Anthony Bosse
email: anthony.bosse@uib.no

Pierre Testor

Nicolas Mayot

Louis Prieur

Laurent Fabrizio D'ortenzio

Hervé Le Mortier

Claire Goff

Laurent Gourcuff

D ' Fabrizio

Ortenzio

Laurent Mortier

Hervé Le Goff

Claire Gourcuff

Laurent Coppola

Héloïse Lavigne

Patrick Raimbault

A submesoscale coherent vortex in the Ligurian Sea: From dynamical barriers to biological implications

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The northwestern Mediterranean Sea is one the few particular places of the world's oceans, where intense atmospheric forcing combined to a weak ocean stratification allows vertical mixing to reach depths (>1500-2000 m). This phenomenon is called open-ocean deep convection and is of critical importance for the ventilation of the deep oceans and has been studied since the 1970s (see [START_REF] Marshall | Open-ocean convection: Observations, theory, and models[END_REF] for a review). It can be divided into three main phases (that however overlap in space and time) [START_REF] Medoc-Group | Observation of Formation of Deep Water in the Mediterranean Sea[END_REF]: the preconditioning consisting in a basin-scale cyclonic circulation causing a doming of isopycnals at its center; the mixing phase, which results from cold and dry winds blowing over the preconditioned area leading to intense heat losses of the ocean and a deepening of the mixed layer (typically several hundreds of watts per squared meter for a couple of days [START_REF] Leaman | Hydrographic Structure of the Convection Regime in the Gulf of Lions: Winter 1987[END_REF]); the spreading phase induced by the restratification of the water column that occurs, when the intense heat losses cease (generally in early spring).

During this last phase, the mixed patch of convected waters breaks up into numerous eddies by conversion of potential energy into kinetic energy through baroclinic instability [START_REF] Gascard | Mediterranean deep water formation baroclinic instability and oceanic eddies[END_REF][START_REF] Legg | A Heton Model of the Spreading Phase of Open-Ocean Deep Convection[END_REF][START_REF] Visbeck | Dynamics of Isolated Convective Regions in the Ocean[END_REF][START_REF] Jones | Restratification after Deep Convection[END_REF].

In particular, Submesoscale Coherent Vortices are formed [START_REF] Mcwilliams | Submesoscale, coherent vortices in the ocean[END_REF]. They are characterized by a small radius, subsurface peak velocities and an extended lifetime (> 1 year). They were found to be involved in the large-scale spreading of newly-formed deep waters toward the western Mediterranean Sea [START_REF] Testor | DEWEX-MERMEX 2013 LEG1 cruise, RV Le Suroît[END_REF]Gascard , 2003, 2006], the Greenland Sea [START_REF] Gascard | Long-lived vortices as a mode of deep ventilation in the Greenland Sea[END_REF] and the Labrador Sea [START_REF] Lilly | Coherent Eddies in the Labrador Sea Observed from a Mooring[END_REF]. In the western Mediterranean Sea, this process has been recognized as being particularly D R A F T March 8, 2017, 5:07pm D R A F T X -5

important: SCVs could transport 30-50% of the newly formed deep waters out of the convective zone [Testor and Gascard , 2006;[START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF]Damien et al., in revision, this issue], while another important part could be transported by the mean circulation [START_REF] Send | Recent observation indicates convection's role in deep water circulation[END_REF].

The strong rotation of SCVs sets transport barriers at that drastically reduce the lateral exchanges between their deep core and the surrounding waters [START_REF] Rhines | How rapidly is a passive scalar mixed within closed streamlines?[END_REF][START_REF] D R A F T ; D R A F T X -46 | Transport by coherent barotropic vortices[END_REF]. As a consequence, they are therefore extremely efficient in transporting physical and biogeochemical tracers characteristics of their generation site over long distances [START_REF] D'asaro | Observations of small eddies in the Beaufort Sea[END_REF]Testor and Gascard , 2003;[START_REF] Bower | Direct observations of formation and propagation of subpolar eddies into the subtropical North Atlantic[END_REF]. As a consequence, they can greatly impact the biogeochemical cycles at a local scale. For instance, [START_REF] Budéus | Structure and effects of a long lived vortex in the Greenland Sea[END_REF] reported a significant increase in the bacteria abundance at great depths within a deep SCVs observed in the Greenland Sea. Durrieu de Madron et al.

[2017] reveal sediments being trapped within cyclonic SCVs in the NW Mediterranean Sea. In oxygen depleted oceans, they have been identified as local spots for denitrification [START_REF] Löscher | Hidden biosphere in an oxygen-deficient Atlantic open-ocean eddy: Future implications of ocean deoxygenation on primary production in the eastern tropical North Atlantic[END_REF]Karstensen et al., in review, 2016] and habitat compression due to their very low oxygen content [START_REF] Lachkar | Eddies reduce denitrification and compress habitats in the Arabian Sea[END_REF]. Especially in tropical oceanic basins, subsurface eddies can be tentatively be detected from space when combined with infrared satellite images [START_REF] Klemas | Subsurface and deeper ocean remote sensing from satellites: An overview and new results[END_REF], even though the surface expression of deep subsurface eddies is often small [START_REF] Ciani | Influence of Deep Vortices on the Ocean Surface[END_REF]. In the Mediterranean Sea, as well as in high latitude environment characterized by small deformation radii of 5-10 km, sampling the fine scale of eddies remnant of wintertime convection is thus very challenging. about 10 km in diameter observed in the NW Mediterranean Sea [START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF].

Winter 2013 was an intense convective year that produced many vortical structures. In this study, we analyze in situ observations collected during summer 2013 in the Ligurian

Sea by a research vessel and a glider in the same SCV. About 10 days after the first survey by the R/V, the glider met by pure luck the same eddy around 30 km to the southwest from the first observation. Both observations have very high similarities in their vertical structure and are separated by a relative close distance in space and time in coherence with the typical drift of SCVs. The intense sampling of the upper 1000 m by the glider combined with full-depth CTD casts and water samples documenting the nutrients concentrations, as well as phytoplankton pigments enable the first detailed study of such a small-scale post-convective vortex.

Data and methods

Basin-scale cruise

Since 2010, sustained observations of the circulation and water properties are carried out within the framework of the MOOSE project (NW Mediterranean Sea Observatory: http://www.moose-network.fr/). The MOOSE-GE cruises aim at providing a yearly snapshot in summer of the open-ocean part of the basin with about 70-100 CTD stations. As an important part of this integrated ocean observing system, gliders are also regularly deployed in the whole sub-basin along repeated sections. The common key objective of the MOOSE observatory is to monitor the deep waters formation in the Gulf of Lions in order to assess its effect on biogeochemical cycles, and on the longer-term environmental and ecosystemic trends and anomalies [Durrieu de [START_REF] Durrieu De Madron | Marine ecosystems' responses to climatic and anthropogenic forcings in the Mediterranean[END_REF].

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The period 2012-2013 was a period of particular intense sampling with 6 basin-scale surveys from July 2012 to September 2013 [Estournel et al., accepted; Testor et al., in revision, this issue].

Hydrographical data: In February 2013, the DEWEX leg 1 was carried out in the NW Mediterranean Sea [START_REF] Testor | DEWEX-MERMEX 2013 LEG1 cruise, RV Le Suroît[END_REF]. With 75 CTD casts distributed over the whole basin, it enables to get a precious picture of the winter deep convection at its climax (see figure 1). In June-July 2013, 72 CTD stations have been collected during the MOOSE-GE 2013 cruise [START_REF] Testor | DEWEX-MERMEX 2013 LEG1 cruise, RV Le Suroît[END_REF]. A profile revealed the presence of a subsurface vortex in the Ligurian Sea (see figure 2). The conductivity, temperature and pressure measurements during those two cruises have been performed using a Seabird SBE911+ CTD probe. The CT sensors have been calibrated by pre-and post-deployment laboratory analysis. After calibration, the absolute accuracy of the measurements is 0.003 for the salinity and 0.001 • C for the temperature. These calibrated CTD casts provide a ground truth for the autonomous underwater gliders.

Lowered ADCP (LADCP):

During the MOOSE-GE 2013 cruise, the rosette was carrying two RDI WH 300 khz LADCPs (up and down looking). 61 LADCP profiles were processed with the LDEO V8b code based on the inversion method developed by Visbeck [2002]. All profiles were inversed at 8 m vertical resolution using both instruments from the surface to the bottom, navigation data from the CTD file and bottom track constraint when available. Precision on horizontal velocities range from 2 to 4 cm s -1 for all validated profiles. Here, we use the LADCP profile carried within the eddy (leg 1, station 7).

Dissolved oxygen:

The rosette was equipped with a SBE43 sensor for dissolved Oxygen (DO), which has been calibrated before the cruises operation and after with

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post-cruises manufacturer calibrations. After calibration, the absolute accuracy of the measurements is about 5 µmol kg -1 . In addition, Winkler titration have been performed on board after seawater sampling. The measurements have been done each day (every 4-5 stations) and the SBE43 sensor has been cleaned after each CTD cast following the manufacturer recommendations [START_REF] Janzen | Getting more mileage out of dissolved oxygen sensors in long-term moored applications[END_REF]. Later on, the Winkler analysis have been used to adjust the SBE43 raw data, as specified by the GO-SHIP group (http://www.goship.org/).

Nutrients: Water samples for nitrate, nitrite, phosphate and silicic acid determination were collected from the Niskin bottles into 20 mL polyethylene flasks and immediately poisoned with 10 µg L -1 mercuric chloride and stored for subsequent laboratory analysis following [START_REF] Kirkwood | Stability of solutions of nutrient salts during storage[END_REF]. Nitrate (NO - 3 ), phosphate (PO 3- 4 ) and silicate (Si(OH) 4 )

ions were analyzed in laboratory by standard automated colorimetric system using a Seal Analytical continuous flow AutoAnalyser III according to [START_REF] Aminot | Dosage automatique des nutriments dans les eaux marines[END_REF]. Inhouse standards regularly compared to the commercially available products (OSIL) were used to ensure the reproducibility of the measurements between the analyses.

Dissolved Inorganic Carbon: For C T (or DIC) measurements, seawater samples were collected into washed 500 mL borosilicate glass bottles, and poisoned with a saturated solution of HgCl 2 . At the end of the cruise, the samples were sent to the SNAPO (Service National d'Analyse des Paramêtres Océaniques du CO 2 : http://soon.ipsl.jussieu.fr/SNAPOCO2/) for analysis. The measurements were performed by potentiometric titration using a closed cell, as described in details in the handbook of methods for the analysis of the various parameters of the CO 2 system in seawater [START_REF] Doe | Handbook of Methods for the Analysis of the Various Parameters of the Carbon Dioxide System in Sea Water; version 2[END_REF]. The precisions obtained for these measurements are 2.2 µmol kg -1 .

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Pigments: The vertical distribution of phytoplankton pigment concentrations was determined through discrete water samples collected with Niskin bottles mounted on the CTD rosette. The discrete water samples were then filtered (GF/F) and High-Performance Liquid Chromatography (HPLC) analyses have been performed to provide a precise determination of the different phytoplankton pigments concentrations. All HPLC measurements used here were conducted at the Laboratoire d Ócéanographie de Villefranche (see [START_REF] Ras | Spatial variability of phytoplankton pigment distributions in the subtropical south pacific ocean: comparison between in situ and predicted data[END_REF] for details on the HPLC method). As in Mayot et al. [submitted, this issue], we used the pigment-based approach proposed by [START_REF] Claustre | The trophic status of various oceanic provinces as revealed by phytoplankton pigment signatures[END_REF] and further improved by [START_REF] Vidussi | Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern mediterranean sea during winter[END_REF] and Uitz et al. [2006] to estimate the contribution of three phytoplankton size classes: micro-, nano-, and pico-phytoplankton (respectively, f micro , Primary production: The phytoplankton primary production was estimated using the bio-optical model described by [START_REF] Morel | Light and marine photosynthesis: a spectral model with geochemical and climatological implications[END_REF]. The euphotic depth was determined from vertical profiles of [Chl a ](z) [START_REF] Morel | Surface pigments, algal biomass profiles, and potential production of the euphotic layer: Relationships reinvestigated in view of remote-sensing applications[END_REF][START_REF] Morel | Bio-optical properties of oceanic waters: A reappraisal[END_REF] and combined with the phytoplankton class-specific photophysiological properties determined by [START_REF] Uitz | Relating phytoplankton photophysiological properties to community structure on large scales[END_REF] (see more details in Mayot et al. [submitted, this issue], supplementary material S1). The model produces an estimate of the primary production associated with each of the three phytoplankton size classes (P micro , P nano and P pico ).

f
f micro = (1.41[F uco] + 1.41[P erid])/ ∑ DP W (1)
f nano = (1.27[HexF uco] + 0.35[ButF uco] + 0.60[Allo])/ ∑ DP W (2) f pico = (1.01[T Chl b ] + 0.86[Zea])/ ∑ DP W (3) with ∑ DP W a

Glider missions

Autonomous oceanic gliders are now an essential part of ocean observing techniques [Testor et al., 2010]. They sample the ocean along a saw-tooth trajectory between the surface and 1000 m. The typical slope of isopycnals are much smaller than the pitch angle of the glider (about ±15-25°), so dives and ascents can be considered as vertical profiles and are separated by typically 2-4 km and 2-4 h depending on the sampling strategy (dives only, or dives/ascents). Having a horizontal speed of 30-40 km per day, they are perfectly suited to sample oceanic features like eddies that propagate slower [START_REF] Martin | Glider observations of kinematics in a Gulf of Alaska eddy[END_REF][START_REF] Frajka-Williams | Physical controls and mesoscale variability in the Labrador Sea spring phytoplankton bloom observed by Seaglider[END_REF][START_REF] Bouffard | Coastal and mesoscale dynamics characterization using altimetry and gliders: A case study in the Balearic Sea[END_REF][START_REF] Bouffard | Sub-surface small-scale eddy dynamics from multi-sensor observations and modeling[END_REF][START_REF] Fan | Observations of Irminger Sea Anticyclonic Eddies[END_REF][START_REF] Pelland | Subthermocline Eddies over the Washington Continental Slope as Observed by Seagliders, 2003-09[END_REF][START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF][START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF][START_REF] Cotroneo | Glider and satellite high resolution monitoring of a mesoscale eddy in the algerian basin: Effects on the mixed layer depth and biochemistry[END_REF]Thomsen et al., 2016]. In the framework of the MOOSE project, gliders are deployed on a regular basis and in particular along the Nice-Calvi section crossing the Ligurian Sea [START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF]. Here, we use two deployments of Slocum gliders along this endurance line: the mission MOOSE T00-23 in January-March and MOOSE T00-26 in June-July 2013.

Hydrographical data:

The gliders were equipped with an unpumped Seabird SBE41CP CTD probe. Direct comparisons with calibrated shipborne CTD measure-

D R A F T March 8, 2017, 5:07pm D R A F T X -11
ments could be done for both deployments following the approach used in [START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF][START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF]. For the summer mission (MOOSE T00-26), we refined the calibration by adjusting the glider data on the calibrated CTD inside the SCV core. Given the very homogeneous SCV core, both platform agree very well: the root mean square (RMS)

difference between 600 and 800 m depth inside the SCV of 0.002 • C in temperature and 0.001 in salinity, which is comparable with the shipborne CTD accuracy. In addition, thermal lag effects of the probe that can affect salinity measurements in the strong summer thermocline have been corrected following [START_REF] Garau | Thermal Lag Correction on Slocum CTD Glider Data[END_REF].

Depth-average currents: From their dead reckoning navigation and GPS fixes made at the surface, gliders deduce a mean current. This latter represents the mean current over each dive and will hereafter be referred as the depth-average currents (DAC). A compass calibration has been carried out before each deployment allowing DAC to be used to reference geostrophic velocities as commonly done (see for instance the previously cited literature). order to minimize the difference between the glider optode and calibrated shipborne measurements. The comparison is made with CTD casts carried out at less than 50 km and 2 days apart from glider measurements for the winter mission and with profiles carried out in the SCV core for the summer deployment. After this calibration procedure the RMS difference between the glider and shipborne measurements at depth was respectively 1.5 and 1.3 µmol kg -1 , which is below the accuracy of absolute shipborne measurement.

Chl-a Fluorescence:

The glider also had a Wet Labs bio-optical fluoremeter. Unfortunately, no direct comparison with HPLC measurements was possible with the glider data, as the short response time of phytoplankton growth imposes a very close match-up in space and time. Alternatively, a calibration method using satellite ocean color was applied [START_REF] Lavigne | Towards a merged satellite and in situ fluorescence ocean chlorophyll product[END_REF]. In this calibration step, fluorescence profiles were also corrected for non-photochemical quenching following [START_REF] Xing | for in vivo chlorophyll fluorescence acquired by autonomous platforms: A case study with instrumented elephant seals in the Kerguelen region (Southern Ocean[END_REF]. With a larger dataset, Mayot et al. [in revision, this issue] tested this method against bottle measurements. Both calibrations gave satisfying and similar results (Mean Absolute Deviation Percent of 23%

with HPLC and 38% with satellite), thus supporting the use of the method of [START_REF] Lavigne | Towards a merged satellite and in situ fluorescence ocean chlorophyll product[END_REF] when direct comparison with in situ data is not possible.

Remote sensing

Surface chlorophyll concentration from level 2 MODIS Aqua product (daily and at 1 km resolution) were extracted over the northwestern Mediterranean Sea from the NASA web site (http://oceancolor.gsfc.nasa.gov/). All the MODIS L2 flags have been applied.

SCV reconstruction

Vortex center detection

D R A F T March 8, 2017, 5:07pm D R A F T X -13
As in [START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF][START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF], glider depth-average currents are used to retrieve the eddy velocity field. A mean advection is estimated by low-passing the along-track DAC using a Gaussian moving average of 35 km variance. The eddy center detection method is then applied on the DAC minus the local advection. In order to find the the eddy center, the following cost function is minimized:

g(x, y) = 1/n ∑ n i=1 [v i • r i (x, y)/∥r i (x, y)∥] 2 with
(x, y) a given position in the horizontal plane, r i (x, y)/∥r i (x, y)∥ the normalized vector linking (x, y) to the location where the depth-average velocities v i are estimated. We choose n = 4 centered around each vortex center to preserve the synoptic character of the sampling (see figure 7 in [START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF] for an illustration of this cost function method).

The SCV center is thus detected five times from June 26 to July 4, 2013 (see figure 2-c).

During that time period, 106 glider profiles and 59 DACs were carried out at less than 20 km of the eddy center. Every profile could then be positioned in the eddy coordinate framework in order to reconstruct its dynamics (see figure 3).

Objective mapping

Full-depth shipborne CTD cast were collected inside the eddy core and outside (see figure 2). Those profiles provide useful informations below 1000 m, the maximum sampling depth of the glider. In order to map the eddy properties (θ, S P and DO) down to the sea floor at about 2500 m, an objective mapping was performed with a spatial decorrelation scale of 6.3 km in the radial and 800 m in the vertical axis (see figure 4) [START_REF] Bretherton | A technique for objective analysis and design of oceanographic experiments applied to MODE-73[END_REF]Le Traon, 1990]. This radial scale results from the eddy radius deduced from the DACs (see caption of figure 3-c) and the vertical scale corresponds to the thickness of the homogeneous core. To perform this analysis, we used all the glider profiles in the top Objective mapping of potential temperature was also performed in the horizontal plane and in the eddy coordinate system (see figure 3-a). For these interpolations, an isotropic decorellation scale of 6.3 km has simply been used.

Eddy dynamics in gradient wind balance

Small scale vortices are generally characterized by a relatively strong horizontal shear (> 0.1f ). Their force balance are thus ageostrophic and the centrifugal force needs to be taken into account, otherwise the velocity are underestimated for anticyclones and overestimated for cyclones [START_REF] Elliott | The Subthermocline Lens D1. Part II: Kinematics and Dynamics[END_REF][START_REF] Penven | Cyclogeostrophic balance in the Mozambique Channel[END_REF][START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF][START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF]. The cyclostrophic velocities v c can be retrieved by solving the quadratic equation expressing the gradient wind balance in a cylindrical coordinate system:

v 2 c (r, z)/r + f v c (r, z) = f v g (r, z)
with r the distance to the eddy center, z the depth, f the Coriolis parameter and v g the geostrophic velocity field. Keeping the relevant solution from this equation then yields:

v c (r, z) = rf 2   -1 + √ 1 + 4v g (r, z) rf   (4)
The negative root of the quadratic equation is excluded as it corresponds to non-stable solutions with vorticity below -f . Note that this equation can be solved only if the geostrophic shear is not too strongly anticyclonic (i.e. 4v g (r, z)/rf < -1). As expected,

D R A F T March 8, 2017, 5:07pm D R A F T X -15
the amplitude of cyclogeostrophic velocities are smaller (respectively larger) than v g for cyclones (resp. anticyclcones). To infer cyclostrophic velocities, absolute geostrophic velocities have thus to be determined first.

Classically, the cross-track geostrophic vertical shear is computed by integrating the thermal wind balance from a smoothed density section. Here, we applied a Gaussian moving average of 3.2 km variance (half of the eddy radius) to the analyzed density field to filter out residual small-scale isopycnals variability without fading the SCV signature. The cut-off length scale is set in accordance with the vortex radius. A modal decomposition on typical density profiles consistently yields a first baroclinic deformation radius of about 6 km. This is relatively small compared to other oceans owing to the low stratification of the northwestern Mediterranean Sea.

For a Gaussian geopotential anomaly, the orbital velocities of the SCV can be written as:

V (r) = V 0 r r 0 e -[( r r 0 ) 2 -1]/2
where V 0 corresponds to the velocity maximum located at the distance r 0 from the center [START_REF] Mcwilliams | Submesoscale, coherent vortices in the ocean[END_REF][START_REF] Pingree | A shallow meddy (a smeddy) from the secondary Mediterranean salinity maximum[END_REF]. We performed a least squares fit of this Gaussian model to the total DAC from the glider in order to estimate V 0 (= 12.2 ± 2.2 cm s -1 ) and r 0 (= 6.3 ± 0.2 km). Observations and parametrized velocity show a good agreement with velocities decreasing close to zero within about three radii (see figure 3-b).

Then, the geostrophic component of total depth-average currents is computed following [START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF], so the geostrophic shear can be correctly referenced from the surface to 1000 m depth (see details in appendix of the latter reference). This method applies when ageostrophy is due to the centrifugal force, which is particularly relevant for small-scale

D R A F T March 8, 2017, 5:07pm D R A F T X -16 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA
SCVs. The geostrophic component is about 20% smaller in magnitude than total ones (9.8 cm s -1 vs 12.2 cm s -1 ).

And finally, cyclostrophic velocities are inferred using (4). If the geostrophic shear is directly referenced without removing the cyclostrophic component, the geostrophic shear becomes too intense for equation (4) to be solved (i.e. 4v g (r, z)/rf < -1).

Note that isopycnal slope below 1000 m is constrained by only two profiles, one representative of the core and the other of the background. Subsequent errors in the eddy velocity field can thus be the result of miscalculating geostrophic shear. The velocity field shown in figure 5-a still fall into the confidence range of LADCP measurements over the whole water column. They seem to be slightly underestimated close to the surface. The RMS difference is 1.9 cm s -1 , which is satisfactory smaller than the LADCP accuracy (mean error of 3.1 cm s -1 in velocity amplitude).

Complementary diagnostics

Vorticity, strain: We computed the relative vorticity from the radial distribution of

cyclogeostrophic velocities v c (r, z): ζ(r, z) = ∇ × v(r, z) = r -1 ∂ r (rv c ) = v c /r + ∂ r v c , as
well as the strain rate: η(r, z) = ∂ r v c -v c /r. It expresses the rate at which adjacent fluid parcels will separate under the action of the flow.

Potential vorticity: The

Ertel's Potential Vorticity (PV, in m -1 s -1 ) is: q ≡ -ζ a • ∇σ/ρ 0 where ζ a = (ζ + f )ẑ
is the absolute vorticity. In the ocean interior (i.e. away from surface and bottom boundaries), the fluid is governed by the inviscid Boussinesq equations and this quantity is conservatively advected [START_REF] Ertel | Ein neuer hydrodynamischer wirbelsatz[END_REF]. In non-frontal regions where lateral density gradients are small, the PV can be written as:

q(r, z) = f N (r, z) 2 (1+ Ro(r, z))/g. D R A F T March 8, 2017, 5:07pm D R A F T BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA X -17

Lateral isopycnic diffusion

The glider collected a remarkable number of profiles (106 at less than 20 km of the center). The glider has sampled the SCV for about 10 days, which is certainly not long enough to measure an evolution of its core. Nonetheless, as we have a good estimate of its age, a lateral eddy diffusion coefficient K ρ can be fitted to the radial distribution of tracers observed along isopycnals across the eddy core. We assume an step-like initial tracer distribution and then solve the diffusion equation in cylindrical coordinates (details are given in appendix A). This model describes the evolution under radial diffusion of a cylinder (radius L) with initial concentration T 0 located in an infinite environment of tracer concentration T ∞ . The cylinder (representing the SCV) then progressively looses its anomalous concentration until reaching T ∞ .

In order to compute K ρ , some parameters have to be specified. L the radius of the initial tracer distribution is chosen as √ 2 ≃ 1.41 eddy radius. This is where vorticity of a Gaussian vortex changes sign. This is also in good agreement with the observed tracer distribution (see figure 6-a). T ∞ the concentration of the surrounding waters is taken as the average between L and 20 km. T 0 is optimized along with K ρ in order for the theoretical profile to fit to observations. By doing this, we allow the tracer concentration to slightly vary at the top and the base of the core, where vertical diffusion can also be at play and would act rather homogeneously within the eddy core.

The analysis is here conducted for θ, S P and DO (see figure 6-a). DO can be considered as a passive tracer below the euphotic layer due to the very low biological activity in absence of sunlight. Dissolved oxygen is probably the most suited tracer, as it exhibits important and consistent lateral gradient across the SCV rim, while temperature and

D R A F T March 8, 2017, 5:07pm D R A F T X -18 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA
salinity gradients vanish close to its equilibrium depth making diffusion estimate impossible. However, it remains uncertain if the SCV has an effect on the bacterial activity as shown by [START_REF] Budéus | Structure and effects of a long lived vortex in the Greenland Sea[END_REF]. If it is the case, DO might not be as conservative as it normally is.

Model validity: Such an approach assumes (1) the vertical diffusion is small compared to horizontal one, and (2) the initial distribution is a step. [START_REF] Mcwilliams | Submesoscale, coherent vortices in the ocean[END_REF] gave roughly similar horizontal and vertical diffusivity coefficient for a typical subsurface SCV. Subsequent fluxes should then be mainly controlled by the tracer gradients. The first point is thus valid within the SCV core between 350 m and 1000 m, where vertical gradients of tracers are very weak (at least one order of magnitude smaller than horizontal ones). The second point is a simplification that would likely cause an overestimation of the diffusivity coefficients. During the dynamical adjustement occurring at the early stage of the SCV's life, sharp gradients will indeed be rapidly smoothed [START_REF] Mcwilliams | Vortex Generation Through Balanced Adjustment[END_REF].

Results

Water mass transformation during winter 2013

Basin-scale context

There are three main water masses in the Western Mediterranean Sea [START_REF] Millot | Circulation in the Western Mediterranean Sea[END_REF].

The fresh (< 38. oxygen minimum when they reach the Western Mediterranean Sea (see figure 1-d and2-d).

The Western Mediterranean Deep Waters (WMDW) eventually fill the rest of the water column to the bottom. Due to its relative small overturning timescale, the Mediterranean Sea is highly sensitive to climate change [START_REF] Somot | Transient climate change scenario simulation of the Mediterranean Sea for the twenty-first century using a high-resolution ocean circulation model[END_REF]. The heat and salt contents of the deep waters have been gradually increasing during the last decades [START_REF] Béthoux | Warming trend in the western Mediterranean deep water[END_REF][START_REF] Krahmann | Longterm increases in western Mediterranean salinities and temperatures: Anthropogenic and climatic sources[END_REF]], with step-like events caused by major deep convection events [START_REF] Schroeder | Abrupt climate shift in the Western Mediterranean Sea[END_REF][START_REF] Houpert | Observations of open-ocean deep convection in the northwestern mediterranean sea: Seasonal and interannual variability of mixing and deep water masses for the 20072013 period[END_REF].

In addition to AW, LIW and WMDW, other less widespread water masses are found.

The Winter Intermediate Waters (WIW), which result from intermediate mixing down to about 300 m maximum (above the LIW layer) in open-ocean [START_REF] Gasparini | The effect of the Eastern Mediterranean Transient on the hydrographic characteristics in the Strait of Sicily and in the Tyrrhenian Sea, Deep-Sea Research Part I: Oceanographic Research D R A F T March 8[END_REF] or in shelf areas of the Gulf of Lions [START_REF] Juza | Origin and pathways of Winter Intermediate Water in the Northwestern Mediterranean Sea using[END_REF] Lions [START_REF] Bosse | Circulation générale et couplage physique-biogéochimie à (sous-)mésoéchelle en Méditerranée Nord-occidentale à partir de données in situ[END_REF].

Winter mixing in the Ligurian Sea

The of the mixed layer (defined using the refined criterion of [START_REF] Houpert | Observations of open-ocean deep convection in the northwestern mediterranean sea: Seasonal and interannual variability of mixing and deep water masses for the 20072013 period[END_REF]). As seen by the glider along the Nice-Calvi section, the mixed layer reaches a maximum depth of about 800 m between the 13 th and 16 th of February (see figure 1-c). Shipborne CTD casts were taken along the same section a few days later on February 19 and 20, while surface layers had already started to restratify after an intense wind event. However, CTD casts collected slightly southwest of the glider section revealed comparable deep mixed layers.

This illustrates the high spatial and temporal variability of the convective area. The center of the Ligurian Sea convective zone could have been located slightly southwest of the Nice-Calvi glider section, as also suggested by satellite images (see figure 8 in [START_REF] Houpert | Observations of open-ocean deep convection in the northwestern mediterranean sea: Seasonal and interannual variability of mixing and deep water masses for the 20072013 period[END_REF]).

In terms of hydrographical characteristics, when the mixed layer was observed deeper than 600 m, it was characterized by a mean potential temperature close to 13.17 The SCV would impact the whole water column down to the bottom, likely due to its important barotropic rotation able to trap old deep waters during its formation.

Interestingly, quite marked LIW are found in the rim of the eddy (θ ∼ 13.45 • C and S ∼ 38.59) compared to typical values found in the Ligurian Sea (see figure 4). Figure 3-a shows the potential temperature at 400 m in an eddy-centered frame where every observation has been rotated according to its orbital velocity and observation date. This horizontal view

shows the heterogeneity of the LIW temperature at the rim of the eddy, unlike the very homogeneous core (see figure 3-b, left panel). Some profiles located between one and two radius reveal temperature reaching 13.61 • C and salinity up to 38.63. Such values are only found along the continental slope off Corsica (see figure 2-c), the boundary circulation along Sardinia and Corsica being known as a major inflow of warm and salty LIW to the NW Mediterranean Sea [START_REF] Millot | The circulation of the Levantine Intermediate Water in the Algerian Basin[END_REF][START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF]. The SCV would have recently been interacting with this LIW vein without being affected, as the core remains very homogeneous while parts of the LIW vein have clearly been extracted and exported to the open-sea.

Dynamical description

Cyclogeostrophic velocities: They show a clear maximum V max = 13.9±2.0 cm s -1 at R = 6.2 ± 0.2 km from the center. The peak velocity is found at 700 m depth where the geostrophic shear (i.e. isopycnals slope) changes sign (see figure 5-a). Close to the surface, velocities are significantly smaller (about 4 cm s -1 at the surface, 7 cm s -1 at 100 m) supported by LADCP measurements. Baroclinic velocities account for about 20% of the total velocities, the rotation of this SCV appears to be mainly barotropic. This could the reason why the SCV also has a signature in the deep waters below its oxygenated

D R A F T March 8, 2017, 5:07pm D R A F T X -23
core. Ageostrophic cyclotrophic velocities reach 3.8 cm s -1 at a radial distance of 4.1 km smaller than the eddy radius. Ageostrophy is maximum at the origin and represents from about 10% at the surface up to ∼45% around 700 m (see figure 5-a, right panel). This confirms the important role of centrifugal effects in the balance of small-scale SCVs.

Rossby Number: When normalized by the planetary vorticity f , the vorticity ζ(r, z)

represents a local Rossby number Ro l (r, z) that quantifies the non-linearity of the flow.

Due to its small radius and intense orbital velocities, the relative vorticity of the SCV reaches pretty high values of -0.80f at the eddy core, close to -f the limit set by inertial instability for barotropic vortices [START_REF] Kloosterziel | Inertial instability in rotating and stratified fluids: barotropic vortices[END_REF]. This value is very similar to -0.85f reported by [START_REF] Prater | A Meddy Off Cape-St-Vincent .1. Description[END_REF] in a small Meddy in the Atlantic. Flow Ro ≡ 2V max /Rf , ends up to be -0.45±0.08, comparable to previous estimates associated with post-convective SCVs in the NW Mediterranean Sea [Testor and Gascard , 2006;[START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF]. [START_REF] Mcwilliams | Submesoscale, coherent vortices in the ocean[END_REF] suggested that SCVs can survive interactions with external flows characterized by weaker horizontal shear. Here, the high vorticity of the SCV could make it survive interactions with boundary flows mostly in geostrophic balance (horizontal shear of about 0.1f or smaller). This also provides a rational explanation for the presence of the warm and salty LIW observed at the rim of the eddy that could result from its interaction with the LIW flow off Corsica (see figure 4 and3). here N ≤ 5f below 500 m (see figure 5-c). This explains why subsurface eddies have a small radius compared to surface mesoscale eddies. The Burger number further quantifies the ratio of the deformation radius to the eddy radius:

Bu ≡ [N H/f R] 2 = [R d /R] 2 .
To compute the Burger number of the SCV, H = 1600 m is defined from the vertical extension of its geopotential anomaly at the center (i.e. larger than 20% of its maximum value at 700 m) and N = (4.0 ± 0.4)f is the mean background stratification between 600 and 800 m. This yields a Burger number of 1.14 ± 0.22, close to unity. In a low stratified ocean, eddies have thus an unusual high aspect ratio (R/H ∼ N/f ∈ [1 : 10]). This is a particular feature shared by many SCVs observed around the world's oceans [START_REF] D'asaro | Observations of small eddies in the Beaufort Sea[END_REF]Timmermans et al., 2008;[START_REF] Bower | Direct observations of formation and propagation of subpolar eddies into the subtropical North Atlantic[END_REF][START_REF] Pelland | Subthermocline Eddies over the Washington Continental Slope as Observed by Seagliders, 2003-09[END_REF][START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF],

which can be theoretically explained in an idealized case [START_REF] Carpenter | Deep mesoscale eddies in the Canada Basin, Arctic Ocean[END_REF].

Effect on stratification and potential vorticity:

The vertical stratification is significantly weakened inside the SCV almost to a factor of 2 with a mean value 2.4f at ∼700 m (see figure 5-c). Although there are few deep observations, the stratification increases close to the bottom, as observed at the base of deep anticyclonic SCVs [START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF]. Combined with the strong negative vorticity, the PV is notably reduced up to a factor of 20 inside the core at the depth of the vorticity maximum and minimum of stratification. The PV reaches values as low as 10 -13 m s -1 , which is one order of magnitude smaller than that of LIW SCVs formed by topographic interaction in the NW Mediterranean Sea [START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF]. The PV conservation between an initial resting water parcel and the final rotating state enables to compute the initial stratification of

D R A F T March 8, 2017, 5:07pm D R A F T X -25
the resting fluid parcel: N ini = N scv √ 1 + Ro l (0, 700) = 1.1f . Such a low value confirms that convective processes might be at the origin of the SCV.

Dynamical barriers

By resolving the diffusion equation, a lateral isopycnic diffusion coefficient could be estimated for each tracer at different depths (see figure 6). Around to the velocity maximum between 550 m and 800 m, the lateral gradient of temperature and salinity is too weak and no estimation is possible. Where it can be estimated, K ρ is 0.22 ± 0.04 m 2 s -1 .

The tracer distribution reaches background values at the radial distance of about √ 2r 0 (= 8.9 km), where the relative vorticity becomes positive. This is also where the strain rate is maximum (see figure 5-b). The dynamical barriers of the SCV seem to start there and extend to the eddy center.

As explain in section 2.5, dissolved oxygen is the only tracer that provides K ρ estimates near the equilibrium depth of the SCV, where the horizontal vertical processes might be the smallest. There is consistent values among the different tracers, except below the core, where oxygen diffusivity seems to slightly diverge. This could the effect of unknown biological processes acting on the oxygen budget of the SCV. Indeed, [START_REF] Budéus | Structure and effects of a long lived vortex in the Greenland Sea[END_REF] showed a stimulation of the bacterial activity in a deep convective SCVs observed in the Greenland Sea. However, this idea remains hard to verify here without dedicated measurements. Furthermore, the base of the SCV's core is a region of stronger stratification and where trapped near-inertial waves could enhance turbulence levels [START_REF] Kunze | The energy balance in a warm-core ring's near-inertial critical layer[END_REF][START_REF] Sheen | Modification of turbulent dissipation rates by a deep southern ocean eddy[END_REF]. Diapycnal mixing could then increase there, pushing to the limit our nately not test this idea. Overall, all estimates agree on the order of magnitude of the diffusion coefficient of 0.2 m 2 s -1 .

Okubo [1971] reviewed estimates of the horizontal eddy diffusivity coefficient associated with oceanic turbulence and its scale dependency ranging 1-100 m 2 s -1 for scales of 1-100 km (see also a nice and more recent review in introduction of [START_REF] Nencioli | In situ estimates of submesoscale horizontal eddy diffusivity across an ocean front[END_REF]).

Here, we quantified the integral effect of unresolved small-sale processes on the erosion of the SCV's core. This has been previously done for Meddies in the Atlantic Ocean:

(∝ L 2 T -1
). The physics of the dissipation of Meddies and post-convective SCVs is likely to involve different processes. While the rim of Meddies is a place of intense layering [START_REF] Meunier | Tracer Stirring around a Meddy: The Formation of Layering[END_REF] and their core is known to be subjected to double diffusive convection and salt-fingering [START_REF] Armi | Two Years in the Life of a Mediterranean Salt Lens[END_REF], the SCV studied here does not exhibit the typical features associated with those processes (horizontal interleaving or vertical staircases in temperature and salinity).

As stated before, [START_REF] Mcwilliams | Submesoscale, coherent vortices in the ocean[END_REF] highlighted the link between the SCV vorticity and its ability to overcome interactions with external flows. Here, the extreme negative vorticity (-0.8f ) sets important dynamical barriers within the core that drastically inhibit lateral exchanges. The background flow is typically characterized by velocities around 10 cm s -1 at 500 m depth and horizontal scales of about 10 km, leading to horizontal shear order of 0.1f . Recently, Damien et al. [in revision, this issue] managed to simulate

D R A F T March 8, 2017, 5:07pm D R A F T X -27
post-convective SCVs of 5 km radius in a realistic high-resolution regional simulation. The SCVs similarly show a slow diffusion of their core properties with an estimated diffusion coefficient of 0.6 m 2 s -1 in coherence with our estimates. They could survived many interactions with external flows before being finally dissipated by the convective event occurring the following winter.

Biogeochemical and biological impacts

Impact on nutrients concentration

The SCV has an important impact on the nutrients distribution (see figure b,c).

Close to the surface, all nutriclines seem to be shallower by 20 to 50 m compared to the background environment leading to an enhancement of the nutrient availability at the base of the euphotic layer. Within the SCV core between 300 m and about 1500 m depth, the three main nutrients (Nitrate, Phosphate, Silicate) are significantly depleted with respective concentrations around 700 m of 6.9, 0.34 and 6.6 µmol L -1 . This is a decrease of 18, 13 and 18% compared to background concentrations. As for other tracers, nutrients remain isolated from the surrounding environment because of the very limited lateral exchanges.

The formation process of the SCV can provide an explanation for these low values.

Indeed, it results from the mixing of nutrients-poor surface waters with richer waters. formed deep waters would certainly have a less marked imprint on the nutrients, whereas shallower Winter Intermediate Water SCVs would be even more nutrients-depleted.

Impact on phytoplankton

The radial distribution of chlorophyll-a measured by the glider is shown in figure 9a. Both [Chl a ] at the deep chlorophyll maximum (DCM) and integrated over the top 200 m reveal much higher concentrations inside the eddy with respectively 1.7 mg m -3 (+113%) and 29 mg m -2 (+38%) (figure 9-b,c). The eddy dynamics seems thus to favor phytoplankton growth, much likely as a result of the isopycnals doming characteristic of cyclonic and "Mode Water" anticyclones [START_REF] Mcgillicuddy | Eddy/wind interactions stimulate extraordinary mid-ocean plankton blooms[END_REF][START_REF] Nencioli | Physical dynamics and biological implications of a mesoscale eddy in the lee of Hawai'i: Cyclone Opal observations during E-Flux III[END_REF].

The isopycnals doming is quite marked at about 100 m deep, while it is dumped closer to the surface due to summer stratification. This can explain why nutriclines are displaced of about 20-50 m increasing the nutrients availability, whereas the DCM only moves by less than 10 m (figure 9-d).

Regarding the phytoplankton size group, HPLC measurements show a clear predominance of nanophytoplankton inside the eddy with a concentration of 0.86 mg m -3 , about twice the median value of 0.44 mg m -3 observed in the Ligurian Sea (see figure 9-e). This is one of the most abundant station for nanophytoplankton, which represents almost 80% of the total chlorophyll-a. Note that the glider fluorometer calibrated with satellite images is in good agreement with the total chlorophyll-a concentration of 1.1 mg m -3 measured by HPLC.

Discussion

Fate and decline of post-convective SCVs

Deep SCVs are among the most coherent circulation features in the ocean and represent local oddities for the diffusion of tracers. For the diffusive cylinder, the tracer concentration will reach half of its initial value after L 2 /0.20K ρ . Given the diffusion coefficient estimated here, it yields a typical lifetime of 28 months. The SCVs here observed 4.5 months after its formation can be considered as still being in its early stage of life. This is new evidence of the extended lifetime of SCVs already observed [Testor and Gascard , 2003;[START_REF] Budéus | Structure and effects of a long lived vortex in the Greenland Sea[END_REF]Testor and Gascard , 2006;[START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF].

For long, it has been considered that lateral intrusions driven by double-diffusion are causing the decay of Meddies. However, new theories on the origin of those intrusions were recently made implying flow instability and stirring processes [START_REF] Hua | Layering and turbulence surrounding an anticyclonic oceanic vortex: in situ observations and quasi-geostrophic numerical simulations[END_REF][START_REF] Meunier | Tracer Stirring around a Meddy: The Formation of Layering[END_REF]. Here, it is hard to see any intrusion at the rim of the SCV, the gradients separating the SCV and the surroundings being pretty sharp for each eddy crossing by the glider (see figure 2-c). Anticyclonic eddies can also trap downward propagating nearinertial waves, as it has already been observed [START_REF] Joyce | Wintertime observations of Subtropical Mode Water formation within the Gulf Stream[END_REF][START_REF] Cuypers | Characterization of turbulence from a fine-scale parameterization and microstructure measurements in the Mediterranean Sea during the BOUM experiment[END_REF][START_REF] Sheen | Modification of turbulent dissipation rates by a deep southern ocean eddy[END_REF]Karstensen et al., in review, 2016]. The energy dissipation of those waves and their influence on the decay of small-scale post-convective SCVs would need to be assessed in future studies with help of complementary turbulence measurements and numerical models.

Deep mixing preconditioning

As SCVs can live for an extended period of time and are very resistant to interactions, they can easily survive until the following winter. Vertical mixing is actually a primary

D R A F T March 8, 2017, 5:07pm D R A F T X -30 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA
generation mechanism of SCVs, but plays also likely an important role in their dissipation. Due to the deformation of isopycnal layers associated with them, they also have an influence on the deepening of the mixed layer [START_REF] Legg | Localization of Deep Ocean Convection by a Mesoscale Eddy[END_REF][START_REF] Lherminier | The Greenland Sea in Water 1993 and 1994: preconditioning for deep convection[END_REF][START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF][START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF]. For an anticyclonic SCV, once the vertical mixing reaches the top of its weakly stratified core, it then requires a lot less buoyancy loss to mix it down to the base of the core.

The heat and salt content anomalies integrated between the center and one eddy radius represent respectively +4.0×10 9 kg of salt and +4.7×10 16 J. This values are comparable to what was found for LIW SCVs by [START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF]. This suggests that post-convective SCVs of Winter Deep Waters can have an equally important role in the vertical and horizontal heat/salt transport across the NW Mediterranean. The large amount of heat and salt they transport can eventually be redistributed within the mixed layer, thus impacting the heat/salt budget of the deep waters, as discussed by [START_REF] Bosse | Spreading of Levantine Intermediate Waters by submesoscale coherent vortices in the northwestern Mediterranean Sea as observed with gliders[END_REF] for LIW SCVs.

Surface signature of a subsurface SCV

The detection of subsurface eddies from space is an active research topic (see [START_REF] Klemas | Subsurface and deeper ocean remote sensing from satellites: An overview and new results[END_REF] for a review). However, in weakly stratified oceans like the Mediterranean Sea characterized by a small deformation radius, gridded altimetry products have a too large decorrelation scale compared to the observed oceanic variability associated with SCVs and standalone along-track measurements that could tentatively resolve them are hard to interpret. In this context, ocean color images can be very useful, as they provide insights at very high resolution (1 km) into the surface dynamics at the only condition that the sky remains cloud-free. Sea surface temperature measured by satellite at high

D R A F T March 8, 2017, 5:07pm D R A F T X -31
resolution have also been examined. The figure 4-a indeed suggests that surface waters are 0.1-0.2 • C colder inside the eddy. However, the summertime heating of the superficial layers very likely prevents such a signal to be captured.

Figure 10 shows the evolution of the surface chlorophyll-a concentration seen by satellite.

It reveals a clear clockwise swirling of a chlorophyll patch around the outer edge of the deep SCV. Despite lower velocities of about 5 cm s -1 , the SCV seems however to act on the surface dynamics (see figure 5-a). Like at great depths, dynamical barriers similarly prevent lateral exchanges between the eddy core and the surroundings. Generally, the surface chlorophyll signal associated with subsurface post-convective SCVs would then be sensitive to the context of its surrounding environment, unlike its subsurface signature characterized by an enhanced deep chlorophyll maximum.

Primary production and carbon sequestration

The primary production is estimated from HPLC measurements by applying a biooptical model [START_REF] Morel | Light and marine photosynthesis: a spectral model with geochemical and climatological implications[END_REF]. It shows an important influence of the SCV compared to other stations carried out in the Ligurian Sea (see figure 9-f). The total primary production reaches 0.76 gC m -2 d -1 about 25% more than the average value in the Ligurian Sea (0.6 gC m -2 d -1 ). The contribution of the different phytoplankton size groups to this elevated primary production again reveals the importance of nanophytoplankton. This can have further implication for the carbon sequestration, as higher productivity also means enhanced export of particulate organic carbon to great depths where it can be remineralized under the action of bacteria. Higher carbon export within mesoscale eddies was already reported in Mediterranean Sea by [START_REF] Moutin | Influence of anticyclonic eddies on the Biogeochemistry from the Oligotrophic to the Ultraoligotrophic Mediterranean (BOUM cruise)[END_REF]. Waite et al.

[2016] recently described an important mechanism that concentrates particulate export

D R A F T March 8, 2017, 5:07pm D R A F T X -32 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA
within mesoscale eddies. The remineralization would imply a gradual increase in the nutrients concentration. The SCV's core however remained nutrients-depleted even after more than 4 months of remineralization.

Dissolved inorganic carbon measurements also reveals a higher concentration within the SCV of about 5-10 µmol kg -1 . As discussed before, this could result from the higher productivity associated with it. Another explanation could be the trapping at depth of organic carbon during wintertime, while the SCV is formed. Indeed, figure 1-c shows a clear signal of chlorophyll-a below the euphotic layer within the mixed layer and down to 1000 m. Phytoplankton cells initially present in the surface layer are then diluted over the mixed layer during active mixing characterized by intense vertical water displacements of ±5-15 cm s -1 [START_REF] Schott | Observations with Moored Acoustic Doppler Current Profilers in the Convection Regime in the Golfe du Lion[END_REF][START_REF] Marshall | Open-ocean convection: Observations, theory, and models[END_REF]Margirier et al., submitted, this issue]. This allows within a few hours the overturning of phytoplankton between the euphotic layer and depths of about 1000 m. During the generation of postconvective SCV, vertical motions cease and phytoplankton would get trapped within the deep core before being converted into inorganic carbon.

Summary and Conclusion

This The SCV has an intense anticyclonic rotation with depth-average currents measured by the glider up to 15 cm s -1 . Those currents were used to detect the eddy center and reconstruct the fine-scale eddy dynamics. The equilibrium depth of the SCV is around 700 m, where cyclogeostrophic peak velocities of 13.9 cm s -1 are estimated at a distance of 6.2 km from the center. The force balance of the eddy is found to be strongly non linear with a Rossby number at the velocity maximum of -0.45. The shear at the origin is even higher and reaches -0.8f . This suggests a great ability of the SCV to overcome the interaction with external flows. The Burger number of the SCV is close to unity indicating a high aspect ratio of this circulation feature. The vertical stratification N is reduced within the core with a mean core stratification of about 2.4f . Due to this low value and to the high anticyclonic vorticity, the potential vorticity of the SCV reaches values as low as 10 -13 m -1 s -1 testifying to the strong mixing occurring during its generation.

The extensive sampling of the eddy core and the knowledge of the age of the eddy enable to estimate a lateral isopycnic coefficient by solving the cylindrical diffusion equation. It yields a diffusive coefficient of 0.22 m 2 s -1 . The diffusive half-life of the eddy is thus of about 2.5 years. So, even after 4.5 months of existence, the SCV can still be considered as being in its early stage of life. Important dynamical barriers drastically reduce lateral

D R A F T March 8, 2017, 5:07pm D R A F T X -34 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA
exchanges between the core of the SCV and the surroundings thus enabling it to keep the characteristics of its origin (i.e. ventilated waters with almost constant temperature and salinity). Furthermore, it has the ability to easily survive until the following winter. As interactions with other flows and diffusive processes have little impact on the SCV, winter vertical mixing is likely to be an important mechanism for the destruction of such very coherent SCVs. In the future, the utilization of turbulence sensors mounted on gliders could unveil the mysteries about the SCVs fate and in particular their interaction with internal waves.

In terms of biogeochemical properties, the SCV core is nutrient-depleted with concentrations in nitrate, phosphate and silicate on average -15% lower than what is found in the surroundings at about 700 m. Nutriclines are shifted toward the surface by about 20-50 m, enhancing the nutrients availability for phytoplankton growth. Consistently, the glider fluorometer and HPLC measurements reveal higher chlorophyll-a concentrations of the deep chlorophyll maximum within the eddy (1.7 mg m -3 , +90%). Furthermore, pigments concentrations show a clear predominance of nanophytoplankton compared to outside. This demonstrates that even deep SCVs have a significant influence on the nutrients distribution and the phytoplankton community. A bio-optical model was also used to characterized the primary production. It was found to be significantly enhanced inside the SCV leading potentially to a higher carbon sequestration.

This study gives the first conjoint physic-biogeochemical description of a post-convective SCV in the NW Mediterranean Sea. Our findings suggest they locally have a great imprint on both physical and biogeochamical cycles. However, their basin-scale impact in particular for the nutrients budget or the phytoplankton distribution still need to be

D R A F T March 8, 2017, 5:07pm D R A F T X -35
assessed. This is an important issue for coupled regional climate model that do not resolve those processes, but still aim at characterizing the evolution of the marine ecosystem in the context of climate change.

Appendix A: The heat equation in cylindrical coordinate

Lets consider the evolution of a tracer T whose concentration is initially constant T = T 0 and confined within a long cylinder of radius R. In this case, the heat equation goes by in its cylindrical form:

∂T ∂t = K 1 r ∂ ∂r (r ∂T ∂r ) (A1)
The desired solution of this equation owes to verify: (1) ∂ r T = 0 at r = 0 as imposed by the cylindrical geometry;

(2) T = T ∞ at r = L as the background domain is supposed to be infinite and thus have a constant tracer concentration.

According to the separation of variables method, we can seek a solution of the form: t). Substituting this into the heat equation yields:

T (r, t) = T ∞ + α(r)β(
1 rα d dr (r dα dr ) = 1 K 1 β dβ dt (A2)
Each side of the equation being a function of an independent variable (r and t), it has thus to be constant. Furthermore, this constant must be negative to prevent β from exponentially diverging in time. Lets call it -λ 2 , we then have:

r 2 d 2 α dr 2 + r dα dr + r 2 λ 2 = 0 and dβ dt + Kλ 2 β = 0 (A3)
The general solution for β is simply: The equation on α is a special case of Bessel's equation, whose only physically meaningful solution has the form: α(r) = α 0 J 0 (λr) where α 0 is another constant and J 0 is the Bessel function of first kind of order zero.

β(t) = β 0 e -λ 2
Since T (r = L, t) = T ∞ , this requires J 0 (λL) = 0. Knowing the zeros of the Bessel function J 0 , one can thus define λ n the eigenvalues of the problem and the particular solutions for the problem: T n (r, t) = T ∞ + A n J 0 (λ n r)e -λ 2 n Dt with A n = α n 0 β 0 . The general solution then writes:

T (r, t) = T ∞ + ∞ ∑ n=1 A n J 0 (λ n r)e -λ 2 n Kt (A4)
To infer the coefficients A n , one can project the initial condition (T (r, t = 0) -T ∞ = T 0 -T ∞ ) onto a particular eigenfunction J 0 (λ m r) and use the orthogonality of each eigenfunction (

∫ [0,L] rJ 0 (λ m r)J 0 (λ n r)dr = 0 if n ̸ = m, = 1 otherwise): ∫ L 0 rJ 0 (λ m r)(T 0 -T ∞ )dr = ∞ ∑ n=1 ∫ L 0 rA n J 0 (λ m r)J 0 (λ n r)dr = A m ∫ L 0 rJ 0 (λ m r) 2 dr(A5)
then knowing that:

∫ [0,L] rJ 0 (λ m r)dr = LJ 1 (λ m L)/λ m and ∫ [0,L] rJ 2 0 (λ m r)dr = L 2 [J 2 0 (λ m L) + J 2 1 (λ m L)]/2 = L 2 J 2 1 (λ m L)/2 , one can explicit the different coefficient A m
and write the final solution of our problem:

T (r, t) = T ∞ + 2(T 0 -T ∞ ) L ∞ ∑ n=1 J 0 (λ n r) λ n J 1 (λ n L) e -λ 2 n Kt (A6)
Acknowledgments.

The hydrographical data were collected and made freely available by the Coriolis project and programmes that contribute to it (http://www.coriolis.eu.org). The cruise data is provided in the reference section along with the associated doi. Vincent Tailliandier is thanked for the calibration of shipborne CTD and providing feedback on the manuscript.

We The geostrophic component of orbital depth-average currents deduced following [START_REF] Bosse | Scales and dynamics of submesoscale coherent vortices formed by deep convection in the northwestern mediterranean sea[END_REF] is also shown by the light black line. Note that outliers plotted in gray have been excluded prior to the curve fitting. Histograms representing the number of observations in 1 km bins are also shown in upper panels. (d) q(r,z) / q out (z)

  By allowing a relatively high horizontal resolution (distance between consecutive profiles 2-4 km), autonomous gliders could characterize the dynamics of post-convective SCVs of D R A F T March 8, 2017, 5:07pm D R A F T X -6 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA

  nano and f pico ) to the total phytoplankton biomass estimated as [Chl a ] the chlorophyll-a concentration. Seven diagnostic pigments were selected as biomarkers of major phytoplankton taxa: fucoxanthin ([F uco]), peridinin ([P erid]), alloxanthin ([Allo]), 19'butanoyloxyfucoxanthin ([ButF uco]), 19'-hexanoyloxyfucoxanthin ([HexF uco]), zeaxanthin ([Zea]) and total chlorophyll-b (chlorophyll-b + divinyl chlorophyll-b = [T Chl b ]) to compute fmicro, fnano, and fpico:

  weighted sum of the seven diagnostic pigments concentration: DP W = (1.41[F uco] + 1.41[P erid] + 1.27[HexF uco] + 0.35[ButF uco] + 0.60[Allo] + 1.01[T Chl b ] + 0.86[Zea]). Eventually, the phytoplankton classspecific vertical profiles of chlorophyll-a were deduced by: [Chl a ] class (z) = [Chl a ](z)f class (z). D R A F T March 8, 2017, 5:07pm D R A F T X -10 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA

Dissolved oxygen :

 oxygen The gliders were equipped with an Anderraa Optode 3835. The raw phase measurements were corrected from a sensor time response estimated by comparing measurements of consecutive up and down profiles. Time delays of 30 s (MOOSE T00-23) and 25 s (MOOSE T00-26) were estimated, the same order of magnitude than the 25 s provided by the manufacturer. Oxygen concentration was then computed using the corrected phase measurements and temperature measurements from the CTD, following the Argo recommendations [Thierry and Bittig, 2016]. As a final calibration step, an offset (respectively 10.0 and 20.3 µmol kg -1 for the missions MooseT00-23 and T00-26) and a slope (respectively 0.016 and -0.0049 µmol kg -1 m -1 ) were least squares fitted in D R A F T March 8, 2017, 5:07pm D R A F T X -12 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA

  .: A POST-CONVECTIVE SCV IN THE NW MED SEA 1000 m and only two full-depth shipborne profiles below. The shipborne CTD cast within the core was positioned at r = 3.8 km from the eddy center by fitting the mean LADCP velocity of the 0-1000 m layer (11.0 cm s -1 ) to the glider DACs (see figure3-c). And the profile representative of the background, taken as the mean profile observed in the Ligurian Sea during the MOOSE-GE cruise (see figure2-b), was positioned at r = 20 km (more than three eddy radius).

  5) and warm (> 15 • C) Atlantic Waters (AW) found in the surface layers (100-200 m in the basin center and deeper along continental slope due to the boundary circulation, see figure 1-c and 2-c). The warm and salty layer of Levantine Intermediate Waters (LIW) at intermediate depths (200-800 m). This water mass is formed in the Eastern Mediterranean Sea and further spread toward the Western Mediterranean Sea through the Sicily channel. Due to their relatively "old" age, they are characterized by an D R A F T March 8, 2017, 5:07pm D R A F T X -19

  glider mission MOOSE T00-23 sampled the Ligurian Sea from January to March at the climax of the deep convection. The figure 1-c shows the progressive deepening D R A F T March 8, 2017, 5:07pm D R A F T X -20 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA

  figure 1-b).

  with large Rossby number close to unity are qualified as submesoscale flows, as they are not completely in geostrophic balance (see a recent review by[START_REF] Mcwilliams | Submesoscale currents in the ocean[END_REF] for more details). The Rossby number of the SCV, estimated at the velocity maximum as

Burger Number :

 : The horizontal scale of oceanic eddies is controlled by the internal deformation radius: R d ≡ N H/f depending on H its vertical extension and N the water D R A F T March 8, 2017, 5:07pm D R A F T column stratification (N 2 ≡ -g∂ z σ/ρ 0 ). The stratification generally decreases with depth:

  simple 1D diffusion model. Again, with no turbulence measurements, we can unfortu-D R A F T March 8, 2017, 5:07pm D R A F T X -26 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA

  [START_REF] Hebert | Evolution of a Mediterranean Salt Lens: Scalar Properties[END_REF] found a lateral eddy coefficient of 5 m 2 s -1 associated with the decay of a 20 km radiusMeddy and McWilliams [1985] 10 m 2 s -1 for a typical 50 km radius Meddy. If Meddies and post-convective SCVs have a comparable lifetime T of a few years, the smaller radius L of SCVs would tend to reduce their associated diffusion coefficient

  Schematically, a 100 m thick surface layer with no nutrients being mixed with 700 m of nutrient-rich waters below would result in a nutrient concentration reduced by about 13%. Following this argument, among the other type of post-convective SCVs described in Bosse et al. [2016], anticyclones with a deep core below 1000 m and cyclones of newly D R A F T March 8, 2017, 5:07pm D R A F T X -28 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA

D

  R A F T March 8, 2017, 5:07pm D R A F T BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA X -29

  study described the dynamical and biogeochamical characteristics of a Submesoscale Coherent Vortex (SCV) formed by deep convection in the Ligurian Sea (NW Mediterranean Sea). It is based on in situ observations collected in late June 2013 during a research cruise (shipborne CTD measurements and water samples analysis) combined with data from an autonomous glider equipped with optode and bio-optical sensors. It was very fortunate that the glider crossed the eddy a few days after the ship, but the opportunity was taken to intensively sample the eddy with the glider. D R A F T March 8, 2017, 5:07pm D R A F T X -33 Its core is made of nearly homogeneous water between 300 and 1200 m depth with θ ≃ 13.18 • C, S P ≃ 38.54 and DO ≃ 200 µmol kg -1 . The high dissolved oxygen concentration of the SCV indicates an origin during the previous wintertime convective episode about 4.5 month prior to its sampling during summer. The presence of very warm and salty Levantine Intermediate Waters around it suggests it has been interacting with the boundary circulation flowing along the continental slope along Sardinia and Corsica.

  Dt where β 0 is a constant. D R A F T March 8, 2017, 5:07pm D R A F T X -36 BOSSE ET AL.: A POST-CONVECTIVE SCV IN THE NW MED SEA

Figure 1 .

 1 Figure 1. (a) CTD casts carried out in the Ligurian Sea during the DEWEX winter cruise in

Figure 2 .Figure 3 .

 23 Figure 2. Same as figure 1 but for the MOOSE-GE 2013 summer cruise and the MOOSE

Figure 4 .Figure 5 .

 45 Figure 4. Hydrography of the SCV. Radial distribution of (a) potential temperature, (b)

Figure 6 .Figure 7 .

 67 Figure 6.Horizontal diffusion of oxygen, heat and salt at the rim of the SCV. (a) The

Figure 8 .

 8 Figure 8. Concentrations of the three main nutrients and carbon measured during the MOOSE-

Figure 9 .

 9 Figure 9. (a) Bin-averaged section across the eddy of the chlorophyll-a concentration measured

  Figure 3.

  Figure 5.

  Figure 6.

  Figure 8.