Data collection was carried out at the BOUSSOLE site (43∘22′ N, 7∘54′ E) in 2013–2015 (Antoine et al., 2006, 2008) and at the DYFAMED site (43∘25′ N, 7∘52′ E) in 1995–1997 (Marty et al., 2002). These sites are 3 nautical miles apart, both located in the Ligurian Sea, one of the basins of the northwestern Mediterranean Sea (Fig. 1). The water depth is ∼2400 m. The prevailing ocean currents are usually weak (< 20 cm s-1), because these sites are in the central area of the cyclonic circulation that characterises the Ligurian Sea. The two sites surrounded by the permanent geostrophic Ligurian frontal jet flow are protected from coastal inputs (Antoine et al., 2008; Heimbürger et al., 2013; Millot, 1999). Monthly cruises are carried out at the same location.

At DYFAMED, fCO2 measurements at 2 m were provided by an anchored floating buoy fitted with a CARIOCA sensor. At BOUSSOLE, measurements were carried out from a mooring normally dedicated to radiometry and optical measurements where two CARIOCA sensors were attached. Both monitored fCO2 hourly at the 3 and 10 m depths (although only one of the two depths was equipped with a functional sensor at some periods); S and T were monitored at the same two depths using a Seabird SBE 37-SM MicroCat instrument. The CARIOCA sensors were adapted to work under pressure in the water column. They were swapped about every 6 months, with serviced and calibrated instruments replacing those which were previously deployed. The accuracy of CARIOCA fCO2 measurements by the spectrophotometric method based on the optical absorbance of a solution thymol blue diluted in seawater is estimated at 2 µatm during both periods. Hood and Merlivat (2001) have reported agreement between the fCO2 measured by CARIOCA buoys, similar to the one deployed at DYFAMED, with ship-based measurements during a number of field programs and with an accuracy of 2 µatm and a precision of 5 µatm.

At Boussole, newly designed fCO2 sensors have been calibrated using in situ seawater samples taken at 5 and 10 m depths during the monthly servicing cruises to the mooring. The total alkalinity (Alk) and DIC of the samples were determined by potentiometric titration using a closed cell according to the method developed by (Edmond, 1970). Certified reference materials (CRMs) supplied by A. G. Dickson (Scripps Institution of Oceanography, San Diego, USA) were used for calibration (Dickson et al., 2007). The accuracy is estimated at 3 µmol kg-1 for both DIC and Alk. fCO2 is calculated using the dissociation constants of Mehrbach refitted by Dickson and Millero (Dickson and Millero, 1987; Mehrbach et al., 1973) and as recommended by Álvarez et al. (2014) for the Mediterranean Sea. Uncertainty in fCO2 derived from an individual sample is expected to be on the order of 5 µatm (Millero, 2007). About eight samples have been used to calibrate each CARIOCA sensor so that the uncertainty of the absolute calibration of each fCO2 CARIOCA sensor is estimated at 1.8 µatm. In addition, we observe that the standard deviation of the difference between the CARIOCA fCO2 and fCO2 computed with the monthly discrete samples (Fig. 2b) is equal to 4.4 µatm, consistent with the expected precision on CARIOCA fCO2 of 5 µatm. Alk and S of the 56 samples taken at BOUSSOLE are linearly correlated according the following relationship; Alk(µmolkg-1)=87.647S-785.5. The standard deviation of the Alk data around the regression line is equal to 4.4 µmol kg-1 (r2=0.89).

Temperature and fCO2 were measured from February 2013 to February 2016. All seasons were well represented, with missing data only in May–July 2013. For some periods, simultaneous measurements were made at the 3 and 10 m depths (Fig. 2a–c).

The range of temperature (Fig. 2a) extends from 13 ∘C in winter up to 27 ∘C in summer, followed by progressive cooling in fall. The coldest temperature, 13 ∘C, results from the winter vertical mixing with the deeper Levantine Intermediate Water (LIW) marked by extremes in temperature and salinity (Copin-Montégut and Bégovic, 2002). Temperature provides the main control of the seasonality of fCO2, from 350 µatm to more than 550 µatm in summer 2013 (Fig. 2b). The fugacity of CO2 in seawater is a function of temperature, DIC, alkalinity, salinity and dissolved nutrients. In the oligotrophic surface waters of the Mediterranean Sea, the effect of nutrients may be neglected. Temperature and DIC have the strongest influences. By normalising fCO2 to a constant temperature, the temperature effect can be removed and changes in fCO2 resulting from changes in DIC can be more easily identified. Figure 2c shows the variability of fCO2 normalised to the constant temperature of 13 ∘C, (fCO2@13) using the equation of Takahashi et al. (1993). The underlying processes that govern the seasonal variability of fCO2@13 are successive winter mixing, biological activity (organic matter formation and remineralisation) and the deepening of mixed layer in fall (Bégovic and Copin-Montegut, 2002; Hood and Merlivat, 2001). Biological processes account for the decline in fCO2@13 observed from March–April to late summer; the ensuing increase in surface fCO2@13 is associated with the deepening of the mixed layer in the fall or convection in winter, as the vertical distribution of fCO2@13 at DYFAMED shows a maximum in the 50–150 m layer. Where a large remineralisation of organic matter occurs, the productive layer is mostly between 0 and 40 m (Copin-Montégut and Bégovic, 2002). The contribution of air–sea exchange is not significant (Bégovic and Copin-Montegut, 2002). Over the period 2013–2015, the air–sea CO2 flux from the atmosphere to the ocean surface is equal to -0.45 mol m-2 yr-1.

During summer 2014, large differences between measurements at 3 and 10 m were observed (Fig. 2a–c between dashed lines). A detailed analysis of the temporal variability during that period underscores the role of inertial waves at the frequency of 17.4 h that create the observed differences between the 2 depths of observations, with the deeper waters being colder and enriched in fCO2@13. Temperature and fCO2@13 variability is dominated by inertial waves. In particular, from 15 to 26 August 2014, the difference in T between the two depths is as large as 7.6 (5.1 ∘C on average). fCO2 decreases on average by 32.7 µatm, corresponding to an increase in fCO2@13 equal to 42.8 µatm.

The 2013–2015 seasonal and inter-annual variability of T, fCO2 and fCO2@13 is illustrated in Fig. 2–f. The larger inter-annual changes in temperature (Fig. 2d) are observed during summer, both at 3 and 10 m depth, while over February and March, a constant value of 13 ∘C is observed as the result of vertical mixing with the LIW. A very large inter-annual variability of fCO2@13 is observed for T < 14 ∘C (Fig. 2f). This is associated with the winter mixing at the mooring site, which is highly variable from year to year. Winter mixed-layer depth (MLD) varies between 50 and 160 m, at the top of the LIW over the 2013–2015 period (Coppola et al., 2016). The variable depth of the winter vertical mixing causes the difference in fCO2@13, as fCO2 increases with depth (Copin-Montégut and Bégovic, 2002). The deepening of the MLD is driven by episodic and intense mixing processes characterised by a succession of events lasting several days, which are related to atmospheric forcing (Antoine et al., 2008) and lead to increase in fCO2@13. Figure 2e illustrates the solubility control of the variability of fCO2, as fCO2 increases when T increases. Another cause of the inter-annual variability of fCO2 for T∼14 ∘C is the timing of the spring increase in biological activity, which differs by a month between years. For instance, the increase happened at the beginning of April in 2013, when T∼15–16 ∘C and by mid March in 2014, when T∼14 ∘C. Another cause is the deepening of the mixed layer due to the fall cooling, which varies by a month between years.

We estimated the DIC and pH changes related to the increase in fCO2@13 measured at the sea surface 18 years apart, assuming a mean salinity equal to 38.2, a mean alkalinity equal to 2562.3 µmol kg-1 following Eq. (1) and a mean in situ temperature (T) equal to 18.25 ∘C. The dissociation constants of Mehrbach refitted by Dickson and Millero (Dickson and Millero, 1987; Mehrbach et al., 1973) were used. pH is calculated on the seawater scale. The uncertainty of dfCO2@13, 3.3 µatm, has been propagated to compute the combined uncertainty in dDIC and dpHSWS. The uncertainties in the equilibrium constants are neglected in this propagation of uncertainties. Likewise, an implicit assumption is that there is no systematic error on DIC and pHSWS derived from fCO2@13 between the two time periods; in particular, mean temperature and salinity remain the same (Sect. 3.2). This is further discussed in Sect. 4.1. We compute an increase in DIC and dDIC equal to 25.2±2.7 µmol kg-1 (1.40±0.15 µmol kg-1 yr-1) and a decrease in pHSWS and dpHSWS equal to -0.0397±0.0042 pHSWS (-0.0022±0.0002 pHSWS yr-1) (Table 2).

The increase in atmospheric fCO2 from 1995–1997 to 2013–2015 was computed from the monthly atmospheric xCO2 concentrations measured at the Lampedusa Island station (Italy) (35∘31′ N, 12∘37′ E) (http://ds.data.jma.go.jp/gmd/wdcgg/, last access: 14 September 2018) (see Eq. 3 in Hood and Merlivat, 2001). Considering a mean annual in situ temperature equal to 18.25 ∘C and an atmospheric pressure of 1 atm, we derived a mean atmospheric fCO2 equal to 355.3±0.8 µatm for 1995–1997 and 389.6±0.9 µatm for 2013–2015, which is an increase of 34.3±2.3 µatm (95 % confidence interval) (Table 2). At this temperature, the change in fCO2 at the sea surface is 41.4±4.1 µatm. Thus the contribution of the increase in atmospheric CO2 is responsible for 84%±5 % of the increase in fCO2 measured in the surface waters. With the same salinity and alkalinity as previously, the measurement of the corresponding change in surface DIC, assuming air–sea equilibrium, would be 20.8±1.3 µmol kg-1 (Table 2).

High-frequency measurements of fCO2 and temperature over two periods of 3 years that are 2 decades apart have allowed the computation of an increase in DIC equal to 25.1±2.3 µmol kg-1 assuming no change in alkalinity. In the range of salinity of the BOUSSOLE samples, 37.9 to 38.5, the alkalinity values computed with Eq. (1) are larger than those predicted by the relationship established for the DYFAMED site, with a mean difference equal to 10±2 µmol kg-1 (Copin-Montégut and Bégovic, 2002). In both cases alkalinity measurements were made with a potentiometric method using the certified reference material supplied by A. G. Dickson for calibration. It is difficult to identify the cause for a possible change in alkalinity between the two periods that are 18 years apart, while no salinity change has been observed. At a coastal site 50 km away from DYFAMED, Kapsenberg et al. (2017) have measured an increase in alkalinity unrelated to salinity over the period from 2007 to 2015. They attribute it to changes in freshwater inputs from land. However, based on data from Coppola et al. (2016), alkalinity in the upper 50 m at DYFAMED did not change significantly from 2007 to 2014 (3.204 µmol kg-1, P=0.0794, r2=0.08). Thus, we cannot conclude whether the difference observed at DYFAMED and BOUSSOLE between the two periods is real or an artifact of measurement techniques. As a sensitivity test, we compute the expected changes in DIC and pH from 1995–1997 to 2013–2015 for a mean alkalinity increase in 10 µmol kg-1. We obtain annual changes of dDIC =+0.46 µmol kg-1 yr-1 and dpH =-0.0001 pH unit yr-1, which are well below errors estimated in Sect. 3.4. Hence, such a change in alkalinity does not significantly affect the increase in DIC and the decrease in pH shown in Table 2.

The increase in sea surface DIC from 1995–1997 to 2013–2015 is 25.2±2.7 µmol kg-1 (Table 2), whereas the expected contribution due to ocean uptake of anthropogenic CO2 is 20.8±1.3 µmol kg-1. In order to interpret the difference between these two values, we examine potential changes that may result from the inter-annual variability in local physical and biological processes or anthropogenic carbon invasion from lateral advection of Atlantic waters.

The annual changes in DIC and pHSWS calculated between 1995–1997 and 2013–2015 are respectively equal to 1.40±0.15 µmol kg-1 and -0.0022±0.0002. At the DYFAMED site, at 10 m, Marcellin Yao et al. (2016) studied the time variability of pH over 1995–2011 based on measurements of T, S, Alk and DIC sampled approximately once a month. They computed a mean annual decrease in pH, -0.003±0.001, which is not significantly different from our estimate. For the global surface ocean, Lauvset et al. (2015) have reported a mean rate of decrease in pH, -0.0018±0.0004 for 1991–2011. This value is also within the limits of uncertainty of the pH change computed in our study.

Bates et al. (2014) examined changes in surface seawater CO2-carbonate chemistry at the locations of seven ocean CO2 time series that have been gathering sustained observations from 15 to 30 years with monthly or seasonal sampling. Six stations are located in the Atlantic and Pacific oceans in a latitudinal band between 10 and 68∘ N. The range of increasing and decreasing annual trends of DIC and pH extends from 0.93±0.24 to 1.89±0.45 µmol kg-1 yr-1 and -0.0014±0.0005 to -0.0026±0.0006, respectively. The Revelle factor of surfaces waters vary from 9–10 in low latitudes to 12–15 in the subpolar time series sites, with higher Revelle factor values reflecting a reduced capacity to absorb atmospheric CO2. The data show that the increase in DIC is not only controlled by the buffer capacity of the water but also by the compounding effects of changes in physical factors like the strengthening of winter mixing or larger air–sea uptake (Olafson et al., 2010).

The increase in DIC computed at DYFAMED is in the upper range of values reported in the other time series. A low Revelle factor of close to 10 characterises the Mediterranean Sea because of its warm and high-alkalinity waters. Moreover, as the result of a relatively short deep-water renewal time estimated to be 20–40 years in the western basin (Schneider et al., 2010), the waters of the Mediterranean Sea have a relatively high capacity to absorb anthropogenic CO2 from the atmosphere and transport it to deep water.

The calculated decrease in pH in the surface water at DYFAMED and in the global ocean are quite similar, despite the higher alkalinity of the Mediterranean Sea. Thermodynamic equilibrium calculations have highlighted the alkalinity's effect on the anthropogenic acidification of the Mediterranean Sea (Palmiéri et al., 2015). Their results show that, notwithstanding a higher total alkalinity, the average anthropogenic change in the surface pH of the Mediterranean Sea does not differ significantly from that of the average of global oceans.