An upgraded carbon-based method to estimate the anthropogenic fraction of dissolved CO 2 in the Atlantic Ocean

Abstract. An upgrade of classical methods to calculate the anthropogenic carbon (Cant) signal based on estimates of the preformed dissolved inorganic carbon (CT

obtain better estimates of preformed properties.This practice also eliminates the need for arbitrary zero-C ant references that are usually based on properties independent of the carbon system, like the CFC content.The long-term variability of preformed total alkalinity (A • T ) has been considered and the temporal variability of the air-sea CO 2 disequilibrium (∆C dis ) included in the formulation.The change of ∆C dis with time has shown to have non-negligible biases on C ant estimates, producing a 4 µmol kg −1 average decrease.The proposed ϕC • T method produces substantial differences in the C ant inventories of the Southern Ocean and Nordic Seas (∼18% of the total inventory for the Atlantic) compared with recent C ant inventories.The overall calculated Atlantic C ant inventory referenced to 1994 is 55±13 Pg C, which reconciles the estimates obtained from classical C • 1 Introduction The world oceans sequestrate annually 2.2±0.4Pg C out of the total 7.4±0.5Pg yr −1 of anthropogenic carbon (hereinafter denoted by C ant ) emitted to the atmosphere from activities such as fossil fuel burning, land use changes, deforestation and cement production (Siegenthaler and Sarmiento, 1993;Sabine et al., 2004;IPCC, 2007).The Atlantic Ocean alone contributes with a share of 38% to the anthropogenic oceanic carbon storage (Sabine et al., 2004) notwithstanding its moderate surface area (29% of the global ocean).
Since C ant cannot be measured directly it has to be deduced from the Total Inor- ganic Carbon (C T ) pool, out of which the anthropogenic signal represents a relatively small fraction (∼3%).To tackle the intricate and full of uncertainties issue of knowing how much C ant there is and where in the ocean is stored the carbon-based "backcalculation" techniques were pioneered (Brewer, 1978;Chen and Millero, 1979).The philosophy behind these methods goes through realizing that the preformed C T (C • T , the existing C T when a water mass is formed) has not remained constant ever since the beginning of the industrial revolution.Surface waters gradually started sensing the effect of rising partial pressures of atmospheric CO 2 (pCO atm 2 ), which forced more of this gas to dissolve (Brewer, 1978).From this perspective, it was argued that the C ant imprint concealed in C • T could be reckoned by deducting from it a preindustrial "zero-C ant " reference, namely C ant =C • T −C • π T (the superscript "π" will denote "at the preindustrial era" hereinafter).
Over the years a series of improvements and contributions have been added to this initial "preformed carbon" C ant estimation approach (Wallace, 2001).These went from more realistic assumptions on water mass equilibration and formation conditions to better estimates of C oπ T and MLR fits from surface or near-surface observations to calculate preformed total alkalinity (A • T ) (Gruber et al., 1996;K örtzinger et al., 1998;P érez et al., 2002;Ríos et al., 2003;Lo Monaco et al., 2005).There exist some approaches that cannot be denoted as C • T -based methods yet they have added to our knowledge of C ant estimation by introducing new constraints.For instance, the transient time distribution (TTD) (Waugh et al., 2006) is an indirect method fully detached from the need of carbon system measurements that assumes there is a distribution of ventilation times (i.e., the TTD) and uses age estimates from CFCs to determine the moment when water masses were last in contact with the atmosphere.
One of the most crucial aspects in any C • T -based approach in order to obtain accurate C ant estimates is reconstructing water mass formation (WMF) conditions as faithfully as possible.This is most relevant for calculating preformed nutrient concentrations and, primarily, A and CFCs at the time of outcropping.The CO 2 air-sea disequilibrium term (∆C dis ) first formal estimation by Gruber et al. (1996) meant a leap forward in the back-calculation technique, albeit with certain caveats (Matsumoto and Gruber, 2005).The C ant was then accordingly re-expressed as the difference between the quasi-conservative tracer ∆C * =(C • T −C π Teq ) and ∆C π dis (C π Teq is the C T in equilibrium with the preindustrial atmospheric CO 2 level of 280 ppm).
The current paper examines some of the above outlined shortcomings that are habitual in C ant back-calculation approaches and proposes some upgrades to them.Special emphasis is placed on assessing the adequacy of the water column region used to reconstruct WMF conditions at large ocean basin scales.Then accordingly, new parameterizations of A • T and ∆C dis are proposed and their long-term variability are given consideration.Finally, the impact of the proposed methodology modifications on previous Atlantic C ant inventory estimates is also addressed.

Dataset
The Atlantic Ocean plays a leading role in the thermohaline circulation context given the numerous deep-water mass formation processes it hosts and it has been selected as an optimal test-bed for the proposed C ant estimation modifications.In total, ten selected cruises to give representative Atlantic coverage were used (Fig. 1 and Table 1).These include the WOCE tracks A02, A14, A16, A17, A20, AR01, I06-Sa and I06-Sb, the CLIVAR A16N legs 1 and 2, the WOCE/CLIVAR OVIDE 2002 and 2004 cruises and the NSeas-Knorr cruise (Bellerby et al., 2005;Olsen et al., 2006).The availability of high-quality carbon system measurements, calibrated with Certified Reference Materials (CRMs), was one of the heavyweight cruise selection criteria.All of the above cruises are part of the Atlantic Synthesis effort made within the CARBOOCEAN Integrated Project framework (http://www.carbon-synthesis.org/).
The data are available from the Global Ocean Data Analysis Project (GLODAP; http: //cdiac.ornl.gov/oceans/glodap/Glodaphome.htm), the Climate Variability and Pre- For the vast majority of the samples, pressure and temperature data come from filtered CTD measurements.Salinity and nutrient data come from analysis of individual Niskin bottles collected with a rosette.All WOCE C T samples kept in the current dataset were analyzed with the coulometric titration technique.The OVIDE cruise C T data was obtained from thermodynamic equations using pH and A T direct measurements and the carbon dioxide dissociation constants from Dickson and Millero (1987).All shipboard A T measurements were analysed by potentiometric titration using a titration system and a potentiometer, and further determined by either developing a full titration curve (Millero et al., 1993;DOE, 1994;Ono et al., 1998) or by single point titration (P érez and Fraga, 1987;Mintrop et al., 2002).The pH measurements were determined using pH electrodes or, more commonly, with a spectrophotometric method (Clayton and Byrne, 1993) adding m-cresol purple as the indicator in either scanning or diode array spectrophotometers.Analytical accuracies of C T , A T and pH are typically assessed within ±2 µmol kg −1 , ±4 µmol kg −1 and ±0.003 pH units, respectively.A downward adjustment of 8 µmol kg −1 in the A T values from WOCE A17 (Table 1) has been suggested by Ríos et al. (2005) after comparing A T data from that cruise with other measurements.Otherwise, the preliminary results from a crossover analysis exercise performed by the CARBOOCEAN Atlantic Synthesis group sustain that no further corrections are needed for the carbon system parameters of the selected cruises.3 Method

The subsurface layer reference for reconstructing water mass formation conditions
It is not until water masses are rapidly capped by the seasonal thermocline and loose contact with the atmosphere that the degrees of O 2 and CO 2 air-sea disequilibria are established and preformed properties are defined.Therefore, any data (but specially surface) collected during this time befalls of incontrovertible value if one is to estimate C ant and infer from such measurements the ∆C dis or any carbon system preformed property, most importantly A • T and C • T .The surface outcropping of water masses is most common in high Atlantic latitudes and typically occurs towards late wintertime.This is the time when minimum seasonal values of temperature, minimum annual air-sea and water column vertical pCO 2 gradients and maximum thickness of winter mixed layers are reached.Unfortunately, the harsh meteorological conditions and the extension of ice covers at high latitudes diminish the number of cruises that can be conducted, making late wintertime surface data scarcely available and providing only sparse spatial coverage.On the contrary and to our profit, the subsurface layer has the advantage of retaining these wintertime WMF conditions quite stable up to sixth months after, when cruises are normally executed.
The surface ocean seasonal cycle has a large sea surface temperature (SST), C T and pCO 2 variability (Bates et al., 1996;Corbi ère et al., 2007).Typical SST oscillations can reach up to 10 • C (Pond and Pickard, 1993) in temperate waters and up to 6 • C in subpolar regions were WMF processes abound (Lab Sea Group, 1998).In the case of pCO 2 , the amplitude of variations ranges between 80 and 160 ppm, which in last instance translates into significant changes of surface C T (Bates et al., 1996;Lef évre et al., 2004;L üger, 2004;Corbi ère et al., 2007).Given such variability the use of surface measurements becomes dubious, even in the case of conservative parameters like θ, S, NO or PO (Broecker, 1974) for parameterizations that aim to characterize outcrop events and their associated WMF conditions.Its use would inevitably lead to reconstructing a manifold of plausible but inaccurate WMF scenarios depending on the sampling date of surface data (Lo Monaco et al., 2005).
As an alternative to the often unavailable surface late wintertime data P érez et al. (2002) and Ríos et al. (2003) used regional data from the 50-200 m layer as a first approximation to the winter mixed layer preformed conditions.It can be easily checked from any climatological database (the World Ocean Atlas 2005-WOA05, for example) how from January through April (typically) surface and subsurface tracer concentrations are more alike than during the rest of the year.Most remarkably, the physical and biological forcing of conservative tracer concentrations in the subsurface layer (100-200 m from hereon) is at least one order or magnitude less than in the case of the surface layer.This means that WMF properties are longer preserved throughout the annual cycle in the 100-200 m domain.Adding to the above arguments, the thermohaline variability of the ocean interior and the subsurface layer are very much alike (Fig. 2).The latter tightly encloses and represents the assortment of water masses existing in the bulk of the Atlantic Ocean, unlike the uppermost 25 m of surface waters.One final and mostly pragmatic aspect yet to relying on subsurface data to recreate WMF conditions is that it greatly reduces the sparseness of data available for parameterizations compared to wintertime surface data.T values despite of the net increases of silicate observed in the area where the equations were applied (Broecker and Peng, 1982;Ríos et al., 1995;P érez et al., 2002).We now investigate how considering different variables and using subsurface data can improve the estimation of A • T .From the selected cruises (Fig. 1), the latitudinal distributions in the subsurface layer  (Friis, 2006) and transform all surface waters close to subsurface conditions.The potential A T (PA T ) term is defined as PA T =A T +NO 3 +PO 4 , after Brewer et al. (1975) and Fraga and Álvarez-Salgado (2005).The main advantage of including PA T instead of A T in parameterizations is that organic matter remineralization has no effect on PA T .However, PA T remains to be a valid alkalinity shift indicator because it is still affected by CaCO 3 dissolution (by a factor of two).One highlight of the distributions in Fig. 3 is how the strong NPA T and silicate gradients at about 50 Where NO=9NO 3 +O 2 (µmol kg −1 ) is the conservative tracer defined by Broecker (1974), and Si is the silicate concentration (µmol kg −1 ).Since this PA T equation has been obtained using subsurface data, the approximation PA T ≈PA

Estimation of
• T can be soundly made, as the used data subset represents best the moment of WMF.Thus, from Eq. (1): A , where NO • 3 =NO 3 −AOU/9 and PO • 4 =PO 4 −AOU/135.AOU stands for Apparent Oxygen Utilization.The O 2 :N=9 and O 2 :P=135 Redfield ratios here used were proposed by Broecker (1974).These remineralization ratios have been satisfactorily applied previously in C ant determination by P érez et al. (2002) in the North Atlantic region.The error of the fit from Eq. (1) has been evaluated in terms of CaCO 3 dissolution (∆Ca), since ∆Ca=0.5(PAT,observed −PA • T ), and is estimated within ±4.6 µmol kg −1 , which is lower than the errors reported in Gruber et al. (1996) Lee et al. (2003).

On the temporal variability of A
• T The well-documented processes of rising sea surface temperature (SST), ocean acidification and changes in CaCO 3 dissolution over the last two centuries come to challenge the now commonly accepted temporal invariability of the A  , 1969), allowing for an even larger atmospheric CO 2 absorption.However, the current rise of the atmospheric CO 2 levels has also lessened the activity of calcifying organisms in surface waters and increased the C T /A T ratio, causing an upward translation of the aragonite saturation horizon (Riebesell et al., 2000;Sarma et al., 2002;Heinze, 2004).As these processes unfold over time they alter the value of preformed A T in the newly formed water masses.
In spite of the buffering capacity of the ocean to quench excess CO 2 , a sustained increase of atmospheric pCO 2 will lead to a large-scale acidification of the ocean that is more readily sensed by the uppermost layers of the ocean, including subsurface.The lowering of seawater pH may have severe consequences for marine biota, especially for those organisms that incorporate carbonate to their exoskeletons and other biomechanical structures (Royal Society, 2005).Heinze ( 2004) has performed a model scenario for the change in global marine biogenic CaCO 3 export production derived from the increasing anthropogenic fraction of atmospheric CO 2 .His laboratory findings were extrapolated to the world ocean using a 3-D ocean general circulation model (OGCM) and the results point to a decrease of 50% in the biological CaCO 3 export production by year 2250 for an assumed A1B IPCC emission scenario (xCO 2 of 1400 ppm).
This result translates into a ∼5% decrease (−0.03 Gt−C CaCO 3 yr −1 ) in the biogenic CaCO 3 export production that would be taking place nowadays.Also, this would pro- for the North Atlantic (Rosenheim et al., 2005).Depending on the author this amount varies from 0.8 to 2.0 Levitus et al., 2001;Curry et al., 2003;IPCC, 2007).The changes in the upper ocean temperature due to global warming would not have an effect on the NPA T due to thermal dependant biogeochemical processes.The hydrological balance affects salinity and alkalinity evenly, meaning that the long time scale salinity shifts in the surface layer do not affect the alkalinity/salinity ratio, i.e., NPA T .In spite of it, using present day θ data in Eq. ( 1) can bias the estimates of preindustrial A • T since any considered water mass would have formed under different values of θ back then in history.At the present day, the NPA T shows a positive rate of increase polewards with respect to SST of −4 µmolkg −1 • C −1 (from data in Fig. 3a and e).Accordingly, if Eq. (1) was to be applied to make historical estimates of A • T using present day values of θ, overestimates in NPA T of ∼4 µmol kg −1 could be introduced.
The decrease of preindustrial A • T due to CaCO 3 dissolution changes and SST shifts was corrected in our calculations according to the expression PA • T =PA T −(0.1 C sat ant +4).Here, C sat ant stands for the theoretical saturation concentration of C ant of the sample, which mostly depends on the atmospheric pCO 2 to which the water mass was exposed during its time of formation.Since we are attempting to quantify the temporal variability of A • T , the C sat ant was used to account for the acidification effects in the above fit because this variable is pCO 2 and, therefore, time dependant.The impact of the combined effects of ocean acidification and SST increase is big enough to be significant in terms of C ant inventory.However, their influence is lower than the uncertainty in C ant determination (normally around ±5 µmol kg −1 , depending on the estimation method).
These minor corrections would be very difficult to quantify directly through measure- on average) in C ant estimates wants to be avoided.Figures 4a and 4b show the ∆Ca calculated using the A • T proposed by Lee et al. (2003) (which it is practically coincident with Gruber et al., 1996) and the A • T from Eq. ( 1).The distribution trends and values of both parameterizations are highly correlated (R 2 =0.77, n=4923).The ∆Ca distributions agree on the accumulation of calcium and increasing alkalinity in deep waters, mainly in the Deep South Atlantic where the oldest water masses are found.However, there is still a significant offset in the ∆Ca fields of 11 µmol kg −1 .The A • T equation from Lee et al. (2003) produces negative ∆Ca in most of the North Atlantic south of its application range limit (latitude <60 • N).Negative values of ∆Ca up to −17 µmol kg −1 are reached, indicating that there is CaCO 3 precipitation in those areas.Nonetheless, there is no evidence that such net precipitation of CaCO 3 predominates over dissolution below the subsurface layer.The review of the global carbonate budget (Milliman et al., 1999;Berelson et al., 2007) shows that a considerable portion of surface-produced calcite (as much as 60-80%) dissolves in the upper 1000 m, above the lysocline, as a result of biological mediation.It has been previously demonstrated by other authors how even though the upper ocean is supersaturated with CaCO 3 , there is a downward increase of the CaCO 3 dissolution (Broecker and Peng, 1982).Additionally, data from sediment traps in the North Atlantic corroborates the dissolution of CaCO 3 in the upper layers of this ocean (Honjo and Manganini, 1993;Martin et al., 1993).The A • T parameterization from this study has satisfactorily produced positive ∆Ca values in the whole Atlantic and low ∆Ca in the Nordic Seas.

Estimation of ∆C dis in the subsurface layer
The disequilibrium between the rapidly increasing atmospheric pCO 2 and the sea surface pCO 2 largely determines the behaviour of the ocean as a CO 2 source or sink.The increasing net uptake of CO 2 by the ocean at a global scale is sustained by an increas- ing air-sea pCO 2 gradient.The ∆C dis can not be measured directly like in the case of A T and must therefore be defined theoretically from observable parameters.The present-day ∆C dis (∆C t dis ) term was first estimated in the context of C ant determination by Gruber et al. (1996), who defined it conceptually as the difference between the C T in the mixed layer at the time of WMF (C • t T ) and the theoretical C T in equilibrium with the corresponding atmospheric pCO 2 (C t T eq ).We applied this definition (Eq.2) to the subset of subsurface data from our selected cruises (Fig. 3f).To obtain C • t T , the measured C T in the described subsurface layer must be corrected for the organic matter remineralization and ∆Ca contributions.The C t T eq term is obtained from thermodynamic equations using subsurface measurements of S, θ, nutrients, AOU, A • T and age estimated from CFC12 concentrations.The water pressure and fugacity terms have been taken into account in the calculation of C t T eq (P érez et al., 2002).The PA

•
T term was calculated applying Eq. ( 1).The shortcoming of the ∆C t dis definition in Eq. ( 2) is its dependence on nonconservative tracers, which is a compulsory and desirable feature in any robust parameterization of oceanographic variables.Hence, the estimated subsurface ∆C dis data (Fig. 3f) are used as input to construct a multilinear regression (MLR) model that uses only conservative variables.The obtained fit is given in Eq. ( 3).The specific parametric coefficients of equation for different temperature and latitude intervals are summarised in Table 2, together with the error estimates of the model.For the case of Central Waters (8≤θ≤18 • C) a distinction between hemispheres has been made because no mixing between Arctic and Antarctic waters takes place in this oceanographic region.It is therefore possible to calculate ∆C dis more accurately through specific equations from the northern and southern hemispheres.In the Equatorial Upwelling region a thermal threshold between warm (θ>18 • C) subsurface waters and colder waters has been also established.The fitted ∆C dis shows a high correlation with the original values calculated using Eq.(2) (R 2 =0.72; n=1934).The uncertainties for the ∆C dis values obtained using conservative variables in Eq. ( 3) are between 4 and 7 µmol kg −1 (average 5.6 µmol kg −1 ; Table 2).

On the temporal variability of ∆C dis (∆∆C dis )
Ever since it was first introduced in the C ant back-calculation equations by Gruber et al. (1996) the main assumption regarding ∆C dis has been its invariability over time (∆C , where "π" stands for preindustrial) for a given oceanic region (Gruber et al., 1996;Gruber, 1998;Wanninkhof et al., 1999;Lee et al., 2003).Conversely, according to Sabine et al. (2004), the C ant inventory is estimated to have a present annual rate of increase of 1.8±0.4Pg C yr −1 .Such C ant uptake and inventory increase is sustained by the increasing air-sea pCO 2 gradient.This means that the atmospheric pCO 2 increases faster than the uptake mechanisms of the ocean can cope with on a yearly basis.This result makes the assumption of invariable ∆C dis rather imprecise (Hall et al., 2004;Matsumoto and Gruber, 2005).
The effects of the temporal variation of ∆C dis (∆∆C dis =∆C t dis −∆C π dis ) on the inventories of C ant have been recently evaluated in Matsumoto and Gruber (2005).
A rate of increase of 1.8±0.amount up to −8.0 µ atm (see Fig. 1 in Biastoch et al., 2007).As estimated by Matsumoto and Gruber (2005) this would correspond to a theoretical average ∆∆C dis of −5.0±1.0 µmol kg −1 that would have developed since the preindustrial era.Accordingly, these authors have suggested a −7% correction factor to the ∆C * estimated C ant inventories in Lee et al. (2003) and Sabine et al. (2004).Matsumoto and Gruber (2005) have proposed a model for the temporal evolution of ∆C dis (see their Fig. 2).On their Eq.( 5) a formal relationship between ∆∆C dis and C ant is given, namely: ∆∆C dis =β/k ex C ant .The term k ex is the globally averaged air-sea gas exchange coefficient for CO 2 (0.065±0.015 mol C m −2 yr −1 µatm −1 according to Broecker et al., 1985).The β is a constant factor that they estimate (0.0065±0.0012 mol C m −2 yr −1 µatm −1 ) from the constraint that the global C ant uptake flux integrated over the industrial period must equal the total inventory of anthropogenic CO 2 in the ocean.Hence, the overall proportionality factor between ∆∆C dis and C ant they obtain is β/k ex ≈0.1.
Observations indicate that ∆C dis varies spatially due to the rapid uptake capacity and solubility changes governed mainly by temperature and wind speed, the biological pump and the vertical mixing.The dilution of transient tracers, in particular C ant and CFCs above the seasonal thermocline strongly depends on the winter mixed layer depth (WMLD) (Doney and Jenkins, 1988).On the subtropical regions, where WMLD is shallow (∼100-200 m), the average C ant content is close to saturation (∼60 µmol kg −1 ).Applying Eq. ( 5) from Matsumoto and Gruber (2005)  mined for different regions by applying the integral constraint to individual isopycnals in order to obtain regional β and by determining the corresponding regional k ex .Next, we propose a simpler method to account for the horizontal (spatial) and vertical (temporal) variability of the β/k ex factor in the area under study.This should provide a correction for the positive bias linked to ∆∆C dis .
The magnitude of ∆∆C dis is assumed to be controlled by the interactions of wind speed, ocean circulation and surface ocean buffering particularly in regions where strong subsurface mixing processes occur.Based on the ∆pCO 2 climatology from Takahashi et al. (2002) it can be stated that the absolute values of ∆∆C dis (|∆∆C dis |) and ∆C dis (|∆C dis |) co-variate with WMLD except in Equatorial warm surface waters.
This empirical result provides a simple process-based argument for trying to express β/k ex as a function of the WMLD and, in so doing, relaxing the assumption of constant β/k ex .Regions with thick WMLs need longer time periods (several years) to equilibrate and therefore tend to have larger interannual disequilibria (no matter whether in the present or in the preindustrial era) (Azetsu-Scott et al., 2003;Fine et al., 2002;Takahashi et al., 2002).Consequently, |∆∆C dis | will tend toward larger values on areas with large |∆C dis |.To a lesser extent than in the high latitudes, the Equator has an anticorrelation between ∆∆C dis and f CO 2 , i.e., it displays negative ∆∆C dis (Matsumoto and Gruber, 2005) and high sea surface f CO 2 values (Takahashi et al., 2002).Knowingly of this exception and given the above argumentation, even if a coarse correlation between the ∆∆C dis and ∆C dis is assumed, Eq. ( 5) in Matsumoto and Gruber (2005) can be re-expressed and re-fitted in terms of C ant and ∆C t dis (Eq.4) to account for the variability of β/k ex .
Furthermore, from Eq. ( 4): a xCO 2 air =375 ppm) is a correction factor that is included to account for the effects of temperature and salinity on the solubility of C ant in the different water masses.The constant term "ϕ" is a proportionality factor and equals the ∆∆C dis /∆C t dis ratio.For simplicity, it has been assumed that "ϕ" is constant elsewhere from the Equator.The Equator is an upwelling region that behaves as a CO 2 source and "ϕ" is assumed to have a positive sign here.Otherwise, the second term in Eq. ( 4) warranties that ∆∆C dis will be assigned low values in low latitudes (where C ant is high and ∆C t dis is low).The C ant /C sat ant ratio in Eq. ( 4) accounts for the temporal variability of ∆∆C dis (Fig. 2 and Eq. ( 5) in Matsumoto and Gruber, 2005) that stems from the fact that C ant increases over time forced by the rising atmospheric CO 2 loads.Hence, the C ant /C sat ant ratio represents the degree of equilibrium between the C T in a given sample and the atmospheric CO 2 concentration at the moment of sampling.This implies that the larger the C ant burden of the water mass is, the larger its ∆∆C dis will be.
The value of the constant proportionality factor "ϕ" in Eq. ( 4) can be calculated using subsurface estimates given that the air-sea CO 2 disequilibrium is established in the upper ocean layers.To estimate it, the subsurface ∆C t dis for the Atlantic is calculated applying Eq. (3) using hydrographical data from the selected cruises that span over a decade (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003) (Fig. 1, Table 1).By averaging the time interval covered in the dataset we get t≈1998 and, therefore, ∆C t dis =∆C 1998 dis in the present study.Next, the C ant in Eq. ( 4) is calculated for subsurface waters applying the CFC-age "shortcut" method with CFC12 data (Thomas and Ittekot, 2001).The average age of the water masses in the Atlantic subsurface layer, including the important outcropping regions, is under 25 years (Fig. 3d).According to Matear et al. (2003), the use of the shortcut method to estimate C ant is suitable in the case of such young waters in the upper ocean layers.Anyhow, the shortcut method is only applied in the present study in this step of estimating "ϕ".Lastly, we take an average ∆∆C dis value for the Atlantic of −5.0±1.0 µmol kg −1 (Matsumoto and Gruber, 2005)  Alternatively, taking this value of ϕ and applying it in Eq. ( 5) yields an average ∆C π dis =−4.5 µmol kg −1 for the Atlantic.This corollary result indicates that during the preindustrial era the average ∆C dis was, on average, less negative than at present.For comparison, Matsumoto and Gruber (2005) obtained average values of ∆∆C dis =−5.5 µmol kg −1 and ∆C π dis =−7.0 µmol kg −1 for the global ocean using synthetic surface data from a 3-D OGCM output.

Modified formulation to estimate C ant
The anthropogenic fraction of C T is traditionally expressed in the back-calculation context as: Where: All terms in Eq. ( 7) are calculated directly from hydrographical data.In the case of PA • T , it is calculated using Eq. ( 1) and applying the proposed A • T correction for CaCO 3 dissolution changes and temperature shifts (Sect.3.3).Then, by substituting Eqs. ( 7) and (8) into Eq.( 6) we get: Finally, by replacing the expression for ∆C The denominator in Eq. ( 10) is always higher than or equal to one and thus lower C ant estimates than those from the ∆C * method will be predicted in most cases.This difference in the estimates will be ultimately modulated by the "weight" of the ∆C t dis term.The presented modification in the methodology and, ultimately, in the formulation is expected to have a significant impact in terms of C ant inventory.The addition of the "ϕ" factor alone represents, on average, a 5 µmol kg −1 decrease in C ant saturated samples.Interestingly, this is in excellent agreement with the average lowering of C ant estimates from the ∆C * method suggested by Matsumoto and Gruber (2005).From hereon, C ant calculations obtained after applying Eq. ( 10) will be referred to as "ϕC method" C ant estimates.
Several in-detail evaluations of the uncertainties attached to C ant estimation with back-calculation approaches have been thoroughly performed in the past (Gruber et al., 1996;Gruber, 1998;Sabine et al., 1999;Wanninkhof et al., 2003;Lee et al., 2003).They all assessed the uncertainty of C ant estimates by propagating random errors over the precision limits of the various measurements required for solving C ant estimation equations.The A • T parameterization here obtained has an associated error that is two times lower than the one proposed by Gruber et al. (1996).In addition, the cruises used to obtain the parameterizations in the present work produced highquality datasets with the help of improved analytical methodologies and the use of certified reference materials in the carbon system measurements.We have performed a random propagation of the errors associated with the input variables necessary to solve Eq. ( 10) and have estimated an overall uncertainty of 5.2 µmol kg −1 for the C ant estimates obtained with the ϕC • T method.For comparison, the overall estimated C ant uncertainties in Gruber et al. (1996) and Sabine et al. (1999)

Calculating A • T and ∆C dis in the water column
To obtain the full-depth A • T and ∆C dis profiles it is necessary to convey into the ocean interior the A • T and ∆C dis calculated for the subsurface layer using Eqs.( 1) and (3), respectively.As discussed in Sect.3.1, applying Eqs. ( 1) and (3) to subsurface data has served so far to identify and establish subsurface A • T and ∆C dis representatives of each intermediate and deep-water mass present in the thermohaline fields from the selected cruises.
Depending on the temperature of each sample, different approaches are followed in this work to achieve optimum A • T and ∆C dis estimates in the whole water column.In the case of water samples above the 5 • C isopleth, Eqs. ( 1) and ( 3) are applied directly to obtain A • T and ∆C dis , respectively.The correction proposed in Sect.3.3 for the temporal variability of A • T is also applied here.For waters with θ<5 • C, A • T and ∆C dis are estimated via an extended Optimum Multiparameter (eOMP) analysis (Poole and Tomczak, 1999;Álvarez et al., 2004).
The main reason for this division is to improve the estimates in cold deep waters where complex mixing processes of Arctic and Antarctic origin waters intervene.The intricate interaction of such water masses uplifts the importance (and complication) of mixing in the lower ocean, backing-up the use of an OMP approach.Moreover, the fact that this region represents an enormous volume of the global ocean (∼86%) confers waters below the 5 • C isotherm the capability of affecting significantly C ant inventories even from potentially small errors in C ant estimates.Consequently, the determination of A • T and ∆C dis in samples with θ<5 • C must be carefully assessed.These are the principal incentives that justify the different procedures used to calculate A • T and ∆C dis in the upper and lower ocean layers.
The type values of A • T for the end-members that make up a water sample could still be calculated applying Eq. ( 1) directly, even in the case of water masses with θ<5 • C.This is because Eq. ( 1) is valid for the temperature range of 0 to 20 • C (Fig. 3a) and also because the subsurface domain faithfully represents the assortment of water masses Introduction

Conclusions References
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Full present in the bulk of the Atlantic Ocean (Fig. 2).Even then, if a water parcel is subject to complex mixing processes it is more appropriate (from a mechanistic point of view) to calculate A • T based on the A • T of the founding end-members and their specific mixing proportions, rather than from direct application of a parameterization such as Eq. ( 1).The same reasoning and modus operandi applies for ∆C dis .The minutia followed in this work for both calculation procedures is given in Appendix A.
Lastly, the saline imprint of the Mediterranean Water (MW) in the North Atlantic can induce to wrong calculations when applying Eqs. ( 1) or (3) directly in waters above the 5 • C isotherm.In these particular cases, the ∆C dis and A • T have to be propagated into the ocean interior by resolving the triangular mix defined by the end-members of Labrador Seawater (LSW), Subpolar Mode Water (SPMW) and MW (Fig. 2).In our selected cruises the samples influenced by MW are located on a wedge of the TS diagram (Fig. 2) that falls outside of the wrapping from subsurface waters.In samples gathered northwards from 15 • N and below 400 m depths the above-mentioned mixing triangle is applied to calculate the mixing percentage of MW.The thermohaline and chemical properties of MW are well documented in the literature (P érez et al., 1993; Álvarez et al., 2005).The A

•
T and ∆C dis type values for the SPMW and LSW were calculated from Eqs. (1) and (3), respectively.For the MW end-member these two type values were determined from the mixing percentages of Eastern North Atlantic Central Water (ENACW) and Mediterranean Overflow Water (MOW) in the Gulf of C ádiz.The θ, S, CFC12 and carbon system data used to calculate the A • T and ∆C dis type values of MOW were sampled in the Strait of Gibraltar and in the Gulf of C ádiz (Rhein and Hinrichsen, 1993;Santana-Casiano et al., 2002).Introduction

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Anthropogenic CO 2 fields of the Eastern Atlantic basin
As a mean of putting the ϕC • T method through the test, the C ant signal is evaluated in a subset of the selected meridional cruises (denoted by star symbols in Fig. 1) that cover the length and are representative of the Eastern Atlantic basin.The obtained results are then compared with previous C ant estimates calculated for the same cruises by Lee et al. (2003) using the classical ∆C * method (Fig. 5a and b).
The broad C ant distribution patterns are quite similar for both methods, except in the Southern Ocean.In this region of discrepancy south from the Polar Front, Lee et al. (2003) calculate C ant concentrations in the whole water column that are too low compared to the ϕC • T estimates.These low ∆C * estimates are substantiated by Lee et al. (2003) from two arguments, namely: a) the hindrance of air-sea CO 2 exchanges caused by the extension of sea ice; b) the short residence times of the newly formed deep water in this region, which are not long enough for the water body to sequestrate significant amounts of C ant .In spite of these arguments, it is still difficult to justify so extremely low values of C ant , given that significant CFC concentrations have been reported along the continental rise and bottom waters in this region (Orsi et al., 2002;Matear et al., 2003;Waugh et al., 2006).Conversely, such evidence supports the moderately low C ant values of about 13±2 µmol kg −1 from the ϕC with the ϕC • T results in Fig. 5a ( V ázquez-Rodríguez et al., 2009).In regions of strong vertical mixing like the Southern Ocean, the back-calculation methods that use deep water masses to establish a C ant =0 baseline can lead to underestimations of the anthropogenic carbon signal because of inappropriate reference choices (Lo Monaco et al., 2005).It is particularly in these regions where the ∆C * method is known to set unrealistic zero-C ant references (Sabine et al., 1999).A strong vertical mixing of very old, free-CFC waters with well-ventilated, CFC-rich wintertime surface waters constitutes a case study for the non-linear dependence between C ant and CFC-derived ages (Matear et al., 2003;Matsumoto and Gruber, 2005).This nonlinearity affects the ∆C dis determination in the ∆C * method and transfers a positive bias to the ∆C dis of deep isopycnal surfaces in the South Atlantic (Gruber, 1998).The ϕC • T method has produced moderately low C ant estimates in the polar and subpolar regions of the section (Southern Ocean and Nordic Seas) mainly due to the influence of the ∆∆C dis term (Fig. 5c).These estimates stem directly from the high |∆C dis | values found in the Southern Ocean and Nordic Seas at present (Fig. 3f).An important advancement of the ϕC • T method in this aspect is that the use of CFCs on the proposed equations is completely unnecessary.

Atlantic inventories of C ant
Although the calculation of a new inventory of C ant is beyond the scope of this study it is still worth discussing the implications of the modifications here proposed.The work from Lee et al. (2003) provides detailed C ant inventories for the Eastern and Western Atlantic basins (Table 5 in Lee et al., 2003) calculated using the ∆C * method estimates in a large number of WOCE-JGOFS sections.In the present work, the specific inventory of C ant from the ϕC • T method was calculated without rejecting negative C ant values that were within a 2σ confidence interval of the determination uncertainties (5.6 µmol kg −1 ).
After Lee et al. (2003), the average specific inventories were determined with a meridional resolution of 10 • for the Eastern Atlantic basin (Fig. 6) using the same cruises as in Sect.4.1.To make results perfectly comparable with Lee et al. (2003), the studied section was referenced to the WOCE/JGOFS canonical year 1994.This was done using the temporal variation of C sat ant as a scaling factor.In addition, the C ant inventories obtained by Gruber (1998) with the ∆C * for the same region during the middle 1980s were also rescaled and referenced to 1994 so as to include them in Fig. 6.
The C ant inventories from Lee et al. (2003) and the one obtained with the ϕC • T method are highly correlated (R 2 =0.95) in the broad 40 • S-30 • N latitude band, notwithstanding the fact there exist regions of discrepancy.The calculated specific inventories in the Iceland basin and the Nordic Seas are ∼20% and ∼40% higher, respectively, than those in Lee et al. (2003) and Gruber et al. (1998).The largest differences in the specific inventory are found in the Nordic Seas and in the Southern Ocean (Fig. 6), as expected from the results in the former section.The ϕC • T method predicts a specific inventory of C ant for the Southern Ocean of 48 mol C m −2 , which is four times higher than the ∆C * ones in Gruber et al. (1998) and Lee et al. (2003).The C ant method intercomparison work from V ázquez-Rodríguez et al. (2009) shows how different independent methods like the TTD (Waugh et al., 2006) or the TrOCA (Touratier et al., 2007) have also calculated higher inventories than the ∆C * approach for the same WOCE lines, supporting the ϕC These estimates are 9 and 16 mol C m −2 higher than the ones computed with the ϕC • T method.Part of these differences can be attributed to the implicitly assumed O 2 equilibrium estate in the ϕC • T method and to the ∆∆C dis approach and fit here proposed (V ázquez-Rodríguez et al., 2009).Also, the ϕC If the ∆∆C dis term here proposed was omitted (i.e., ϕ=0) then an average decrease of 6.8±2.8 mol C m −2 in the specific inventory of C ant would result (that is, 12% of the average C ant inventory) (Fig. 6).This is in good agreement with the average 7% reduction factor proposed in Matsumoto and Gruber (2005).On the other hand, the long-term variation of A • T produces an increase on the average specific inventory of 8.3±2.0 mol C m −2 .It must also be noticed that the influences of the ∆∆C dis term and the long-term variation of A • T in C ant inventories vary little with latitude (Fig. 6).
The specific inventories for the Eastern and Western Atlantic basins are thoroughly detailed in Table 5 from Lee et al. (2003) for the same 10 • latitude bands in this study.From that table, the inventories from the two Atlantic basins appear to be highly correlated (East inv.=1.069West inv.−3.467: R 2 =0.9246).By calculating a west/east inventory ratio and applying it to our Eastern Atlantic results, we were able to come up with an estimate of the total inventory of C ant for the Atlantic Ocean.In so doing, the uncertainties associated with the extrapolation due topographic effects would affect our results in the same manner as they would affect the ones in Lee et al. (2003).It must be noticed that the inventories between 50 • -70 • S and 60 • -70 • N estimated from our C ant estimates are directly applied to calculate the total inventory.Knowingly of the caveats associated with the above practices, an estimate of 55±13 Pg C for the Atlantic C ant total inventory was finally obtained for the ϕC • T method.This result is substantially higher than recently calculated C ant inventories (∼18% larger) mainly due to the differences found in the Southern Ocean and Nordic Seas (V ázquez-Rodríguez et al., 2009).Introduction

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Conclusions
The ϕC • T method is a process-oriented geochemical approach that attempts to account for the nature and evolution of the phenomena that ultimately have affected the C ant storage in the ocean since the 1750s.It considers from the biogeochemistry of the marine carbon cycle to the mixing and air-sea exchange processes that control the uptake of C ant by the ocean.It also considers the spatiotemporal variability of the A • T and ∆C dis terms.The subsurface layer reference for WMF conditions has served to produce high-performance parameterizations of A • T and ∆C dis that can be used to estimate C ant without the need of any additional and arbitrary zero-C ant references.Overall, the proposed method upgrades translate into significant impacts on C ant inventories and bring closer together the estimates obtained from classical C • T -based methods and newly introduced C ant calculation approaches like the TrOCA or the TTD (V ázquez- Rodríguez et al., 2009).
This modified method to calculate C ant has the potential to be further improved by considering some of the following: a) incorporating a model of the spatial variability of the R C stoichiometric ratio, which is presently assumed to be constant; b) applying a more robust and elaborate eOMP mixing analysis to convey the A • T and ∆C dis into the ocean interior.The OMP should include more end-members in accordance with the complexity of the circulation and mixing phenomena that occur in the Atlantic and, particularly, in the Southern Ocean; c) Refining the proposed ∆∆C dis model.
Regarding ∆∆C dis , clear discrepancies between the estimates from this study and Matsumoto and Gruber (2005) have been described for the subtropical gyres.In addition, some studies (Lef èvre et al., 2004;Olsen et al., 2006) point towards a net decrease of the ∆f CO 2 gradient in the subpolar gyres, which is likely caused by the recent changes of the Northern North Atlantic circulation patterns (Curry and Mauritzen, 2005).This ∆f CO 2 trend would be opposite to one that can be expected from the WMLD approximation adopted in this work.Thence, a further refined function for ∆∆C dis based on observations or synthetic data from OGCMs would be desirable.This Introduction

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Full discrepancy between the detected decrease in the pCO 2 gradient and the supposed increase in ∆C dis over time could stem from the separation between the natural and anthropogenic CO 2 signal.Unfortunately, these signals are impossible to discern using observational data and can only be estimated with the help of 3-D OGCMs.This is intended as prospective work.

Appendix A
The eOMP analysis is a method used to estimate the mixing proportions of a set of end-members that make up a particular water sample.It is desirable (but not compulsory) that the end-members are actually source water types (SWT) to grant some robustness to the eOMP.The use of eOMP is recommended (compared with the classical OMP) when the water mass analysis has a basin-wide breadth, or if the SWTs are to represent conditions in WMF regions remote from the region under investigation, meaning that biogeochemical changes can no longer be disregarded and have to be included in the analysis.
To resolve the mixing problem, the eOMP approach poses a set of linear equations built from conservative and non-conservative variables (Table 3) to conform an equation system that is solved by minimizing its residuals using a non-negative least square routine.In this study the tracers taken as conservative are θ, S and silicate whilst the non-conservative ones are oxygen, nitrate and phosphate.The conservative behaviour of silicate is assumed for eOMP resolution purposes given the high silicate values of the southern end-members compared to the northern ones (Table 3).Consciously of such north-south silicate gradient, assuming a conservative behaviour for silicate constitutes a plausible approximation because its biological perturbation would be negligible compared to the variability generated by the physical mixing.Each equation in to highly weighed equations are largely minimized (Poole and Tomczak, 1999).An inherent constraint to the system of equations is that the number of end-members that can be considered in an eOMP to resolve their mixing really depends on the number of variables available.Hence, given the set of seven (six plus the mass constraint) eOMP equations in Table 3, six end-members were defined in this work to resolve the mixing through the length of the Eastern Atlantic basin.They have been named as N1, N2, S1, S2, Weddell Sea Deep Water (WSDW) and Circumpolar Deep Water (CDW) (Figs. 2 and 7).
The mixing of northern water masses in the Eastern Atlantic basin has been simplified in this work by defining the N1 and N2 end-members (Figs. 2 and 7).Although none of them represents any known water source, they were characterized from the observed upper limits of the salinity and temperature variability ranges.Rigorously speaking, N1 is made up of about 13% of MW and 87% of LSW, which is one of the most important components of NADW.The N2 end-member has very similar thermohaline characteristics to the Denmark Strait Overflow Water (DSOW) that forms in the Greenland Sea (Strass et al., 1993).The Iceland-Scotland Overflow Water (ISOW: 1.9 • C, 34.98) ( Álvarez et al., 2004) can also be found along the mixing line established between N1 and N2.
On the Southern Ocean end, the linear mixing of different proportions of the S1 and S2 end-members can yield several water masses that form in the upper South Atlantic, namely: Antarctic Intermediate Water (AAIW), Sub-Antarctic Mode Water (SAMW), Ice Shelf Water (ISW) and Winter Water (WW) (Brea et al., 2004;Lo Monaco et al., 2005).Moreover, some deep-waters like the CDW and the Weddell Sea Deep Water (WSDW) are also found on this end of the Atlantic (Figs. 2 and 7).The CDW forms from the mixing of WSDW with deep waters from the three major oceans in the Antarctic Circumpolar Currents (Broecker et al., 1985;Onken, 1995;Brea et al., 2004).On the other hand, WSDW is formed from the mixing of ISW and the overlying Warm Deep Water in the Weddell Sea (Onken, 1995).The thermohaline type values of CDW listed in Table 3 were taken from measurements made at the Drake Passage (Broecker et al., 1985).In the case of the type values for nitrate, phosphate and silicate for the six end-members in Fig. 7, they were obtained by extrapolation of the ad hoc properties from regression lines with S and θ (Poole and Tomczak, 1999).Afterwards, these preliminary type values were run through an iterative process as in Álvarez et al. (2004) in order to refine the estimates.
The A • T and ∆C dis type values in Table 3 were calculated by first identifying each end-member within the subsurface layer and then applying Eqs. ( 1) and ( 2), respectively.In the case of CDW, the former procedure to calculate A • T and ∆C dis cannot be applied.Even though the θ and S type values of this end-member are enclosed within the observed thermohaline subsurface variability (Figs. 2,3a and b), the fact that this water mass forms off-bounds the Atlantic basin from the mixing of WSDW with deep waters from the three major oceans requires treating it separately.The θ-S type values for CDW here used (Table 3) were obtained from measurements at the Drake Passage (Broecker et al., 1985).To estimate the ∆C dis and A • T type values, the CDW was decomposed into its constituent proportions of North Atlantic Deep Water (NADW), Antarctic Intermediate Water (AAIW) and WSDW, after Broecker et al. (1985).According to Broecker et al. (1985) the CDW is formed by deep mixing of 25%, 45% and 30% of Northern component, Southern component and AAIW, respectively.The Southern component in Broecker et al. (1985) corresponds with the WDSW end-member in the present work, while the so-called Northern component is made up of 60% of N1 and 40% of the N2 end-members in this study.Finally, the AAIW in Broecker et al. (1985) would correspond to a mix of 93% of S1 and 7% of S2.
The obtained eOMP results show high correlation coefficients (R 2 , Table 3) and low standard errors of the residuals (Table 3) with the measured tracer concentrations.This means that the simplified mixing model here presented is able to reproduce with a high degree of confidence the physical and chemical variability observed in the Eastern Atlantic basin.In terms of reliability, the results here obtained are comparable to those in other studies, such as in Karstensen and Tomczak (1998) or Álvarez et al. (2004), for example.flow Water by mixing in the East Greenland Current, J. Geophys.Res., 98, 6907-6919, 1993. Takahashi, T., Sutherland, S. C., Sweeney, C., Poisson, A., Metzl, N., Tilbrook, B., Bates, N., Wanninkhofe, R., Feely, R. A., Sabine, C., Olafsson, J., and Nojiri, Y., Global sea-air CO 2 flux based on climatological surface ocean pCO 2 , and seasonal biological and temperature effects, Deep Sea Res.Pt.II, 49, 1601II, 49, -1622II, 49, , 2002.Thomas, H. and Ittekkot, V.: Determination of anthropogenic CO 2 in the North Atlantic Ocean using water mass ages and CO 2 equilibrium chemistry, J. Mar. Sys., 27, 325-336, 2001. Touratier, F., Azouzi, L., and    The correlation coefficient (R 2 ) between eOMP results and observed properties and the standard errors of these estimates are also listed.All type values and standard errors are given in µmol kg −1 except for θ ( • C) and S. Notice that neither the A • T nor the ∆C dis equations (dark grey shade) belong to the system of equations for the eOMP (no weight assigned).The type values here listed were calculated a posteriori and are given as reference for the end-members here chosen.          2 showing the end-members defined to resolve the eOMP and the mixing lines between North Atlantic, South Atlantic and Southern Ocean waters.In order to differentiate Arctic waters from Antarctic waters in the mixing problem the samples were colour-graded according to their latitude of precedence.

•
T and the extent of air-sea CO 2 and O 2 equilibria.The original backcalculation methods assumed full-saturation of water masses in terms of oxygen, CO 2 T parameterizations have been previously proposed, like the ones from Gruber et al. (1996) or Millero et al. (1998), based on surface A T observations gathered normally during the summer or spring.It has been shown by other authors that these parameterizations yield systematic negative ∆A T =A T −A • Given this definition, positive ∆C dis values represent sea outgasing of CO 2 and negative values indicate CO 2 uptake by the ocean.The subsurface ∆C dis distribution in Fig. 3f resembles very much the one derived from the pCO 2 climatology of Takahashi et al. (2002) except for the high latitude areas, where the climatology lacks data (especially during wintertime).
∆C t dis =a + b(θ−10) + c(S−35) + d (NO−300) + e(PO−300) 4 Pg C yr −1(Sabine et al., 2004) would produce an annual increase on the average oceanic C ant specific inventory of 0.46 mol C m −2 yr −1 .Knowing that the globally averaged gas exchange coefficient for CO 2 is ∼0.052±0.015mol C m −2 yr −1 µatm −1(Naegler et al., 2006), implies that the global average air-sea ∆f CO 2 induced by the anthropogenic CO 2 fraction would Introduction would yield a ∆∆C dis ≈−6 µmol kg −1 .Likewise, subpolar regions with WMLD of ∼500 m or larger have average C ant concentrations of ∼40µmol kg −1 .The estimated ∆∆C dis as of Matsumoto and Gruber (2005) would be of −4 µmol kg −1 .However, model-derived synthetic data given in Fig. 8b from Matsumoto and Gruber (2005) yield estimates of∆∆C dis ≈0 and −10 µmol kg −1 for the subtropical areas and subpolar areas, respectively.These contradictions suggest that the proportionality factor β/k ex should not be constant.Matsumoto and Gruber (2005) have acknowledged the effects of their approximation and have indicated a possible improvement for it: β/k ex could be deter- 5) The term of C ant saturation (C sat ant =S/35(0.85θ+46.0), and calculate the mean of Atlantic subsurface estimates for the "C ant /C sat ant |∆C t dis |" part in Eq. (4) (−9.5±0.3 µmol kg −1 is obtained).Considering the above calculations, a value of ϕ=0.55±0.10 is finally

π
dis given in Eq. (5) into Eq.(9) and rearranging terms, we obtain a modified back-calculation equation for estimating C ant :C ant = ∆C * −∆C t dis 1 + ϕ ∆C t dis /

•
T method.To add to the discussion, LoMonaco et al. (2005) have presented estimates of C ant in the Southern Ocean of 20 µmol kg −1 on average, which are even higher than the ϕC • T values for the bottom samples south of the Antarctic polar front.Lo Monaco et al. (2005) applied a classical back-calculation approach in which the effect of sea-ice on air-sea oxygen equilibrium was considered.In addition, their method implicitly parameterizes the ∆∆C dis although they consider a homogeneous spatial distribution of it, like for the air-sea O 2 disequilibrium case on ice-covered surface waters.Nevertheless, their C ant distributions along the WOCE I06-Sb line are in very good agreement −1 ) are located in the subtropical gyres, where C ant estimates are close to saturation values.This represents a clear discrepancy with model results presented by Matsumoto and Gruber (2005) of approx.−2 µmol kg −1 for the same area.Nonetheless, these warm surface waters (above 13 • C) represent only ∼3.6% of the Atlantic volume and this divergence would yield a minor dissimilarity of 0.023 Gt of C ant in terms of total inventory.Alternatively, the ∆∆C dis values in the high latitudes are moderate (around 4 and 6 µmol kg −1 for the Southern Ocean and Nordic Seas, respectively).These results are in good agreement with the surface ∆∆C dis estimates shown in Matsumoto and Gruber (2005) and will have a remarkable impact in terms of inventory because of the penetration of moderate amounts of C ant in the large volume of the Southern Ocean.

•
T method does not consider the ∆C dis and A • T as constant terms, like the method in Lo Monaco et al. (2005).Considering the above-cited elements could decrease C ant inventories from Lo Monaco et al. (2005) in roughly 6-9 mol C m −2 and get them closer to the rest of estimates.

Fig. 1 .
Fig. 1.Map showing Atlantic cruises used to characterise the subsurface layer.The cruises denoted by stars were also selected for testing the adequacy of proposed modifications in C ant estimation (Sect.4).

Figure 4 .Fig. 2 .Figure 5 .Fig. 3 .
Figure 4. T/S diagram of the Atlantic from the studied data set.Red circles represent South Atlantic sub-surface waters; blue circles are North Atlantic sub-surface waters.The smaller dark dots represent all water column (depth >200 dbar) T/S samples.The smaller light grey dots are the uppermost 25 meters surface waters showing a clear distinction from the rest of the tighter bulk of samples.The thick yellow diamonds joined by the red line are the endmembers that define the mixing triangle used to resolve the influence of MW.The thick orange triangles joined by the green line are the end-members used in the OMP mixing analysis applied to waters with θ<5º C (refer to section 4.3.2 for details).

Figure 6 .
Figure 6.Distributions of computed CaCO 3 dissolution (µmol•kg -1 ) using: a) the A T º parameterization from L'03; and b) the A T º parameterization given in equation (1) fro m this study.

Fig. 5 .
Fig. 5. C ant distributions (µmol kg −1 ) of the Eastern Atlantic basin calculated with: (a) The ϕC • T method and (b) The ∆C * method as of Lee et al. (2003) for latitudes below 60 • N, where their A • T parameterization is valid.Negative C ant estimates are omitted and shown as blank areas.The thick white isoline in (a) and (b) is the 5 • C isotherm to indicate the regions where A •T and ∆C dis are calculated with different procedures, according to the ϕC • T method.The effect of the "ϕ" term in individual C ant estimates is shown in (c) (in µmol kg −1 ).This was calculated by subtracting C ant calculated from Eq. (10) with ϕ=0 and then ϕ=0.55.The results have been referenced to 1994.

Figure 10 .Fig. 6 .
Figure 10.Comparison of specific C ant inventories (mol C•m -2 ) for the Eastern Atlantic calculated using: The ∆C* method from GSS'96 (green line); The ∆C* method as of L'03 (blue line); The ϕC T º method (red line).All three inventories have been averaged by latitude bands and referenced to 1994, after L'03.Orange line with open circles depicts the combined effects of CaCO 3 and temperature shifts introduced in PA T º.The grey line with open squares represents the individual contribution of the φ term to the ϕC T º specific inventory when φ=0.

Figure 7 .
Figure 7.A detailed view of the cold (θ <5 ºC) end from the TS diagram in Fig. 4 that is used to spot the end-members defined to resolve the eOMP.The samples are color coded according to their latitude of precedence to differentiate Arctic and Antarctic waters in the mixing problem.

Fig. 7 .
Fig. 7.A detailed view of the cold end (θ<5• C) of the TS diagram in Fig.2showing the end-members defined to resolve the eOMP and the mixing lines between North Atlantic, South Atlantic and Southern Ocean waters.In order to differentiate Arctic waters from Antarctic waters in the mixing problem the samples were colour-graded according to their latitude of precedence.
and in Figures are 9 and 6 µmol kg −1 , respectively.Figures Table3was properly weighed according to the following criteria: tracers having the most accurate analytical determinations and/or lowest environmental variability were assigned the largest weights.By doing so, the residuals associated Introduction

Table 1 .
Goyet, C.: CFC-11, ∆14C and 3 H tracers as a means to assess anthropogenic CO 2 concentrations in the ocean, Tellus, 59B, 318-325, doi:10.1111/j.1600-List of selected Atlantic cruises (Fig.1).Only data collected at depths greater than 100 m was used for calculations.Surface layer data was discarded to avoid the influence of seasonal variability on C ant estimates.
Acronyms and superscripts denote the following: a Y=measured values available; b N=measured values unavailable; c NA=no adjustment made; d Y+Calc=When direct measurements were unavailable, A T was calculated from C T and pH measurements, using the thermodynamic relationships of the carbon system; e =Correction in µmol kg −1 , after ORNL/CDIAC 148 report Introduction

Table 2 .
Coefficients and statistics for the Multilinear Regression (MLR) of ∆C dis vs. conservative parameters (Eq.3).Except for θ ( • C) and S, all other variables and standard errors are given in µmol kg −1 .N stands for the number of valid points used for the fit, and R 2 is the correlation coefficient of the adjustment.The standard error of the estimate was calculated as

Table 3 .
The equations, weights and type values of the selected end-members for the eOMP.