Particulate organic carbon budget of the Gulf of Lion shelf (NW Mediterranean) using a coupled hydrodynamic-biogeochemical model

The Gulf of Lion shelf (NW Mediterranean) is one of the most productive areas in the Mediterranean Sea. A 3D coupled hydrodynamic-biogeochemical model is used to study the mechanisms that drive the particulate organic carbon (POC) budget over the shelf. A set of observations, including temporal series from a coastal station, remote sensing of surface 10 chlorophyll-a, and a glider deployment, is used to validate the distribution of physical and biogeochemical variables from the model. The model reproduces well the time and spatial evolution of temperature, chlorophyll, and nitrate concentrations and shows a clear annual cycle of gross primary production and respiration. Knowing the physical and biogeochemical inputs and outputs terms, the annual budget of the POC in the Gulf of Lion is estimated and discussed. We estimate an annual net primary production of ~200 10 tC yr at the scale of the shelf. The primary production is marked by a coast-slope increase with 15 maximal values in the eastern region. Our results show that the primary production is favored by the inputs of nutrients imported from offshore waters, representing 3 and 15 times the inputs of the Rhône in terms of nitrate and phosphate. Besides, the EOFs decomposition highlights the role of solar radiation anomalies and continental winds that favor upwellings, and inputs of the Rhône River, on annual changes in the net primary production. Annual POC deposition (19 10 tC yr) represents 10% of the net primary production. The delivery of terrestrial POC favored the deposition in front of the Rhône mouth and the 20 mean cyclonic circulation increases the deposition between 30 and 50 m depth from the Rhône prodelta to the west. Mechanisms responsible for POC export (24 10 tC yr) to the open sea are discussed. The export off the shelf in the western part, from the Cap de Creus to the Lacaze-Duthiers canyon, represented 37% of the total POC export. Maximum values were obtained during shelf dense water cascading events and marine winds. Considering surface waters only, the POC was mainly exported in the eastern part of the shelf through shelf waters and Rhône inputs, which spread to the Northern Current during 25 favorable continental wind conditions. The Gulf of Lion shelf appears as an autotrophic ecosystem with a positive Net Ecosystem Production and as a source of POC for the adjacent NW Mediterranean basin. The undergoing and future increase in temperature and stratification induced by climate change could impact the trophic status of the GoL shelf and the carbon export towards the deep basin. It is crucial to develop models to predict and assess these future evolutions. https://doi.org/10.5194/bg-2021-82 Preprint. Discussion started: 6 April 2021 c © Author(s) 2021. CC BY 4.0 License.


The importance of continental margins in the organic carbon budget
Continental margins are of particular interest concerning the input, production, deposition, and export to the deep open ocean of particulate organic carbon (POC) (Bauer and Druffel, 1998;Liu et al., 2010). These buffer regions often show high biological productivity, induced by solar radiation and nutrients availability from river inputs and coastal upwellings (Legendre, 1990;Dagg et al., 2004;Lohrenz et al., 2008). The input of terrigenous POC and this high productivity make these 35 coastal zones areas of high organic matter deposition (Gao and Wang, 2008;Dagg et al., 2008). Hydrodynamic processes such as upwelling, dense water cascading, slope current could favor the lateral transport of POC towards the open sea and deeper environments (Lapouyade and Durrieu de Madron, 2001;Thunell et al., 2007;Sanchez-Vidal et al., 2008). The understanding of the input, deposition, and export of POC is thus essential to estimate the carbon budgets of coastal areas at a world scale.

40
Besides, modeling the POC dynamics in coastal and shelf systems needs the integration of several processes interacting with each other, as a land-sea continuum (riverine organic carbon and nutrient inputs) and hydrodynamical forcings on POC production and transport in the water column. A realistic simulation of the hydrodynamical processes in the coastal area is essential to reproduce the spatiotemporal changes in POC conditions (Hofmann et al., 2011). Among those processes, circulation patterns and stratification dynamics are considered to be extremely important to describe the POC horizontal 45 advection, impacted by water mass upwelling, and shelf-open ocean water mass exchanges, as well as to be able to describe the vertical gradients in nutrient conditions that control the POC production (primary production) and the POC deposition (Liu and Chaï, 2009).

Regional settings
The Gulf of Lion shelf (GoL) in the NW Mediterranean is a wide continental shelf ( Fig. 1, area of approximately 10 000 km²) 50 strongly influenced by freshwater and particulate matter inputs from the Rhône River (Fig. 1). The Rhône River is characterized by a mean annual discharge of 1,700 m 3 s -1 , which makes the GoL one of the most river-impacted areas of the Mediterranean (Naudin et al., 1997;Maillet et al., 2006;Ludwig et al., 2009). Sadaoui et al. (2016) estimated a total suspended solid flux around 8.4 10 6 t yr -1 from which approximately 1% is considered as POC (see Table 2 in Durrieu de Madron et al., 2000).
During floods, terrestrial inputs from the Rhône create a surface plume that spreads southward across the shelf by surface 55 currents driven by continental (westerly/northerly) winds or is constrained along the coast during marine (easterly) winds.
Besides, Rhône inputs also feed a bottom nepheloid layer that favors local sediment deposition (Many et al., 2018). The Gulf of Lion is bordered on the continental slope by the Northern Current associated with the general circulation of the western Mediterranean basin (Petrenko et al., 2008).
In terms of biological net primary production (NPP), the Gulf of Lion is one of the most productive areas in the Mediterranean Sea (together with the North Adriatic and the Alboran Sea) (Bosc et al., 2004). It is an exception in this oligotrophic system, which is relatively impoverished in nutrients concerning the open ocean. The annual production in the GoL shelf has been estimated to be in the range of 80-150 gC m -2 yr -1 (90-165 10 4 tC yr -1 considering a shelf area of 1.1 10 10 m 2 ) (Durrieu de 65 Madron et al., 2000), which is similar to the production in the adjacent deep-water formation area (Lefevre et al., 1997;Ulses et al., 2016;Kessouri et al., 2018).
The main mechanisms that drive POC deposition in the Gulf of Lion are widely described in Auger et al. (2011). The authors highlighted the contribution of organic detritus to 80-90% of the total POC deposition whereas the contribution of living particles (phytoplankton) was estimated to approx. 10-20%. Besides, the authors estimated that the contribution of terrestrial 70 particulate organic carbon corresponds to less than 17 % of the total of POC deposition, with the main deposition occurring in front of the Rhône mouth during floods. On the other hand, the predominant influence of marine biological production on POC deposition over the entire shelf is highlighted.
The Gulf of Lion is considered as a source of POC to the basin of the NW Mediterranean sea (Durrieu de Madron et al., 2000;75 Ulses et al., 2008b;Ulses et al., 2016). It is a very dynamic system, marked by low residence times (Mikolajczak et al., 2020) where wind-induced currents are important for POC horizontal advection. Coastal hydrodynamic conditions are influenced by the circulation along the continental slope, the Northern Current (Petrenko et al., 2003), the freshwater inputs from the Rhône (Marsaleix et al., 1998;Estournel et al., 2001), the wind-driven circulation over the shelf (Estournel et al., 2003;Petrenko, 2003;Petrenko et al., 2005;Ulses et al., 2008a), and the formation and cascading of shelf dense water (Dufau-Julliand et al., 80 2004;Ulses et al., 2008c).
It is however noticeable that the values of the POC budget terms have been determined based on local observations and/or during limited periods. The inter-annual variability of the environmental conditions (wind velocity, heat flux, temperature, etc.) as well as episodic events (floods, storms, water mass upwellings) are also expected to play a key role in changes in the 85 POC budget over the shelf and need to be quantified.

Objective of this study
The objective of this present work is to estimate the POC budget on the Gulf of Lion shelf and to improve our understanding of the mechanisms that control this budget based on a coupled hydrodynamical-biogeochemical model over a pluriannual period. The 2011-2016 period was characterized by high annual changes in environmental conditions, particularly during 90 winters, which are key periods in the water mass export and mixing, and phytoplankton bloom triggering (see winter heat fluxes and winds in Fig. 1 Fig. 1). It is expected that these variations in these environmental conditions, that may influence the availability of nutrients 95 in the surface layer, and hence the phytoplankton growth will affect the POC budget on the shelf, which remains seldom quantified at the scale of the shelf and during contrasted years.
In this paper, we present the numerical model used to carry out this study, particularly its validation against multiplatform observations including time series from a coastal station, remote sensing of surface chlorophyll-a, and a glider deployment to 100 describe the vertical distributions of physical and biogeochemical conditions. After describing the environmental conditions, we then estimate the POC budget of the shelf during the 2011-2016 period, and detail and discuss the variability of the nutrient availability, primary production, the deposition over the shelf, and the cross-shelf transport of POC towards the deep basin and the Catalan margin over this period marked by contrasted meteorological, hydrodynamic and fluvial conditions. https://doi.org/10.5194/bg-2021-82 Preprint. Discussion started: 6 April 2021 c Author(s) 2021. CC BY 4.0 License. The Rhône River is shown by a black line. SOMLIT Banyuls station is shown in red. The path of the glider during the April/May 2013 deployment is shown in magenta. The limit of the shelf studied in this work is specified by the 120 m isobath. The thick blue and orange lines show the limit of the boundaries used to estimate water, nutrients, and particulate organic carbon transports in the eastern and western part of the shelf, respectively. The boundary of the model grid is shown in red on the inserted Mediterranean map. Bottom: Meteorological and fluvial forcings for 110 each year simulated: the winter (DJF) mean wind rose (m s -1 ), winter surface heat flux (W m -2 ), and annual Rhône River discharge (m 3 s -1 ) are specified.

The model
The three-dimensional model results from the off-line forcing of the biogeochemical Eco3M-S model by the regional 115 circulation SYMPHONIE model. These two models and the coupling procedure are described thereafter.

The hydrodynamic model
The SYMPHONIE model (Marsaleix et al., 2006; is a 3-D primitive equation, free surface, and generalized sigma vertical coordinate model. This model was previously used to simulate the hydrodynamic conditions in the Mediterranean Sea and specific processes as the Rhone river plume dynamics (Estournel et al., 1997;Reffray et al, 2004), coastal dense water 120 formation (Ulses et al., 2008c), wind-induced circulation over the Gulf of Lion shelf (Estournel et al., 2003;Petrenko et al., 2008;Ulses et al., 2008a), shelf-slope exchanges and along-slope circulation (Bouffard et al., 2008;Mikolajczak et al., 2020).
The numerical grid of the model is the same as in the study of Briton et al. (2018). It consists of a curvilinear bipolar (Bentsen et al, 1999) Arakawa C-grid with 40 vertical sigma levels (Mikolajczak et al., 2020). The bipolar grid presents a horizontal resolution between 300 m and 500 m over the shelf, and gradually decreases to several km towards the south of the domain 125 along the Algerian coast. This configuration allows us to have more than half of the total points of the grid over the shelf while keeping the open boundaries far from the study area, the Gulf of Lion.
River runoffs were considered using measured daily values for French rivers (Banque Hydro database, www.hydro.eaufrance.fr), the Ebro (SAIH Ebro database, www.saihebro.com), and mean annual value for the others. The implementation of rivers in the model was described in Estournel et al. (2009). Atmospheric forcings were generated by the 130 hourly fields (wind speed and direction, pressure, air temperature and humidity, solar and downward longwave radiation and precipitation) provided by the ECMWF (European Centre for Medium-Range Weather Forecasts) forecasts. We used the bulk formula of Large and Yeager (2004) to estimate the surface turbulent fluxes.
The period simulated with the SYMPHONIE model runs from 1 July 2011 to 31 December 2016. The initial state and the open boundary conditions were generated by a "parent" simulation (SYMPHONIE) that began two months earlier than the "child" 135 simulation. The open lateral boundary conditions of the child model consist of radiative conditions reinforced by a lateral restoring layer towards the hydrodynamic fields of the parent model (Marsaleix et al, 2006). The parent model covers the Mediterranean basin. Its average horizontal resolution is 4 km. It is initialized with the Mercator Ocean International operational center hydrodynamic fields using the stratification index correction method described in Estournel et al. (2016).

The biogeochemical model 140
The Eco3M-S model is a multi-plankton and multi-nutrient dynamics model (Ulses et al., 2016) that simulates the dynamics of the biogeochemical cycles of biogenic elements (carbon, nitrogen, phosphorus, silicon, and oxygen) and plankton groups.
We used the "Source Splitting" coupling method (Butenschön et al., 2012), which consists of an off-line forcing of the 145 biogeochemical model by the daily averaged outputs of the physical model. It is then assumed that biogeochemical properties do not significantly impact hydrodynamics and we used a time step of 10 minutes for the advection and diffusion of biogeochemical variables.
Rhône River nutrient inputs (nitrate, ammonium, phosphate, silicate, and dissolved organic carbon) were determined using in situ daily data (Mistrals-Sedoo database, http://mistrals.sedoo.fr/MOOSE/). Concentrations of dissolved organic phosphorus 150 and nitrogen and particulate organic carbon were estimated from this dataset and the relations found in the literature (Moutin et al., 1998;Sempéré et al., 2000). The Orb, Aude, and Herault rivers monthly data were extracted from the Naïades database (Agence de l'eau, http://www.naiades.eaufrance.fr/) and were interpolated on the period of the simulation with a daily resolution. At the other river (Tech, Têt, Agly) mouths, climatological values were used according to Ludwig et al. (2010).
The deposition of organic and inorganic matter from the atmosphere was based on the low estimations of Ribera d 'Alcala et 155 al. (2003). Finally, the pelagic-benthic coupling of inorganic nutrients was made using the meta-model described in Soetaert et al. (2001). An adjustment of this model was made according to Pastor et al. (2011).
As for the hydrodynamic model, the initial state and the open boundary conditions were generated by a "parent" simulation (Eco3M-S) that encompassed the whole Mediterranean Sea. This latter simulation was forced by the same daily fields from the SYMPHONIE model as used for the "child" regional hydrodynamic model (see 2.1.1). This ensures the coherence of the 160 physical and biogeochemical fields at the open boundaries of the child regional model. The period simulated with the Eco3M-S regional model runs from 1 August 2011 to 31 July 2016.

Satellite data 170
Spatial maps of daily chlorophyll-a concentrations, with a 1 km resolution, were obtained using products from Moderate Resolution Imaging Spectroradiometer (MODIS). Products, analysis, and calibrations used were provided by IFREMER Nausicaa services and OC5 IFREMER algorithms for Chl-a concentrations from Gohin (2011). We then estimated the daily spatial median surface chlorophyll-a concentration (in µg L -1 ) using a filter to discard images with more than 50% occupied by clouds over the GoL and discarding surface chlorophyll-a data for depth lower than 20 m since these data could be affected 175 by residual contamination from turbidity despite dedicated treatment.

Glider-based measurements
The glider-based time series (Testor et al., 2018) consist of lines of 25 to 50 km long that run across the shelf from the coast (30 m depth) to the shelf edge (100 m water depth) in the vicinity of the Lacaze-Duthiers canyon head (SW Gulf of Lion) (see glider path in Fig. 1). The autonomous glider was a coastal Teledyne Webb Research Slocum (Davis et al., 2002) that moved 180 at an average speed of 20-30 cm s −1 in a sawtooth-shaped trajectory between 1 m below the surface and 1-2 m above the seabed. The glider was equipped with an un-pumped Seabird 41-CP CTD providing temperature, depth, and conductivity data.
Salinity was derived following the equation of EOS-80. We then derived the Brunt-Väisälä frequency (N² expressed in s -2 ), which was used as an indicator of the thermal stratification (see details in Many et al. (2018)).
A Wetlabs FLNTU sensor provided turbidity (expressed in NTU) and fluorescence of chlorophyll-a (factory calibrated and 185 expressed in μg L − 1 ) measurements based on backscattering measurements at 700 nm. Turbidity measurements from the FLNTU (λ = 700 nm) optical sensor of the glider were used to estimate the particulate backscattering coefficients bbp 700 , which were used to correct fluorescence data from the nonphotochemical quenching (NPQ) (Sackmann et al., 2008;Behrenfeld et al., 2009). The correction applied was determined using the night and day bbp 700 and fluorescence profiles (see details in Thomalla et al. (2018)). 190

Observations/model comparisons at the Banyuls SOMLIT station
Comparisons of simulated surface and bottom temperature and salinity with those measured at the Banyuls SOMLIT station for the period 2011-2016 are presented in Fig. 2. The highly significant correlation (i.e. coefficient of determination R²>0.8 for surface data and R²>0.6 for bottom data, p<0.01), the RMSD inferior to 0.6, and normalized standard deviation of approx.

Surface Chlorophyll-a comparison between MODIS and model for the period 2011-2016
The comparison of the daily mean value of the surface chlorophyll-a, measured from MODIS and extracted from the model at the same points and days, averaged over the GoL shelf is shown in Fig. 4. We obtain mean chlorophyll-a concentrations from 220 MODIS and the simulation of 0.39 (±0.23) and 0.35 (±0.24) µg L -1 over the 2011-2016 period. The relationship between the binned data shows a very good agreement between the model and the observations (slope=0.8; R²=0.97; p<0.01) with a mean bias of 0.04 µg L -1 . The model reproduces well the seasonality of the surface chlorophyll-a with the main maximum during the spring period (approx. 1 µg L -1 at the end of March) and a secondary maximum in fall (approx. 0.6 µg L -1 ). The spatial patterns with high concentrations in the river plumes were also correctly reproduced (see the bottom panel in Fig. 4). Some 225 discrepancies, however, exist, in particular during spring, where the model could overestimate the surface chlorophyll-a concentrations.

Glider/Model comparison
The comparison between the data from the glider deployment in April/May 2013 and those extracted from the model at the same time and position is shown in Fig. 5. Overall, the comparison shows a good agreement between the descriptions of 235 temperature, salinity, and chlorophyll-a conditions in the model and glider data, with mean biases of 0.33 °C, 0.17, and 0.001 µg L -1 respectively. This period was characterized by the establishment of the water column stratification. Temperature, salinity, and Brunt-Väisälä frequency derived from the glider data reflect the vertical stratification that controlled the chlorophyll-a vertical distribution. The model accurately reproduces these vertical thermal and chlorophyll-a distributions, although some differences exist, such as the intensity of the stratification (see the Brunt-Väisälä frequency in Fig. 5) 240 Chlorophyll Volume transport is assessed in Fig. 7 through two unequal sections that close off the Gulf of Lion shelf (see Fig. 1). Besides, the water column is each time divided into two parts, above (Fig. 7a) and below (Fig. 7b) 60 m corresponding roughly to the 265 depth of the nutricline in summer (Kessouri et al., 2017). The "western" section corresponds to the area known to be responsible for deep export by cascading (sometimes down to the bottom of the basin ~2500 m) during cold winters (Ulses et al., 2008c;Durrieu de Madron et al., 2013). This export is restricted to 300-400 m during mild winters and also during eastern storms, which blow predominantly in autumn and produce a downwelling in the Cap de Creus Canyon (Ulses et al., 2008a;Mikolajczak et al., 2020). The other section hereafter named "eastern" for the sake of simplicity is known in the eastern part as an intrusion 270 zone of the Northern Current (Conan et al., 1998), while in the center of the shelf, exchanges with the Northern Current have also been (more rarely) documented (Estournel et al., 2003). It is also the area where the Rhone plume most often exits the shelf under prevailing NW to N wind conditions (Gangloff et al., 2017;Many et al., 2018).

Nutrients and phytoplankton
External inputs of inorganic nutrients -Cross-shelf transport of NO 3 (similar results are observed for PO 4 and are not shown) computed along the GoL shelf boundary (the boundary is indicated in Fig. 1) shows the import of nutrients all year round from adjacent seas (22.8 ± 2.3 10 4 tN yr -1 and 2.92 ± 0.30 10 4 tP yr -1 ) (see yellow lines in Fig. 8 and details in Table 1). Nutrients were mainly imported from offshore through the deep layer on the eastern part of the shelf and all year round (Fig. 8b) with a 290 maximum in fall and winter (4-6 10 4 tN month -1 ), especially in 2012, 2013, and 2015. These imports in the deep layer of the shelf were much stronger than the exports which took place mainly in fall and winter and to the west while they were almost nil in spring and summer. In the surface layer, imports and exports were low all year round except in winter for export, which then was of the same order or even higher than in the deep layer. Besides, strong inputs from rivers took place in fall, winter, and spring (not shown). The Rhône inputs represented 95/96 % of the total river inputs. Nitrate river inputs are estimated to 295 7.1 ± 1.3 10 4 tN yr -1 with maximum values in 2012-2013 (Table 1). Phosphate river inputs are estimated to 0.19 ± 0.04 10 4 tP yr -1 (max. in 2012-2013, Table 1).       Table 1). The nutrient stock was minimum in summer during the stratified period ( Fig. 9a-b). The upper layer was depleted in nutrients and the nutriclines were located at ~ 60 m depth (Fig. 9d-e). A deep chlorophyll maximum (DCM) with concentrations of 0.5 mg m 3 was present between 40 and 60 m depth (Fig. 9f). From September onwards, events of vertical mixing associated with northerly gales led to injections of nutrients into the upper layer through the nutricline (Fig. 9a-b) and erosion of the DCM. 315 In November/December, nutrient stocks increased sharply (Fig. 9a-b) and nutrient profiles became homogeneous over the water column (Fig. 9d-e). Nutrient stocks reached their maximum between the end of December and February when a significant inter-annual variation is found. During this winter period with minimal solar radiation (Fig. 6a), the vertical mixing drove the phytoplankton cells downward where the light intensity was low (Fig. 9f). The phytoplankton biomass was then minimal (Fig. 9c). Superimposed on this seasonal feature, at the monthly scale, significant decreases in chlorophyll stocks 320 were observed in some years in November and December, clearly linked to periods of low solar radiation. From February onwards, as solar radiation increased again, the model predicted a strong increase in phytoplankton biomass in the upper layer and a decrease in nutrient stocks. The chlorophyll concentration became maximum in March/April (value between 0.8 and 1.3 mg m -3 ) when the water column restratified (Fig. 9f). In April, DCM reformed when nutrients began to be depleted in the surface layer. It gradually deepened with the deepening of the nutriclines. The phytoplankton biomass decreased. 325

POC fluxes
The time series of the simulated monthly POC fluxes for the five years is shown in Fig. 10 (spatially integrated over the GoL 335 shelf). Related annual estimates of physical (cross-shelf transport and deposition) and biogeochemical POC fluxes are synthesized in Table 2. GPP (gross primary production) was maximum during spring and summer (~15000 tC day -1 ) and decreased in winter ( ~5000 tC day -1 ) (Fig. 10a). A highly significant correlation of 0.87 (p<0.01) is found between GPP and solar radiation. The increase in solar radiation yielded the onset of the late winter/spring GPP (Fig. 10a). Overall, we estimate to 402.8 ± 5.0 10 4 tC yr -1 the POC produced through the GPP at the scale of the shelf. 340 The total respiration, which corresponds to the transformation of POC and DOC to dissolved inorganic carbon (DIC) by phytoplankton, zooplankton, and bacteria, followed the pattern of the GPP with maximum values during late spring and summer (Fig. 10b). In detail, autotrophic respiration, in addition to the exudation to DOC, led to a quantity of POC degraded or recycled in the water column by the producers of about 207.2 ± 6.6 10 4 tC yr -1 (51% of the GPP). This entailed a net primary production (NPP) of 195.6 ± 8.2 10 4 tC yr -1 . The NPP followed the same patterns during all years with minimum productivity 345 in winter (~3000 tC day -1 ) and maximum during bloom onset in spring (~8000 tC day -1 maximum in April 2012 and June 2013) (Fig. 10e). Besides, 226.5 ± 5.5 10 4 tC yr -1 of OC were remineralized by the heterotrophic respiration (79% from bacteria activity). The net metabolism, i.e. the Net Ecosystem Production (NEP, Fig. 10c), which is the difference between the GPP and the community respiration, shows that the ecosystem was productive overall, with NEP estimates of about 89.3 ± 3.3 10 4 tC yr -1 at the scale of the shelf (Table 2). 350 POC fluxes from river inputs were highly variable in time and mainly related to floods of the Rhône River, which locally brought more than 5000 tC day -1 during episodic events (Fig. 10d). Overall, it yielded a quantity of POC delivered from rivers of about 13.6 ± 9.8 10 4 tC yr -1 with a large inter-annual variability of 72%.
Cross-shelf transport of POC computed along the GoL shelf boundary (Fig. 10f)  At last, POC fluxes from the rivers and the biological activity highly contributed to POC deposition over the shelf (Fig. 10g, correlation of R = 0.53 and R = 0.52 (p<0.001), respectively). The five years show the role of the NPP on the temporal background with POC deposition between 400 and 800 tC day -1 over the shelf. Besides, episodic inputs from rivers during 360 floods increased POC deposition to more than 800 tC day -1 at the scale of the shelf in May and June 2013. The different contributions to the POC deposit led to a total of about 19.3 ± 1.2 10 4 tC yr -1 .

Figure 10: Time series for the five simulated years of POC fluxes (in tC day -1 ) from a) monthly gross primary production, b) monthly total respiration, c) monthly net metabolism (NEP), d) daily rivers input, e) monthly net primary production, f) monthly transport
365 across the shelf boundary, and g) monthly deposition.
https://doi.org/10.5194/bg-2021-82 Preprint. Discussion started: 6 April 2021 c Author(s) 2021. CC BY 4.0 License. Table 2: Annual POC budget (stock in 10 4 tC and fluxes in 10 4 tC yr -1 ) of the Gulf of Lion shelf. Cross-shelf net transport across the shelf boundary (indicated in Fig. 1) is specified. By convention net transport off the shelf is shown by a negative value.

Spatial variability of the annual NPP over the shelf and interannual variability
The vertically integrated NPP for the 2011-2016 period simulated is presented in Fig. 11. The NPP was not uniform over the shelf. Minima were located along the coast for depth lower than 50 m and showed values in the range of 50-100 gC m -2 yr -1 .
Further offshore, the NPP increased to 150-200 gC m -2 yr -1 all over the shelf with maximum values close to the shelf break 375 (120m depth, ~200 gC m -2 yr -1 ). While a trend exists between the NPP and the depth, local maxima were located at the eastern entrance of the shelf and in front of the Rhône mouth with values of approx. 250 gC m -2 yr -1 in the ROFI (Region Of Freshwater Influence). The annual anomalies (Fig. 11) show that the first two years (2011-2012 and 2012-2013) of the simulation were more productive than the rest of the simulated years with mean NPP anomalies of +9 gC m -2 yr -1 . Conversely, the 2013-2016 period 385 showed a lower NPP with mean anomalies of -7 gC m -2 yr -1 . In detail, our results show that there are maximum anomalies in particular areas of the Gulf of Lion, namely inside the Rhone ROFI, along the coast, and over the southwestern external part of the shelf.

Spatial variability of the annual POC deposition over the shelf
The POC deposition over the shelf averaged over the 5 years simulated and its annual anomalies are presented in Fig. 12. Our 390 estimates yielded an averaged POC deposition of 19.3 gC m -2 yr -1 . As for the NPP, the deposition of POC was not uniform over the shelf. It was maximum in front of the river mouths, in particular the Rhône river mouth, with values of about 30 gC m -2 yr -1 . The POC deposit decreased from 20 gC m -2 yr -1 in the middle of the shelf, between 20 and 60 m depth, to 10 gC m -2 yr -1 at the shelf break.
The annual anomalies (Fig. 12) show that during the first two years (2011-2012 and 2012-2013) of the simulation POC 395 deposition was higher than the rest of the simulation with mean anomalies of +0.9 and +0.3 gC m -2 yr -1 . Conversely, the 2013-

Cross-shelf transport of POC 405
Over the 2011-2016 period, the annual net POC transport off the shelf was estimated to 24.0 10 4 tC yr -1 . We detailed the transport through different sections of the GoL shelf boundary shown in Fig. 13.
Results highlight the preferential area of the southwestern part of the Gulf of Lion shelf (approx. 10% of the total boundary), which corresponded to 37% of the total POC net transport off the shelf considering the whole water column (8.9 10 4 tC yr -1 ).
Within this western section, the transport was carried out mainly through the Cap de Creus Canyon (CC in Fig. 13, 18% of the 410 total export) and towards the Catalan shelf to the south of the GoL (CS in Fig. 13, 19% of the total export). Besides, our results also show the balanced net transport in the Lacaze-Duthiers canyon (LD in Fig. 13).
Considering only surface waters (0-60 m depth), the POC net transport, oriented towards the open sea and adjacent shelf, amounted to 13.6 10 4 tC yr -1 , 57% of the total export, and mainly occurred in the eastern and central parts of the shelf. The temporal variability of the POC net transport is shown in Fig. 14. The results show the variability of the export of POC to the open sea through the surface layer (Fig. 14a, <60m depth) or the bottom layer (Fig. 14b, >60m depth). They also show the opposite functioning between the eastern and western parts of the shelf, and in both layers, as in water exchanges. 425 In the surface layer (Fig. 14a), the overall net transport (yellow line) was in the range of 0-0. In the bottom layer (Fig. 14b), the overall net transport was lower than in the surface layer with residual export in fall and winter and episodic imports without seasonality. Exports occurred mainly in the western part of the shelf. They reached maximum values in winters 2012, 2013, 2015 (maximum of ~0.4 10 5 tC month -1 ), and also in falls with slightly lower values.
During spring and summer, deep imports of POC in the west occurred, slightly compensated by deep exports in the east. Fig. 13. b)

Discussion
A first multi-year assessment with a 3D coupled hydrodynamic-biogeochemical model was presented to quantify POC fluxes on the Gulf of Lion shelf. The model reproduces well the annual cycle of nutrient and phytoplankton concentrations in the Gulf of Lion shelf. The coupling of hydrodynamic-biogeochemical models highlights the role of physical processes as stratification and winter mixing, which impact nutrients dynamics in the upper layer in agreement with previous observational 445 (Diaz et al., 2000) and modelling studies (Tusseau-Vuillemin et al., 1998;Herrmann et al., 2013) in the NW Mediterranean region. Dynamics in phytoplankton biomass are then well represented through the spring bloom, the summer DCM, and the erosion of the DCM in fall, related to the stratification and nutricline dynamics.

Annual cycle of nutrients and physical forcings
We have highlighted the year-round import of nutrients on the shelf from offshore waters of about 22 10 4 tN yr -1 for nitrate 450 and 3 10 4 tP yr -1 for phosphate that represent 3 and 15 times more, respectively, than annual Rhône inputs (7 10 4 tN yr -1 -0.2 10 4 tP yr -1 ), the difference between nitrate and phosphate being explained by the very high N:P ratio in Rhone river inputs (approx. 80). Minimal values estimated in summer can be attributed to weak water exchanges in the deeper layer at this season ( Fig. 7). In fall, exchanges increase (>20 000 tN month -1 ; 2500 tP month -1 ) as water exchanges take place on a thicker layer including the nutricline (Fig. 7-9). Most often these events correspond to fall marine storms. It seems that they can also be 455 partly attributed to the rapid increase in the transport of the Northern Current in November, which corresponds to the activation of its East Corsica branch (Carret et al., 2019). This increase would favor intrusions of the Northern Current on the shelf.
Autumn is the beginning of the period also including winter during which the nutrient stocks increase by a factor of 2 to 3 partly due to the low consumption associated with the low solar radiation. Besides, the first two winters were also marked by significant net imports of nutrients on the shelf from February to April 2012 and March 2013. Winter 2012 was marked by 460 extremely dense shelf water formations followed by intense cascading in the canyon of Cap de Creus (Durrieu de Madron et al., 2013). However, as shown in Fig. 7-8, the export of nutrients through dense shelf water cascading in the south-western region was exceeded by nutrient inputs in the eastern part of the shelf where about 30 000 tN month -1 were advected for 3 months (February-April 2012). In March 2013, the strong nutrient input corresponds to the interaction between offshore convection, which produced high nutrient concentrations throughout the open-sea water column (nitrate concentration up to 8 465 µmol L -1 near the surface vs. 3 µmol L -1 over the shelf, see Kessouri et al. (2017)), and a strong easterly storm that advected these nutrients onto the shelf through the surface and deep layers. Our results are consistent with the results of the modeling study by Tusseau-Vuillemin et al. (1998) who showed such export through dense water cascading, as well as shelf enrichment with nutrients advected from the open-sea convection area.
Throughout the year, it is remarkable that all the physical processes described here, whether they correspond to water input 470 from the eastern or western part of the shelf, at the surface, or in the deep layer, result in a net import of nutrients to the Gulf of Lion shelf. This reveals a systematic consumption of nutrients during the transit of the water masses on the shelf, the water leaving the shelf being poorer than the incoming water. The Gulf of Lion shelf is therefore generally a reactor that consumes the nutrients imported from the open sea all year round to produce planktonic biomass. In more detail, since nutrients are imported mainly under the nutricline, they probably play a major role in stratified periods (summer and autumn) sustaining the 475 production in the DCM and feeding upwelling at the coast. In contrast, in winter, despite high nutrient inputs from the open ocean, the ecosystem is less productive due to low solar radiation and vertical mixing that further reduces the exposure of cells to light. During this season, the dynamics of the shelf linked to the strong winds, combining vertical mixing and Ekman transport towards the open sea, leads to a vertical circulation of nutrients that enter through the bottom and exit through the surface layer, generally with little benefit for the ecosystem. 480 The primary production is thus impacted by the nutrient availability in the photic layer imported not only from local bottom waters by vertical mixing or by the rivers but also and importantly from offshore waters, particularly from the Northern Current and even from the deep convection region through marine storms induced circulations (Conan et al., 1998;Tusseau-Vuillemin et al., 1998).

Biological production 485
Considering a shelf area of approx. 10 000 km 2 , we estimate an averaged NPP of 196 gC m -2 yr -1 . This result is in line with previous studies in the NW Mediterranean that estimated an annual NPP in the range of 80-150 gC m -2 yr -1 using local and punctual in situ measurements (Cruzado et Velasquez, 1990;Lefevre et al., 1997;Conan et al., 1998;Durrieu de Madron et al., 2000), or the range of 160-300 gC m -2 yr -1 from remote sensing (Bosc et al., 2004;Olita et al., 2011), or of 75-250 gC m -2 yr -1 using biogeochemical models (Lazzari et al. 2012;Teruzzi et al. 2018). Our estimates are also in the upper range of NPP 490 observed over shelves in mid-latitude areas as in the Bering Sea, the North Sea, and the Mid-Atlantic Bight (100-150 gC m -2 yr -1 , see details in Hofmann et al. (2011)).
The high productivity and the recycling of organic matter during the year were highlighted. Positive NEP values all year round (max. NEP of ~5000 tC d -1 during April 2015) show that the GoL shelf acted as a sink of DIC (source of organic carbon) regarding the pelagic planktonic ecosystem (i.e. the biological term). Besides, the NEP decreased during fall and was minimum 495 in winter due to the decrease of the GPP while the total respiration recycled the OC. Negative daily NEP values (not shown) occurred in December 2012 and 2014, and in November 2013, which shows that the GoL shelf ecosystem episodically acted as a source of DIC (Sempéré et al., 2000). Our annual estimate of 89.3 ± 3.3 10 4 tC yr -1 is 43% higher than the estimate of Sempéré et al. (2000).
Primary production at the annual scale shows a weak interannual variation with a standard deviation of 4%. It shows a strong 500 spatial variability with a range from 50 gC m -2 yr -1 in the very shallow regions, to 200 gC m -2 yr -1 on the outer shelf and 250 gC m -2 yr -1 in the eastern part of the shelf. The main spatial variability with a coast-open sea gradient is caused by the increasing reservoir of available nutrients with depth. This spatial pattern is consistent with the study of Macias et al. (2018) showing maximal primary productivity in the deeper and eastern regions of the shelf. Along with this general pattern, changes in environmental variables are expected to play a role in the changes in the NPP over the shelf. Hence, we aim at identifying the 505 key biogeochemical, hydrodynamic, and atmospheric indicators, which could potentially explain the additional spatiotemporal variability in NPP over the simulated period. To that end, we determined the Empirical Orthogonal Functions (EOFs) decomposition and the major Principal Components (PCs) of NPP weekly anomalies (Fig. 15) (see detail in Olita et al. (2011) and Daewel and Schrum (2017)).

515
The first EOF explains 64% of the NPP variability with positive values over the entire shelf, and higher values in the eastern region, and along the continental slope. Its temporal variability (PC 1 ) follows the pattern of the temporal variability of the solar radiation with a correlation of 0.43 (p<0.001) (Fig. 15). Besides, the second EOF explains 14% of the NPP changes with an opposite behavior between the coastal area (<50m deep, mainly in the Bay of Marseille and the SW part of the GoL) and the 520 central part of the shelf (see Fig. 15). Its temporal variability (PC 2 ) is significantly correlated with the weekly anomalies of wind intensity. At last, the third EOF explains 9% of the NPP changes with the opposite behavior between the Rhône ROFI and the rest of the shelf. It is related to the temporal variability of the Rhône river NO 3 anomalies (PC 3 , see Fig. 15 -bottom panel, same results are observed with PO 4 anomalies). PCs are thus related to processes that drive the nutrients concentrations, controlling the primary production: 525 -EOF 1 /PC 1 : changes in NPP over the entire shelf are positively correlated to solar radiation. This indicates that the primary production over the shelf is controlled by the nutrients available on one hand (see 5.1), and regulated by the anomalies of solar radiation (i.e. light intensity). Maximum production periods thus occur when inputs of nutrients are high (from offshore waters or Rhône River) and are concomitant with periods of strong solar radiation positive anomalies (Legendre, 1990). 530 -EOF 2 /PC 2 : changes in NPP in the bay of Marseille and along the coast of the GoL are positively correlated to the wind speed. This indicates the role of wind-induced coastal upwellings in the supply of nutrients to the surface layer that locally favors the primary production (Lefevre et al., 1997;Fraysse et al., 2014), and wind-induced eastern storms when the nutrient-rich Rhone plume is pushed towards the coast and flows southwestward (Ulses et al., 2008a) and may in certain cases be diluted towards the east (Gatti et al., 2006). 535 -EOF 3 /PC 3 : changes in NPP in the Rhône ROFI are positively correlated with the Rhône nutrient input anomalies (same results with PO 4 , not shown). It shows the role of the Rhône floods in the supply of nutrients to the gulf, which locally increases the NPP (Minas and Minas, 1989;Durrieu de Madron et al., 2003).

The deposition and offshore export of POC
In terms of POC deposition (Fig. 12), the model reproduces the high accumulation rates observed in front of the Rhône mouth 540 (Cathalot et al., 2013). Besides, the cyclonic circulation favors the alongshore dispersion of the terrestrial material from the Rhône River along the 30-50 m isobaths (Got and Aloisi, 1990;Durrieu de Madron et al., 2000). Annual changes can be related to changes in Rhône terrestrial POC inputs to the shelf (minimum inputs in 2011-2012 and maximum inputs in 2012-2013 corresponding to minimum and maximum deposition in front of the Rhône mouth) as well as to the inter-annual variability of the NPP (see above) that drove the deposition of POC over the shelf (max. NPP in 2011(max. NPP in -2012 in agreement with Auger et al. 545 (2011). Besides, it is also noteworthy that these results do not take into account possible wave-induced sediment resuspension processes during storms, which participate in changes in sediment deposition areas (Bourrin et al., 2015). The future development of a fully coupled hydrodynamic, sedimentary, and biogeochemical model could provide a better description of the dynamics of POC deposition, in particular on the inner shelf (0-30 m). Among the deposited sediments, the average remineralization rate of POC was estimated to 70% leading to a loss by the degradation of about 13.5 (+/-1.2) 10 4 tC yr -1 in 550 the sediment (Table 2). This result is in line with Accornero et al. (2003) and Pastor et al. (2011), who estimated a mean remineralization rate of 60% in the Gulf of Lion, and with Durrieu de Madron et al. (2000), who estimated a total loss by the degradation of 33.8 (+/-16.1) 10 4 tC yr -1 at the water-sediment interface.
Our results have highlighted the first order of importance of the cyclonic circulation that occurs over the shelf and that favors water and POC export in the southwestern part of the shelf (~2900 tC yr -1 km -1 across the western boundary compared to ~850 555 tC yr -1 km -1 for the eastern one). They agree with the results from previous studies, which showed the important water and particulate matter export in this part of the shelf due to the winter coastal circulation (Estournel et al., 2003;Ulses et al. 2008c) and episodic marine storm events (Ulses et al., 2008a;2008b;Bourrin et al., 2015). Lapouyade and Durrieu de Madron (2001) estimated from in-situ measurements a mean transport of 3.3 10 4 tC month -1 (12.8 kg s -1 ) in winter that drastically decreased to 0.2 10 4 tC month -1 (0.8 kg s -1 ) during the summer. These estimates are of the same order as those obtained here, with mean 560 winter and summer POC transport of 2.3 10 4 and 0.5 10 4 tC month -1 .
The estimates of POC transport for individual parts of the western slope (see Fig. 13) demonstrate the importance of the Cap de Creus Canyon area and the adjacent narrow part of the shelf (CS in Fig. 13) in the export of POC off the GoL (4.2 and 4.6 10 4 tC yr -1 , respectively). It is also remarkable that this transport is maximum in winters 2011-2012 and 2012-2013, during a period marked by several cascading events (Durrieu de Madron et al., 2013) and marine storms (Bourrin et al., 2015). Indeed, 565 this part of the shelf is an active area in the export of POC towards the open sea and the deeper environments as highlighted in Puig et al. (2008) and Sanchez-Vidal et al. (2008). Besides, it is noticeable that the Lacaze-Duthiers canyon area shows a balanced net transport of POC with maximum imports in summer 2013 and 2015 and low exports in winters. It probably highlights the balance existing between the inputs from the open sea during the stratified period and continental winds that generate anticyclonic eddies in this area (Estournel et al., 2003;Hu et al., 2011), and outputs from transport during extreme 570 events as storms and dense-shelf waters cascading (Palanques et al., 2006).
We estimate that approx. 4.6 (+/-2.8) 10 4 tC yr -1 was exported towards the Catalan margin and the Gulf of Rosas by-passing the Cap de Creus Canyon. This value, which represents approx. 20% of the total net transport off the shelf, shows a significant contribution of POC from the GoL to this area. Future studies could focus on the balance between POC inputs from the southwestern part of the GoL and from local rivers (as Tordera, Ter, and Fluvia rivers), estimated at 0.13 10 4 tC yr -1 by Sanchez-575 Vidal et al. (2013). Observations in this part of the shelf could also validate our estimates in this area, which has been seldom instrumented from now.
Considering surface waters, the impact of the steady northwestern wind that favors offshore water exports through eddies and intrusions of the Northern Current has been identified as the main factor regulating surface shelf-slope exchanges in this area (Estournel et al., 2003;Petrenko, 2003). The surface export of POC is also related to the spread of the Rhône River plume 580 towards the open sea during floods and surface currents favorable conditions (Gangloff et al., 2019;Many et al., 2018). The high concentrations of POC in the plume therefore actively contribute to offshore exports through the Northern Current during these episodic events.

Conclusion
A 3D coupled hydrodynamic-biogeochemical model was used to estimate the POC budget of the Gulf of Lion shelf, and to 585 understand the mechanisms responsible for its spatiotemporal variability over the period 2011-2016. The validation of the model was performed using existing data from a multi-platform observation system. A good agreement between model results and observations at different space and time scales was shown. The model represents the high dynamical character of the Gulf of Lion shelf in terms of hydrodynamic (stratification/winter mixing) and biogeochemical conditions (nutrients, chlorophyll and POC dynamics). 590 Spatial, seasonal and inter-annual changes in the different POC input and output terms were identified. Model results highlight the high NPP occurring in the GoL shelf (196 10 4 tC yr -1 ) with maximum values in spring and in the outer shelf, in particular in the eastern region. The interannual variability of the NPP at the Gulf of Lion scale is especially low (SD = 4%) and monthly interannual anomalies in NPP are mainly explained by changes in the intensity of solar radiation. Our results also show that the nutrient enrichment from the general circulation and the open sea (22 10 4 tN yr -1 and 3 10 4 tP yr -1 ), representing on average 595 3 times for nitrate, and 15 times for phosphate, the inputs from the Rhone, favors the phytoplankton growth over the entire shelf. Coastal upwelling as well as inputs for the Rhone also contribute locally and to a lesser extent to changes in NPP. The positive NEP values during a large part of the year show that the GoL annually acts as a sink of DIC regarding the pelagic planktonic ecosystem.
Rivers contribute to the POC delivery to the shelf with a mean value of 19 10 4 tC yr -1 representing 10% of the NPP, and strong 600 changes induced by floods (72% inter-annual variability). At last, we have shown the high dynamical character of the GoL shelf waters, which results in strong cross-shelf transport of POC oriented off-shelf (24 10 4 tC yr -1 ). Our estimates have shown that 57% of the export occurred in the surface layer through the eastern and central part of the shelf, and 43% below 60 m mostly through the western part of the shelf and favored by marine winds in fall and cascading events in winter.
At the scale of the western Mediterranean Sea, our results show the crucial role of the Gulf of Lion shelf, which acts as a 605 reactor that consumes the inorganic nutrients imported from the open sea to produce organic matter all year round. A part of the produced organic matter is exported by the coastal circulation towards the Catalan shelf and the open sea, yielding to the enrichment in POC of adjacent coastal waters, the Northern Current and the deeper basin. The autotrophic status of the ecosystem along with the highly dynamical character of the area, marked by low residence times and shelf-slope processes as dense shelf water cascading, suggest that the GoL shelf could act as a sink for atmospheric CO 2 and favor carbon sequestration. 610 The future coupling of the model presented in this work with a carbonate system module describing the dynamics of dissolved inorganic carbon and estimating the air-sea CO 2 fluxes could allow a better understanding and a quantification of the source/sink role of atmospheric CO 2 on the shelf. This work represents the first step for further investigations and quantifications of phenomena such as the impact of climate change on cascading events and bottom export, or the effect of reduced nutrient inputs from coastal rivers. 615 the SOMLIT network (Service d'Observation en Milieu Littoral; http://somlit.epoc.u-bordeaux1.fr/fr). We thank the SOERE 620 MOOSE for supporting and providing long-term observation data in the Gulf of Lion. We especially thank the French glider team, P. Testor, and F. Bourrin for their help on the glider data processing.