Climatological variations of total alkalinity and total dissolved inorganic carbon in the Mediterranean Sea surface waters

Abstract

A compilation of data from several cruises between 1998 and 2013 was used to derive polynomial fits that estimate total alkalinity (A${}_{\mathrm{T}}$) and total dissolved inorganic carbon (C${}_{\mathrm{T}}$) from measurements of salinity and temperature in the Mediterranean Sea surface waters. The optimal equations were chosen based on the 10-fold cross-validation results and revealed that second- and third-order polynomials fit the A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ data respectively. The A${}_{\mathrm{T}}$ surface fit yielded a root mean square error (RMSE) of $\pm$ 10.6 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$, and salinity and temperature contribute to 96 % of the variability. Furthermore, we present the first annual mean C${}_{\mathrm{T}}$ parameterization for the Mediterranean Sea surface waters with a RMSE of $\pm$ 14.3 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$. Excluding the marginal seas of the Adriatic and the Aegean, these equations can be used to estimate A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ in case of the lack of measurements. The identified empirical equations were applied on the 0.25${}^{\circ }$ climatologies of temperature and salinity, available from the World Ocean Atlas 2013. The 7-year averages (2005–2012) showed that A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ have similar patterns with an increasing eastward gradient. The variability is influenced by the inflow of cold Atlantic waters through the Strait of Gibraltar and by the oligotrophic and thermohaline gradient that characterize the Mediterranean Sea. The summer–winter seasonality was also mapped and showed different patterns for A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$. During the winter, the A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ concentrations were higher in the western than in the eastern basin. The opposite was observed in the summer where the eastern basin was marked by higher A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ concentrations than in winter. The strong evaporation that takes place in this season along with the ultra-oligotrophy of the eastern basin determines the increase of both A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ concentrations.

Introduction

The role of the ocean in mitigating climate change is well known, as it absorbs about 2 Pg C yr${}^{-\mathrm{1}}$ of anthropogenic CO${}_{\mathrm{2}}$ (Wanninkhof et al., 2013). Worldwide measurements of surface seawater CO${}_{\mathrm{2}}$ properties are being conducted as they are important for advancing our understanding of the carbon cycle and the underlying processes controlling it. For instance, the buffer capacity of the CO${}_{\mathrm{2}}$ system varies with temperature, the distribution of total inorganic carbon, and total alkalinity (Omta et al., 2011).

Our understanding of the open-ocean CO${}_{\mathrm{2}}$ dynamics has drastically improved over the years (Rödenbeck et al., 2013; Sabine et al., 2004; Takahashi et al., 2009; Watson and Orr, 2003). However, our understanding of marginal seas such as the Mediterranean remains poor due to the limited measurements combined with the enhanced complexity of the land–ocean interactions. In the Mediterranean Sea, available measurements of the carbonate system are still scarce and only available in specific regions such as the Alboran Sea (Copin-Montégut, 1993), the Gibraltar Strait (Santana-Casiano et al., 2002), the DYFAMED (Dynamics of Atmospheric Fluxes in the Mediterranean Sea) time series in the Ligurian Sea (Bégovic and Copin-Montégut, 2002; Copin-Montégut and Bégovic, 2002; Touratier and Goyet, 2009), and the Otranto Strait (Krasakopoulou et al., 2011). Large geographical distribution of CO${}_{\mathrm{2}}$ data are often confined to cruises with a short sampling period (Álvarez et al., 2014; Goyet et al., 2015; Rivaro et al., 2010; Schneider et al., 2007; Touratier et al., 2012). Numerical models have provided some insights into the carbon dynamics in the Mediterranean Sea (Cossarini et al., 2015; D'Ortenzio et al., 2008; Louanchi et al., 2009), but it remains important to constrain the system from in situ measurements to validate their output.

The scarcity of the CO${}_{\mathrm{2}}$ system measurements in the Mediterranean Sea make it difficult to constrain the CO${}_{\mathrm{2}}$ uptake in this landlocked area and also limits our understanding of the magnitude and mechanisms driving the natural variability on the ocean carbon system (Touratier and Goyet, 2009). Empirical modelling has been successfully used to study the marine carbon biogeochemical processes such as the estimation of biologically produced O${}_{\mathrm{2}}$ in the mixed layer (Keeling et al., 1993), estimation of global inventories of anthropogenic CO${}_{\mathrm{2}}$ (Sabine et al., 2004), and estimation of the CaCO${}_{\mathrm{3}}$ cycle (Koeve et al., 2014). Empirical algorithms were also used to relate limited A${}_{\mathrm{T}}$ and C${}_{\text{T}}$ measurements to more widely available physical parameters such as salinity and temperature (Bakker et al., 1999; Ishii et al., 2004; Lee et al., 2006). The A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ fields can then be used to calculate pCO${}_{\mathrm{2}}$ fields and thus predict the CO${}_{\mathrm{2}}$ flux across the air–sea interface (McNeil et al., 2007).

Previous empirical approaches to constrain A${}_{\mathrm{T}}$ in the Mediterranean Sea have only covered selected cruises (Schneider et al., 2007; Touratier and Goyet, 2009) or local areas such as the DYFAMED time-series station or the Strait of Gibraltar (Copin-Montégut, 1993; Santana-Casiano et al., 2002). As for C${}_{\mathrm{T}}$, empirical models have only been applied to data below the mixed layer depth (MLD) following the equation of Goyet and Davis (1997) at the DYFAMED time-series station (Touratier and Goyet, 2009) or using the composite data set from Meteor 51/2 and DYFAMED (Touratier and Goyet, 2011). Lovato and Vichi (2015) also proposed an optimal multiple linear model for C${}_{\mathrm{T}}$ using the Meteor 84/3 full water column data. To the best of our knowledge the reconstruction of C${}_{\mathrm{T}}$ in surface waters has not been yet performed in the Mediterranean Sea. This is probably due to the lack of measurements available for previous studies to capture the more complex interplay of biological, physical and solubility processes that drive C${}_{\mathrm{T}}$ variability in the surface waters.

In this study we have compiled CO${}_{\mathrm{2}}$ system measurements from 14 cruises between 1995 and 2013, which allowed us to constrain an improved and new empirical algorithm for A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ in the Mediterranean Sea surface waters. We also evaluated the spatial and seasonal variability of the carbon system in the Mediterranean Sea surface waters by mapping the 2005–2012 annual and seasonal averages of surface A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ using the 0.25${}^{\circ }$ climatologies of salinity and temperature from the WOA13.

Methods

Surface A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ data in the Mediterranean Sea

Between 1998 and 2013, there were multiple research cruises sampling the seawater properties throughout the Mediterranean Sea. This includes parameters of the carbonate system, more specifically A${}_{\mathrm{T}}$, pH, and C${}_{\text{T}}$ and physico-chemical properties of in situ salinity and temperature. In this study we have compiled surface water samples between 0 and 10 m depth, totaling 490 and 400 measurements for A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ respectively (Table 1).

List of available carbonate system datasets for the Mediterranean Sea.

Data set	Period	Area	Carbonate system	Data points	Reference
			parameters
Prosope	Sep–Oct 1999	Mediterranean Sea	A${}_{\mathrm{T}}$ and pH	20	Bégovic and Copin (2013)
Meteor 51/2	Oct–Nov 2001	Eastern Mediterranean	A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$	16	Schneider and Roether (2007)
Meteor 84/3	Apr 2004	Southern Mediterranean	A${}_{\mathrm{T}}$, C${}_{\mathrm{T}}$ and pH	16	Tanhua et al. (2012)
Carbogib 2-6	2005–2006	Gibraltar Strait	A${}_{\mathrm{T}}$ and pH	28	Huertas (2007a, b, c, d, e)
Gift 1–3	2005–2006	Gibraltar Strait	A${}_{\mathrm{T}}$ and pH	12	Huertas (2007f, g, h)
Transmed	Jun 2007	Eastern Mediterranean	A${}_{\mathrm{T}}$ and pH	20	Rivaro et al. (2010)
Sesame IT-4	Mar–Apr 2008	Northern Mediterranean	A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$	16	SeaDataNet
Boum	Jun–Jul 2008	Mediterranean Sea	A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$	75	Touratier et al. (2012)
Pacific-Celebes	2007–2009	Mediterranean Sea	A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$	22	Hydes et al. (2012)
Moose-GE	May 2010	Ligurian Sea	A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$	44	SeaDataNet
Hesperides	May 2013	Gibraltar Strait	A${}_{\mathrm{T}}$	10	Perez et al. (2013)
MedSeA	May 2013	Southern Mediterranean	A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$	59	Goyet et al. (2015)
DYFAMED time series	1998–2013	Ligurian Sea	A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$	152	Oceanological Observatory
					of Villefranche-sur-Mer

Polynomial model for fitting A${}_{\mathbf{T}}$ and C${}_{\mathrm{T}}$ data

Two polynomial equations for fitting A${}_{\text{T}}$ or C${}_{\mathrm{T}}$ from salinity (S) alone or combined with sea surface temperature ($T$) in the surface waters (0–10 m) of the Mediterranean Sea were chosen from the results of the 10-fold cross-validation method (Breiman, 1996; Stone, 1974). This type of analysis was previously performed by Lee et al. (2006) for general relationships of A${}_{\mathrm{T}}$ with salinity and temperature. This model validation technique is performed by randomly portioning the data set into 10 equal subsamples. One subsample is used as the validation data and the nine remaining subsamples are used as training data. The cross-validation process is then repeated 10 times, with each of the 10 subsamples used exactly once as the validation data. In this manner, all observations are used both for training and validation, and each observation is used for validation only once. The best fit is chosen by computing the residuals from each regression model and computing independently the performance of the selected optimal polynomial on the remaining subsets.

The analysis was applied for polynomials of order 1–3, and the optimal equation was chosen based on the lowest root mean square error (RMSE) and the highest coefficient of determination ($r^{\mathrm{2}}$). High-order polynomials (4 and above) were discarded because they can be oscillatory between the data points, leading to a poorer fit to the data.

The data set consists of 490 and 400 data points for A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ respectively (Table 1). To ensure the same spatial and temporal coverage of the polynomial fits, the same training data set was retained for both A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$. This was performed by selecting stations were both parameters were simultaneously measured, yielding 360 data points (Fig. 1). To validate the general use of the proposed parameterizations we tested the algorithms with measurements which are not included in the fits (validation data set). For A${}_{\mathrm{T}}$, the validation data set consists of 130 data points which are formed from the testing subset of the 10th fold (40 data points) and from cruises where A${}_{\mathrm{T}}$ was measured without accompanying C${}_{\mathrm{T}}$ (90 data points). For C${}_{\mathrm{T}}$, the validation data set is the same as the testing subset of the 10th fold (40 data points).

Spatial distribution of data points used to initiate the fits of A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$.

[Figure omitted. See PDF]

Climatological and seasonal mapping of A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$

The climatological and seasonal averages of salinity (Zweng et al., 2013) and temperature (Locarnini et al., 2013) in 0.25 $\times$ 0.25${}^{\circ }$ grid cells were downloaded from the WOA13. The 7-year averages (2005–2012) and the summer–winter seasonality of A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ fields were mapped at 5 m depth by applying the respective derived algorithms in their appropriate ranges of S and $T$. The summer seasonality is defined as the average of the months of July, August, and September. The winter seasonality is defined as the average of the months of January, February, and March.

Results and discussion

Fitting A${}_{\mathrm{T}}$ in the Mediterranean Sea surface waters

In the surface ocean the A${}_{\mathrm{T}}$ variability is controlled by freshwater addition or the effect of evaporation, and salinity contributes to more than 80 % of the A${}_{\mathrm{T}}$ variability (Millero et al., 1998). In the Mediterranean Sea, several studies have shown that the relationship between A${}_{\mathrm{T}}$ and S is linear (Copin-Montégut, 1993; Copin-Montégut and Bégovic, 2002; Hassoun et al., 2015b; Jiang et al., 2014; Rivaro et al., 2010; Schneider et al., 2007). In other studies, the sea surface temperature ($T$) has been included as an additional proxy for changes in surface water A${}_{\mathrm{T}}$ related to convective mixing (Lee et al., 2006; Touratier and Goyet, 2011).

The results of the 10-fold cross-validation analysis revealed that the optimal model for A${}_{\mathrm{T}}$ is a second-order polynomial in which A${}_{\mathrm{T}}$ is fitted to both S and $T$ (Eq. 1). $$\begin{array}{cc}& {\mathrm{A}}_{\text{T}}=2558.4+49.83\left(S,-,38.2\right)-3.89\left(T,-,18\right)\\ & & -3.12(S-38.2{)}^{\mathrm{2}}-1.06(T-18{)}^{\mathrm{2}}.\end{array}$$ valid for $T$ > 13 ${}^{\circ }$C and 36.30 < S <39.65; n = 375; $r^{\mathrm{2}}$ $=$ 0.96; and RMSE $=$ 10.6 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$,

A linear relationship between A${}_{\mathrm{T}}$ and S yields a higher RMSE (14.5 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$) and a lower $r^{\mathrm{2}}$ (0.91) than Eq. (1). In a semi-enclosed basin such as the Mediterranean Sea, the insulation and high evaporation as well as the input of rivers and little precipitation leads to a negative freshwater balance (Rohling et al., 2009). The resulting anti-estuarine thermohaline circulation could explain the contribution of temperature to the A${}_{\mathrm{T}}$ variability (Touratier and Goyet, 2011).

The residuals of the training data set used to generate the second-order polynomial fit for A${}_{\mathrm{T}}$ are presented in Fig. 2a. Most of the A${}_{\mathrm{T}}$ residuals (340 out of 375) were within a range of $\pm$ 15 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$). However, 35 residuals were high up to $\pm$ 30 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$). Applying the A${}_{\mathrm{T}}$ algorithm to the testing data set (Fig. 2b) yields a mean residual of 0.91 $\pm$ 10.30 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$), and only six data points have residuals higher than $\pm$ 15 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$). Furthermore, to make sure that the A${}_{\mathrm{T}}$ algorithm does not overfit the data, we tested the difference in means between the RMSE and residuals between the training set compared to the testing set. The results show that for both the RMSE and mean residual, we cannot reject the null hypothesis (that assumes equal means) between the training and validation data sets (Table 2).

The comparison of the RMSE reported by other studies with that of Eq. (1) does not indicate if the parameterization developed here has advanced or not on previous attempts in the Mediterranean Sea. In that order, we independently applied each of the previous equations on the same training data set used to develop Eq. (1) and then computed the RMSE and $r^{\mathrm{2}}$ for every one (Table 3). The results show that Eq. (1) has a lower RMSE and a higher $r^{\mathrm{2}}$ than all of the parameterizations presented in Table 3. For instance, the general relationship of Lee et al. (2006) applied to the data set of this study yields an RMSE as high as $\pm$ 40.50 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$. The RMSE of other studies developed strictly in the Mediterranean Sea varied from $\pm$ 13.81 to $\pm$ 26.11 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ using the equations of Touratier and Goyet (2011) and Schneider et al. (2007) respectively.

Mean difference $t$ test for the A${}_{\mathrm{T}}$ algorithm between the training and validation data sets

	Training data set	Validation data set
RMSE ($\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$)	10.60	10.34	Mean difference $t$ test:
			$H$ $=$ 0; $p$ $=$ 0.83
Mean residual ($\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$)	2.64 $\times$ 10${}^{-13}$ $\pm$ 10.57	0.91 $\pm$ 10.30	Mean difference $t$ test:
			$H$ $=$ 0; $p$ $=$ 0.42

Performance of the different parameterizations for the estimation of A${}_{\mathrm{T}}$ applied independently to the training data set of this study.

Region	Parameterization	RMSE ($\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$)	$r^{\mathrm{2}}$	Reference
Alboran Sea	A${}_{\mathrm{T}}$ $=$ 94.85(S) $-$ 1072.6	$\pm$ 16.61	0.92	Copin-Montégut (1993)
DYFAMED site	A${}_{\mathrm{T}}$ $=$ 93.99(S) $-$ 1038.1	$\pm$ 16.31	0.92	Copin-Montégut and Bégovic (2002)
Strait of Gibraltar	A${}_{\mathrm{T}}$ $=$ 92.28(S) $-$ 968.7	$\pm$ 16.48	0.92	Santana-Casiano et al. (2002)
Mediterranean Sea	A${}_{\mathrm{T}}$ $=$ 73.7(S) $-$ 285.7	$\pm$ 26.11	0.68	Schneider et al. (2007)
DYFAMED site	A${}_{\mathrm{T}}$ $=$ 99.26(S) $-$ 1238.4	$\pm$ 18.53	0.91	Touratier and Goyet (2009)
Western Mediterranean	A${}_{\mathrm{T}}$ $=$ 95.25(S) $-$ 1089.3	$\pm$ 16.97	0.92	Rivaro et al. (2010)
Eastern Mediterranean	A${}_{\mathrm{T}}$ $=$ 80.04(S) $-$ 499.8	$\pm$ 14.58	0.91
Mediterranean Sea	A${}_{\mathrm{T}}$ $=$ 1/(6.57 $\times$ 10${}^{-\mathrm{5}}+$1.77 $-$ 10${}^{-\mathrm{2}}$) $/$S $-$(5.93 $-$ 10${}^{-\mathrm{4}}$(ln$\left(\mathit{\theta }\right))$ / ${\mathit{\theta }}^{\mathrm{2}}$)	$\pm$ 13.81	0.92	Touratier and Goyet (2011)
Global relationship (subtropics)	A${}_{\mathrm{T}}$ $=$ 2305 $+$ 58.66 (S $-$ 35) $+$ 2.32 (S $-$ 35)${}^{\mathrm{2}}$ $+$ 1.41 ($T-20$) $+$ 0.04 ($T-20$)${}^{\mathrm{2}}$	$\pm$ 40.50	0.26	Lee et al. (2006)

Map of the residuals of the A${}_{\mathrm{T}}$ algorithm (Eq. 1) applied to the (a) training and (b) testing data sets.

[Figure omitted. See PDF]

By applying directly the previous parameterizations to our training data set, the calculated RMSEs are significantly higher than the ones reported in their respective studies. For instance the reported RMSE in Lee et al. (2006) for subtropical oceanic regions is $\pm$ 8 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ and that of Schneider et al. (2007) for the Meteor 51/2 cruise is $\pm$ 4.2 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$. This shows that previous models were constrained by their spatial coverage, time span, and used data sets. In fact the previous equations were calculated in local areas such as the Alboran Sea (Copin-Montégut, 1993), the Strait of Gibraltar (Santana-Casiano et al., 2002), and the DYFAMED Site (Copin-Montégut and Bégovic, 2002; Touratier and Goyet, 2009). On a large scale, equations were applied using limited data sets such as the Meteor 51/2 cruise in October–November 2001 (Schneider et al., 2007), the Transmed cruise in May–June 2007 (Rivaro et al., 2010), and the Meteor 51/2 and DYFAMED time-series stations (Touratier and Goyet, 2011).

The proposed algorithm including surface data from multiple cruises, and on a large time span, presents a more representative relationship to estimate A${}_{\mathrm{T}}$ from S and $T$ than the previously presented equations (Table 3). In Eq. (1), $T$ and S contribute to 96 % of the A${}_{\mathrm{T}}$ variability and the RMSE of $\pm$ 10.6 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ presents a significant improvement of the spatial and temporal estimations of A${}_{\mathrm{T}}$ in the Mediterranean Sea surface waters (mean difference $t$ test, $H$ $=$ 1; $p$ $=$ 0.04).

Fitting C${}_{\mathrm{T}}$ in the Mediterranean Sea surface waters

The surface C${}_{\mathrm{T}}$ concentrations are influenced by lateral and vertical mixing, photosynthesis, oxidation of organic matter and changes in temperature and salinity (Poisson et al., 1993; Takahashi et al., 1993). All these processes are directly or indirectly correlated with sea surface temperature (Lee et al., 2000). Hence, the parameterization of C${}_{\mathrm{T}}$ includes both physical (S and $T$) and/or biological parameters (Bakker et al., 1999; Bates et al., 2006; Koffi et al., 2010; Lee et al., 2000; Sasse et al., 2013).

The results of the 10-fold cross-validation analysis showed that a first-order polynome fits C${}_{\mathrm{T}}$ to S and $T$ with an RMSE of 16.25 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ and $r^{\mathrm{2}}$ $=$ 0.87. These values are comparable to the RMSE and $r^{\mathrm{2}}$ found by previous empirical approaches applied in the eastern Atlantic (Bakker et al., 1999; Koffi et al., 2010). However, we found that a third-order polynome improved the RMSE and $r^{\mathrm{2}}$ of the equation compared to the first-order fit (Eq. 2). Hence we will retain the large data set used to develop Eq. (2), where temperature and salinity explain 90 % of the C${}_{\mathrm{T}}$ variability encountered in the Mediterranean Sea surface waters. The remaining 10 % could be attributed to the biological and air–sea exchange contributions to the C${}_{\mathrm{T}}$ variability. $$\begin{array}{cc}& C_{\text{T}}=2234+38.15\left(S,-,38.2\right)-14.38\left(T,-,17.7\right)-4.48\\ & (S-38.2{)}^{\mathrm{2}}-1.43\left(S,-,38.2\right)\left(T,-,17.7\right)+9.62\\ & (T-17.7{)}^{\mathrm{2}}-1.10(S-38.2{)}^{\mathrm{3}}+3.53(T-17.7)(S-38.2{)}^{\mathrm{2}}\\ & & +1.47(S-38.2)(T-17.7{)}^{\mathrm{2}}-4.61(T-17.7{)}^{\mathrm{3}},\end{array}$$ valid for $T$ > 13 ${}^{\circ }$C and 36.30 < S < 39.65; n $=$ 375, $r^{\mathrm{2}}$ $=$ 0.90; and RMSE $=$ 14.3 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$.

The C${}_{\text{T}}$ parameterization developed in this study (Eq. 2) showed a higher uncertainty than that of A${}_{\mathrm{T}}$ regarding both RMSE and $r^{\mathrm{2}}$. The estimation of C${}_{\mathrm{T}}$ in the mixed layer adds a high uncertainty due to the seasonal variability (Sabine et al., 2004). Also in surface waters, the C${}_{\mathrm{T}}$ are directly affected by air–sea exchange, and their concentrations will increase in response to the oceanic uptake of anthropogenic CO${}_{\mathrm{2}}$.

Previous models accounted for the anthropogenic biases in the C${}_{\mathrm{T}}$ measurements by calculating the C${}_{\mathrm{T}}$ rate of increase (Bates, 2007; Lee et al., 2000; Sasse et al., 2013; Takahashi et al., 2014). However, in a study, Lee et al. (2000) also did not correct the C${}_{\text{T}}$ concentrations for regions above 30${}^{\circ }$ latitude such as the Mediterranean Sea. In the following we will assess the importance of accounting or not for anthropogenic biases in the C${}_{\mathrm{T}}$ measurements. In that order we downloaded the monthly atmospheric pCO${}_{\mathrm{2}}$ concentrations measured from 1999 to 2013 at the Lampedusa Island station (Italy) from the World Data Centre for Greenhouse Gases (http://ds.data.jma.go.jp/gmd/wdcgg/). Following the method described by Sasse et al. (2013), we corrected the C${}_{\mathrm{T}}$ measurements to the nominal year of 2005 and applied the same 10-fold cross-validation analysis using data with and without anthropogenic $C_{\text{T}}$ corrections. We found that the RMSE of the C${}_{\mathrm{T}}$ model trained using measurements with anthropogenic corrections is 13.9 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$, which is not significantly different from the model trained using measurements without anthropogenic corrections (Eq. 2; RMSE $=$ 14.3 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$).

The yearly increase of C${}_{\mathrm{T}}$ concentrations is difficult to assess due to the wide spatial distribution of the training data set used to generate Eq. (2). Hence, we will refer to the monthly C${}_{\mathrm{T}}$ concentrations measured between 1998 and 2013 at the DYFAMED time-series station. We found that the rate of increase in $C_{\text{T}}$ concentrations at the DYFAMED site was 0.99 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ yr${}^{-\mathrm{1}}$ (Fig. 3), which is consistent with the anthropogenic $C_{\text{T}}$ correction rate used in the previous studies of Lee et al. (2000), Bates (2007), and Sasse et al. (2013).

The rate of increase in C${}_{\mathrm{T}}$ concentrations of 0.99 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ yr${}^{-\mathrm{1}}$ as well as the RMSE difference of $\pm$ 0.4 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ between the two models (with or without anthropogenic corrections) are both smaller than the uncertainty of the C${}_{\mathrm{T}}$ measurements of at least $\pm$ 2 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (Millero, 2007). A recent study also showed that the uncertainty of the C${}_{\mathrm{T}}$ measurements can be significantly higher than $\pm$ 2 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$, as most laboratories reported values of C${}_{\mathrm{T}}$ for the measures that were within a range of $\pm$ 10 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ of the stated value (Bockmon and Dickson, 2015).

Mean difference $t$ test for the C${}_{\mathrm{T}}$ algorithm between the training and validation data sets

	Training data set	Validation data set
RMSE ($\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$)	14.3	16.2	Mean difference $t$ test:
			H $=$ 0; $p$ $=$ 0.04
Mean residual ($\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$)	$-$1.5 $\times$ 10${}^{-12}$ $\pm$ 14.2	4.5 $\pm$ 17	Mean difference $t$ test:
			H $=$ 0; $p$ $=$ 0.06

Rate of increase applied to correct the C${}_{\mathrm{T}}$ measurements in reference to the year 2005.

[Figure omitted. See PDF]

Between 1998 and 2013, the C${}_{\mathrm{T}}$ concentrations measured at the DYFAMED time-series station showed a slightly increasing trend ($r^{\mathrm{2}}$ $=$ 0.05). The increase in C${}_{\mathrm{T}}$ concentrations in response to elevated atmospheric CO${}_{\mathrm{2}}$ was masked by the high seasonal variations. For example, during the year 1999 the variation in C${}_{\mathrm{T}}$ concentrations reached as high as 100 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (Fig. 4a). Also, there is a clear seasonal cycle of C${}_{\mathrm{T}}$ in the DYFAMED station (Fig. 4b). In the summer, the C${}_{\mathrm{T}}$ starts to increase gradually, reaching a maximum of 2320 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ during the winter season, after which a gradual decrease is observed to reach a minimum of 2200 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ by the end of spring. The seasonal cycle can be explained by the counter effect of temperature and biology on the C${}_{\mathrm{T}}$ variations. During the spring, the increasing effect of warming of pCO${}_{\mathrm{2}}$ is counteracted by the photosynthetic activity that lowers the C${}_{\mathrm{T}}$. During the winter, the decreasing effect of cooling on pCO${}_{\mathrm{2}}$ is counteracted by the upwelling of deep waters rich in C${}_{\mathrm{T}}$ (Hood and Merlivat, 2001; Takahashi et al., 1993). This shows that the C${}_{\mathrm{T}}$ concentrations were more affected by the seasonal variations than by anthropogenic forcing.

(a) Temporal and (b) seasonal variations of C${}_{\mathrm{T}}$ measured at the DYFAMED time-series station between 1998 and 2013.

[Figure omitted. See PDF]

Considering the small differences in the RMSE obtained by the two models, the uncertainties in the C${}_{\mathrm{T}}$ measurements, and the clear signal of the seasonal variations, no corrections were made to account for the rising atmospheric CO${}_{\mathrm{2}}$ concentrations. Also, the dynamic overturning circulation in the Mediterranean Sea plays an effective role in absorbing the anthropogenic CO${}_{\mathrm{2}}$ and transports it from the surface to the interior of the basins (Hassoun et al., 2015a; Lee et al., 2011).

The residuals of the data set used to generate the third-order polynomial fit for C${}_{\mathrm{T}}$ are presented in Fig. 5a. Most of the C${}_{\mathrm{T}}$ residuals (330 out of 360) were within a range of $\pm$ 18 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$). In contrast, only few residuals (12 out of 360) reached up to $\pm$ 50 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$). Applying the C${}_{\mathrm{T}}$ algorithm to the testing data set (Fig. 5b) yields a mean residual of 4.5 $\pm$ 17 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$), which is close to the uncertainties of our C${}_{\mathrm{T}}$ relationship. The high residuals observed in this study are consistent with the results of the optimal multiple linear regression performed by Lovato and Vichi (2015), where the largest discrepancies between observations and reconstructed data were detected at the surface layer with RMSE higher than $\pm$ 20 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$. To make sure that the C${}_{\mathrm{T}}$ algorithm does not overfit the data, we conducted the same analysis performed on the A${}_{\mathrm{T}}$ data sets. The results show that for both the RMSE and mean residual we cannot reject the null hypothesis (that assumes equals means) between the training and validation data sets (Table 4).

Considering the high uncertainties of the C${}_{\mathrm{T}}$ measurements, the seasonal variations, and the anthropogenic forcing, Eq. (2) presents the first parameterization for C${}_{\mathrm{T}}$ in the Mediterranean Sea surface waters, with an RMSE of $\pm$ 14.3 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ (1$\mathit{\sigma }$) and a $r^{\mathrm{2}}$ $=$ 0.90 (Eq. 2).

Spatial and seasonal variability of A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ in surface waters

The ranges of the 2005–2012 average annual climatologies of WOA13 are from 35.91 to 39.50 for S and from 16.50 to 23.57 ${}^{\circ }$C for $T$ (Locarnini et al., 2013; Zweng et al., 2013). However, a wider range is observed for the seasonal climatologies, especially during the winter season where $T$ ranges from 9.05 to 18.43 ${}^{\circ }$C. The estimations of A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ in surface waters from Eq. (1) and (2) respectively are only applicable in the appropriate ranges of $T$ > 13 ${}^{\circ }$C and 36.3 < S < 39.65. Hence, the surface water's A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ concentrations were mapped only where $T$ and S were within the validity range of Eq. (1) and (2) respectively. Excluding few near-shore areas and the influence of cold Atlantic waters in winter, the ranges in which Eq. (1) and Eq. (2) can be applied are within those of the climatological products of $T$ and S of the WOA13 (Fig. 6).

Comparison of the predicted C${}_{\mathrm{T}}$ values from the C${}_{\mathrm{T}}$ algorithm given in Eq. (2) with measurements which are (a) included or (b) excluded when deriving the fit.

[Figure omitted. See PDF]

The 7-year averages (2005–2012) of (a) sea surface salinity and (b) sea surface temperature climatological fields of the WOA13 (Locarnini et al., 2013; Zweng et al., 2013).

[Figure omitted. See PDF]

The mapped climatologies for 2005–2012 at 5m depth show a strong increase in the eastward gradient for both A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ with the highest concentrations always found in the eastern Mediterranean (Fig. 7). The minimum values of 2400 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ for A${}_{\mathrm{T}}$ and 2100 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ for C${}_{\mathrm{T}}$ are found near the Strait of Gibraltar and the maximum values of 2650 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ and 2300 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ are found in the Levantine and Aegean sub-basins for A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ respectively.

The A${}_{\mathrm{T}}$ parameterization of this study detects a clear signature of the alkaline waters entering through the Strait of Gibraltar that remains traceable to the Strait of Sicily as also shown by Cossarini et al. (2015). In the eastern basin the positive balance between evaporation and precipitation contributes to the increasing surface A${}_{\mathrm{T}}$. Local effects from some coastal areas such as the Gulf of Gabes and riverine inputs from the Rhone and Po rivers are also detected.

Our results for surface A${}_{\mathrm{T}}$ have a similar spatial pattern and range as the annual climatology of Cossarini et al. (2015) which simulates surface A${}_{\mathrm{T}}$ values from 2400 to 2700 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$. The main difference is marked in the upper ends of the Adriatic and Aegean sub-basins where our algorithm predicts A${}_{\mathrm{T}}$ values around 2400–2500 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$, whereas the analysis of Cossarini et al. (2015) yields a maximum of 2700 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ in these regions. Regressions in regions of high alkaline riverine inputs indicate a negative correlation between alkalinity and salinity (Luchetta et al., 2010). Hence, eastern marginal seas such as the Adriatic and Aegean sub-basins have high A${}_{\mathrm{T}}$ concentrations due to the freshwater inputs having enhanced alkalinity loads (Cantoni et al., 2012; Souvermezoglou et al., 2010). This shows the sensitivity of our algorithms to temperature and salinity especially in areas that are more influenced by continental inputs such as the Po and other local rivers in the northern Adriatic and inputs of the brackish Black Sea water through the Dardanelles Strait as well as by the river runoff from the Greek and Turkish mainland in the northern Aegean (Fig. 7a).

The 7-year averages of spatial variability for (a) surface A${}_{\mathrm{T}}$ predicted from Eq. (1) and (b) surface C${}_{\mathrm{T}}$ predicted from Eq. (2), applied to the 2005–2012 climatological fields of S and $T$ from the WOA13.

[Figure omitted. See PDF]

Distribution of the summer–winter differences of (a) surface A${}_{\mathrm{T}}$ predicted from Eq. (1) and (b) surface C${}_{\mathrm{T}}$ predicted from Eq. (2), applied to the 2005–2012 climatological fields of S and $T$ from the WOA13.

[Figure omitted. See PDF]

At the surface, the basin-wide distributions of C${}_{\mathrm{T}}$ are affected by physical processes and their gradient is similar to that of A${}_{\text{T}}$ (Fig. 7b). The lowest C${}_{\mathrm{T}}$ concentrations are found in the zone of the inflowing Atlantic water and increases toward the east in part due to evaporation as also shown by Schneider et al. (2010). Our results for surface C${}_{\mathrm{T}}$ have a similar range as the optimal linear regression performed by Lovato and Vichi (2015) which estimates surface C${}_{\mathrm{T}}$ values from 2180 to 2260 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$. Moreover, the results show that the Mediterranean Sea is characterized by C${}_{\mathrm{T}}$ values that are much higher (100–200 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ higher) than those observed in the Atlantic Ocean at the same latitude (Key et al., 2004).

Overall, the western basin has a lower surface C${}_{\mathrm{T}}$ content than the eastern basin, which could be explained by the eastward decrease of the Mediterranean Sea trophic gradient (Lazzari et al., 2012). The higher rate of inorganic carbon consumption by photosynthesis in the western basin can lead to the depletion of C${}_{\mathrm{T}}$ in the surface waters, whereas the ultra-oligotrophic state in the eastern basin can lead to a high remineralization rate that consumes oxygen and enriches surface waters with C${}_{\mathrm{T}}$ (Moutin and Raimbault, 2002).

The magnitude of the seasonal variability between summer and winter for A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ is shown in Fig. 8. Unlike the 7-year averages, the seasonal climatological variations (2005–2012) of A${}_{\mathrm{T}}$ have different spatial patterns than those of C${}_{\mathrm{T}}$. Overall the summer–wintertime differences for A${}_{\mathrm{T}}$ have an increasing eastward gradient (Fig. 8a). The largest magnitudes are marked in the Alboran Sea with differences reaching up to $-$80 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$; the negative difference implies that during the winter inflowing surface Atlantic water has higher A${}_{\mathrm{T}}$ concentrations than in summer. Higher wintertime than summertime A${}_{\mathrm{T}}$ concentrations are also observed in the Balearic, Ligurian and the south-western Ionian sub-basins but with a less-pronounced seasonality ($\sim$ $-$30 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$). For these three sub-basins, the C${}_{\mathrm{T}}$ has a higher summer–winter magnitude than A${}_{\text{T}}$ ($\sim$ $-$70 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$). The winter cooling of surface waters increases their density and promotes a mixing with deeper water. Thus, the enrichment in wintertime likely reflects the upwelling of deep waters that have accumulated A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ from the remineralization of organic matter, respiration, and the dissolution of CaCO${}_{\mathrm{3}}$. The seasonality is more pronounced for C${}_{\mathrm{T}}$, which likely reflects the stronger response of C${}_{\mathrm{T}}$ to biological processes than A${}_{\text{T}}$ (Takahashi et al., 1993).

In the Algerian sub-basin and along the coasts of Tunisia and Libya, the seasonality is inverted with higher A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ concentrations prevailing in the summer. The African coast is an area of coastal downwelling during the winter season. However, during summer the coastal upwelling appears in response to turning of the wind near the coast toward the west (Bakun and Agostini, 2001). In general, the magnitude of the A${}_{\mathrm{T}}$ seasonal variability is higher in summer than in winter for the eastern basin and more particularly in the Ionian and Levantine sub-basins. During this season, strong evaporation takes place, which induces an increase of A${}_{\mathrm{T}}$ concentrations (Schneider et al., 2007). In the eastern basin, the high evaporation during the summer has a smaller effect on the C${}_{\mathrm{T}}$, and magnitudes reach their maxima in the Levantine sub-basin ($\sim$ $+$ 20 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$). During wintertime the western basin and the south-east of Sicily appear to be dominated by higher C${}_{\mathrm{T}}$ concentrations than the rest of the eastern basin, where the summer C${}_{\mathrm{T}}$ concentrations prevail (Fig. 8b). During winter the high C${}_{\mathrm{T}}$ concentrations that coincide with low sea surface temperature in the western basin could result from the deepening of the mixed layer and could be enhanced by the upwelling associated with the Tramontane–Mistral winds that blow from the south of France and reach the Balearic Islands and the Spanish coast.

Summary

The A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ algorithms are derived from a compilation of 490 and 426 quality controlled surface measurements respectively, collected between 1999 and 2013 in the Mediterranean Sea. A second-order polynomial relating A${}_{\mathrm{T}}$ to both S and T yielded a lower RMSE ($\pm$ 10.4 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$) and a higher $r^{\mathrm{2}}$ (0.96) than a linear fit deriving A${}_{\mathrm{T}}$ from S alone. This confirmed the important contribution of temperature to the A${}_{\mathrm{T}}$ variability. Hence, temperature should be included in future algorithms to help better constrain the surface A${}_{\mathrm{T}}$ variations. The proposed second-order polynomial had a lower RMSE than other studies when we applied their respective algorithms to the same training data set. In this study we propose an improved and more global relationship to estimate the A${}_{\mathrm{T}}$ spatial and temporal variations in the Mediterranean Sea surface waters.

The C${}_{\mathrm{T}}$ parameterization is a first attempt to estimate the surface variations in the Mediterranean Sea. A third-order polynomial is suggested to fit the C${}_{\mathrm{T}}$ to $T$ and S with a RMSE of $\pm$ 14.3 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$. The biological contributions to the C${}_{\mathrm{T}}$ variations were less pronounced than the physical processes. The contributions of to the physical processes and biology to the C${}_{\mathrm{T}}$ variability were 90 and 10 % respectively. In terms of anthropogenic forcing, the C${}_{\mathrm{T}}$ rate of increase of 0.99 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ yr${}^{-\mathrm{1}}$ was significantly lower than the uncertainty of the measurements than can reach $\pm$ 10 $\mathrm{\mu }$mol kg${}^{-\mathrm{1}}$ between different laboratories. Moreover, the C${}_{\text{T}}$ concentrations were more affected by the seasonal variations than the increase of atmospheric CO${}_{\mathrm{2}}$.

We propose to use Eqs. (1) and (2) for the estimation of surface A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ in the Mediterranean Sea when salinity and temperature of the area are available and are in the appropriate ranges of the equations. However, in the eastern marginal seas, especially the northern Adriatic and northern Aegean, there is a need to develop a more specific equation that minimizes the errors in these areas. Hence, it is important to enrich the existing data set by an extensive sampling program such as the Med-SHIP initiative (CIESM, 2012) in order to improve the modelling of the carbonate system over the whole Mediterranean Sea.

Acknowledgements

The authors would like to thank all parties that have contributed to the data provision.

• The Sesame IT4 and Moose-GE cruise data were provided through SeaDataNet – Pan-European infrastructure for ocean and marine data management (http://www.seadatanet.org).

• The DYFAMED time series have been provided by the Oceanological Observatory of Villefranche-sur-Mer (L. Coppola). This project is funded by CNRS-INSU and ALLENVI through the MOOSE observing network.

• The Transmed cruise data were provided by P. Rivaro, A. Russo, and V. Kovacevic. The Transmed cruise is part of the VECTOR project, funded by the Ministry of Education, University and Research, the Ministry of Economy and Finance, the Ministry of the Environment and Protection of Natural Resources, and the Ministry of Agriculture and Forestry with an Integrated Special Fund for Research (FISR).

• The MedSEA 2013 cruise data were provided by the University of Perpignan Via Domitia, Institut de Modélisation et d'Analyse en Géo-Environnements et Santé, ESPACE-DEV (C. Goyet and A. E. R. Hassoun). This project was funded by the EC Mediterranean Sea Acidification in a changing climate project (MedSeA; grant agreement 265103).

• We would also like to thank the SNAPO-CO${}_{\mathrm{2}}$ (Service National d'Analyse des paramètres Océaniques du CO${}_{\mathrm{2}}$) for their contribution in measuring some of the A${}_{\mathrm{T}}$ and C${}_{\mathrm{T}}$ samples.

The authors are also grateful to the National Council for Scientific Research (CNRS) in Lebanon for the PhD thesis scholarship granted to Gemayel Elissar.Edited by: C. Heinze