical of upwelling extent in this
region. In this case, the coarse atmospheric forcing resolution can be
emphasized as the major error source. Figure 2b shows the temporal
variation of the spatial averaged bias:
SSTlong,lat(t)=1(NiNj)∑i=1,j=1Ni,NjSSTi,j,t,
where NiNj is the number of grid points in space. The shading
around the curves represents the spatial standard deviation:
σSST(t)=1(Ni-1)(Nj-1)∑i=1,j=1Ni,Nj(SSTi,j-<SST>lon,lat(t))2.
At this regional scale and on average over the full domain, we do not observe
significant permanent bias in the simulation. Both simulations and
observations have the same average and temporal variations in surface temperature with a
developed seasonal cycle with maximum temperature in August and September and
the coldest waters at the end of winter in March. The largest differences can be
noticed during the onset of the seasonal stratification in May–June.
After this first overview on SST, two contrasted dates (summer and winter)
are displayed in Fig. 3 for SST and sea surface salinity (SSS). In summer
(Fig. 3a), the model reproduces the warm pool in the south-eastern part of
the Bay of Biscay with temperature exceeding 21 ∘C (Lazure et al.,
2009). In front of Brittany (48.2∘ N, 5.6∘ W), the position
of the Ushant tidal front (Le Boyer et al., 2009; Renaudie et al., 2011;
Pasquet et al., 2012) with cold waters in the vicinity of the coast and
warmer water outside the front is reproduced by model simulations. In winter,
colder (Fig. 3b) and fresher (Fig. 3d) waters above the inner shelf related
to river plume extent do not exceed 9 ∘C and salinity of 34.8.
Furthermore, in Fig. 3, turbulent activity (eddies, filaments) can be
noticed during summer and winter in the deeper region but also over the
continental shelf.
As a more focused illustration, freshwater exports in the open ocean, as
described in Reverdin et al. (2013), appear in the present experiment
(Fig. 4). The elongated freshwater filaments extending to the south-west in
the southern part of the Bay of Biscay (44∘ N, 3.5∘ W)
represent an observed signal of cross-slope exchanges. Reproducing these
exports is a significant step forward in our simulations, thanks to the
higher spatial resolution (1 km vs. 4 km in previous experiments). Indeed,
the spatial resolution appeared as a key issue to better resolve these
exchanges between the continental shelf and the open ocean.
Average modelled seasonal circulation (a: winter,
b: spring, c: summer, d: autumn) for surface
layers (0–50 m depth) over the period 2001–2010 (for clarity purposes,
fields have undersampled and 1 over 50 grid points are plotted). Gray lines
represent 500, 200, 100 and 50 m isobaths.
Vertical hydrological structure
The hydrological content of the simulation is evaluated through comparisons
with available observations in 2010 from the CORA-IBI (COriolis ocean
database for ReAnalysis – Ireland–Biscay–Iberia, Szekely et al., 2017) database. Considered
vertical profiles can be divided into two sources: Argo (Argo, 2000; Riser et
al., 2016) profiles in the open ocean and RECOPESCA (Leblond et al., 2010;
Charria et al., 2014; Lamouroux et al., 2016) profiles on the continental
shelf.
Figure 5 shows the difference between observed and modelled profiles for
the year 2010 in temperature and salinity in the top layers. In temperature, the
model reproduces the vertical structure with a small average misfit of 0.015
and a 0.45 ∘C root mean square error (RMSE) between 0 and 20 m
depth (Fig. 5a), -0.11 ∘C (1.23 ∘C for RMSE) between 20
and 40 m depth (Fig. 5b) and 0.25 ∘C (1.17 ∘C RMSE)
between 40 and 100 m depth (Fig. 5c). This misfit can be observed in the
distribution in Fig. 5. Following the uncertainties around the thermocline
(i.e. a few metres of differences in the thermocline depth will induce large
difference between model and observations) the misfit distribution is larger
below 20 m depth. Similar behaviour is observed in salinity with the larger
spread for the layer 20–40 m depth. In salinity, the average misfit is
smaller at the surface (-0.024 for the layer 0–20 m depth,
RMSE = 0.27; Fig. 5d) and above 100 m depth (0.025 for the layer 40–100 m depth,
RMSE = 0.28; Fig. 5e and f) than between 20 and 40 m depth where the
average difference is larger (0.176, RMSE = 0.59). Considering the RMSE,
we confirm that the maximum of error is located in mid-depth layers
(20–40 m) and can be locally important. Part of the error can be attributed
to the colocation approach assuming that we will reproduce the same features
at the same time and place in the simulations, but choices for the
configuration (e.g. smoothed bathymetry, coarse atmospheric forcings) can
contribute to increasing the observed error between model and local in situ
observations. However, following the distributions, with biases of different
signs following the depth, no systematic bias exists in the numerical
experiment.
Comparison of the 1-day mean and depth averaged along-shore and
cross-shore velocity components between ADCP measurements (black) and
BACH1000_100lev currents (blue) at the location of ASPEX4
(Fig. 7a and b) above the continental shelf and ASPEX10 (Fig. 7c and d) above the continental slope. The orientation of the along-shore and
cross-shore components is relative to the bathymetry.
Bay of Biscay general circulation
Concerning the general circulation in the region, three levels of
comparisons are detailed. As a synoptic view, the seasonal circulation in
the surface layer is computed to be compared with existing climatologies
(e.g. Charria et al., 2013). Then, to highlight circulation patterns
occurring at short timescales as poleward jets over the continental shelf
(e.g. Batifoulier et al., 2012; Kersalé et al., 2015) and the vertical
structure of the currents, modelled fields are compared with ADCP observations during the ASPEX campaign (Le Boyer et
al., 2013; Kersalé et al., 2015) and the front of the Arcachon Bay during
the ARCADINO campaign (Batifoulier et al., 2012).
At seasonal scale, Fig. 6 shows the circulation integrated over the first 50 m
depth for the whole simulation. This average circulation over 10 years can be
compared with the climatology (processed from observation from 1992 to 2009)
derived from drifters in Charria et al. (2013). In winter (Fig. 6a), the
contrasted velocities with weak current over the continental shelf and more
intense structures in the open ocean clearly appear. The poleward slope
current with values lower than 10 cm s-1 is reproduced. In spring
(Fig. 6b), the reversal of circulation with an equatorward slope current is
simulated. This circulation remains sustained in summer (Fig. 6c) with a
reinforcement of equatorward currents over the continental shelf. Following
wind regime evolution and the transition period in September–October (SOMA
seasonal response; Pingree et al., 1999), autumn circulation (Fig. 6d)
highlights, on average, the poleward slope current close to the 500 m isobath.
These average circulation features are then in agreement with the
drifter-derived seasonal climatology (Charria et al., 2013).
Another source for validating the modelled circulation comes from ADCP
deployments in the region. During the ASPEX project, 10 current-meter
moorings were deployed from July 2009 to August 2011. The mooring location
was distributed over the continental shelf and the upper section of the shelf
break. Mooring features and observations from the project are described and
analysed in Le Boyer et al. (2013) and Kersalé et al. (2015).
Evolution of meridional velocity component in m s-1 of the
BACH1000_100lev model during July–August 2008 (a) at the ARCADINO ADCP
location. ADCP observations for the same periods are represented
(b).
Two ASPEX ADCP moorings have been selected to compare evolution of current
velocities with modelled fields: no. 4 on the continental shelf and no. 10 on
the continental slope (see positions in Fig. 1). We can notice that the
length of the considered time series for comparison is both limited by the
duration of the numerical experiment (2001–2010) and the technical issues in
data sampling (lack of measurements for the end of the ASPEX10 time series).
Two-dimensional linear spatial interpolation on model output velocity components
at each sigma level is made on the geographical position/location of the
mooring. Then, the zonal and meridional components of modelled velocities are
projected on along-shore and cross-shore component at each sigma level. In
the aim to compare the depth-averaged velocity on both model outputs and in
situ data, vertical integration of the two velocity components is made on
almost the whole water column
The first record is located near the
bottom. Records located in the surface layer thickness (corresponding to
20 % of the mooring depth) have been removed due to noisy measurements.
.
Vertical integration of the model outputs is also made on the water column
between the minimum and maximum depths defined previously.
Surface modelled relative vorticity for 28 July 2003 (a) and
27 February 2010 (b). The yellow rectangle limits the targeted region
for diagnostics.
In Fig. 7, the modelled and observed currents are represented. A general
agreement following the current directions and amplitudes is observed with
correlations between 0.6 and 0.69 for along-shore components. For the
cross-shore component, representing the less intense currents, in ASPEX4
(Fig. 4b), the direction of the current is well reproduced but the amplitude
remains generally smaller in simulations (RMSE = 0.024 m s-1). At
ASPEX10 (Fig. 4d), the cross-shore weak circulation is not reproduced, with a
correlation between model and observation equal to 0.09, due to the mesoscale
circulation in this area (e.g. Solabarrieta et al., 2014; Caballero et al.,
2016). The agreement between observations and numerical simulation is
improved for dominant along-shore currents. Indeed, amplitudes are very
similar in both ASPEX sites (except during autumn 2009; Fig. 4a and c). The
direction and direction changes are also very well reproduced (the
correlation for ASPEX4 is equal to 0.6 and for ASPEX10 to 0.69), even at high
frequency, which was not expected following the coarse atmospheric forcings
used for the simulation.
Other comparisons have been performed with an ADCP mooring during the
ARCADINO experiment. This mooring, located on the Aquitaine shelf (south of
45∘ N; Fig. 1), has been used to highlight poleward coastal jets up
to 32 cm s-1 (Batifoulier et al., 2012). Similar events are modelled in
our numerical experiments with smaller amplitudes (Fig. 8). In 2008, a
poleward along-shore current appears around 15 August 2008 (Fig. 8) in
observations. From in situ ADCP measurements (Batifoulier et al., 2012),
there is also a velocity maximum between 16 and 20 August 2008. In the
modelled fields, the jet is reproduced but velocities are weaker and the
event starts earlier in the simulation. The jet is also deeper in the model
(20–40 m depth with maximum velocities ∼ 16 cm s-1) than in
observations with a maximum above 30 m depth. When model forcings are
explored, we explain this event with similar conditions to those observed in
Batifoulier et al. (2012). Indeed, westerly winds are blowing from the 6 to
8 August (with intensities 8 to 12 m s-1) along the Spanish
coast to set up the circulation resulting in the poleward jet following the
explained process in Batifoulier et al. (2012).
These illustrations of the modelled fields and comparisons with available
observations show the ability and the limits of our numerical experiment to
reproduce the coastal ocean dynamics at high resolution in the Bay of
Biscay. Based on these fields, the interannual variability at (sub)mesoscales
can be explored.
Interannual variability of (sub)mesoscale instabilities in surface
layers
The present study aims to characterize the interannual variability of the
(sub)mesoscale dynamics and discuss the possible processes explaining
this variability. Before considering these interannual scales, the seasonal
features are described for a given year.
Seasonal scale
To explore the (sub)mesoscale activity, the vertical component of the
relative vorticity (referred as relative vorticity) has been first analysed.
From these dynamical fields, we can infer the intensity of rotating
structures and their spatial distribution.
In Fig. 9, the surface relative vorticity from analysed simulations at
different contrasted time steps is represented. From these maps, different
patterns can be noticed. First, the contrast between the deep open ocean and
the shallow continental shelf is clearly visible for the different periods.
In summer 2003 (Fig. 9a), over the continental shelf, the internal waves are
observed in the northern part of the domain spreading from the shelf break
(around 47.5–48∘ N, 7–5∘ W). In the southern part of the
continental shelf (south of 48∘ N), small structures related to
local drivers (e.g. edge of region of freshwater influence, wind bursts;
O. Yelekci et al., personal communication, 2016) are developed. These
structures can be seen through large relative vorticity values over the outer
part of the continental shelf between the 100 m isobath (Fig. 6) and the shelf
break (Fig. 1). In contrast, in winter (Fig. 9b), small-scale features
are more concentrated in the inner shelf (the first half of the continental
shelf closer to the coast with water shallower than 100 m depth) under the
influence of large winter river inputs (e.g. mainly from the Loire and Gironde
rivers).
Relative vorticity averaged over 150 m depth and spatially
averaged for the years 2004 and 2005 (a). Map of the surface relative
vorticity for 2 March 2004 (b) and 15 August 2004 (c).
Power spectrum (computed for each latitude and averaged over
longitudes and time during the considered month) from surface relative
vorticity for the year 2010 (a). Numbers in the legend correspond to the
months in the year 2010. Time series of the regressed spectral slope from the
power spectrum of surface relative vorticity in 2010 (b). Spectral
slopes have been computed considering wavelengths from 7 to 132 km.
When we consider the open ocean over the abyssal plain, contrasted situations
with structures with smaller relative vorticity in summer (Fig. 9a) and more
intense small vortices in winter (Fig. 9b) are clearly observed. Smaller
features (eddies and filaments with spatial scales lower than 40 km) are
fully developed in winter. In summer, typical spatial scales are larger
than in winter. More large-scale vortices are simulated during this season.
The spatial spectral analysis over the domain (Fig. 11) confirms the largest
small-scale (< 50 km wavelength) variance peaks in winter (maximum
in March) and the minimum variance at small scale in summer (July).
Vertical velocity averaged over 150 m depth and spatially averaged
for the years 2004 and 2005 (a). Map of the vertical velocity at 4 m depth
for 2 March 2004 (b) and 15 August 2004 (c).
Vertical profile of w′b′ averaged over the studied subdomain
(described in Fig. 9) during the winter season (January–February–March) in
2005. The dashed line represents the mixed layer depth averaged for the same
period over the considered region.
Interannual variability (from 2003 to 2010) of spatially averaged
vertical velocity (a), relative vorticity (b), temperature (the red dashed
line is the average annual cycle during the modelled period) (c) and
salinity (d) integrated over 150 m depth. The considered domain is given in
Fig. 9.
Based on Fig. 10, representing the years 2004 and 2005, a picture of the
annual evolution of the relative vorticity intensity can be drawn considering
a spatial average of the absolute relative vorticity over the region
highlighted in Fig. 9 (yellow rectangle). Based on the spatial average
integrated over 150 m depth
This depth (150 m) has been defined
to include most of the mixed layer depth in winter. As it is used for the whole
time series (including stratified seasons), the maximum mixed layer depth
(around 200 to 250 m on average) has not been taken as a reference.
(Fig. 10a), a maximum is observed during the end of winter (February–March)
followed by a period (June–September) corresponding to a minimum of averaged
relative vorticity. The horizontal patterns (Fig. 10b and c) associated with
these average time series confirm the larger range of relative vorticity
values related to small-scale structures. In summer (Fig. 10c), intensity of
eddies is decreased with larger-scale features (e.g. structures with a length
scale larger than 50 km). This decrease in the intensity of the modelled
field can also be described through the surface relative vorticity spectra
computed from each month (Fig. 11). These spectra have been computed every
day over the limited domain (yellow rectangle in Fig. 9) using a 2-D fast Fourier
transform and then averaged over the considered month. These spectra clearly
show the seasonal variation of the variance with a maximum in March and a
minimum in July. An increase in the variance of small scales (lower than
50 km) is also observed through a change in the curve slope observed in
November, January and March compared with May, July and September.
Following the relative vorticity fields (i.e. related to vortices, fronts,
filaments), vertical motions can also be explored. The role of structures at
(sub)mesoscale on these vertical motions can be highlighted by the
exploration of vertical velocities (significant vertical velocity patterns
are mainly at submesoscales and mesoscales). Indeed, in Fig. 12a, a similar
seasonal cycle with relative vorticity is observed with a maximum of
integrated vertical velocity at the end of winter (February–March) and a minimum
in summer (June–September). Based on the spatial patterns of the vertical
velocity fields (Fig. 12b and c), intense and small structures are observed
at the end of winter (Fig. 12b) that have developed with small typical length scales. In
summer, positive and negative vertical velocity patterns are more elongated
due to aggregated patterns (Fig. 12c) and less activity at small scale.
A vertical signature of the fluctuations in the (sub)mesoscale regimes can be
inferred from the (sub)mesoscale component of the vertical buoyancy flux
(w′b′, where w is the vertical velocity and b the buoyancy) computed
following
w=w‾+w′b=b‾+b′,
with
b=-g(ρ-ρ0)ρ0,
where w‾ and b‾ are filtered field using a 2-D
convolution with a Hanning window of 40 km length scale. w′b′ is then
representing spatial scales smaller than 40 km.
The diagnostic (w′b′) translates the conversion rate of available potential
energy to eddy kinetic energy (e.g. Boccaletti et al., 2007; Fox-Kemper et
al., 2008a, b), which tends to be maximal in the mixed layer in the case of
vertical velocities related to mixed layer instabilities (Boccaletti et al.,
2007; Stone, 1966, 1970). In Fig. 13, the vertical profile of w′b′ averaged
over the studied subdomain during the winter season (January to March) shows a
maximum (reaching, on average, 3.1 × 10-10 m2 s-3)
in surface layers corresponding to the mixed layer.
Following the seasonal description, 10 years of high-resolution simulations
allow consideration of the interannual variations.
Interannual scale
The different regimes modelled in 2004 and 2005 are also observed during the
whole simulated period (2003–2010; the first 2 years are not taken into
account considering a spin-up period). Indeed, in Fig. 14a (vertical
velocity) and 14b (relative vorticity), a maximum appears generally at the end of
winter at the same time for both quantities. The intensity of the maximum
displays interannual fluctuations with larger values in 2004 (only for
vertical velocity), 2005, 2006, 2009 and 2010. In contrast, 2003, 2007
and 2008 are characterized by a weaker (sub)mesoscale activity. The maxima
are in phase with the coldest period in temperature, and the most extreme
values in vertical velocity and relative vorticity correspond to the
most extreme cold values in temperature compared with the annual cycle
(Fig. 14c) before the spring warming and the beginning of seasonal
stratification. The most extreme vertical velocities are simulated during
winter 2005 with a peak in the beginning of March 2005. In contrast, positive
anomalies in temperature are modelled from September 2007 to May 2008. For
winter before (beginning of 2007) and during this period (winter 2008),
minimum vertical velocities and relative vorticity are observed over the
8-year period. In 2009, the winter situation comes back to cold sea
temperature anomalies related with more intense vertical velocities and
relative vorticity.
Time series of the regressed spectral slope from the power
spectrum of surface relative vorticity from 2003 to 2010. Spectral slopes
have been computed considering wavelengths from 7 to 132 km.
(a) Averaged mixed layer depth in the studied region (Fig. 9).
(b) Vertical profiles of w′b′ averaged over the same domain during winter
seasons (January–February–March).
As we consider an area not under direct influence of major river runoffs (far
from the slope dynamic barrier), the salinity (Fig. 14d) does not exhibit a
regular seasonal cycle. Indeed, the main sources of freshwater in the Bay of
Biscay come from river discharges. These discharges follow a seasonal
cycle with a maximum flow at the end of winter not simulated over the
analysed domain. Furthermore, the evaporation–precipitation budget (related
to the more intense and frequent cyclonic weather systems in winter) does not
induce large variations at seasonal scales in the region but fluctuates
interannually depending the atmospheric conditions.
The role of the different spatial scales in this interannual variability is
explored through the analysis of the slope of the power spectrum of surface
relative vorticity. Figure 15 shows the shallowest slopes (larger than
k-0.4) occurring in autumn/winter (from November to March). In contrast,
slopes values are steeper (between k-1.2 and k-1.4) in
spring with a minimum in May or June. The interannual variability of this
minimum (corresponding to steepest slopes) is limited and values are very
similar following the year. Concerning the shallowest winter slopes, the
value is decreasing with time but the limited number of simulated years does
not allow conclusion to the significance of this trend. The monthly seasonal
cycle is very stable every year. However, we can notice that in 2004 the
shallowest slopes are reached earlier (in November) than during the other
years (December, January or February). The interannual variability of the
spectral slope gives then an overview of the evolution of the distribution of
spatial scales.
Discussion
Model simulation, validated with available observations, exhibits a seasonal
cycle related to small-scale features in the deep part of the Bay of Biscay.
This region, despite low levels of eddy kinetic energy (e.g. Caballero et
al., 2008; Charria et al., 2013), is the location of development of mixed
layer instability dynamics similar to those observed in the western Pacific Ocean
(e.g. Sasaki et al., 2014), the western North Atlantic (e.g. Mensa et al.,
2013; Callies et al., 2015) and the eastern North Atlantic (e.g. Thompson et
al., 2016). Following the analogy, the features from mixed layer
instabilities (Boccaletti et al., 2007) are confirmed by the maximum of
activity simulated at the end of winter when vertical buoyancy fluxes at
(sub)mesoscale are the most intense and with a maximum of conversion rate
between available potential energy and eddy kinetic energy at (sub)mesoscale
in the mixed layer depth
The criterion selected for the mixed layer
depth is a threshold value of density from a near-surface value at 10 m
depth equal to 0.03 kg m-3 following de Boyer Montégut et
al. (2004).
(Fig. 13). These instabilities drive a conversion in kinetic
energy of the stored potential energy in winter and can lead to reinforcing the
seasonal stratification.
Statistics on the northerly and southerly winds during winters
(January–February–March). Based on atmospheric forcings, the percentages of
occurrence of northerly (in blue) and southerly (in red) winds are
represented.
Therefore, in a realistic modelling framework, these results corroborate the
suitable spatial (1 km) and vertical resolutions (100σ levels) to
solve the (sub)mesoscale realistic features resulting from mixed layer
instabilities. Indeed, Soufflet et al. (2016), based on ROMS simulations in a
baroclinic jet test case, showed the sensitivity of the vertical buoyancy
flux to the spatial resolution (20, 10, 5 and 2 km) with a maximum mixed
layer buoyancy flux for the higher-resolution model. In the present study,
the reproducibility of the results balancing between the winter unstable field
and summer smoothed mesoscale activity after 10 years of simulation further
shows the interest of the O(1 km) scale in regional modelling. Previous
interannual experiments with 4 km spatial resolution (not shown) also
confirm the improvements.
The system described in the Bay of Biscay then follows a scheme where
end-of-winter mixed layer instabilities will feed the eddy kinetic energy in
the region. However, interannual fluctuations are clearly visible (Fig. 14)
and can have an effect on the intensity of instabilities. A first link has
been established between the winter mixed layer depth and the submesoscale
activity. Indeed, Fig. 16a, representing the averaged mixed layer depth in
the studied region, is correlated with the evolution of the relative
vorticity and associated vertical velocities (Fig. 14a and b). The maximum
intensity of vertical velocities is related to the maximum depth of the mixed
layer. This relationship can be explained by the amount of available
potential energy stored following these deep mixed layers. Following the
potential impact of such fluctuations (maximum average vertical velocities
can be doubled following the considered year) on the mixing and then on
systems under this pressure (e.g. biogeochemistry), identifying the source of
such variability becomes a key point to forecasting seasonal small-scale
dynamics. A first driver potentially explaining deeper mixed layer depth for some
years is the mechanical energy input (e.g. Duhaut and Straub, 2006; Huang et
al., 2006; Elipot and Gille, 2009) related with the wind stress and the
surface ocean velocity (the surface ocean velocity effect is generally
smaller than the wind stress impact). Variations of this large-scale source
of energy have been explored in the Bay of Biscay and do not explain the
interannual variations of the mixed layer depth in the region (not shown).
The alternative source of convective processes deepening the mixed layer
depth in winter is the heat fluxes (mostly latent and sensible heat fluxes in
winter in the region following Somavilla et al., 2011). During the simulated
period, the extremely cold and dry winter in 2005 (Somavilla et al., 2009,
2011, 2016) explains the deepest average mixed layer depth over the domain.
This winter was very specific with dominant northerly wind (Fig. 17)
advecting cold air in the Bay of Biscay. This cold air mass influences the
air–sea temperature gradient and then the associated heat fluxes. This
extreme winter is associated with the largest vertical buoyancy flux at
(sub)mesoscale (Fig. 16b). Following the same behaviour, the years 2009 and
2010 also reach deep mixed layer depth maxima (deeper than 250 m;
Fig. 16a) associated with an intense associated vertical buoyancy flux.
Similarly, the year 2010 is associated with an important occurrence of
northerly winds (Fig. 17). The modelled deep mixed layer for these years was
observed by Hartman et al. (2014) from in situ Argo vertical profiles in the
Bay of Biscay. These specific years (2009 and 2010) were also associated with
cold winters.
On the contrary, 2007 and 2008 had shallower mixed layer depth maxima
(Fig. 16a) associated with a reduced maximum of vertical buoyancy flux at
(sub)mesoscale (Fig. 16b). These shallower mixed layers are related to warm
winters causing warming of the surface ocean and a decrease in winter mixing.
Indeed, during winter 2007, the surface air temperature was probably the
highest recorded during the past 500 years (Luterbacher et al., 2007).
Winter 2006 is an intermediate state due to the remaining effect of sea
surface temperature anomaly during winter 2005 (Dummousseaud et al., 2010).
The analysis can be extended to the distribution of the dominant spatial
scales. Based on power spectra and the evolution of the spectral slopes
(Fig. 15), the analysis does not show interannual evolution in the
distribution of spatial scales except at the end of 2004 where we can observe that
the maximum slope is reached in November, earlier than during other analysed
years. During the whole period, slopes remain located between k-0.4 and
k-1.4. This range is in agreement with modelling studies based on
similar resolutions. For example, in Brannigan et al. (2015), spectral slopes
for surface velocities for simulation with similar resolution (1 and 2 km)
are located between k-2 and k-4. Taking into account the velocity
derivative in the relative vorticity, slopes from the present study are
equivalent to slopes between k-2.4 and k-3.4 in surface velocities.
Based on these distributions, the potential impact of large-scale
interannual variability on the small-scale features is mainly observed for
extreme conditions (e.g. autumn 2004/winter 2005) where the early decrease
of the slope translates to an anticipated increase of the variance at
small scales.
Conclusions
With the rise of numerical capabilities, coastal dynamics can be explored at
regional scale over pluri-annual periods keeping a high spatial resolution
needed to solve at the (sub)mesoscale. Based on a 1 km spatial resolution numerical
experiment over 10 years, we explored the (sub)mesoscale dynamics in the Bay
of Biscay and its interannual evolution.
Before exploring interannual variability for few-kilometre scales, the
ability of the model to reproduce multi-scale processes (from intermittent
events to average circulation) has been shown, including sustaining a coherent
circulation after 10 years of simulation.
Based on these products, and despite low levels of eddy kinetic energy linked
with an eastern boundary circulation system, the seasonal cycle in the
turbulent regimes with a smaller scale at the end of winter and a maximum in relative
vorticity and vertical velocities at the end of winter (in March) is shown. The
source of these small-scale structures is associated with mixed layer
instabilities.
Then, the investigations focused on interannual variability in the
(sub)mesoscale are linking the evolution in the maximum of small-scale
vertical velocities with the maximum mixed layer depth reached
during the ongoing winter. Differences between intensities of
(sub)mesoscale activity can then be related to the winter conditions
explaining mixed layer dynamics. Cold winters are characterized by deeper
mixed layer depth (2005, 2009 and 2010), with the coldest winter in 2005,
which induced a shift in the North Atlantic heat budget and circulation
(Somavilla et al., 2016). These cold winters are associated with more
intense baroclinic instabilities inducing vertical velocities at the
(sub)mesoscale and an early increase of small-scale variance (November in
2004). In contrast, the years 2006–2008 represent warm winters (with the
warmest in 2007), a shallow mixed layer and a weak generation rate of eddy
kinetic energy.
Therefore, this experiment shows a straight impact of large-scale
ocean–atmosphere heat fluxes on the intensity of (sub)mesoscale activity in
a region under coastal influence. This new insight in understanding the
(sub)mesoscale in coastal regions, thanks to high-resolution numerical
modelling, will contribute understanding of small-scale fluctuations in
biogeochemical production.
The model configuration and the source codes are available
in Thetten et al. (2017). The CORA-IBI dataset is available in Szekely et
al. (2017). SEVIRI remotely sensed sea surface temperature data are available
at http://www.osi-saf.org/lml/pres_SST. ASPEX ADCP data are published
in Le Boyer et al. (2013). ARCADINO data are published in Batifoulier et
al. (2012).
In the MARS3D model, the set of primitive equations (Lazure and Dumas, 2008)
is obtained based on usual assumptions (Boussinesq and shallow-water
assumptions) in a hydrostatic framework. As the model is based on vertical
sigma coordinates, equations are rewritten in a sigma coordinate framework,
where (Song and Haidvogel, 1994)
(z=ζ),
with (z=-H), where σ is the vertical coordinate and D is the height of water
column, with D=H+ζ. H is the depth of the fluid at rest; ζ is
the sea surface elevation. z and σ increase upwards. The result is
that at the sea surface (z=ζ) and σ=0. In contrast, at the
sea floor (z=-H) and σ=-1 .
We have noted the L operator as
L(A)=u∂A∂x+v∂A∂y+w∂A∂σ.u is the zonal velocity, v the meridional velocity and w is the
vertical velocity in the sigma coordinate framework (x,y,σ) with
w=1Dw-σ∂ζ∂t-uσ∂ζ∂x+σ-1∂H∂x-vσ∂ζ∂y+σ-1∂H∂y.
The set of primitive equations is then in Cartesian coordinates:
1D∂p∂σ=-ρg∂u∂t+L(u)-fv=-g∂ζ∂x-1ρ0∂Pa∂x+πx+1D∂nzD∂u∂σ∂σ+Fx∂v∂t+L(v)+fu=-g∂ζ∂y-1ρ0∂Pa∂y+πy+1D∂nzD∂v∂σ∂σ+Fy∂ζ∂t+∂Du∂x+∂Dv∂y+∂Dw∂σ=0∂DT∂t+∂DuT-kx∂T∂x∂x+∂DvT-ky∂T∂y∂y+∂DwT-kzD2∂T∂σ∂σ=1ρ0CP∂I∂σ∂DS∂t+∂DuS-kx∂S∂x∂x+∂DvS-ky∂S∂y∂y+∂D(wS-kzD2∂S∂σ)∂σ=0.
The equation of state relates density to salinity, temperature and pressure:
ρ=FS,T,p,
where F is a non-linear function (not stated explicitly here; Jackett and
McDougall, 1995).
From Eq. (1) and introducing the buoyancy b=-gρ-ρ0/ρ0 within a sigma coordinate framework, the zonal and
meridian components of the baroclinic pressure gradient (πx,πy) are
πx=∂∂xD∫σ1bdσ+bσ∂D∂x-∂H∂xπy=∂∂yD∫σ1bdσ+bσ∂D∂y-∂H∂y.
The horizontal friction terms are
Fx=1D∂∂xDνx∂u∂x+1D∂∂xνx∂H∂x-σ∂D∂x∂u∂σ+1D∂∂σνx∂H∂x-σ∂D∂x∂u∂x+1D∂∂σνxD∂H∂x-σ∂D∂x2∂u∂σFy=1D∂∂yDνy∂v∂y+1D∂∂yνy∂H∂y-σ∂D∂y∂v∂σ+1D∂∂σνy∂H∂y-σ∂D∂y∂v∂y+1D∂∂σνyD∂H∂y-σ∂D∂y2∂v∂σ,
where x, y and σ are the Cartesian coordinates of the framework
u (zonal velocity), v (meridian velocity) and w∗ (vertical velocity),
respectively; H(x,y) is absolute value of bottom position;
S, T and p are, respectively, salinity, temperature and pressure.
f=2Ωsinφ is the
Coriolis parameter, Ω=2π/86164 rad s-1 Earth's rotation
frequency, g gravity, b=-g(ρ-ρ0)/ρ0 buoyancy, ρ=ρ(S,T,p) seawater density, ρ0 reference density, Cp sea
water heat capacity, I shortwave heat fluxes, nz vertical eddy viscosity,
kz vertical eddy diffusivity, νx and νy horizontal eddy
viscosity, kx and ky horizontal eddy diffusivity.
The boundary conditions are expressed as
Boundary conditions atBoundary conditions atthe surface σ= 0the bottom σ=-1nzD∂u∂σ=τsxρ0nzD∂u∂σ=τbxρ0nzD∂v∂σ=τsyρ0nzD∂u∂σ=τbyρ0kzD∂T∂σ=QTρ0Cpkz∂T∂σ=0kz∂S∂σ=0kz∂S∂σ=0w∗= 0w∗=0
where QT is the heat flux at the air–sea interface, (τsx,τsy)=ρaCdsW(Wx,Wy) are
the surface stress components with
ρa=1.25kgm-3CdS=0.016,
where (Wx,Wy) is the wind velocity vector at 10 m above the sea surface.
(τbx,τby)=ρ0CdBu(u,v) are the bottom stress components with
CdB=κlnz+H+z0z02,
where κ refers to the Von Karman constant and z0 the bed
roughness.
The authors declare that they have no conflict of
interest.
Acknowledgements
This study is part of the LEFE/GMMC project ENIGME. Model experiments have
been performed with one of the GENCI (French Big National Equipment Intensive
Computing) computational resources administered at CINES (National Computing
Center for Higher Education). The computing time of this study costs 3.6
million core hours. We would like to thank Arnaud Le Boyer and Pascal Lazure
for providing ASPEX data. Remotely sensed sea surface temperature data are
provided by OSI-SAF (http://www.osi-saf.org/) and belong to EUMETSAT.
Data processing has been performed using the open-source Python library
VACUMM. We also thank Bernard Le Cann, Louis Marié and Christophe Maes
for the insightful discussions. Special thanks are given to Liam Brannigan
and an anonymous reviewer for their very constructive comments.
Edited by: A. J. George Nurser
Reviewed by: Liam Brannigan and one anonymous referee
ReferencesAgoumi, A.: Modélisation du régime thermique de la Manche, Manche,
PhD Thesis, Ecole Nationale des Ponts et Chaussées,
https://pastel.archives-ouvertes.fr/tel-00523011, 255 pp., 1982.
André, X., Le Reste, S., and Rolin, J.-F.: Arvor-C: A Coastal Autonomous
Profiling Float, Sea Technol., 51, 10–13, 2010.Argo: Argo float data and metadata from Global Data Assembly Centre (Argo
GDAC), SEANOE, 10.17882/42182, 2000.Batifoulier F., Lazure P., and Bonneton P.: Poleward coastal jets induced by
westerlies in the Bay of Biscay, J. Geophys. Res.,
117, C03023, 10.1029/2011JC007658, 2012.
Berger, H., Dumas, F., Petton, S., and Lazure, P.: Evaluation of the hydrology
and dynamics of the operational mars3d configuration of the Bay of Biscay,
Mercator Ocean – Quartely Newsletter, 49, 60–68, 2014.
Berrisford, P., Dee, D. P., Poli, P., Brugge, R., Fielding, K., Fuentes, M.,
Kållberg, P. W., Kobayashi, S., Uppala, S., and Simmons, A.: The ERA-Interim
archive Version 2.0, ERA Report Series 1, ECMWF, Shinfield Park, Reading, UK, 2011.Boccaletti, G., Ferrari, R., and Fox-Kemper, B.: Mixed layer instabilities and
restratification, J. Phys. Oceanogr., 37,
2228–2250, 10.1175/JPO3101.1, 2007.
Brannigan, L., Marshall, D. P., Naveira-Garabato, A., and Nurser, A. G.: The
seasonal cycle of submesoscale flows, Ocean Model., 92, 69–84, 2015.Caballero, A., Pascual, A., Dibarboure, G., and Espino, M.: Sea level and Eddy
Kinetic Energy variability in the Bay of Biscay, inferred from satellite
altimeter, J. Mar. Syst., 72, 116–134,
10.1016/j.jmarsys.2007.03.011, 2008.Caballero, A., Rubio, A., Ruiz, S., Le Cann, B., Testor, P., Mader, J., and
Hernández, C.: South-Eastern Bay of Biscay eddy-induced anomalies and
their effect on chlorophyll distribution, J. Mar. Syst.,
162, 57–72,
10.1016/j.jmarsys.2016.04.001, 2016.Callies, J., Ferrari, R., Klymak, J. M., and Gula, J.: Seasonality in
submesoscale turbulence, Nat. Commun., 6, 6862,
10.1038/ncomms7862, 2015.
Capet, X., Campos, E. J., and Paiva, A. M.: Submesoscale activity over the
Argentinian shelf, Geophys. Res. Lett., 35, 2008a.Capet, X., McWilliams, J. C., Molemaker, M. J., and Shchepetkin, A. F.: Mesoscale
to Submesoscale Transition in the California Current System, Part I: Flow
Structure, Eddy Flux, and Observational Tests, J. Phys.
Oceanogr., 38, 29–43, 10.1175/2007JPO3671.1, 2008b.Capet, X., McWilliams, J. C., Molemaker, M. J., and Shchepetkin, A. F.: Mesoscale
to Submesoscale Transition in the California Current System, Part II:
Frontal Processes, J. Phys. Oceanogr., 38, 44–64,
10.1175/2007JPO3672.1, 2008c.Charria, G., Lazure, P., Le Cann, B., Serpette, A., Reverdin, G., Louazel, S.,
Batifoulier, F., Dumas, F., Pichon, A., and Morel, Y.: Surface layer circulation
derived from Lagrangian drifters in the Bay of Biscay, J. Mar.
Syst., 109/110, S60–S76,
10.1016/j.jmarsys.2011.09.015, 2013.
Chelton, D. B., Deszoeke, R. A., Schlax, M. G., El Naggar, K., and Siwertz,
N.: Geographical variability of the first baroclinic Rossby radius of
deformation, J. Phys. Oceanogr., 28, 433–460, 1998.Costoya, X., deCastro, M., Gómez-Gesteira, M., and Santos, F.: Mixed Layer
Depth Trends in the Bay of Biscay over the Period 1975–2010, PLoS ONE, 9,
e99321, 10.1371/journal.pone.0099321, 2014.de Boyer Montégut, C., Madec, G., Fischer, A. S., Lazar, A., and
Iudicone, D.: Mixed layer depth over the global ocean: An examination of
profile data and a profile-based climatology, J. Geophys. Res.-Ocean., 109,
C12003, 10.1029/2004JC002378, 2004.
Duhaut, T., Honnorat, M., and Debreu, L.: Développements numériques
pour le modele MARS, PREVIMER report-Ref: 06/2 210 290, 2008.
Duhaut, T. H. A. and Straub, D. N.: Wind stress dependence on ocean surface
velocity: implications for mechanical energy input to ocean circulation, J.
Phys. Ocean., 36, 202–211, 2006.Dumousseaud, C., Achterberg, E. P., Tyrrell, T., Charalampopoulou, A.,
Schuster, U., Hartman, M., and Hydes, D. J.: Contrasting effects of
temperature and winter mixing on the seasonal and inter-annual variability
of the carbonate system in the Northeast Atlantic Ocean, Biogeosciences, 7,
1481–1492, 10.5194/bg-7-1481-2010, 2010.Dussurget, R., Birol, F., Morrow, R., and De Mey, P.: Fine Resolution Altimetry Data
for a Regional Application in the Bay of Biscay, Mar. Geod., 34,
447–476, 10.1080/01490419.2011.584835, 2011.Elipot, S. and Gille, S. T.: Estimates of wind energy input to the Ekman
layer in the Southern Ocean from surface drifter data, J. Geophys. Res.,
114, C06003, 10.1029/2008JC005170, 2009.
Ferrari, R.: A frontal challenge for climate models, Science,
332, 316–317, 2011.Fox-Kemper, B., Ferrari, R., and Halberg, R.: Parameterization of Mixed Layer
Eddies, Part I: Theory and Diagnosis, J. Phys. Oceanogr., 38, 1145–1165,
10.1175/2007JPO3792.1, 2008a.Fox-Kemper, B., Ferrari, R., and Halberg, R.: Parameterization of Mixed Layer
Eddies, Part II: Prognosis and Impact, J. Phys. Oceanogr., 38, 1166–1179,
10.1175/2007JPO3788.1, 2008b.
Gill, A. E.: Atmospheric-Ocean Dynamics, Academic Pres, 1982.
Haidvogel, D. B. and Beckmann A.: Numerical Ocean Circulation Modeling.
Imperial College Press, 1999.Hartman, S. E., Hartman, M. C., Hydes, D. J., Jiang, Z.-P., Smythe-Wright, D., and
González-Pola, C.: Seasonal and inter-annual variability in nutrient
supply in relation to mixing in the Bay of Biscay, Deep-Sea Res. Pt.
II, 106, 68–75,
10.1016/j.dsr2.2013.09.032, 2014.
Huang, R. X., Wang, W., and Liu, L. L.: Decadal variability of wind-energy
input to the world ocean, Deep-Sea Res. Pt. II, 53, 31–41, 2006.
Jackett, D. R. and McDougall, T. J.: Minimal Adjustment of Hydrostatic
Profiles to Achieve Static Stability, J. Atmos. Ocean. Tech., 12, 381–389, 1995.Kersalé, M., Marié, L., Le Cann, B., Serpette, A., Lathuilière,
C., Le Boyer, A., Rubio, A., and Lazure, P.: Poleward along-shore current
pulses on the inner shelf of the Bay of Biscay. Estuarine, Coast. Shelf Sci.,
179, 155–171, 10.1016/j.ecss.2015.11.018, 2015.Klein, P., Lapeyre, G., Capet, X., Le Gentil, S., and Sasaki, H.: Upper Ocean
Turbulence from High-Resolution 3D Simulations, J. Phys.
Oceanogr., 38, 1748–1763, 10.1175/2007JPO3773.1, 2008.
Kolmogorov, A.: Dissipation of energy in the locally isotropic turbulence,
Proceedings mathematical and physical sciences, The Royal Society, London,
1941.Lazure P. and Dumas F.: An external–internal mode coupling for a 3D
hydrodynamical model for applications at regional scale (MARS), Adv.
Water Resour., 31, 233–250,
10.1016/j.advwatres.2007.06.010, 2008.Lazure, P., Garnier, V., Dumas, F., Herry, C., and Chifflet, M.: Development of a
hydrodynamic model of the Bay of Biscay, Validation of
hydrology, Cont. Shelf Res., 29,
985–997, 10.1016/j.csr.2008.12.017, 2009.Le Boyer, A., Charria, G., Le Cann, B., Lazure, P., and Marié, L.: Circulation
on the shelf and the upper slope of the Bay of Biscay, Cont. Shelf
Res., 55, 97–107, 10.1016/j.csr.2013.01.006, 2013.Luterbacher, J., Liniger, M. A., Menzel, A., Estrella, N., DellaMarta, P.
M., Pfister, C., Rutishauser, T., and Xoplaki, E.: Exceptional European
warmth of autumn 2006 and winter 2007: historical context, the underlying
dynamics, and its phonological impacts, Geophys. Res. Lett., 34, L12704,
10.1029/2007GL029951, 2007.Lyard, F., Lefevre, F., Letellier, T., and Francis, O.: Modelling the global
ocean tides: modern insights from FES2004, Ocean Dynam.,
56, 394–415, 10.1007/s10236-006-0086-x, 2006.
Marchesiello, P., McWilliams, J. C., and Shchepetkin, A.: Open boundary
conditions for long-term integration of regional oceanic models, Ocean
Model., 3, 1–20, 2001.McWilliams, J. C.: Submesoscale, coherent vortices, Rev.
Geophys., 23, 165–182, 10.1029/RG023i002p00165, 1985.
Mesinger, F. and Arakawa, A.: Numerical methods used in atmospheric models,
GARP Publications Series, No. 17, World Meteorological Organization, 1976.Molemaker, M. J., McWilliams, J. C., and Dewar, W. K.: Submesoscale Instability
and Generation of Mesoscale Anticyclones near a Separation of the California
Undercurrent, J. Phys. Oceanogr., 45, 613–629,
10.1175/JPO-D-13-0225.1, 2015.
Molines, J. M., Barnier, B., Penduff, T., Treguier, A. M., and Le Sommer, J.:
ORCA12.L46 climatological and interannual simulations forced with DFS4.4:
GJM02 and MJM88, Drakkar Group Experiment report GDRI-DRAKKAR-2014-03-19,
2014.
Pasquet, A., Szekely, T., and Morel, Y.: Production and dispersion of mixed
waters in stratified coastal areas, Cont. Shelf Res., 39, 49–77, 2012.Pingree, R. D. and Le Cann, B.: Anticyclonic eddy X91 in the southern Bay of
Biscay, May 1991 to February 1992, J. Geophys. Res., 97, 14353–14367,
10.1029/92JC01181, 1992a.
Pingree, R. D. and Le Cann, B.: Three anticyclonic Slope Water Oceanic eDDIES
(SWODDIES) in the Southern Bay of Biscay in 1990, Deep-Sea Res. Pt. A, 39,
1147–1175, 1992b.Pingree, R. D., Sinha, B., and Griffiths, C. R.: Seasonality of the European
slope current (Goban Spur) and ocean margin exchange, Cont. Shelf
Res., 19, 929–975, 10.1016/S0278-4343(98)00116-2, 1999.Porter, M., Inall, M. E., Green, J. A. M., Simpson, J. H., Dale, A. C., and Miller, P. I:
Drifter observations in the summer time Bay of Biscay slope current, J. Mar. Syst., 157, 65–74,
10.1016/j.jmarsys.2016.01.002, 2016.
Renaudie, C., Morel, Y., Hello, G., Giordani, H., and Baraille, R.:
Observation and analysis of mixing in a tidal and wind-mixed coastal
region, Ocean Model., 37, 65–84, 2011.Reverdin, G., Marié, L., Lazure, P., d'Ovidio, F., Boutin, J., Testor, P.,
Martin, N., Lourenco, A., Gaillard, F., Lavin, A., Rodriguez, C., Somavilla, R.,
Mader, J., Rubio, A., Blouch, P., Rolland, J., Bozec, Y., Charria, G.,
Batifoulier,
F., Dumas, F., Louazel, S., and Chanut, J.: Freshwater from the Bay of Biscay
shelves in 2009, J. Mar. Syst., 109/110, Supplement
S134–S143, 10.1016/j.jmarsys.2011.09.017, 2013.Rodi, W. and Mansour, N. N.: Low Reynolds number k-ε modelling
with the aid of direct simulation data, J. Fluid Mechan., 250,
509–529, 10.1017/S0022112093001545, 1993.
Rodi, W.: Turbulence Models and Their Application in Hydraulics: A
State-of-the-Art Review, 3rd Edn., IAHR Monograph, Balkema,Rotterdam,
Netherlands, 1993.Sasaki, H., Klein, P., Qiu, B., and Sasai, Y.: Impact of oceanic-scale
interactions on the seasonal modulation of ocean dynamics by the atmosphere,
Nat. Commun., 5, 5636, 10.1038/ncomms6636, 2014.
Solabarrieta, L., Rubio, A., Castanedo, S., Medina, R., Charria, G., and
Hernández, C.: Surface water circulation patterns in the southeastern
Bay of Biscay: New evidences from HF radar data, Cont. Shelf
Res., 74, 60–76, 2014.Somavilla, R., González-Pola, C., Rodriguez, C., Josey, S.
A., Sánchez,
R. F., and Lavín, A.: Large changes in the hydrographic structure of the
Bay of Biscay after the extreme mixing of winter 2005, J. Geophys. Res., 114,
C01001, 10.1029/2008JC004974, 2009.Somavilla, R., González-Pola, C., Ruiz-Villarreal, M., and Montero,
A. L.: Mixed layer depth (MLD) variability in the southern Bay of Biscay,
Deepening of winter MLDs concurrent with generalized upper water warming
trends?, Ocean Dynam., 61, 1215, 10.1007/s10236-011-0407-6, 2011.Somavilla, R., González-Pola, C., Schauer, U., and Budéus, G.: Mid-2000s
North Atlantic shift: Heat budget and circulation changes, Geophys. Res.
Lett., 43, 2059–2068, 10.1002/2015GL067254, 2016.
Song, Y. and Haidvogel, D. B.: A semi-implicit ocean circulation model
using a generalized topography-following coordinate system, J. Comp. Phys.,
115, 228–244, 1994.Soufflet, Y., Marchesiello, P., Lemarié, F., Jouanno, J., Capet, X.,
Debreu,
L., and Benshila, R.: On effective resolution in ocean models, Ocean
Model., 98, 36–50, 10.1016/j.ocemod.2015.12.004, 2016.Szekely, T., Bezaud, M., Pouliquen, S., Reverdin, G., and Charria, G.:
CORA-IBI, Coriolis Ocean Dataset for Reanalysis for the Ireland-Biscay-Iberia
region, SEANOE, 10.17882/50360, 2017.
Theetten, S., Vandermeirsch, F., and Charria, G.: BACH1000_100lev-51 : a
MARS3D model configuration for the Bay of Biscay, SEANOE,
10.17882/43017, 2017.
Thompson, A. F., Lazar, A., Buckingham, C., Naveira Garabato, A. C.,
Damerell, G. M., and Heywood, K. J.: Open-ocean submesoscale motions: A full
seasonal cycle of mixed layer instabilities from gliders, J.
Phys. Oceanogr., 46, 1285–1307, 2016.Tulloch, R., Marshall, J., Hill, C., and Smith, K. S.: Scales, Growth Rates, and
Spectral Fluxes of Baroclinic Instability in the Ocean, J. Phys.
Oceanogr., 41, 1057–1076, 10.1175/2011JPO4404.1, 2011.
van Aken, H. M.: Surface currents in the Bay of Biscay as observed with
drifters between 1995 and 1999, Deep-Sea Res. Pt. I, 49, 1071–1086, 2002.