Temporal trends in oceanic dissolved inorganic carbon (DIC) and δ13C-DIC were reconstructed along five isopycnals in the upper 1000 m of the North Atlantic Ocean using a back-calculation approach. The mean anthropogenic DIC increase was 1.21 ± 0.07 μmol kg−1 yr−1 and the mean 13C decrease was −0.026 ± 0.002‰ yr−1, both in good agreement with the results from previous studies. The observed δ13C-DIC perturbation ratio is −0.024 ± 0.003‰ (μmol kg−1)−1. Our results indicate that the North Atlantic is able to maintain equilibrium with the anthropogenic perturbation for DIC and follows it with decadal time lag for δ13C. A CFC-calibrated one-dimensional isopycnal advection-diffusion model is used to evaluate temporal DIC and δ13C trends and perturbation ratios of the reconstructions. We investigate the time history of the air-sea CO2 and 13C disequilibria in the North Atlantic and discuss the importance of physical and biological processes in maintaining them. We find evidence that the North Atlantic Ocean is characterized by enhanced uptake of anthropogenic CO2. Also, we use the model to examine how the time rate of change of δ13C depends on changes in the temporal evolution of δ13C in the atmosphere. The model evolution explains the curious result that the time rate of change of surface water δ13C in the North Atlantic Ocean can exceed that observed concurrently in the atmosphere. Finally we introduce a powerful way of estimating the global air-sea pCO2 disequilibrium based on the oceanic δ13C-DIC perturbation ratio.
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 Human activities, such as burning of fossil fuels and land use changes, have emitted (and will continue to emit) anthropogenic CO2 that is strongly depleted in the carbon isotope 13C due to the preferential uptake of the light carbon isotope 12C during the photosynthetic carbon fixation by plants. The resulting dilution of the atmospheric 13C/12C ratio by anthropogenic CO2 emissions is known as the “13C Suess effect” in analogy to (anthropogenic and natural) removal effects for the radioactive carbon isotope 14C in atmospheric CO2 first described by Suess . The oceanic 13C Suess effect, i.e., the decrease of the δ13C of dissolved inorganic carbon (DIC) as a consequence of CO2 exchange with the atmosphere, provides a means of quantifying the oceanic uptake rate of anthropogenic CO2 [Quay et al., 1992; Heimann and Maier-Reimer, 1996; Bacastow et al., 1996].
 Direct observation of anthropogenic changes in DIC and δ13C-DIC is hampered by a huge natural background (DIC) as well as significant seasonal and interannual variability and thus has only been feasible at two time series stations [e.g., Bates et al., 1996; Bacastow et al., 1996; Winn et al., 1998; Gruber et al., 1999; Bates, 2001]. Quantification of the oceanic Suess effect has proven to be particularly difficult due to the scarcity of quality historical δ13C data. However, several promising methods have been proposed that exploit the information contained in oceanic 13C measurements to quantify the ocean's uptake rate of CO2 [Quay et al., 1992; Tans et al., 1993; Bacastow et al., 1996; Heimann and Maier-Reimer, 1996; Gruber and Keeling, 2001]. In most of these the determination of the oceanic 13C Suess effect is critical. This importance has stimulated development of a method to determine the oceanic 13C Suess effect from present-day data only using a back-calculation technique to reveal preformed δ13C-DIC values, whose temporal changes are estimated from water mass ages based on concurrent CFC measurements [Sonnerup et al., 1999b].
 As pointed out by Heimann and Maier-Reimer  the strong similarity of the atmospheric perturbation histories of CO2 and 13C (Figure 1) implies that the penetration of both oceanic perturbations must be similar. The relationship between changes in DIC and δ13C-DIC in the ocean should therefore reflect the atmospheric perturbation history of these tracers convoluted by the relative equilibration rates of these two tracers. Keir et al.  have pointed out that the global relationship between oceanic DIC and δ13C-DIC changes provides a constraint on CO2 exchange times between the atmosphere and the terrestrial biosphere. Unfortunately, knowledge of the relation between oceanic δ13C and DIC changes is inadequate. Because the equilibration times of DIC and δ13C between surface ocean and atmosphere differ by one order of magnitude, variability in surface water residence time with respect to gas exchange and circulation results in spatial variability of the oceanic δ13C-DIC perturbation ratio. While the global relationship may lie near 0.016‰ (μmol kg−1)−1 [Heimann and Maier-Reimer, 1996], a recent study found that this ratio can vary substantially and could be as low as 0.007‰ (μmol kg−1)−1 over much of the southern ocean [McNeill et al., 2001].
 In this paper, we use the back-calculation approach of Sonnerup et al. [1999b] and extend it to DIC to estimate “preformed” δ13C-DIC and DIC values along five isopycnals in the North Atlantic Ocean. Using apparent CFC ages we reconstruct the temporal changes in these preformed properties. Next we explore the relationship between preformed DIC changes and preformed δ13C changes in the North Atlantic Ocean. We use a simple, one-dimensional (1D) thermocline ventilation model to evaluate this relationship from a thermodynamic perspective and in the context of other published results. Finally we discuss the utility of our North Atlantic δ13C-DIC perturbation ratio in determining exchange times in the terrestrial biosphere and in quantifying ocean uptake of fossil-fuel CO2.
 Our analyses were carried out using the data acquired during the 1993 Ocean Atmosphere Carbon Exchange Study (OACES) cruise of R/V Malcolm Baldrige from 5°S to 65°N along 20°–29°W in the North Atlantic (4 July–30 August 1993). The data were retrieved from the NOAA Atlantic Oceanographic and Meteorological Laboratory (Miami, Florida, USA) public data server (http://www.aoml.noaa.gov/ocd/oaces/bottle_data.html).
 A systematic offset in the Winkler oxygen data was removed by adding 7.5 μmol kg−1, as suggested in the data description file and by Wanninkhof et al. . Apparent oxygen utilization (AOU) was calculated as the difference between the oxygen solubility (calculated after Weiss ) at the sample's temperature and salinity, and the sample's measured oxygen concentration. Although the measurement error of oxygen (after correction of the systematic offset) is only ∼1 μmol kg−1, the error in AOU is dominated by the error in the assumption of oxygen saturation at the surface outcrop. Gruber et al.  estimated an error of 4 μmol kg−1 based on the observed deviation of wintertime surface oxygen concentrations from saturation.
 Dissolved inorganic carbon (DIC) was measured by coulometric titration following extraction of the CO2 with an automated system known as SOMMA [Johnson et al., 1993]. Total alkalinity (AT) was determined by potentiometric titration with a system described in detail by Millero et al. . Based on regular measurements of certified reference material provided by Andrew Dickson from Scripps Institution of Oceanography (La Jolla, California, USA) the estimated accuracy of the carbon system parameters is 1.5 μmol kg−1 for DIC and 2.5 μmol kg−1 for AT [Millero et al., 1998; Wanninkhof et al., 1999].
 The δ13C-DIC samples were poisoned with HgCl2 immediately after collection. The CO2 was extracted to 100 ± 0.5% using a helium stripping technique at the University of Washington, and the 13C/12C ratio of the extracted CO2 was later measured on a Finnigan MAT 251 isotope ratio mass spectrometer. The overall precision of δ13C analyses was ± 0.02‰ based on replicate analyses of standards and seawater samples [Quay et al., 1992].
 Shipboard analyses of chlorofluorocarbons CFC-11 (CCl3F) and CFC-12 (CCl2F2) were performed by a purge-and-trap extraction technique followed by gas chromatography with electron capture detection [Bullister and Weiss, 1988]. The precision of these analyses, based on measurements of replicate samples, is 0.01 pmol kg−1 or 1%, whichever is greater. Apparent CFC ages were obtained by converting measured CFC concentrations to equivalent air concentrations using known solubility relationships [Warner and Weiss, 1985]. These concentrations are compared with the atmospheric concentration history [Walker et al., 2000] to obtain an apparent CFC age [Doney and Bullister, 1992].
 Water column data from all stations along the transect were interpolated linearly onto isopycnal surfaces from samples collected above and below. A history of annual mean atmospheric CO2 concentrations was constructed from the Mauna Loa record of Keeling and Whorf , covering the period from 1959 to the present, and the Siple Station ice core data of Neftel et al.  for the period 1744–1953. The 1000-year high precision record of Francey et al.  provided the history of atmospheric δ13C-CO2. A sixth order polynomial fit function for the CO2 versus δ13C-CO2 relationship (Figure 1) described by Francey et al.  was used to compute a history of annual mean δ13C-CO2 from the combined Mauna Loa/Siple Station CO2 record.
 Climatological data for temperature, salinity, wind speed, and mixed layer depth were used to estimate the outcrop latitude of each modeled isopycnal, and to force the advection-diffusion model. Sea surface temperature [Levitus and Boyer, 1994] and salinity [Levitus et al., 1994] were taken from the Word Ocean Atlas 1994 (monthly 1° by 1° averages) and used to compute the wintertime maximum density along the meridional section. The location, where a wintertime density matching the isopycnal density was found, was taken as the outcrop location of that isopycnal. At each isopycnal's outcrop location representative data for sea surface temperature and sea surface salinity were taken from the World Ocean Atlas 1994 climatology data. Representative wind speed data (monthly 2° by 2° averages) were retrieved from the Comprehensive Ocean-Atmosphere Data Set (COADS) Release 1 Data Set. Finally, mixed layer depths, calculated with a fixed density criterion (Δσ = 0.125 kg m−3), were taken from the World Ocean Atlas 1994 additional data [Monterey and Levitus, 1997].
3. Reconstruction of DIC0 and δ13C0 Along Isopycnals
3.1. Calculation Procedures
 The calculation of preformed DIC (DIC0) and δ13C-DIC (δ13C0) values, i.e., values which formed during the last contact with the atmosphere, requires quantification of biologically mediated changes in these quantities after removal from atmospheric contact. Biologically mediated changes in DIC are due to remineralization of organic matter and dissolution of biogenic carbonates at depth. A sample's AOU can be converted into the concurrent DIC increase using the stoichiometric Corg/−O2 ratio of respiration, also referred to as “Redfield” ratio [Redfield, 1934; Redfield et al., 1963]. By definition, the DIC change due to carbonate dissolution is half the resulting change in total alkalinity [Pilson, 1998]. The latter can be estimated from the difference between the observed sample alkalinity (ATmeas) and the preformed alkalinity (AT0) in the water mass' outcropping area. A minor correction has to be applied to take account of the proton flux associated with the respiration of organic matter, which can be regarded as an in situ titration of total alkalinity. This correction is calculated from the Redfield N/−O2 ratio of respiration and AOU. Hence, as originally suggested by Brewer , DIC0 can be calculated as follows:
 The calculation of preformed DIC further requires estimation of a sample's preformed alkalinity (AT0). This is feasible on the basis of a multilinear regression on temperature and salinity. For details see Appendix A.
 Calculation of preformed δ13C-DIC (δ13C0) is similar to that of DIC0, except it requires estimates of the isotopic composition of the added organic matter and inorganic carbon [Kroopnick, 1985]
where δ13C is the δ13C of DIC, δ13Corg is the δ13C of organic matter produced during primary production, and is the δ13C of biogenic carbonates. The latter is typically within ± 1‰ of δ13C of surface seawater DIC [Bonneau et al., 1980]. Hence, calcification and carbonate dissolution have very little effect on the δ13C and, unlike for DIC0, the alkalinity terms in equation (3) can be neglected [Sonnerup et al., 1999b]
Equation (4) thus only requires knowledge of the δ13C of organic matter produced during primary production. As an approximation we used the δ13C of particulate organic matter which is typically of the order of −20‰ in most of the world oceans. We calculated δ13Corg values for two latitude belts covering the study area from the data compiled by Goericke and Fry : Equator-20°N: −19.8 ± 0.9‰; 20°–65°N: −21.1 ± 1.8‰.
3.2. Isopycnal DIC0 and δ13C0 Distributions
 We have chosen five isopycnals (σθ = 26.60, 26.80, 27.00, 27.20, and 27.40 kg m−3) along the 20°–29°W meridional transect in the North Atlantic, which are found at depths between 90 and 950 m (Figure 2) and thus in a domain of the ocean which is dominated by wind-driven circulation. Estimated outcrop locations cover the latitude range 36°–59.5°N. Apparent CFC-11 ages in subsurface samples at the outcrop locations are 1–6 years (Figure 3) and increase southward to maximum values of 22–45 years at 5°–10°N. CFC concentrations reached values near the detection limits (0.005–0.01 pmol kg−1) only at the southern edge on the deepest isopycnal σθ = 27.40. Given the significantly longer atmospheric history of the CO2/13C perturbation, all waters encountered on these isopycnals during this cruise must contain some anthropogenic CO2.
 Preformed DIC (DIC0) and δ13C-DIC (δ13C0) were calculated using equations (2) and (4). Regressions of DIC0 and δ13C0 versus the apparent CFC-11 age show fairly consistent trends on all isopycnals (Figure 4). The mean DIC0 versus CFC-11 age trend of 1.21 ± 0.07 μmol kg−1 yr−1 (Table 1) corresponds reasonably well with direct observations of the DIC increase: 1.7 μmol kg−1 yr−1 at the Bermuda Atlantic Time series Study (BATS) site [Bates et al., 1996] and 0.72–1.37 μmol kg−1 yr−1 at the Hawaii Ocean Time series (HOT) site [Winn et al., 1998]. It is slightly faster than the equilibrium DIC increase of 1.0 μmol kg−1 yr−1 calculated for a mean Revelle factor of 9.5 and a mean annual increase in atmospheric CO2 concentrations of 1.5 ppmv yr−1 [Keeling and Whorf, 2000].
Table 1. The Temporal Change of DIC0 and δ13C0 Based on Apparent CFC-11 Ages for Five Isopycnals on a Meridional Section Along 20°–29°W in the North Atlantic Ocean
Temporal DIC0 Trend
Temporal δ13C0 Trend
Data, μmol kg−1 yr−1
Model, μmol kg−1 yr−1
Data, ‰ yr−1
Model, ‰ yr−1
1.25 ± 0.09
−0.024 ± 0.002
1.12 ± 0.07
−0.027 ± 0.003
1.23 ± 0.06
−0.029 ± 0.002
1.28 ± 0.05
−0.025 ± 0.001
1.17 ± 0.05
−0.026 ± 0.001
1.21 ± 0.07
0.96 ± 0.05
−0.026 ± 0.002
−0.029 ± 0.003
 The mean δ13C0 versus CFC-11 age trend of −0.026 ± 0.002‰ yr−1 compares favorably with trends of −0.025 ± 0.002‰ yr−1 at Station “S” near Bermuda [Bacastow et al., 1996; Gruber et al., 1999] and −0.025 ± 0.002‰ yr−1 at station ALOHA (23°N, 158°W) in the North Pacific Ocean [Gruber et al., 1999]. Quay et al.  found a trend of −0.020‰ yr−1 (0.4‰ over the 20-year period 1970–1990) in the Pacific Ocean. The reconstruction of the method of Sonnerup et al. [1999b] on σθ = 27.2–27.4 in the North Atlantic was based on the same technique and data set but restricted to a smaller latitude band, only four data points, and gave slightly slower temporal changes of −0.018 ± 0.002‰ yr−1. Our temporal δ13C0 trend almost exactly matches the atmospheric Suess effect of −0.027 ± 0.001‰ yr−1 for the period 1962–1993 (calculated from the southern hemisphere 13CO2 record of Francey et al. ), and is indicative of a rather slow overturn of local surface waters in the North Atlantic Ocean [Bacastow et al., 1996]. All of these estimates based on changes in δ13C-DIC are higher that the 0.018‰ yr−1 change found in a Sclerosponge further south near Jamaica (18°N, 77°W) during 1970–1990 [Druffel and Benavides, 1986; Böhm et al., 1996].
 Generally, our temporal trends of DIC0 and δ13C0 fall on the high end of the range of published values. They should be regarded as upper limits because CFC-11 ages of >25 yr are biased young due to the non-linear trend in atmospheric CFC-11 prior to 1968 [Doney and Bullister, 1992; Sonnerup, 2001]. This effect is likely negligible on the shallow isopycnals σθ = 26.6 and 26.8, but on deep isopycnals may explain some of the discrepancy with the results of the study of Sonnerup et al. [1999b], which were restricted to ages of ≤17 years in the North Atlantic.
 Another potentially biasing effect is two-end-member mixing that occurs along the isopycnals. As no mixing correction was applied, any difference between northern and southern end-member values of preformed DIC and δ13C lead to a bias in the inferred temporal changes of DIC0 and δ13C0. Clearly, the smaller the differences in the end-member preformed values, the smaller is the resulting bias. Körtzinger et al. [2001a] provide end-member values for potential temperature θ and DIC of three isopycnals (σθ = 27.0–27.2) in the Atlantic Ocean which can be used to assess the size of the mixing error. The fractions of the northern (fN) and southern end-member (fS) present at the southern edge of our data domain can be calculated from the end-members' preformed temperatures (θN0 and θS0) and the potential temperature θ at the southern edge
 Based on these calculations, on isopycnals σθ = 27.0 and 27.2 about 40% of southern end-member water has been admixed at the southern edge around 5°–10°N. As the differences in present-day DIC0 between the northern and southern end-member are about 11 μmol kg−1, the mixing-related DIC change along the sampled part of the isopycnals is 4–5 μmol kg−1 at most. Based on this comparison of present-day DIC end-members, the resulting bias in the observed temporal tends of DIC0 is <10%. As this bias tends to decrease the temporal trend, it partially offsets the bias toward faster changes favored by underestimation of water mass ages. Wintertime surface δ13C-DIC values are in the same range (1.7–2.2‰, Figure 2 in Gruber et al. ) in the isopycnals' outcrop areas in the northern (36°–60°N) and southern (40°–50°S) hemispheres. Hence mixing likely has an even smaller effect on temporal δ13C0 trends. In summary, although we cannot rule mixing biases out, we conclude that they are small and may be compensated by the previously discussed errors in apparent CFC ages.
 The “preformed-preformed” relationship between δ13C0 and DIC0 is fairly consistent on all isopycnals with a mean value of −0.024 ± 0.003‰ (μmol kg−1)−1 (Figure 5 and Table 2). This implies larger relative δ13C decreases than the model results of Heimann and Maier-Reimer  using the three-dimensional Hamburg model of the oceanic carbon cycle HAMOCC 3. Their global ocean model results split into two trends of −0.016 and −0.019‰ (μmol kg−1)−1 (calculated from their Figure 6), which may reflect some regional variability. Keir et al.  found a slope of −0.016‰ (μmol kg−1)−1 for a group of stations in the Northeast Atlantic Ocean based on anthropogenic CO2 [Körtzinger et al., 1998] and their reconstruction of anthropogenic δ13C changes based on phosphate. Combination of temporal trends of DIC and δ13C at stations BATS and HOT/ALOHA (see above) yields perturbation ratios of −0.015‰ (μmol kg−1)−1 and −0.024‰ (μmol kg−1)−1, respectively. These numbers, however, have a large uncertainty mainly due to the errors of the DIC trends. In the Southern Ocean, the δ13C0 to DIC0 change ratio was much smaller, ranging from 0.015 ± 0.005‰ (μmol kg−1)−1 at 42°S down to 0.007 ± 0.005‰ (μmol kg−1)−1 at 54°S [McNeill et al., 2001].
Table 2. The “Preformed-Preformed” Relationship Between δ13C0 and DIC0 for Five Isopycnals on a Meridional Section Along 20°–29°W in the North Atlantic Ocean
CFC age range, yr
δ13C0 versus DIC0
Data, ‰ (μmol kg−1)−1
Model, ‰ (μmol kg−1)−1
−0.026 ± 0.006
−0.026 ± 0.004
−0.022 ± 0.001
−0.022 ± 0.001
−0.022 ± 0.002
−0.024 ± 0.003
 The theoretical relationship between δ13C and DIC in an ocean fully equilibrating with the CO2 and 13C perturbations is shown in Figure 6. The tracer relationship shows two distinct slopes of −0.024 ± 0.001 and −0.032 ± 0.001‰ (μmol kg−1)−1 during 1006–1968 and 1971–1993, respectively. This change in the slope between the atmospheric perturbations around 1970 (Figure 1) can already be seen in the record of Francey et al.  who do not offer an explanation for it. However, this slope change exactly coincides with the time when – based on the results of several models [McGuire et al., 2001] – the terrestrial biosphere changed dramatically from more or less neutral to a net CO2 sink. It can be speculated that the change in the atmospheric tracer relationship (and in the ocean) reflects the change in the net terrestrial CO2 flux.
 The different perturbation relationships for the two time periods are reflected in our isopycnal reconstructions which range in apparent water mass ages between 22 years on shallow isopycnals (σθ = 26.60) and >45 years on deeper isopycnals (σθ = 27.40) and exhibit steeper slopes on younger isopycnals (σθ = 26.60 and 26.80). Our results show δ13C0 versus DIC0 slopes which are steeper than those found by Heimann and Maier-Reimer  and Keir et al.  and closer to a scenario where the surface ocean DIC and δ13C changes are in equilibrium with the atmosphere. Such a situation is likely not typical for the global ocean, and the North Atlantic may thus represent an upper extreme in the observed perturbation ratio. The inferred slow overturning in the North Atlantic can only be explained by the thermohaline circulation which leads to a net northward near surface transport of waters which remains in contact with the atmosphere for a considerable period of time, obviously long enough to permit full equilibration with both tracer signals. We study the reason for this finding using a numerical advection-diffusion model in section 4. We will also discuss the implications of these results in more detail in section 6.
4. Modeling of DIC0 and δ13C0 Along Isopycnals
4.1. Advection-Diffusion Model
 We use an advective-diffusive scheme to describe the meridional evolution of chemical tracers such as CFC-11 and CFC-12, and to reconstruct anthropogenic changes of DIC and the 13C/12C ratio of DIC along selected isopycnal horizons in the Atlantic Ocean
Here C represents the tracer concentration, v is the equatorward meridional component of the along-isopycnal advection velocity, K is the along-isopycnal eddy diffusivity, t is time, and x is the meridional distance.
 The model uses a 1° latitudinal spacing and is marched forward in time using a 1-month time step. The temporal change of tracer concentrations is calculated using centered in time, centered in space (CTCS, or “leapfrog”) differencing of the advection terms and the DuFort-Frankel scheme for the diffusion terms [Fletcher, 1988; Sonnerup et al., 1999a]. Here we run the model beginning in 1934 and 1765 for CFCs and anthropogenic CO2/13C, respectively. The model's transport parameters, v and K, are varied to fit the CFC-11 and CFC-12 distribution in 1993, as measured during the OACES cruise, to the North Atlantic Ocean (20°W). The CFC-calibrated model is then used to predict the distribution of anthropogenic DIC and δ13C changes.
 The boundary condition applied at the outcrop box assumes that the surface seawater remains at the degree of equilibrium with atmospheric CFC-11 and CFC-12 observed on these isopycnals at the outcrop location during the 1993 cruise. We assumed an outcropping period of 3 months for CFCs and used winter month averages (JFM) of climatological T and S. The calibration of the model's transport parameters is sensitive to the along-isopycnal slope of the CFC profile rather than absolute CFC concentrations. The model calibration is nearly insensitive to the length of the outcropping period. Using a 12 month per year outcropping period, with annual means of T and S, yielded virtually identical velocities and diffusivities as the 3 months per year outcrop and required only 5–10% higher saturation levels. We apply a zero diffusive flux boundary condition for CFC, DIC, and δ13C-DIC at the southern boundary, where no meridional gradients in these properties were observed (Figures 3 and 9).
 For all isopycnals, CFC saturation was within 8% of equilibrium with the 1993 atmosphere (92–107%). Transport within the subtropical gyre is dominated by advection, and CFC gradients largely reflect the near-linear increase in atmospheric CFC concentrations during the 1970s and 1980s. Advection velocity is thus determined by the slope of the CFC gradient. Based on the shape of the CFC-11 distribution on each isopycnal, several regimes – here identified as “subpolar”, “intermediate”, and “subtropical” – can be identified and were assigned individual velocities. Figure 7 schematically depicts the different regions as defined for each isopycnal. Values of model parameters are summarized in Table 3.
Table 3. Model Parameters (Advection Velocity, Eddy Diffusivity, CFC Saturation at the Outcrop) Used in the Advection-Diffusion Modela
DIC0 was calculated from preformed alkalinity (derived from T and S) by assuming equilibrium with the pre-industrial atmosphere. The carbon system parameters reflect the characteristics of the marine CO2 system at the outcrop location.
Abbreviations “SP”, “IN”, and “ST” refer to the “subpolar”, “intermediate” and “subtropic” model regions, respectively (see Figure 7).
As the ocean takes up anthropogenic CO2, some of its buffer capacity is consumed. As a consequence, the Revelle factor increases at equilibrium by about 10% and the carbonate fraction decreases by around 21% (1765–1993). In the model we used the means between pre-anthropogenic and 1993 Revelle factors.
 South of the tropical-subtropical front (16°–26°N), which represents the front between North (NACW) and South Atlantic Central Water (SACW) [Klein and Tomczak, 1994], the flow is predominantly zonal and we assumed that meridional transport here is due solely to along-isopycnal eddy diffusion. As a result, diffusivities are slightly sensitive to the location of the southern boundary which was placed in the center of the no-CFC-gradient regime and moved northward from 6°N to 9°N on successively deeper isopycnals. Diffusivities were adjusted to yield the best fit to the data south of the tropical-subtropical front and decrease with increasing depth from 1900 to 700 m2 s−1 (Table 3). These numbers compare well with literature values from 1800 m2 s−1 [Jenkins, 1991] to 500 m2 s−1 [Armi and Stommel, 1983]. Individual isopycnal diffusivities were assumed to be constant over the full meridional extent of the model.
 Our simple 1D-advection-diffusion model does not include the possibility of diapycnal mixing, which might account for part of the discrepancy between model results and reconstruction. However, Speer  demonstrated that diapycnal mixing is weak (indistinguishable from zero) in the thermocline (σθ = 26.6–27.6) of the North Atlantic Ocean. Furthermore the area investigated is not influenced by boundaries, passages etc. that might give rise to strong cross-isopycnal mixing. Sonnerup et al. [1999a] found that diapycnal CFC fluxes accounted for <15% of CFC ventilation into the subtropical Pacific thermocline. On the other hand, Klein and Tomczak  found evidence for unidirectional diapycnal mixing in the front between NACW and SACW (near 15°N on our section), which they attributed to double diffusion. This process, however, is likely to affect only shallower isopycnals (σθ ≤ 27.00) in the frontal region.
 The importance of zonal transports, which cannot be represented by our meridional advection-diffusion model, has to be assessed. We compared our meridional transect with CFC, DIC, and δ13C data (where available) from several zonal transects intersecting at 51°N (R/V Meteor cruises 39/2 + 4 in 1997 [Körtzinger et al., 1999]), at 48°N (R/V Meteor cruises 30/2 in 1994 [Körtzinger et al., 1998] and 39/3 in 1997), and at 24.5°N (OACES 24N North Atlantic Cruise in 1998, http://www.aoml.noaa.gov/ocd/oaces/24n98.html). In the upper 1000 m of the eastern North Atlantic basin these sections show very little zonal variability of all three tracers (CFC, DIC, and δ13C). Significant gradient are evident not only near the European/African shelf and above the mid-Atlantic ridge but also at deeper levels. Based on these findings we estimate that biases due to zonal transports are likely small overall.
4.2. Model Simulation of Anthropogenic CFC, 13CO2, and 13CO2 Perturbations
4.2.1. Calculation Procedures
 Our CFC-calibrated advection-diffusion model is used to describe the along-isopycnal penetration of the perturbation signals of CO2 and 13C into the North Atlantic Ocean. Atmospheric histories of CO2 and 13CO2 are prescribed at the outcrop where the resulting air-sea net flux of CO2 and 13CO2 is calculated. The model is initialized with CO2 and 13C in equilibrium with the pre-industrial atmosphere (as outlined in Appendix B). Processes that kept the real pre-industrial surface ocean CO2 system at a certain degree of air-sea disequilibrium (e.g., biology, mixing) are not reflected in the model and affect the predicted DIC and δ13C-DIC values as discussed below. For anthropogenic DIC and δ13C-DIC it was found that an outcropping period of 12 months was required in order for the model ocean to take up realistic amounts of CO2. Therefore we used annual climatological means of T, S, mixed layer depth, and wind speed in the model runs for DIC and δ13C.
 The net flux of CO2, F12, across the air-sea interface can be described by a bulk formula
where k is the transfer (or piston) velocity, KH is the solubility of CO2 in seawater, and pCO2g and pCO2sea are the partial pressures of CO2 in seawater and air, respectively. In order to simplify calculations, we used the mole fraction of CO2 in dry air (xCO2) instead of the partial pressure (pCO2). These two quantities are linked by the total barometric pressure and the water vapor saturation partial pressure (see caption of Figure 6). If no surface skin temperature effect is present, Patm and pH2Osat are identical for pCO2g and pCO2sea and the use of xCO2 instead of pCO2 represents only a very small error in F12, ranging from −0.5% to +2% over the temperature range 4–26°C (at P = 1 atm). The solubility of CO2, KH, was calculated following the study of Weiss . For the wind speed dependence of the transfer velocity k, we used the quadratic parameterization for climatological winds of Wanninkhof . It should be noted that this bulk formula is strictly only valid for total CO2, i.e., the sum of 12CO2 and 13CO2. We assume this equation also to be valid for 12CO2 as this represents about 98.9% of the CO2.
 The net flux of 13CO2, F13, across the air-sea interface can be described in a similar fashion
where αk is the kinetic fractionation factor for 13CO2 gas exchange, αaq − g is the equilibrium fractionation factor for CO2 gas dissolution, and αDIC − g is the fractionation factor between seawater DIC and CO2 in air. and RDIC represent the 13C/12C ratios of CO2 in air and DIC, respectively. More details on the derivation of equation (8) and the parameterizations used for the fractionation factors are given in Appendix C.
 The fluxes of 12CO2 and 13CO2 are calculated according to equations (7) and (8) at every time step. These fluxes per unit area of the air-sea interface (μmol m−2 month−1) are then converted into water column concentration changes of DIC and DI13C (both in μmol kg−1) by using the annual mean mixed layer depth (mld) and density (ρ). As the model advects and diffuses the tracer DIC, the air-sea exchange itself depends on the concentration difference of CO2 across the air-sea interface (equation (7)), so a conversion has to be made back and forth between DIC and pCO2. This was done using the Revelle (or homogeneous buffer) factor fR, which represents the quotient of the relative increases in pCO2 and DIC at equilibrium and constant temperature, salinity, and alkalinity [Sundquist et al., 1979]
From this, the pCO2sea change was calculated
 Similarly, the change in the DI13C inventory (= RDICDIC) is calculated from F13, and the resulting change in RDIC is derived from ΔDI13C and ΔDIC. The complete calculation procedure for DIC and RDIC is shown in Figure 8.
 The Revelle factor is not a constant. As the ocean takes up anthropogenic CO2, the Revelle factor increases and the ocean's CO2 uptake capacity decreases. The total increase of the Revelle factor since pre-industrial times is on the order of 10%. We use the mean of the factors for 1765 and 1993, calculated assuming equilibrium with the atmosphere. The simplification of using a constant mean rather than a variable Revelle factor has very little consequence on the results. The difference in modeled 1993 meridional DIC gradient between a constant and a variable Revelle factor is 0.1–0.5 μmol kg−1 across the whole section.
4.2.2. Model Results for DIC0 and δ13C0
 The CFC-calibrated advection-diffusion model was used to predict DIC and RDIC changes from pre-industrial equilibrium as a consequence of the prescribed measured atmospheric perturbation. As the model does not include biologically mediated CO2 changes, the model parameters DIC and RDIC are directly comparable to the properties DIC0 and δ13C0 (expressed as RDIC0) reconstructed from field data. This assumes, of course, that values chosen for −O2/Corg, −O2/N, AT0, and δ13Corg in equations (2) and (4) represent actual conditions in the Northeast Atlantic Ocean, and that wintertime oxygen saturation levels are indeed close to 100% for all the isopycnal outcrops.
 Magnitude and shape of the temporal change of DIC0 and δ13C0 as well as the δ13C0-DIC0 relationship are generally in very good agreement with the reconstruction (Figure 9 and Tables 1 and 2). The modeled temporal change of DIC0 of 0.96 ± 0.05 μmol kg−1 yr−1 is about 20% smaller than the reconstructed change (Figure 4 and Table 1) but in close agreement with the equilibrium increase of 1.0 μmol kg−1 yr−1 for a Revelle factor of 9.5. The modeled δ13C0 temporal change of −0.029 ± 0.003‰ yr−1, however, agrees well with both the reconstruction (Figure 4 and Table 1) and the atmospheric trend (−0.027 ± 0.001‰ yr−1).
 The model δ13C0-DIC0 relationship has a slope of −0.030 ± 0.003‰ (μmol kg−1)−1 which is 25% steeper than the reconstructed slope (Table 2). This difference is due primarily to the difference between reconstructed and modeled temporal DIC0 changes. A closer look at the model results reveals that the two different equilibrium trends for the pre-1970 and post-1970 periods (Figure 6) are mirrored in the model output (Table 2). The change in the mean δ13C0-DIC0 slopes is determined by the range in water mass ages found on a particular isopycnal, i.e., by the degree to which the two different periods are represented on that isopycnal.
 The model surface seawater pCO2 at the outcrop closely follows the atmospheric pCO2 (Figure 10). The developing small air-sea pCO2 disequilibrium in the model reaches maximum values between 0.6 μatm (σθ = 26.60) and 1.5 μatm (σθ = 27.40) during the last 30 years. This is on the order of the annual increase of atmospheric pCO2 (1.5 μatm) and reflects the 1-year equilibration timescale of CO2. In contrast, the model outcrop δ13C does not keep pace with the atmospheric perturbation. Although initialized at equilibrium, modeled δ13C develops a significant air-sea disequilibrium (Figure 10) increasing with time toward maximum values between −0.19‰ (σθ = 26.60) and −0.32‰ (σθ = 27.40). Like for pCO2, this disequilibrium is building up very slowly as the rate of change in atmospheric δ13C-CO2 remains moderate. Around the middle of the 20th century the rate of change in δ13C-CO2 increases significantly reaching maximum values during the 1970s. The maximum air-sea disequilibrium during the last decades is about ten times the annual atmospheric δ13C-CO2 decrease (−0.027‰ yr−1) beautifully reflecting the 10-year equilibrium timescale of 13C.
 This variable air-sea disequilibrium for δ13C explains the increase in the modeled temporal δ13C0 trend from −0.025‰ yr−1 on isopycnal σθ = 27.40 to values below −0.030‰ yr−1 on the shallowest isopycnals (Table 1). While the latter comprise an age range of only 20 years, apparent water mass ages on isopycnal σθ = 27.40 span a range of more than 40 years (Figure 4). As the model 13C air-sea disequilibrium shows a maximum in the early 1980s and decreases thereafter, it is possible for the oceanic Suess effect to be even greater than the atmospheric Suess effect for the last 10–15 years. During this period the oceanic δ13C change not only follows (with roughly a 10-year time lag) the atmospheric Suess effect of −0.025 ± 0.001‰ yr−1 but partially compensates the higher disequilibrium that has built up during the 1970s. The shorter time window sampled on the shallowest isopycnals reflects this enhanced Suess effect more than does the longer time window of deeper isopycnals which reflects the opposite situation in the 1960s and 1970s, when the oceanic Suess did not keep pace with the atmospheric Suess effect and a growing air-sea disequilibrium was found (Figure 10).
5. Air-Sea Disequilibria
5.1. The Air-Sea Disequilibrium of CO2
 There is disagreement over the absolute values of DIC0 between model results and data. This is due to the fact that, unlike the model ocean, the real ocean in most places is not in equilibrium with the atmosphere nor has it been in pre-industrial times [Sarmiento and Sundquist, 1992]. Modeled and reconstructed DIC0 values are in close agreement only on the deepest isopycnal σθ = 27.40 (Figure 9). Going up in the water column, modeled DIC0 is increasingly lower than reconstructed DIC0. On the shallowest isopycnal σθ = 26.60, a mean DIC0 difference of around 11 μmol kg−1 (17°–26°N) is found which corresponds to a surface pCO2 difference of about 22 μatm. The disequilibrium increases with decreasing age and is generally largest for waters having been ventilated most recently. The disagreement between modeled and reconstructed DIC0 is always smallest or even nonexistent at the southern edge indicating that the surface ocean in the outcropping area was closer to equilibrium at the time these oldest waters were last ventilated. Hence, the reconstructed along-isopynal DIC0 change is higher than what is expected from the atmospheric CO2 increase alone which is in agreement with the results from BATS [Bates et al., 1996; Bates, 2001].
 The more-than-expected increase in DIC could be explained by a combination of two factors – the non-linearity of the marine CO2 system and the strong undersaturation typically found in the North Atlantic Ocean. Our results as well as model results [e.g., Meier-Reimer and Hasselmann, 1987; Sarmiento et al., 1992] indicate that the surface ocean is able to follow the atmospheric CO2 perturbation. The corresponding increase in surface DIC, however, not only depends on the atmospheric CO2 increase itself but also on the natural CO2 disequilibrium maintained by other processes. For an ocean area remaining significantly undersaturated with respect to atmospheric CO2 while following the secular CO2 rise, the total DIC increase for a given atmospheric change is higher than for an ocean starting at equilibrium. Accordingly a naturally supersaturated ocean area will show a smaller anthropogenic DIC signal. Being initialized at equilibrium, our model cannot represent this effect, which should be contained though in the reconstructions.
 The North Atlantic Ocean (north of 30°–35°N) is significantly undersaturated with respect to atmospheric pCO2 [Takahashi et al., 1995, 1997, 2002]. This strong CO2 sink results from the combined effects of biological carbon uptake and the cooling of water moving northward as part of the subtropical gyre circulation and of the thermohaline circulation. The North Atlantic Ocean should thus be one of the primary ocean regions to be characterized by an enhanced DIC increase. Obviously the opposite would be true for natural source regions such as the tropical oceans. Our North Atlantic Ocean results may therefore represent an upper extreme in the global context.
 An enhanced uptake of anthropogenic CO2 could also be caused by possible climate feedback mechanisms [Joos et al., 1999] which might already be at work in the real ocean. While this is entirely possible, it is hard to detect such feedbacks in the field. If acting as proposed, however, the feedback mechanisms should become more important and more readily detectable as climate change progresses.
5.2. The Air-Sea Disequilibrium of δ13C
 There is also disagreement between the absolute values of δ13C0 of model results and the reconstruction, indicating that the surface ocean is not at air-sea equilibrium for 13C. It is well established that there are several processes at work that keep the surface ocean from achieving isotopic equilibrium [Broecker and Maier-Reimer, 1992]. Four primary factors can be identified that can cause air-sea disequilibrium of 13C: (1) export production of organic matter, (2) mixing/upwelling of subsurface water into the mixed layer, (3) net air-sea exchange of CO2 [Lynch-Stieglitz et al., 1995], and (4) the temperature dependence of the equilibrium fractionation between DIC and CO2 in the air (αDIC-g).
 In the following we try to explain observed patterns of (measured and reconstructed) surface water δ13C-DIC in the North Atlantic Ocean. For this purpose, we looked at five data sets (Figure 11): δ13C measured on surface samples (upper 20 m) taken during the OACES cruise in July/August, reconstructed δ13C0 values from subsurface samples near the outcrop locations of the five isopycnals, and the equilibrium surface δ13C at climatological mean, maximum, and minimum outcrop temperatures in equilibrium with the 1993 atmosphere.
 Measurements of surface δ13C were made on samples taken during summertime (July/August 1993). In contrast, our reconstructed δ13C0 values reflect wintertime ventilation conditions. In the absence of any seasonality in surface δ13C values, these two data sets should coincide. This seems to be the case in the southern part of the section (south of approximately 30°N), which is essentially a permanently oligotrophic system that does not show significant wintertime surface nutrient concentrations nor a winter-to-summer drawdown of surface DIC [Körtzinger et al., 2001b]. A similarly small seasonality in surface ocean δ13C has been reported by Gruber et al.  for the Bermuda time series station at 32°N (seasonal δ13C cycle of 0.2–0.3‰).
 North of about 35°N, the elevation of summer δ13C above wintertime δ13C0 is primarily due to export production of organic matter, which has already fully depleted nitrate and phosphate south of 57°N at the time of the measurement (August 1993). In contrast, nitrate (2.0–5.9 μmol kg−1) and phosphate (0.29–0.45 μmol kg−1) were still available north of 57°N comprising roughly 25–50% of wintertime surface concentrations. Consequently, δ13C values are less strongly elevated above wintertime preformed δ13C0 values. Both measured δ13C and reconstructed δ13C0 seem to converge around 30–35°N, the transition region toward the permanently oligotrophic system further south [see also the work of Körtzinger et al., 2001b].
 Measured surface δ13C-DIC values are in the range 1.4–1.9‰ everywhere along the transect representing isotopic air-sea equilibrium only around 60°N. Toward the south surface δ13C-DIC is increasingly enriched in 13C by up to 2‰ above air-sea equilibrium. Reconstructed preformed δ13C0 is near atmospheric equilibrium (at annual mean T) around 47°N (outcrop of isopycnal σθ = 27.00). The enrichment of preformed δ13C0 above air-sea equilibrium south of 47°N can be attributed to two major factors: export production of organic carbon from the mixed layer and the temperature dependence of as documented in the equilibrium curves of Figure 11.
 The observed meridional trend in preformed δ13C0 with lower (reconstructed) values in the north and higher (measured) values toward south, however, cannot be explained by export production alone. One possible candidate for maintaining this gradient could be air-sea exchange of CO2. Annual net CO2 fluxes following the study of Takahashi et al.  are near zero (±1 × 1012 g C yr−1 for 4° (latitude) × 5° (longitude) area) south of 35°N but show significant net uptake north of here (3–7 × 1012 g C yr−1 for 4° × 5° area). Our simple model calculations, however, indicate that the net CO2 flux is less depleted in 13C at low temperatures. Furthermore the depletion in the net CO2 flux increases with decreasing ΔpCO2. Thus our tests indicate that net uptake of CO2 in the North Atlantic is likely not a major contributor to the observed meridional δ13C0 gradient.
 We also looked into the δ13C signature of the upward DIC flux (calculated at each station from the δ13C-DIC slope of samples in the upper 200 m). In the southern half of our section this upward DIC flux is characterized by δ13C values of −14 ± 2‰. In the northern part, however, the DIC is much more depleted with δ13C values of −22 ± 1‰. Such differences can be explained by the winter mixed layer depth, which does not exceed values of 40 m south of 20°N and increases moderately to about 200 m toward 45°N. Around 45°N a steep increase in maximum wintertime mixed layer depths is observed with maximum values of up to 700 m (Figure 2). This pronounced gradient in winter mixed layer depth has consequences on the characteristics of the surface ocean CO2 system. In the area of shallow mixing, the DIC source from below the mixed layer does not mirror the isotopic signature of particle flux and is probably more strongly influenced by advection and lateral processes. Where winter mixed layers are deep, the carbon system may be more self-contained, i.e., most of the respiration of exported particles and thus most of the imprint of its 13C signature occurs within a depth horizon that is reentrained into the mixed layer during wintertime. This indicates that the upward DIC flux may contribute significantly to the observed meridional gradient in preformed δ13C0.
6. The δ13C0 and DIC0 Relationship
 The “preformed-preformed” relationship between δ13C0 and DIC0 is useful in several ways. First of all, the relationship provides a link between the change of the oceanic carbon inventory and the 13C Suess effect. If representative of the world ocean, it can be used for direct conversion between global inventory changes of DIC and 13C. This relationship thus provides a means of cross-checking independent inventory estimates and potentially a powerful constraint on model-based simulations.
 Second, Keir et al.  demonstrated that the “preformed-preformed” relationship can be used to constrain the size of the exchangeable terrestrial biosphere, i.e., that part of the terrestrial biosphere (e.g., vegetation, wood, detritus) which actively exchanges with the atmosphere on the timescale of the atmospheric CO2 perturbation. Keir et al.  adapted the atmosphere, ocean, and terrestrial biosphere 12CO2 and 13CO2 budget of Quay et al.  to examine the relationship between δ13C0 (Δδs) and DIC0 (ΔCT)
where δ* and δs0 are the mean δ13C values of fossil fuel source CO2 and pre-industrial ocean DIC (here CT), respectively. Δδa and Δδb are the changes since pre-industrial times in atmospheric δ13C-CO2 values and terrestrial biosphere δ13C values, respectively. Ma0 and Mb0 denote pre-industrial carbon inventories of the atmosphere and the terrestrial biosphere, respectively. ΔMa is the change in the atmospheric carbon inventory while ΔMs denotes the change of the oceanic carbon inventory. Actual values chosen for these parameters are shown in Table 4.
Table 4. Values Employed in Mass Balance Calculation After Equation (11)
1 ppmv CO2 = 2.2 Pg C.
Calculated using the pre-industrial atmospheric δ13C-CO2 and an ocean-wide average εDIC-g of 8.59 (at area-weighted mean SST of 18.4°C).
 Following this approach, the δ13C0-DIC0 relationship (Δδs/ΔCT in equation (11)) can be calculated as a function of the total ocean CO2 uptake (ΔMs) for different sizes of the exchangeable terrestrial biosphere covering the range of possible scenarios from no exchangeable carbon (Mb0 = 0 Pg C) to fully exchangeable carbon (Mb0 = 2000 Pg C). Using the airborne fraction (ΔMa/(ΔMa + ΔMs)) of 0.58 from the work of Sarmiento et al. , the 128 Pg C increase of the atmospheric carbon reservoir corresponds to a total ocean CO2 uptake of 91 Pg C. With this cumulative ocean uptake, the reconstructed δ13C0-DIC0 slope of −0.024 ± 0.003‰ (μmol kg−1)−1 indicates that less than half of the total carbon stored in the terrestrial biosphere (520 ± 500 Pg C of a total of 2050 Pg C, Siegenthaler and Sarmiento ) has been actively exchanging with the atmosphere during period 1960–1993 (Figure 12).
 However, the ∼12% uncertainty in the δ13C0-DIC0 slope (plus the additional uncertainty associated with the parameters in equation (11)) precludes a reliable determination of the size of the exchangeable carbon reservoir using this approach (Figure 12). Also, for reasons outlined above, we expect the North Atlantic δ13C0-DIC0 slope to be significantly larger than the ocean's average, and thus this estimate of the mass of the exchanging terrestrial carbon reservoir is likely too small. A precise determination of the mass of the exchanging terrestrial carbon therefore awaits additional estimates of the δ13C-DIC perturbation ratio such that global coverage and higher precision can be achieved.
 Another potentially useful application of the δ13C0-DIC0 relationship stems from the fact that the air-sea disequilibrium of δ13C can be estimated with better precision than the air-sea CO2 disequilibrium or ΔpCO2. The average global air-sea disequilibrium of δ13C of −0.62 ± 0.1‰ [Gruber and Keeling, 2001; P. D. Quay et al., Anthropogenic changes of the 13C/12C of dissolved inorganic carbon in the ocean as a tracer of CO2 uptake, submitted to Global Biogeochem. Cycles] is generally larger than seasonal and spatial variability of δ13C in the surface ocean. In contrast, the average ΔpCO2 of around 8 μatm (inferred from a global net CO2 uptake of 2 Pg C yr−1) is up to an order of magnitude smaller than seasonal and spatial pCO2 variability in the surface ocean [Takahashi et al., 1997]. The reconstructed ratio of the oceanic δ13C0 and DIC0 perturbations can be used to estimate the mean air-sea ΔpCO2. For this purpose, it is converted into the ratio of 13C and 12C concentration changes (ΔDI13C/ΔDIC), which equals the ratio of the net air-sea fluxes of 13CO2 and 12CO2 (see equations (8) and (7), respectively)
 We can estimate the air-sea ΔpCO2 after solving equation (12) for pCO2sea, using global area-weighted means of sea surface temperature (18.4°C [Levitus and Boyer, 1994]) and salinity (34.75 [Levitus et al., 1994]) to calculate the fractionation factors, the mean 1960–1993 atmospheric CO2 concentration (pCO2g ≅ xCO2g = 335.3 ppmv), and atmospheric δ13C-CO2 (−7.3‰), a global gas exchange rate weighted air-sea δ13C disequilibrium of −0.62 ± 0.10‰ [Gruber and Keeling, 2001; Quay et al., submitted] and our δ13C0-DIC0 slope of −0.024 ± 0.003‰ (μmol kg−1)−1. For this set of values we find a global mean air-sea ΔpCO2 of 5.4 ± 1.1 μatm, which yields a global net uptake of CO2 on the order of 1.6 ± 0.3 Pg C yr−1 when the exchange coefficient kKH = 0.067 moles CO2 m−2 yr−1 μatm−1 after the method of Tans et al.  is used.
 This result for the global mean ΔpCO2 and the net uptake of anthropogenic CO2 is not suited to provide a better global estimate of the oceanic uptake of anthropogenic CO2 as the North Atlantic is not representative of the world ocean. A global mean of the δ13C0-DIC0 relationship would likely be less steep [McNeill et al., 2001] and thus yield a higher net oceanic CO2 uptake in better agreement with the current understanding. Also, the value of −0.62 ± 0.10‰ applied here for the global air-sea δ13C disequilibrium may not be valid for the whole period of time that is represented in our analysis. A box-diffusion simulation of ocean 12CO2 and 13CO2 uptake indicates that during the time period over which our δ13C0-DIC0 relationship was determined (late 1960s to 1993), the air-sea disequilibrium increased by about −0.3‰ [Quay et al., submitted]. Using an air-sea disequilibrium of −0.47‰, roughly representative of 1980, instead yielded a ΔpCO2 of 4.1 μatm and an ocean uptake of 1.2 Pg C yr−1 by the same approach as above. An improved determination, based on observations of the temporal evolution of the air-sea δ13C disequilibrium, awaits analysis of planned CLIVAR repeat hydrography cruise data over the coming decade. These cruises will also provide opportunities to reconstruct δ13C and DIC changes based on multiparameter approaches [Sabine et al., 1999; Sonnerup et al., 2000; McNeill et al., 2001].
 Finally, in order to make the estimated ΔpCO2 compatible with ΔpCO2 measurements (such as in the form of the compilation of the work of Takahashi et al. ), the pre-industrial CO2 disequilibrium that arises from an imbalance between (inorganic and organic) carbon inputs through rivers and carbon losses through sedimentation has to be taken into account. The complications associated with this approach for determining the global mean ΔpCO2 are beyond the scope of this paper and will be discussed in more detail as more determinations of the required carbon system parameter become available. We merely demonstrate here that knowledge of the mean oceanic perturbation ratio has the potential to provide relatively precise, model-independent CO2 uptake estimates.
 Using the back-calculation approach of Sonnerup et al. [1999b] for δ13C and extending it to total dissolved inorganic carbon we calculated the temporal change of DIC and δ13C along five isopycnals in the upper 1000 m of the North Atlantic Ocean. The anthropogenic changes of 1.21 ± 0.07 μmol kg−1 yr−1 (DIC) and −0.026 ± 0.002‰ yr−1 (δ13C) during 1950–1993 are in good agreement with results from previous studies. That they seem to be on the high end of the range of published values can be explained by the fact that apparent CFC ages are biased young for ages > 25 years. Based on estimated end-member characteristics we find no evidence for significant mixing biases on DIC0 or δ13C0. The observed δ13C0-DIC0 perturbation ratio of −0.024 ± 0.003‰ (μmol kg−1)−1 in the North Atlantic Ocean is significantly higher than databased on other oceanic regions, and the global mean from model results.
 We used a simple 1D model calibrated to CFCs to investigate reasons why the North Atlantic DIC and δ13C change rates may be larger than the global average. Our model results indicate that in the case of CO2, surface waters are able to stay close to equilibrium with the anthropogenic perturbation. For DIC, the observed temporal change slightly exceeds the thermodynamically driven equilibrium uptake. This points toward an enhancement of the uptake of anthropogenic CO2. The oceanic 13C perturbation follows the atmospheric 13C history with a roughly decadal lag due to the long equilibration time-scale of 13C. Our model results suggest that this delay can cause the δ13C0-DIC0 slope to exceed that found in the atmospheric time history due to a recent decrease of the atmospheric δ13C decrease rate.
 We were able to reproduce temporal DIC0 and δ13C0 trends as well as the δ13C0-DIC0 relationship reasonably well using the 1D advection-diffusion. Significant biases due to the influence of zonal transports on tracer fields could be ruled out, and scaling calculations indicated that our isopycnal analysis was not strongly biased by end-member mixing effects. Absolute values of DIC0 and δ13C0 were not well reproduced by the model because the real ocean is not in equilibrium with the atmosphere while the model was initiated at equilibrium. The actual air-sea disequilibrium for CO2 and 13C in the North Atlantic Ocean is maintained by biological carbon export, CO2 gas exchange, and circulation processes that are not represented in the model.
 Because of the one order of magnitude difference in the two tracers' timescale for equilibration between the surface mixed layer and the atmosphere – 1 year for DIC and 10 years for DI13C – reconstructions of DIC0 and δ13C0 provide useful information about processes controlling air-sea CO2 disequilibrium conditions. The situation found in the North Atlantic, where reconstructed anthropogenic DIC and δ13C changes can reasonably well be explained by prevailing disequilibrium conditions, may not be representative of the world ocean. In regions where surface water exposure times to the atmosphere are short relative to the equilibration timescale of δ13C significantly less steep perturbation ratios can be expected.
 Precise knowledge of the global ocean's DIC0-δ13C0 relationship would not only provide powerful constraints on changes of the oceanic carbon inventory and the 13C Suess effect, but could be used to constrain the size of the exchangeable terrestrial carbon reservoir and most notably to estimate the mean air-sea pCO2 equilibrium. Our results of these applications using the North Atlantic results only are in general agreement with the current understanding of the perturbed oceanic carbon cycle. The results are indicative of a rather slow overturning in the North Atlantic that can be viewed as a manifestation of the thermohaline circulation. As the perturbation ratio found in the North Atlantic is likely not representative of the world ocean, these results are shown to demonstrate the potential of these approaches, and to encourage further work in determining the global δ13C0-DIC0 perturbation ratio and air-sea δ13C disequilibrium.
Appendix A:: Calculation of Preformed Alkalinity
 The calculation of preformed DIC (equations (1) and (2)) requires estimation of a sample's preformed alkalinity (AT0). Unlike DIC, seawater alkalinity is not affected by the invasion of (anthropogenic) CO2 from the atmosphere and preformed alkalinity should therefore have remained constant over the time span of the anthropogenic perturbation. Surface seawater alkalinity shows quasi-conservative behavior, and it is common practice [e.g., Millero et al., 1998] to normalize total alkalinity to a constant salinity (nAT = AT35/S) and use the observed nAT − θ relationship (equation (A1), for 10 < θ < 21°C) to calculate AT0 at a salinity of 35
This practice, however, neglects the fact that the AT–S relationship is characterized by a significant intercept representing the freshwater end-member (equation (A2)). By implicitly assuming a zero intercept in the normalization procedure spurious variance is added to the salinity normalized alkalinity. In this study, traditionally normalized alkalinity ((nAT = AT35/S)) deviated by −8 to 4 μmol/kg from the alkalinity normalized using the slope of the AT–S relationship (equation (A2)) over the observed salinity range (S = 36.6 − 34.5).
Equation (A2) provides a more accurate means of salinity normalization. Over the temperature range 10°–21°C, alkalinity normalized using equation (A2) does not show a temperature dependence (slope = 0.02 ± 0.10). The temperature dependence observed for traditionally normalized alkalinity (equation (A1)) thus appears to be largely fortuitous and due to the spurious variance added by the normalization procedure itself. For temperatures above 21°C even alkalinities normalized using equation (A2) retain some temperature dependence. Thus a multilinear regression of total alkalinity on temperature and salinity (equation (A3), 10 < θ < 28°C) provides a more robust means of estimating preformed alkalinity over the whole range of sea surface temperatures. In all present calculations equation (A3) was used instead of equation (A2)
Appendix B:: Calculation of DIC and δ13C Air-Sea Equilibrium
 The equilibrium DIC value was calculated from (annual mean) outcrop T and S, preformed alkalinity AT0 (equation (A3)), and the pre-industrial CO2 mole fraction (xCO2 = 276.9 ppmv in 1765) by applying the thermodynamic relationships of the marine CO2 system and assuming no pre-industrial pCO2 air-sea disequilibrium. All CO2 system calculations were carried out using the software program of Lewis and Wallace  and the carbonic acid dissociation constants after the work by Mehrbach et al.  (refit by Dickson and Millero ). This calculation procedure also yielded values for the Revelle factor, fR, and the carbonate fraction of DIC, , representing the surface ocean CO2 system at each isopycnal's outcrop. Both properties are needed in air-sea exchange parameterization for CO2 and 13C as described below.
 For 13C, the equilibrium fractionation between DIC and gaseous CO2 has to be taken into account, which depends on temperature and carbon speciation within the marine CO2 system. Zhang et al.  measured the equilibrium enrichment (εDIC-g) of 13C in seawater DIC and obtained the following empirical function for T = 5 − 25°C and = 0.05 − 0.20
The δ13C of surface seawater DIC in equilibrium with the pre-industrial atmosphere (δ13Cg = −6.30‰ in 1765) can then be calculated using climatological T at each isopycnal's outcrop
Appendix C:: Bulk Formula for Net Air-Sea Exchange of 13CO2
 The bulk formula for the net air-sea exchange of 13CO2, F13, can be derived from the bulk formula for the net air-sea exchange of 12CO2 (equation (7))
where and represent the 13C/12C ratios of CO2 in air and seawater (CO2(aq)), respectively, and KH13 is the solubility of 13CO2. Equation (C1) illustrates that F13 not only depends on the CO2 gradient but also on the isotopic disequilibrium. The 12C and 13C flux properties are related through the kinetic fractionation factor of CO2 gas transfer, αk, and the equilibrium fractionation factor for CO2 gas dissolution αaq−g
 The δ13C measurements were made with support of the NOAA/OACES program under grant NA86GP0104. Arne Körtzinger is particularly grateful to Paul Quay for providing the opportunity to work at the University of Washington, and to the Deutsche Forschungsgemeinschaft for funding this research stay. Finally we would like to acknowledge the comments of two anonymous reviewers, which helped to improve the manuscript. This is JISAO contribution number 837.