2.1 The numerical model

2.2 Observations used for the model assessment

2.3 Statistical analysis

In order to quantify the performance of the model in its ability to represent the dynamics of dissolved oxygen for the study period, we computed four complementary metrics following the recommendations of Allen et al. (2007): (1) the SD ratio ($r_{\mathit{\sigma }}=\frac{{\mathit{\sigma }}_o}{{\mathit{\sigma }}_m}$ where σ_m and σ_o are the SD of model outputs and observations, respectively); (2) the Pearson correlation coefficient,

where K is the number of observations, $y_k^o$ is the observation k, $y_k^m$ is the corresponding model output k, and $\stackrel{\mathrm{‾}}{y^o}$ and $\stackrel{\mathrm{‾}}{y^m}$ are the mean of observations and model outputs, respectively; (3) the normalised root-mean-square error,

and (4) the percentage bias ($\text{PB}=\frac{\stackrel{\mathrm{‾}}{y^m}-\stackrel{\mathrm{‾}}{y^o}}{\stackrel{\mathrm{‾}}{y^o}}\times \mathrm{100}\mathit{\%}$). The model results are compared with the observations at the same dates and positions.

3.1 Comparisons to cruise observations

The comparisons of modelled wind velocity and ocean model outputs with in situ observations from the high-frequency SACES are shown in Fig. 2. Modelled wind provided by ECMWF and used to force the hydrodynamic model and to calculate the air–sea oxygen flux is highly correlated with the observations (R=0.96, p value <0.01). The low values of NRMSE (13.9 %) and percentage bias (−0.5 %) show the accuracy of this variable, found for all ranges of value. Regarding the surface ocean variables, we obtain statistically significant correlations equal to 0.64, 0.83 and 0.83 (p value <0.01), between observed and modelled values of, respectively, surface temperature, salinity and dissolved oxygen concentration. The NRMSEs are equal to 2.0 %, 0.3 % and 5.2 %, respectively. The percentage biases remain negligible for temperature (−0.7 %), salinity (0.002 %) and dissolved oxygen concentration (−1.2 %).

Figure 2Time evolution during DEWEX Leg1 (in February 2013, a, c, d and e) and Leg2 (in April 2013, b, f) cruises of observed (red) and modelled (blue) (a and b) wind velocity (m s⁻¹), (c) surface temperature (^∘C), (d) surface salinity, and (e, f) surface dissolved oxygen concentration (µmol kg⁻¹). Trajectories of the measurements during DEWEX Leg1 and Leg2 cruises are indicated on inserted maps. Modelled wind velocity was provided by ECMWF. No surface temperature and salinity data are available over the period of DEWEX Leg2. The metrics indicated for the modelled wind velocity and surface oxygen concentration were calculated for both DEWEX Leg1 and Leg2 periods.

Figures 3 and 4 compare the observed and modelled dissolved oxygen concentration for the stations sampled during the DEWEX and MOOSE-GE cruises, respectively, at the surface (between 5 and 10 m) and along the south–north transect passing across the convection area (stations encircled in black in Fig. 3). Overall, the simulation correctly reproduces the spatial and temporal variability of the oxygen concentration observed at the surface and in the water column during and between the three cruises. During wintertime, the model simulates low surface oxygen concentrations (<220 µmol kg⁻¹) in the open sea of the Gulf of Lion and the Ligurian Sea, areas that coincide with the deep vertical mixing regions (Estournel et al., 2016a; Kessouri et al., 2017) (Fig. 3a and b). Figure 4a shows the oxygen homogenisation of the whole water column between 41.5 and 42.3^∘ N, the core of the deep-convection area. Concentrations above 240 µmol kg⁻¹ are modelled in the surface layer on the shelf and in the south at the Balearic front, in accordance with the observations (Figs. 3a, b and 4a). The model also agrees with observations showing a layer of low oxygen concentration (minimum concentration <185 µmol kg⁻¹ at depths around 500 m) located between 150 and 1500 m, mainly in the LIW (300–800 m), outside the deep-convection area (Fig. 4a). The metrics confirm the good agreement between model outputs and observations with a significant spatial correlation of 0.81 and 0.61 (p value <0.01), an NRMSE of 5.3 % and 15.7 %, and a negligible percentage bias of −1.1 % and 0.01 %, respectively, at the surface and along the south–north transect.

Figure 3Surface dissolved oxygen concentration (µmol kg⁻¹) observed (a, c and e) and modelled (b, d and f) over the (a and b) DEWEX Leg1 (1–21 February 2013), (c and d) DEWEX Leg2 (5–24 April 2013) and (e and f) MOOSE-GE (11 June–9 July 2013) cruise periods. The black-outlined dots correspond to the measurement stations shown in Fig. 4.

Figure 4Comparison between model outputs and observations on a transect crossing the deep-convection area (stations are circled in black in Fig. 3a, c and e) over the (a and b) DEWEX (Leg1: 10–12 February 2013, Leg2: 8–10 April) and (c) MOOSE-GE (27 June–5 July 2013) cruise periods. The left column shows observed and modelled profiles at 42 and 40.3^∘ N. The right column shows vertical section of dissolved oxygen concentration (µmol kg⁻¹) along the transect; the model is represented by background colours and observations are indicated in coloured circles.

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During the spring cruise period, the model represents high dissolved oxygen values (>240 µmol kg⁻¹) at the surface throughout the region, as observed (Fig. 3c and d). The increase in modelled oxygen concentration in the surface layer between both campaigns is in agreement with observations (Figs. 3a–d and 4a, b). A zone of low oxygen concentration in the intermediate waters is present in the convection area in both datasets (Fig. 4b). However, it is worth noting that this zone of low oxygen concentration is heterogeneous in its magnitude and thickness both in model outputs and in observations, and it is not similarly distributed in space in the model compared to the measurements. At the surface and along the transect, the spatial correlation coefficients between modelled and observed dissolved oxygen are equal to 0.59 and 0.30 (p value <0.01), respectively, the NRMSE to 4.6 % and 19.3 %, respectively, and the percentage biases to −1.2 % and −4.4 %, respectively.

The north–south gradient, with lower surface concentrations in the south of the deep-convection area, observed during the stratified period (i.e. MOOSE-GE cruise period in June–July), is then well reproduced by the model (Fig. 3e and f). The minimum zone is more established than in spring in both in situ data and model results (Fig. 4c). Both sets of data represent a maximum in the subsurface at depths around 50 m, close to the deep chlorophyll maximum (shown in Fig. 5 in Kessouri et al., 2018), although an underestimation of its magnitude is visible between 41.5 and 42^∘ N in the model (Fig. 4c). We find a spatial correlation coefficient of 0.64 and 0.96 (p value <0.01), an NRMSE of 3.2 % and 3.5 %, and a negligible percentage bias (absolute values ≤0.4 %) between model outputs and observations at the surface and along the north–south transect, respectively.

Figure 5The left column shows oxygen inventory integrated from the surface to 1800 m depth (a and b) or 1000 m (c) (mol m⁻²) in Argo float measurements (cyan) and model outputs (black) along Argo (a) 6901467, (b) 6901470 and (c) 6901487 float trajectories. The right column shows trajectories of corresponding Argo float.

The metrics computed using all station data from the three cruises are given in Table 1. The modelled dissolved oxygen concentration is significantly correlated with the observed concentration (R≥0.81, p<0.01), in particular for the winter period when the pattern of the oxygen distribution appears to be primarily shaped by deep-convection processes, shown to be accurately represented by Estournel et al. (2016a). The model results show low percentage biases (PB <1 %), low NRMSE (<8 %), and SD ratios ranging between 1.13 and 1.35, which indicate a larger variability in the observations than in the model outputs.

Table 1Statistical analysis of model results: Pearson correlation coefficient (R), normalised root-mean-square error (NRMSE), percentage bias (PB) and SD ratio, calculated between modelled dissolved oxygen concentrations and observations from DEWEX winter and spring cruises and the MOOSE-GE summer cruise and from Argo-O₂ platforms.

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3.2 Comparison to Argo float data

The model accurately reproduces the magnitude of oxygen inventory in the water column and its time evolution observed using Argo floats during the study period (Fig. 5). The model simulates the increase observed between early December and late February. This increase is estimated at ≈20 mol m⁻² over a layer from the surface to 1800 m, along the trajectory of the float 6901467 (Fig. 5a), and at ≈10 mol m⁻² over a layer from the surface to 1000 m, along the trajectory of the float 6901487 (Fig. 5c), both floats being located in the Gulf of Lion at that period. The oxygen inventory remains high during the month of March and then decreases significantly from early April to early June, in model outputs and Argo observations. In both datasets, the decrease reaches up to 20 mol m⁻² over 1800 m along the path of the Argo float 6901470 in the Gulf of Lion (Fig. 5b) and is less pronounced (≈10 mol m⁻²) along the trajectory of the float 6901467 in the Balearic Sea (Fig. 5a). More moderate decreases are then simulated and observed until September along all float trajectories. The statistical analysis shows that, in terms of oxygen inventory, significant correlation coefficients are obtained between the model outputs and the three float observations ($\mathrm{0.64}<R<\mathrm{0.83}$, p value <0.01), NRMSEs are smaller than or equal to 2.4 %, and the absolute values of percentage bias are smaller than or equal to 2 % (Fig. 5). In terms of dissolved oxygen concentration in the water column, we obtain significant correlation coefficients ($\mathrm{0.56}<R<\mathrm{0.93}$, p value <0.01), NRMSEs smaller than 10.5 %, percentage biases smaller than 1 %, and SD ratios close to 1 for floats 6901470 and 6901487 and of 1.37 for float 6901467 (Table 1).

5.1 Seasonal cycle of dissolved oxygen

The good agreement found between model results and in situ measurements (Sect. 3) gave us confidence in the model that we use here to analyse the evolution of the oxygen inventory in the deep-convection area and to quantify the relative contribution of each oxygen flux in its variation: exchanges at the air–sea interface, as well as physical and biogeochemical fluxes in the ocean interior. Based on the evolution of vertical mixing and the phytoplankton growth in the study area, Kessouri et al. (2017) divided the study period into four sub-periods. The first period from September to the end of November, which we will refer to as the autumn period, is characterised by a stratified water column (mean MLD <50 m) and respiration dominating primary production (Kessouri et al., 2018). The second period, from the end of November to the end of March, referred to here as the winter period, is characterised by a sustained vertical mixing (mean MLD >50 m). The third period, called spring, ran from late March to early June. It corresponds to the period of restratification of the water column (Estournel et al., 2016a) and of the peak of the phytoplankton bloom at the sea surface followed by the formation of a deep chlorophyll maximum (Kessouri et al., 2018). The last period, summer, from early June to September, is characterised by a strong stratification (mean MLD <20 m) and the permanent presence of a deep chlorophyll maximum below 40 m depth (Kessouri et al., 2018). In the following, we will analyse the dynamics of dissolved oxygen for these four periods. The time evolution of daily oxygen budget terms is shown in Fig. 6d–f, while the time evolution of cumulative oxygen fluxes and the resulting variation in oxygen inventory for the upper (surface to 150 m) and deeper (150 m to bottom) layers is presented in Fig. 8. The biogeochemical term of the budget is defined as the sum of oxygen production through photosynthesis and of oxygen consumption through respiration by phytoplankton, zooplankton and bacteria and through oxidation of ammonium (nitrification) (see Eq. 1). The physical term is decomposed into two modes of transport: a net lateral transport due to advection (positive values correspond to an input for the deep-convection area) and a net vertical downward transport at the interface between the two layers, at 150 m depth, due to advection and turbulent mixing. Finally, the time evolution of the dissolved oxygen concentration and the oxygen saturation anomaly, ΔO₂, averaged over the convection area is shown in Fig. 9.

Figure 8Time series from September 2012 to September 2013 of the oxygen inventory (black line) and cumulative air–sea flux (red line), downward transport (dark blue), lateral transport (positive values: input for the convection area, light blue), and biogeochemical flux (green line) in the (a) upper (surface to 150 m) and (b) deeper (150 m to bottom) layer. Unit: mol m⁻².

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Figure 9Time evolution of (a) the dissolved oxygen concentration (µmol kg⁻¹) and (b) the oxygen saturation anomaly (%), with mixed-layer depth (m) indicated by the black line, all horizontally averaged over the deep-convection area.

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5.2 Annual oxygen budget

Figure 10 illustrates the oxygen budget of the NW Mediterranean convection area over the period September 2012 to September 2013. At the annual scale, the deep-convection area is a net sink of oxygen for the atmosphere, estimated at 20.0 mol O₂ m⁻². A total of 88 % (17.7 mol O₂ m⁻²) of this amount was injected into the ocean interior during the period when the deep-convection process took place.

Figure 10Schematic showing the terms of the annual oxygen budget (mol O₂ m⁻²) for the north-western Mediterranean deep-convection area over the period from September 2012 to September 2013. F_A–S: air-to-sea flux; F_H: net horizontal transport; F_v 150: net downward transport at the base of the euphotic layer (150 m); F_B: net biogeochemical production; Δ∫O₂: variation in oxygen inventory. Positive fluxes are inputs for the deep-convection zone. The terms of the budget are estimated for the upper euphotic layer (surface to 150 m) and the deeper aphotic layers (150 m to bottom).

The annual net biogeochemical production of oxygen in the euphotic layer (0–150 m) is estimated at 1.6 mol O₂ m⁻². The net annual NCP (net community production, defined as gross primary production minus community respiration in the euphotic zone) is estimated at 3.9 mol O₂ ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$, yielding autotrophy in this area. In the deeper layers (150 m–bottom) an oxygen consumption of 3.8 mol O₂ m⁻² was associated with respiration of heterotrophic organisms by 70 % and oxidation of ammonium by 30 %. This led to an annual net biogeochemical consumption of 2.2 mol O₂ m⁻² over the whole water column.

The model indicates that 27.1 mol m⁻² of O₂ was exported from the upper layer to deeper layers. This net transport toward the bottom occurred during 68 % of the events of deep vertical mixing of oxygen-rich surface waters with oxygen-poor underlying waters. Finally, the budget shows that the deep-convection area appears as a net source for dissolved oxygen for the rest of the western Mediterranean Sea with an annual net horizontal transport of 15.0 mol O₂ m⁻². This transport breaks down into an input of 5.3 mol O₂ m⁻² in the upper layer and an export of 20.3 mol O₂ m⁻² in the deeper layer.

At the end of the annual cycle, a negligible decrease (0.3 mol m⁻², i.e. 0.05 %) in the oxygen inventory of the upper euphotic layer is found, while 3.1 mol m⁻² (i.e. 0.66 % of the inventory) was stored in the deeper water masses.

6.1 Air–sea oxygen flux

Our model results indicate that the NW Mediterranean deep-convection area was a net sink for the atmospheric oxygen at a rate of 20.0 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ between September 2012 and September 2013 and at a rate of 280 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$ (17.7 mol m⁻² over 63 d) during the 2013 deep-convection period. Inside the area, the annual air–sea flux shows strong spatial heterogeneity, with a range extending from 2.7 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ at the periphery to 36.0 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ in the centre. Considering its sea surface area (61 720 km²), the NW deep-convection zone received 1233 Gmol of oxygen from the atmosphere over the period September 2012 to September 2013, including 1090 Gmol during the winter 2013 intense vertical mixing period. We showed that the strong oxygen ingassing was essentially driven by a high undersaturation ($<-\mathrm{10}$ %) and intense northerly winds during the deep-convection period.

Nevertheless, uncertainties in the net uptake rate remain. First, uncertainties are linked to errors in modelled ocean surface variables (dissolved oxygen, temperature and salinity) and wind velocity used for the calculation of the air–sea flux. The comparisons of model results with in situ high-frequency measurements at the surface during the period of maximum flux (deep-convection period) indicate a bias of less than or close to 1 % and a NRMSE smaller than 14 % for the wind velocity, surface temperature, salinity and oxygen concentration (Sect. 3.1). A second source of uncertainty is linked to the parameterisation chosen for the calculation of the gas transfer velocity. In the standard run, we used the cubic dependence with wind speed parameterisation proposed by Wanninkhof and McGillis (1999). Sensitivity analyses were performed using eight other parameterisations for the calculation of air–sea flux (Wanninkhof, 1992, 2014; Woolf, 1997; Nightingale et al., 2000; Wanninkhof et al., 2009; Stanley et al., 2009; Liang et al., 2013; Bushinsky and Emerson, 2018; see Sect. 2.1.2). Estimates of annual air–sea flux, as well as flux and amount of atmospheric oxygen captured by the study area during the deep-convection period, calculated with all these parameterisations are gathered in Table 2. All estimates show a net sink for atmospheric oxygen for the study area. They range from 14.2 to 21.5 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ at the annual scale, with a mean value of 17.7±2.8 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$, and from 188 to 285 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$, with a mean value of 242±38 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$, during the deep convection. Both estimates in the standard run are in the upper range of all estimates. Considering all estimates, we determine an uncertainty (SD) of 15 %–16 % for the annual and convection period air–sea flux. This uncertainty, associated with the parameterisation of the gas transfer velocity, propagates to the estimates of vertical and lateral transport of oxygen in the ocean interior. Depending on the gas transfer parameterisation used, at the annual scale, downward export below the euphotic zone ranges from 22.0 to 27.9 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ (mean value: 25.1±2.2 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$), and lateral transport ranges from 4.8 to 6.1 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ (mean value: 5.6±0.5 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$) in the euphotic layer and from −17.1 to −20.6 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ (mean value: $-\mathrm{19.0}\pm \mathrm{1.3}$ $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$) in the aphotic layer. During the deep-convection event, downward export below the euphotic zone ranges from 223 to 302 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$ (mean value: 265±30 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$). The uncertainty on the transport terms of the annual budget thus remains smaller than 12 %. The values of the NRMSE between cruise observations and modelled dissolved oxygen from sensitivity tests are found very close to the NRMSE obtained for the standard run. Slightly smaller NRMSE values (≈10 %) are found only for the winter DEWEX-Leg1 cruise period using the parameterisations of Wanninkhof and McGillis (1999), Woolf (1997), Stanley et al. (2009), and Liang et al. (2013), which give a higher oxygen transfer than the other parameterisations. Previous studies on oxygen air–sea flux in deep-convection zones recommended the use of parameterisations with high transfer during periods of strong wind and convection (Copin-Montégut and Bégovic, 2002; Körtzinger et al., 2008b; Koelling et al., 2017; Atamanchuk et al., 2020). Atamanchuk et al. (2020), comparing flux estimates based on several parameterisations, found that these flux estimates may vary by an order of magnitude and warned of the possibility of a strong underestimation of air–sea oxygen flux in biogeochemical models that do not include bubble-mediated terms. In our study, the range of estimates obtained with both types of parameterisations, those that are only diffusive and those that include bubble-mediated terms, is similar. Although the parameterisation of Wanninkhof and McGillis (1999) used in our standard run does not include an explicit bubble-mediated transfer term, it provides estimates of air–sea fluxes close to those obtained with the bubble-flux-inclusive one of Stanley et al (2009), preferred by Atamanchuk et al. (2020) in their Labrador Sea study. The strong undersaturation obtained in the north-western Mediterranean during the convection period, between −10 % and −20 %, may explain a greater contribution of the diffusive flux compared to the air injection by bubbles. Moreover, winter conditions are less extreme than in the Labrador Sea where strong wind speeds of more than 13.8 m s⁻¹ were encountered for at least 40 d. In the NW Mediterranean Sea and in winter 2012/13, only 13 % of the convection area was characterised by a number of days with wind speeds >13.8 m s⁻¹ varying between 30 and 35 d. An experimental study of flux measurements in this region over a whole year would allow a better assessment of the contribution of air injection in the total air–sea flux and hence of the different parameterisations of gas transfer.

Table 2Estimates of air-to-sea oxygen flux (F_A–S) for the period September 2012–September 2013 and during the deep convection (15 January–8 March, 15–24 March), using different parameterisations of gas transfer velocity.

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Previous studies based on in situ observations have proposed estimates for the air–sea oxygen flux in the study area. Our modelled seasonal cycle of air–sea oxygen flux agrees with the results of Copin-Montégut and Bégovic (2002) and Coppola et al. (2018) in the Ligurian Sea, at the DYFAMED site, who observed an annual cycle with a net ingassing from December to March and net outgassing from April to November. In the Ligurian Sea the deep-convection process does not occur each winter. When occurring, it is generally shorter and shallower than in the centre of the Gulf of Lion, the core of dense water formation. Coppola et al. (2018) using temperature, salinity and oxygen monthly profiles and the gas transfer parameterisation of Ho et al. (2006) estimated for the period 1994–2014 a monthly air-to-sea flux varying from −15.1 to 14.8 mol O₂ ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$, with an annual mean value of −2.6 mol O₂ ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$. Over this 20-year period, the authors identified one winter, winter 2005/2006, with intense vertical mixing reaching the deep layers, and four winters (1999, 2000, 2006 and 2013) with moderate vertical mixing reaching intermediate depths. From the difference in O₂ inventory between December 2005 and April 2006, they deduced that 24 mol m⁻² of atmospheric O₂ was injected between 350 and 2000 m at a rate of 300 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$. At the same site, Copin-Montégut and Bégovic (2002) estimated an air–sea ingassing of 5 and 2.6 mol O₂ m⁻², respectively, for the moderate cold winters 1999 (for 26 d, rate of 190 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$) and 2000 (for 23 d, rate of 110 $\mathrm{mmol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$), respectively, using in situ surface measurements of oxygen in winter and the formulation of gas transfer velocity from Wanninkhof and McGillis (1999). Those estimates were twice as small as their observation of variation in the oxygen content in the first 600 m of depth, namely 11 and 15 mol m⁻² (in 1 month) for winters 1999 and 2000, respectively. Those authors suggested an underestimation in their estimates due to low-frequency measurements and an underestimation of the gas transfer coefficient. At the same location, for the study period, we found a net oxygen ingassing of 9.2 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ at the annual scale and 135 mmol O₂ ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$ during the period of deep-convection events (63 d) (Fig. 7d). Thus our calculation of atmospheric oxygen uptake in the Ligurian Sea is close to the ones of Copin-Montégut and Bégovic (2002) for moderate convective winters. Our estimates in the centre of the Gulf of Lion, where convection reached the deep waters, with values of 20–28 mol O₂ m⁻² during deep convection are also close to the estimate by Coppola et al. (2018) for the intense vertical mixing winter 2005/2006 in the Ligurian Sea.

Finally, our model calculation of air–sea oxygen flux for the NW Mediterranean is in the same range found for other worldwide deep-convection areas. At the centre of the Labrador Sea, Körtzinger et al. (2008b) found an annual air–sea ingassing of 10.0±3.1 mol O₂ ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ over the period 2004/2005, using in situ observations at the K1 mooring site and the Wanninkhof (1992) parameterisation. By quantifying the relative contribution of biogeochemical and lateral fluxes, Koelling et al. (2017) estimated an oxygen ingassing of 29.1±3.8 mol m⁻² over winter 2014/2015 at the same mooring site K1. Wolf et al (2018) derived from Argo float observations in the Labrador Sea mean air–sea fluxes with a large range of values varying from 5.7 to 22.8 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ using various parameterisations. Using parameterisations including bubble-mediated fluxes (Liang et al., 2013; Yang et al., 2017), their estimates of atmospheric oxygen uptake ranged from 21.6 to 36.6 mol m⁻² for the convective winter 2003/2004. Based on measurements of oxygen from a moored profiler and Argo floats and on the Stanley et al. (2009) parameterisation, Atamanchuk et al. (2020) estimated an annual air–sea flux of oxygen of 19.3±3.4 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ for the year 2016/2017. For the Irminger Sea, Maze et al. (2012) estimated an abiotic air–sea oxygen flux of 13±3 $\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ for the years 2002, 2004 and 2006, using an optimisation method and observations from three surveys and Word Ocean Atlas 2009.

6.2 The role of the NW deep-convection area in the ventilation of the western Mediterranean Sea

Open-sea convection and shelf dense water cascading (Canals et al., 2006; Ulses et al., 2008b) in the NW Mediterranean are the main mechanisms for the ventilation of the entire western Mediterranean Sea. Over the past decades, several observational studies reported increases in O₂ concentration in deep water masses at several sites in the western Mediterranean where deep convection did not occur and where winter vertical mixing was limited to surface or intermediate levels. Coppola et al. (2018) associated the high concentrations of O₂ observed in deep layers of the Ligurian Sea in 1994 and 2005, when convection was limited to intermediate waters, with the arrival of deep water formed in the open sea of the Gulf of Lion or formed on the Gulf of Lion shelf and cascading down to the deep basin. Using measurements from five cruises, Schroeder et al. (2008a) documented an abrupt increase in heat, salt and O₂ inventory of deep waters in an extensive area of the western Mediterranean, occurring in 2005 and 2006. The authors attributed these changes, referred to as the western Mediterranean Transient (hereafter WMT; Zunino et al., 2012), to the propagation of the new dense waters formed in the NW deep-convection area during the winters 2004/2005 and 2005/2006, when severe weather conditions caused intense dense water formation (Lopez-Jurado et al., 2005; Schroeder et al., 2006). The study of Schroeder et al. (2008a) showed the presence of these new O₂-rich deep waters in the Balearic Sea, the Ligurian Sea and in the Algerian sub-basin in June 2005 and their propagation to the whole Algerian sub-basin and the west of the Alboran Sea in October 2006. New oxygenated waters were also observed in the entire deep layers of the Algerian sub-basin in 2011 (Schneider et al., 2014; Stöven and Tanhua, 2015), 2014 (Keraghel et al., 2020), 2016 and 2018 (Li and Tanhua, 2020). Moreover, the results of Li and Tanhua (2020) showed a ventilation of the deep waters of the Tyrrhenian Sea through an overflow of well-oxygenated water masses from the Algerian basin into the deep layer, between 2011 and 2016.

Somot et al. (2016) found that winter 2012/13 is one of the five winters over the 33-year period 1980–2013 showing high dense water formation rates (above 0.6 Sv), using the CNRM-RCSM4 model. According to their estimates, the cumulative volume of dense water formed over the winters 2011/2012 (0.45 Sv) and 2012/13 (0.7 Sv), amounting to 1.15 Sv, may be close to the volume of dense water formed in winter 2004/2005 of 1.2 Sv. As a result, these successive 2012 and 2013 deep-convection events could have been responsible for a similar ventilation as the one observed after the event of 2005 (Schroeder et al., 2008b; Schneider et al., 2004; Stoven and Tanhua, 2015), assuming similar air–sea exchanges.

Our modelling study indicates that, over the period September 2012 to September 2013, the upper layer of the NW deep-convection area captured 5.3 mol O₂ m⁻² from the surrounding regions, in addition to the 20.0 mol m⁻² of oxygen from the atmosphere, while the deeper layers released 20.3 mol m⁻² toward the adjacent seas (Sect. 5.2). Considering the deep-convection surface area of 61 720 km², the lateral transport led to a gain in the upper layer of 330 Gmol yr⁻¹ in the convection area and a loss of 1250 Gmol yr⁻¹ towards the adjacent deep areas. As a result, the NW convection area appears as a source of 920 Gmol yr⁻¹ of oxygen for the rest of the western basin for the period 2012/13. Lateral O₂ inputs in the upper layer occurred mainly from February to September with two peak periods, in early March, a calm period between two convective events, and in April, during restratification. These imports were mainly related to eddies produced by the baroclinic instability that was triggered at the periphery of the convection zone when strong wind ceased (Killworth, 1976; Testor et al., 2018). These inputs from the peripheral zone contributed to the vertical export of oxygen to the aphotic layer. First in the short term, the oxygen imported between two convection events was exported at depth by the following events. At longer timescales (April–September), the convection area was also fed by the peripheral zones and in turn produced a vertical export to the aphotic layer. These exchanges were of lower intensity and concerned shallower layers but are not negligible when integrated over the year. Regarding the lateral transport in the deeper layer, our model outputs show that the O₂-rich dense waters formed in the NW deep-convection area propagated towards the Balearic Sea, first at intermediate depths (150–800 m) from the beginning of the winter mixing period and then through deep layers (800 m to bottom) from mid-February (not shown). These water masses then mostly flowed towards the south of the western basin, while a smaller part was advected back in the convection area through mesoscale circulations counteracting the effect of the intrusions of low-oxygen LIW during the restratification period, in increasing the oxygen inventory of intermediate waters (not shown). A preferential pathway to the south of the basin was the one along the eastern coast of Minorca in the Algerian sub-basin, in agreement with previous observational and modelling studies that examined the spreading of waters formed in winter in the NW region (Pinot and Ganachaud, 1999; Schroeder et al 2008b; Beuvier et al., 2012). Our simulated circulation of oxygen in the western basin is also consistent with the study of Piñeiro et al. (2019), who reported the arrival of new dense water masses formed in the deep-convection area east of Minorca over the 2011–2013 period using temperature and salinity observations at the hydrographic stations RADMED. In our model outputs, the offshore Balearic Sea (bathymetry >1000 m, surface area: 19 700 km²) and Algerian sub-basin (bathymetry >1000 m, surface area: 171 610 km²) experienced an increase in their oxygen inventory, during and after the NW deep-convection events, receiving oxygen through lateral transport (271 and 1276 Gmol, respectively) while the amounts of oxygen captured at the air–sea interface during the period of intense vertical mixing were smaller in those areas than in the NW deep-convection area by a factor of 10 and 3, respectively (i.e. 104 and 385 Gmol versus 1090 Gmol for the NW deep-convection area). This suggests that an important part of the oxygen absorbed at the air–sea interface of the NW deep-convection area, exported first vertically towards its deeper layers and then horizontally towards the adjacent regions, was stored, at least temporarily, in the Algerian sub-basin.

Finally, our results demonstrate that the total oxygen supply by air–sea exchanges in the NW deep-convection region for the period 2012/13 (1233 Gmol yr⁻¹), which was then mainly released to adjacent seas in the aphotic layer, constitutes a major source of oxygen at the scale of the whole Mediterranean Sea. Indeed this supply is close to the biogeochemical oxygen consumption within the Mediterranean Sea estimated at 1545 Gmol yr⁻¹ by Huertas et al. (2009) using in situ measurements at the Strait of Gibraltar over the period 2005–2007.

The present study of the period 2012/13 constitutes a first step in our analysis and quantification of the oxygen budget for the western Mediterranean Sea. Previous observational studies (Coppola et al., 2018; Mavropoulou et al., 2020) over periods of 20 years or more showed that the mean oxygen concentration in the western Mediterranean and in particular in the NW deep-convection area is subjected to a strong interannual variability, mainly in response to the variability of deep convection, the latter being influenced by transient changes such as the WMT event. A deeper analysis of the physical processes involved in the vertical and horizontal transport in the convection zone as well as of the spreading of the oxygen-enriched dense waters, formed in the NW deep-convection area, in the western basin and toward the Atlantic Ocean through the Gibraltar Strait will be conducted in further studies using a numerical simulation with extended domain and period.

6.3 Net community production

Our budget calculation shows that in this region characterised by intense vertical mixing the biogeochemical terms remained very low compared to the air–sea oxygen flux over the period 2012/13. Our modelling results indicate that the net biogeochemical production of oxygen in the euphotic layer was positive from mid-December to the end of July and negative the rest of the year. It was maximum during the spring bloom from mid-March to mid-April. We estimate a net annual NCP (in the upper layer) of 46.8 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ (3.9 molO₂ ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$; see Eq. 1). This indicates a net autotrophy for the euphotic layer of the NW Mediterranean deep-convection area over the period September 2012–September 2013. If consumption of oxygen through nitrification is considered, net biogeochemical production amounted to 1.6 mol O₂ ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$. It is worth noting that nitrification, discussed in Kessouri et al. (2017), who estimated a nitrogen budget using the same coupled model, accounts only for 7 % of the total oxygen consumption but for 60 % of the NCP, suggesting that this process should be considered when estimating NCP from oxygen concentration.

Our value of NCP is higher than the net downward export of organic carbon at the base of the euphotic layer estimated at 35 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ (25 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ for particulate organic carbon and 10 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ for dissolved organic carbon) by Kessouri et al. (2018) over the same period and using the same coupled model. Also using the same coupled model, Kessouri et al. (2017), who analysed the nitrogen cycle over the study period, obtained a new primary production varying from 65 to 77 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ in the deep-convection zone. By analysing the carbon, nitrogen and oxygen cycles, the NW deep-convection region is always found to be an autotrophic ecosystem. The discrepancies in magnitude obtained depending on the element considered reflect different dynamics for these elements in the euphotic layer, possibly due to variable ${\mathrm{O}}_{\mathrm{2}}:\mathrm{C}:\mathrm{N}$ ratios in biogeochemical production and consumption processes as shown by Copin-Montégut (2000) in the Ligurian Sea using high-frequency measurements.

Our estimate of NCP is smaller than the estimate of 85.2 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ in the Ligurian Sea at the DYFAMED site over the period 1994–2014 by Coppola et al. (2018) using monthly observations. It is close to the estimate by Ulses et al. (2016) of 42.8 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ over the period 2003–2008 using the same numerical model and considering an area extending to the whole offshore NW Mediterranean and a 100 m thick upper layer. It is also similar to the previous estimates of new primary production by Severin et al. (2014) varying from 46 to 63 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ over the period February–March 2011, based on in situ nutrient concentrations.

NCP is often used to estimate the strength of the biological pump and the potential capacity of a system to capture atmospheric CO₂. Although the NW deep-convection pelagic ecosystem appears as a net annual sink for atmospheric CO₂ from our modelling results and previous studies (Coppola et al., 2018; Ulses et al., 2016), the role of this region in terms of carbon sequestration remains highly uncertain. Deep convection generates a strong downward transport of organic carbon below the euphotic layer (Ulses et al., 2016; Kessouri et al., 2018). A large amount of organic carbon transferred below the euphotic zone is then consumed and demineralised after deep convection (Santinelli et al., 2010), leading to an increase in CO₂ inventory into the deeper reservoir that could be raised back in the euphotic layer during the following deep-convection events as shown in the Atlantic Ocean by Körtzinger et al. (2008a) and in the Pacific Ocean by Palevsky et al. (2016). Episodes of oversaturation of sea surface pCO₂ related to atmospheric pCO₂ were reported during short wind gusts and intense vertical mixing events in the Ligurian Sea (Copin-Montégut et al., 2004; Merlivat et al., 2018) and in the central Gulf of Lion open sea (Touratier et al., 2016). The authors explained those oversaturation episodes by the increase in CO₂ concentration at the ocean surface induced by the mixing of surface CO₂-poorer waters with deep CO₂-rich waters. Those punctual observations suggested short releases of CO₂ by the ocean induced by deep convection. On the other hand, using a 0.5^∘ resolution array of coupled 1D hydrodynamic–biogeochemical models of the upper layer in the Mediterranean Sea over the period 1998–2004, D'Ortenzio et al. (2008) estimated that the NW region is a sink for atmospheric CO₂ in winter and at the annual scale (between 12 and 24 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$) and found that biogeochemical processes dominate air–sea exchanges and mixing processes in this region most of the year. In another region of deep convection, the Labrador Sea, DeGrandpre et al. (2006) and Körtzinger et al. (2008b) also found an annual uptake of atmospheric CO₂ that amounted to 55.2 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ for the period 2000–2001 and 32.4±9.6 g C ${\mathrm{m}}^{-\mathrm{2}}{\mathrm{yr}}^{-\mathrm{1}}$ for the period 2004–2005, using mooring observations (and also a 1D biogeochemical model for DeGrandpre et al., 2006).

In the study area, our results show that lateral transport dominated the budget of oxygen during the restratification period when deep dense waters spread in the western basin and LIW reintegrated the deep-convection zone. This suggests that coupled 3D biogeochemical–physical models, including a carbonate system module, could be useful tools to complete the previous 1D studies of dissolved inorganic carbon dynamics and integrate on an annual scale the exchanges at the air–sea interface by taking into account lateral transport and mesoscale structures influencing the spreading of water masses and their compounds during convection and restratification phases and impacting the budgets.