The Eco3M-CarbOx biogeochemical model was developed to represent the dynamics of the seawater carbonate system and plankton food web in the BoM. The model was implemented using the Eco3M (Ecological Mechanistic and Modular Modelling) platform (Baklouti et al., 2006). The model structure used is based on an existing model of the plankton ecosystem (Fraysse et al., 2013), including a description of carbon (C), nitrogen (N), and phosphorus (P) marine biogeochemical cycles. The Eco3M-CarbOx model includes 22 prognostic state variables that are split into several compartments: phytoplankton, heterotrophic bacteria, detrital particulate organic matter, labile dissolved organic matter, nutrients (ammonia, nitrate, and phosphate), dissolved oxygen, and carbonate system variables (Fig. 1). In this study, the state variables of the Eco3M-CarbOx model only change over time (i.e., usually termed “model 0D”); they are representative of the time evolution of a sea surface water cell, but this biogeochemical model is not coupled with a hydrodynamic model.

The model presented in this study includes a set of new developments and improvements in the realism of the plankton web structure and process formulations compared to the model of Fraysse et al. (2013). In order to improve the representation of chlorophyll concentration in the Bay of Marseille the phytoplankton is divided into two groups: one with some ecological and physiological traits of the Synechococcus cyanobacteria, which is one of the major constitutive members of pico-autotrophs in the Mediterranean Sea (Mella-Flores et al., 2011), and another with traits of large diatoms, which are generally observed during spring blooms at mid-latitudes (Margalef, 1978). For both of the phytoplankton, there is a diagnostic chlorophyll a variable related to the phytoplankton C biomass, the phytoplankton N-to-C ratio, and the limiting internal ratio fQN (Faure et al., 2010; Smith and Tett, 2000; Table B2, Appendix B). The functional response of primary production was modified using another formulation of the temperature limitation function which takes into account the optimal temperature of growth for each phytoplankton group. The exudation of phytoplankton was modified taking into account the intracellular phytoplankton ratio. For the uptake of matter by bacteria and the remineralization processes the dependence on the intracellular bacteria ratio was modified. A temperature dependence of all biogeochemical processes was added to take into account the effects of rapid and strong variations of seawater temperature on plankton during episodes of upwelling, for instance, that are usually observed in the BoM. Also certain parameters in some formulations were modified owing to the alterations of some formulations (Table B4, Appendix B).

Additionally, a carbonate system module was developed and three state variables were added: dissolved inorganic carbon (DIC), total alkalinity (TA) and the calcium carbonate (CaCO3) implicitly representing calcifying organisms. The knowledge of DIC and TA allows the calculation of the pCO2 and pH (total pH scale) diagnostic variables, necessary for resolving all the equations of the carbonate system. These equations use apparent equilibrium constants, which depend on temperature, pressure, and salinity (Dickson, 1990a, b; Dickson and Riley, 1979; Lueker et al., 2000; Millero, 1995; Morris and Riley, 1966; Mucci, 1983; Riley, 1965; Riley and Tongudai, 1967; Uppström, 1974; Weiss, 1974). The details of the resolution of carbonate system module are given in Appendix A. For this module three processes were also added: the precipitation and dissolution of calcium carbonate and the gas exchange of pCO2 with the atmosphere. Based on the review of Middelburg (2019), it is considered that (i) TA decreases by 2 moles for each mole of CaCO3 precipitated, by 1 mole for each mole of ammonium nitrified, by 1 mole for each mole of ammonium assimilated by phytoplankton, and TA increases by 2 moles for each mole of CaCO3 dissolved, and by 1 mole for each mole of organic matter mineralized by bacteria in ammonium (Table B2, Appendix B); (ii) DIC is consumed during the photosynthesis and calcification processes and is produced by respiration (of phytoplankton, zooplankton, and bacteria) and the CaCO3 dissolution processes. Moreover, the dynamics of DIC are altered by the CO2 exchanges with the atmosphere (Table B2, Appendix B). The air–sea CO2 fluxes are calculated from the pCO2 gradient across the air–sea interface and the gas transfer velocity (Table B3, Appendix B) estimated from the wind speed and using the parametrization of Wanninkhof (1992).

In the Eco3M-CarbOx model, zooplankton is considered as an implicit variable. However, a closure term based on the assumption that all of the matter grazed by the zooplankton and higher trophic levels return as either organic or inorganic matter by excretion, egestion, and mortality processes is taken into account (Fraysse et al., 2013). The model considers a “non-Redfieldian” stoichiometry for phytoplankton and bacteria. All the biogeochemical model formulations, equations, and associated parameter values are detailed in Appendix B.

The BoM is located in the eastern part of the Gulf of Lion, in the northwestern Mediterranean Sea (Fig. 2). The city of Marseille, located on the coast of the BoM, is the second largest city of France, with a population of ca. 1 million. The Rhône River, which flows into the Gulf of Lion, is the greatest source of freshwater and nutrients for the Mediterranean Sea, with a river mean flow of 1800 m3s-1 (Pont et al., 2002). Several studies highlight the eastward intrusion events from the Rhône River plume in the BoM under east and southeasterly wind conditions, which favor biological productivity (Fraysse et al., 2014; Gatti et al., 2006; Para et al., 2010). The biogeochemistry of the BoM is complex and highly driven by hydrodynamics. For example, north–northwesterly winds induce upwelling events which bring cold and nutrient-rich waters upward (Fraysse et al., 2013). Moreover, the oligotrophic Northern Current occasionally intrudes into the BoM (Petrenko, 2003; Ross et al., 2016).

Despite the presence of several marine protected areas around the BoM (the Regional Park of Camargue, the Marine protected area Côte Bleue, and the National Park of Calanques), it is strongly impacted by diverse anthropogenic forcing, because industrialized and urbanized areas are located all along the coast. From the land, the BoM receives nutrients and organic matter from the urban area of the Aix–Marseille metropolis (Millet et al., 2018), the industrialized area of Fos-sur-Mer (one of the biggest oil-based industry areas in Europe), and the Berre Lagoon, which is eutrophized (Gouze et al., 2008; Fig. 2c). From the atmosphere, the BoM is subject to fine-particle deposition and greenhouse gas emissions (including CO2) from the nearby urban area, and it also receives effluents from the Aix–Marseille metropolis.

The modeled variables of the carbonate system (DIC, TA, pH, and pCO2) and chlorophyll a are hereafter compared to observations collected at the SOLEMIO station (Figs. 2c and 3), which is a component of the French national monitoring network (Service d'Observation en Milieu Littoral – SOMLIT, http://somlit.epoc.u-bordeaux1.fr/fr/, last access: January 2020). Major biogeochemical parameters have been recorded since 1994. Carbonate chemistry variables (pH, pCO2, DIC, and TA), sampled every 2 weeks, have been available since 2016.

In the present work, the Eco3M-CarbOx model was run for the whole year of 2017. This year was chosen because in situ data of carbonate systems (DIC, TA, pH, and pCO2) are available for the whole year at the SOLEMIO station (Fig. 2c). The biogeochemical variables were initialized using in situ data from winter conditions (Table B1, Appendix B). The model was forced by time series of sea surface temperature and salinity, wind (at 10 m), light, and atmospheric CO2 concentrations. The sea temperature time series is from in situ hourly data recorded at the Planier station (Fig. 2c). For salinity, hourly in situ data from the SOLEMIO station and from the CARRY buoy were used (Fig. 2c). Wind and light hourly time series were extracted from the WRF meteorological model at the SOLEMIO station (Yohia, 2017). Finally, we used hourly atmospheric CO2 values from in situ measurements recorded at the Cinq Avenues station (CAV station; Fig. 2b) by the AtmoSud Regional Atmospheric Survey Network, France (https://www.atmosud.org, last access: August 2019). This simulation is the reference simulation (noted S0). As highlighted previously, Rhône River plume intrusions (due to wind-specific conditions) have an impact on the dynamics of primary production (Fraysse et al., 2014; Ross et al., 2016) and then on the seawater carbonate system. Moreover, the seawater temperature and atmospheric CO2 variations control the seawater CO2 dynamics via the solubility equilibrium and gas exchange with the atmosphere (Middelburg, 2019). In order to quantify the impact of different forcing, several simulations (hereafter noted S), which are summarized in Table 1, were conducted:

Impact of seawater temperature increase, S1. The forcing time series of in situ temperatures was shifted by +1.5 ∘C (Cocco et al., 2013).

In this work, we calculated the daily mean values of state variables, statistical parameters, and mean fluxes of modeled processes throughout the year and over two main hydrological periods: the stratified and mixed water column periods. The stratified water column (SWC) is defined with a temperature difference between the surface and bottom of more than 0.5 ∘C (Monterey and Levitus, 1997). For the simulated year (2017), the SWC period lasts from 10 May to 20 October. The mixed water column (MWC) period corresponds to the rest of the year.

Following the recommendations of Rykiel (1996), three criteria were considered to evaluate the performance of our model:

Does the model reproduce the timing of the observed variations of carbonate system at the seasonal timescale?

Over most of the studied period, the model simulates lower chlorophyll a concentrations than the in situ observations, especially during the MWC period (Fig. 3a). Two maxima of chlorophyll a concentrations are observed in situ: the first one at ca. 1.71 mgm-3 in March and the second one at ca. 0.68 mgm-3 in May. They are both linked to Rhône River plume intrusions. Several in situ maxima between 0.50 and 0.70 mgm-3 are observed between March and April (at the end of the MWC period), and they signaled the spring bloom event (Table 2 and Fig. 3a). The biogeochemical model quantitatively reproduces the spring bloom observed at the end of the MWC period (Fig. 3a) with a maximum value of ca. 0.69 mgm-3. The model does not catch the two aforementioned maxima of chlorophyll, and it contains a low WSS and a strong bias (0.37 and +0.22 mgm-3, respectively – Table 2).

On the whole, the seasonal variations of the seawater pCO2 are correctly simulated by the biogeochemical model (Fig. 3b), even if the values are rather overestimated during the MWC period. From January to February, the model reproduces the slight decrease in the observed pCO2, and from February to March it reproduces the increase in pCO2 even if the amplitude of this increase remains smaller. In mid-April, during the simulated spring bloom period, the observed drop in pCO2 and increase in pH are also spotted in the model (Fig. 3b and c). The model especially succeeds in reproducing the observed increase in relation to high temperatures during the SWC period. The reduction of the CO2 solubility due to thermal effects mostly explains the increase in pCO2 during the SWC period. The strong SD of modeled values during the SWC period can be explained by the rapid changes in temperature, probably due to upwelling usually occurring at this time of the year (Millot, 1990). The range of modeled pCO2 values (345–503 µatm) encompasses the range of observed values (358–471 µatm; Table 2). The statistical analysis provides a mean bias of +23 µatm, and a WSS of 0.69 (Table 2).

The seasonal dynamic of pH is mostly reproduced by the model, and in particular, the decrease during the SWC period (Fig. 3c). However, the modeled pH is generally underestimated throughout the year, except during the SWC period, with a mean bias of -0.015 (Table 2). The seasonal range is captured by the model with a minimum value during the SWC period (7.994 vs. 8.014 for observations; Table 2) and a maximum one during the MWC period (8.137 vs. 8.114 for observations; Table 2). The statistical analysis highlights an index of agreement between the in situ data and the model outputs higher than 0.70 (Table 2).

The seasonal variations of DIC show the highest values during the MWC period and a decrease (increase) during the beginning (the end) of the SWC period (Fig. 3d). The lowest values are observed during September. The Eco3M-CarbOx model closely matches the seasonal dynamic by reproducing the range of extreme observed values (Table 2). The mean bias is also small (-8.48 µmolkg-1; Table 2). More than 70 % (0.73; Table 2) of modeled DIC concentrations are in statistical agreement with the corresponding observations.

The seasonal cycle of measured TA does not show a clear pattern (Fig. 3e). Large variations of values ranging between 2561 and 2624 µmolkg-1 (Table 2) are observed, whatever the hydrological season being considered. The biogeochemical model provides almost constant values of around 2570 µmolkg-1 all throughout the year, which is lower than in situ data. With a low WSS index of agreement and a large mean bias (Table 2), the model is not able to confidently reproduce the observed variations of TA (Fig. 3e and Table 2).

For the year 2017, the values of temperature vary between 13.3 and 25.9 ∘C (Fig. 4a). The DIC variations closely match those of temperature (correlation coefficient -0.75). For example, the spring increase in temperature leads to a decrease in DIC concentrations (Fig. 4a and c), and the minimum values are reached at the end of SWC period. Over the simulated period, the air–sea CO2 fluxes (Faera) vary between -14 and 17 mmolm-3d-1, with a weakly positive annual budget of +6 mmolm-3yr-1 (or +0.017 mmolm-3d-1, Table 3). Then, the BoM waters would act as a net source of CO2 to the atmosphere on an annual basis. However, on a seasonal basis, the BoM waters would change from a net sink during the MWC period (Faera < 0; Table 3) to a net source during the SWC one (Faera > 0; Table 3).

On an annual basis, the gross primary production (GPP) and total respiration (R) are balanced, leading to a null average net ecosystem production (NEP; NEP = GPP-R) (Fig. 4f and Table 3). The intensity of autotrophic respiration (Ra) is lower than that of primary production (annual mean of 0.065 vs. -0.413 mmolm-3d-1, respectively – Table 3), while the zooplankton and bacterial respiration account for an average of 0.348 mmolm-3d-1 (Table 3). On a seasonal basis, the model highlights an ecosystem dominated by autotrophy during the MWC period (NEP > 0; Table 3) and heterotrophy during the SWC period with higher flux values (NEP < 0; Table 3). The biogeochemical fluxes show the strongest variations along the SWC period, following those of temperature (Fig. 4f). The maximum GPP occurs in April and is correlated with the maximum chlorophyll concentration. At this time, the ecosystem is autotrophic (NEP > 0; Fig. 4b and f) and is a net sink for atmospheric CO2, which explains the DIC and seawater pCO2 decreases during the bloom period (Fig. 4c–e)

When looking in detail at the 2017 temperature and salinity time series (Fig. 4a), several crucial events can be seen occurring, including freshwater intrusions (e.g., 15 March and 6 May) into the BoM and large variations of temperature in relation to upwelling events or latent heat losses due to wind bursts. The largest freshwater intrusion from the Rhône River plume occurs in mid-March, with a minimum observed salinity of ca. 32.5 at the SOLEMIO station (Fig. 4a). During this event, the seawater pCO2 decreases and pH increases concomitantly (Fig. 4c and d). Then, seawater appears to be temporarily under-saturated in CO2, and the BoM waters thus act as a sink for atmospheric CO2 at the time of intrusion (Fig. 4e).

During the SWC period, upwelling events quickly cool the surface seawater. In two days, from 25 to 27 July, the water temperature drops from 24.7 to 16.9 ∘C (Fig. 4g). The decrease in temperature corresponds to the increase in DIC concentrations (Fig. 4i). Concomitantly, the value of seawater pCO2 decreases from 497 to 352 µatm, and pH increases from 7.99 to 8.12 (Fig. 4i and j). This event quickly changes the BoM waters from a source to a sink for atmospheric CO2 (from +17 to -14 mmolm-3d-1; Fig. 4k), and also from a net heterotrophic to a net autotrophic ecosystem (Fig. 4l).

The evaluation of model skill vs. in situ data highlights that the modeled pH, pCO2, and DIC are in acceptable agreement with observations (Fig. 3). The seasonal variations observed for the different variables are captured by the model, including for example the seasonal decrease in DIC and pH during the SWC period, in relation to the increase in pCO2, and the inverse scenario during the MWC period. The chlorophyll content variability is not well reproduced, especially during spring (Fig. 3a), even taking into account the nitrate supply from the Rhône River plume intrusion (Fig. 7c). This is due to the multiple origins of chlorophyll, organic matter, and nutrients in the BoM that are not accounted for in the Eco3M-CarbOx model: autochthonous marine production, and allochthonous origins from the Rhône and Huveaune River plumes (Fraysse et al., 2013). The observed variations and levels of TA are not correctly simulated by the model (Fig. 3f). The study of Soetaert et al. (2007) highlights that the main variations of TA in the marine coastal zones are linked to freshwater supplies and marine sediments. The present study does not take into account the inputs of TA from the Rhône River and the water–sediment interface, and it may explain why the TA variable is not correctly predicted by our model.

The contribution of each biogeochemical process to the DIC variability can be assessed using the presented model: the aeration process contributes to 78 % of the DIC variations, and all biogeochemical processes together contribute to 22 % (Table 3). As mentioned by Wimart-Rousseau et al. (2020), the model suggests that the seawater pCO2 variations and associated fluxes would be mostly driven by the seawater temperature dynamics. Moreover, the seasonal variations of the air–sea CO2 flux are in agreement with some previous field studies (De Carlo et al., 2013; Wimart-Rousseau et al., 2020), which measured a weak oceanic sink for atmospheric CO2 during winter and a weak source to the atmosphere during summer.

The model results reveal that temperature would play a crucial role in controlling two counterbalanced processes: (1) the carbonate system equilibrium and (2) the phytoplankton growth. The increase in temperature during SWC leads to a higher pCO2 in seawater due to the decrease in the CO2 solubility (Middelburg, 2019) and, at the same time, the fixation of DIC by phytoplankton is favored, leading to a decrease in the pCO2 level. The imbalance between the latter two processes leads to a change in the ecosystem status (autotrophic or heterotrophic) and the corresponding behavior as a sink or source to the atmosphere. In case of a 1.5 ∘C rise over the whole year, the temperature variation has a very small impact on the carbonate system dynamics. However, it favors the autotrophic processes and strengthens the oceanic sink of atmospheric CO2 during the bloom of phytoplankton (Fig. 5e and j).

In line with several previous works on the northwestern Mediterranean Sea (De Carlo et al., 2013; Copin-Montégut et al., 2004; Wimart-Rousseau et al., 2020), the model also suggests that the status of the Bay of Marseille regarding sink or source for CO2 could change at high temporal frequency (i.e., hours to days). Bursts of north–northwestern winds lead to sudden and sharp decreases in seawater temperature (< 2 d; Fig. 4g) either directly by latent heat loss through evaporation at the surface (Herrmann et al., 2011) or indirectly by creating upwelling (Millot, 1990), with the consequences of a decrease in the seawater pCO2 values (Fig. 4j) and, in fine, an alteration of the CO2 air–sea fluxes. Model results suggest that the fast variations of temperature could lead to rapid changes of the sink vs. source status in this coastal zone (Fig. 4k). Moreover, Fraysse et al. (2013) highlight that upwelling in the BoM favors ephemeral blooms of phytoplankton by nutrient supplies up to the euphotic layer and would, in turn, contribute to the seawater pCO2 decrease. North and northwestern winds through latent heat losses and/or upwelling events could then enhance the sink for atmospheric CO2 due to the temperature drop and nutrients inputs. However, these results remain preliminary because in our experimental design only the cooling effect of upwelling on the carbonate balance is taken into account. But concomitantly, upwelling usually bring nutrients and DIC at the surface and these supplies could also perturb the balance of the carbonate system. A further coupling of the Eco3M-CarbOx model with a tridimensional hydrodynamic model would certainly enable the multiple effects of upwelling on the dynamics of the carbonate system in this area to be embraced and the results presented in this study to be refined.

High wind speeds (> 7 ms-1) amplified the gaseous exchange of CO2 considerably (De Carlo et al., 2013; Copin-Montégut et al., 2004; Wimart-Rousseau et al., 2020). The model highlights that a strong wind event of 3 d has a significant impact on the seawaterpCO2 values during a longer period of ca. 15 d (Fig. 6). A combination of high atmospheric pCO2 values and high wind speeds would then favor the sink for CO2 into the waters of the BoM. The aeration process also depends on the choice of the formulation of the gas transfer velocity (k600). In this study, the formulation of Wanninkhof (1992) is used and depends of the wind speed at 10 m above the water surface. However, the current velocity could favor the gas exchange, and suspended matter concentration could limit the gas exchange (Abril et al., 2009; Upstill-Goddard, 2006; Zappa et al., 2003). Due to the important heterogeneity of physical and biogeochemical forcings in coastal zones, other factors that control the air–sea gas exchange should certainly be taken into account.

The simulation with intrusions of the Rhône River plume shows that inputs of nitrate cause a drop of seawater pCO2 owing to the nutrient supply favoring the phytoplankton development (Fig. 7). In this scenario, the oceanic sink of atmospheric CO2 is enhanced. But rivers also supply TA (e.g., Gemayel et al., 2015; Schneider et al., 2007) and DIC (e.g., Sempéré et al., 2000) that shift the carbonate system equilibrium toward a pCO2 decrease and a DIC increase (Middelburg, 2019). Taking into account these further supplies may sensibly modify the modeled carbonate balance in the BoM. A next step to the present work will be to design more realistic numerical experiments to refine the results obtained in this preliminary study. The intrusions of the Rhône River plume also induce a salinity decrease in the BoM waters, which leads to a drop in the pCO2 levels in the model. This drop of pCO2 is due to the decrease in the CO2 solubility when salinity decreases (Middelburg, 2019).

In the scenario of forcing the model by using urban atmospheric pCO2 time series, the air–sea gradient increases, and then it enhances the status of the BoM as a sink for atmospheric CO2. As suggested by the in situ study of Wimart-Rousseau et al. (2020), the Eco3M-Carbox model highlights the crucial role of the coastal ocean in an urbanized area, and with an increase in atmospheric CO2, the CO2 uptake by the coastal ocean may increase. This result is in line with the studies of Andersson and Mackenzie (2004) and Cai (2011), which predict an increase in the intensity of the CO2 sink and a potential threat to coastal marine biodiversity in coastal areas owing to high atmospheric CO2 levels.