The data used in this study were collected at three cruises carried out in the Nordic seas in 2002 and 2003. The 2002 cruise of I/B Oden, the 2002 cruise of R/V Knorr, and the 2003 cruise of R/V G.O. Sars. The expocodes for the cruises are 77DN20020420, 316N20020530, and 58GS20030922, respectively. A map of the Nordic seas with the stations occupied on these three cruises is provided in Figure 1. The data have been described by Olsen et al. , Jeansson et al. , and Jutterström et al.  and only a brief summary of their stated precision and accuracy is provided here. The precision of the DIC and alkalinity data (Alk) have been estimated to approximately ±1 μmol kg−1 and accuracy was ensured by analyses of certified reference material (CRM) supplied by A. Dickson, Scripps Institution of Oceanography, USA [Jutterström et al., 2008; Olsen et al., 2006]. Oxygen and CFC data were all obtained with a precision of ∼1% [Jutterström et al., 2008]. The data from the three cruises are included in the CARINA data synthesis product [Key et al., 2010] and they have been found to be internally consistent [Falck and Olsen, 2010; Jeansson et al., 2010; Olsen et al., 2009; Olsen, 2009a, 2009b], except the CFC-12 data obtained at the G.O. Sars cruise, which should be adjusted by a factor of 0.95 [Jeansson et al., 2010]. This adjustment was applied to the data used in the work presented here. To avoid complications due to the seasonal cycle and the recent decline in the atmospheric CFC concentrations, only data from deeper than 250 m are used for the calculations presented here.
2.2. TTD Method
 The TTD framework applies to passive tracers with a time-dependent surface history. For these, the interior ocean concentrations at location r and time t can be expressed as (assuming steady transport and uniform c0 over the source region)
where c0 is the time-dependent surface history of the tracer in question and G(r, τ) is the distribution of transit times (the TTD) at the location. Here we use three passive tracers, CFC-11, CFC-12, and anthropogenic CO2. For the two former, the surface history was determined using the atmospheric history compiled by Walker et al. , and solubility calculated from temperature and salinity according to Warner and Weiss , assuming a surface saturation of 98% which is consistent with the observations of Jutterström et al. . The DICant history was determined as the difference between the preindustrial equilibrium DIC and that at time τ, using updated Law Dome and Mauna Loa atmospheric CO2 mole fraction records. This requires estimates of preformed alkalinity, Alk0, and these were obtained from salinity using the relationships specifically determined for the Nordic seas by Nondal et al. . Preformed silicate and phosphate was set to 8 and 1 μmol kg−1, respectively, typical concentrations of Nordic seas surface water in winter as determined from the CARINA data set [Key et al., 2010; Olafsson and Olsen, 2009]. The CO2 system calculations were carried out using CO2sys [Lewis and Wallace, 1998] for Matlab [van Heuven et al., 2009] using the constants of Mehrbach et al.  refit by Dickson and Millero .
 The TTD is approximated by an inverse Gaussian distribution [Hall et al., 2002; Waugh et al., 2004, 2006]
where Γ is the mean age of the water sample, Δ is the width of the TTD, and τ is the age of the water, the transit time. When the ratio between Δ and Γ is known the TTD can be determined by using a single transient tracer. For our DICant calculation we use observations of CFC-12, combined with an estimate of Nordic seas Δ/Γ, derived as described in section 2.3.
2.3. Determination of TTD Parameters
 The ratio between Δ and Γ describes the shape of the TTD. Large ratios imply broad TTDs indicating that propagation of surface signals occurs over a wide range of transit times. The smaller the ratio the less mixing and, thus, the narrower range of transit times. The special case Δ/Γ = 0 indicates that tracer signals are propagated into the ocean interior through pure bulk advection. The ratio, which reflects the degree of ocean mixing, is expected to vary and must be determined on regional scales.
 To constrain Δ/Γ for the Nordic seas we follow the approach of Waugh et al. , i.e., by comparing the relationship between tracer ages. Tracer concentrations in themselves could have been compared in order to remove the effect of the nonlinear relationship between concentration and age that is typical for many tracers. However, this approach did not provide any additional information, and we chose to compare the ages to enable direct comparison of our results with those of Waugh et al. .
 By the tracer age we mean the age estimate that is obtained by comparing the concentration in seawater with the atmospheric history of the tracer in question
where c(t) is the interior concentration, c0 is the surface concentration history, and τ is the tracer age. This assumes that tracer signals are propagated into the ocean interior through pure bulk advection so that a single transit time rather than a distribution of transit times describes the timescale of ocean transport from one location to another, i.e., Δ/Γ = 0. Any given Δ/Γ value will lead to a specific relationship between tracer ages from tracers with different surface histories, and the true Δ/Γ value can be identified by comparing observed tracer age relationships with theoretical ones, i.e., those expected for given Δ/Γ values [Waugh et al., 2004]. For the North Atlantic, for instance, Waugh et al.  constrained Δ/Γ to 0.75 or larger using this approach. Assuming a Δ/Γ of unity has since then become more or less a routine [Waugh et al., 2006; Tanhua et al., 2009].
 As shown by Waugh et al.  not all tracer pairs are equally suitable for constraining Δ/Γ. Pairs with surface histories that differ in shape results in the strongest constraint. For instance, the pair CFC-11 and CFC-12 does not impose strong constraints on Δ/Γ. This is also the case for the Nordic seas, as is illustrated in Figure 2 which compares the observed relationships between Nordic seas τCFC-11 and τCFC-12 values with the theoretical relationships between these tracer ages estimated for different Δ/Γ values. The pattern is more or less similar to that observed in North Atlantic data by Waugh et al. [2004, Figure 3a], and it imposes little, if any constraint on the Δ/Γ values. In fact, the observed relationships do not appear compatible with any of the theoretical ones for ages less than 25 years. The same was observed in the North Atlantic data presented by Waugh et al. , and they proposed that it was caused by different surface saturations of these two tracers. However, assuming different surface saturation affects the observed and theoretical CFC-11-CFC-12 relationships equally. Therefore, invoking different surface saturations for the two tracers did not make the observed relationships fall at the family of theoretical ones. We therefore believe that this feature may indicate that the data for at least one of the two CFC components are slightly biased (∼5%, section A1). This possibility does not have any large influence on our results, as is fully evaluated in Appendix A.
Figure 2. Relationship between Nordic seas τCFC-12 and τCFC-11 determined by comparing pCFC (from measured CFC and the equation of Warner and Weiss , assuming 98% saturation) with the atmospheric CFC history of Walker et al.  through equation (3). Solid lines show the theoretical relationships determined for TTDs with Δ/Γ ranging from 0.25 to 2 by steps of 0.25. The Δ/Γ = 0.25 curve has been labeled. A Δ/Γ = 0 corresponds to τCFC-11 − τCFC-12 = 0 over the whole range of τCFC-12. The breaks in the relationships and negative τCFC-11 − τCFC-12 values at τCFC-12 of approximately 15 years or less are the result of the recent decline of atmospheric CFC-11 and CFC-12 concentrations. This prohibits determination of a unique tracer age for samples within the range of declining values, and τCFC-11 and τCFC-12 were set to zero in these periods. The period is longer for CFC-11 than for CFC-12.
Download figure to PowerPoint
 Waugh et al.  evaluated the ability of several tracer pairs to constrain Δ/Γ, illustrated in their Figure 8. It is evident from their Figure 8 that CFC-12 and a radioactive tracer with a decay rate similar to the atmospheric CO2 growth rate is one of the more suitable pairs. This implies that the pair τCFC-12 − τCO2 would impose strong constraints on Δ/Γ. This strategy is followed in the present study.
 To use CO2 as an age tracer, i.e., to find the carbon dioxide tracer age, we employ the conceptual framework of the ΔC* approach of Gruber et al.  for estimating anthropogenic carbon concentrations. This framework assumes pure bulk advection which allows for the separation of observed inorganic carbon concentrations into (1) the water sample's equilibrium concentration when at the surface, (2) the degree of disequilibrium the water sample had when at the surface, which is assumed to be constant over time, and (3) the change of dissolved inorganic carbon concentration that has taken place since the water parcel left the surface, associated with remineralization and calcium carbonate dissolution
The term holds a time stamp, and this allows for the calculation of the CO2 tracer age. The approach requires an independent estimate of DICdiseq and has not, as far as we are aware, been described in the literature. The lack of this implementation is a result of the far from homogenous surface distribution of CO2 saturation degree [e.g., Takahashi et al., 2009]. However, for the Nordic seas this can be circumvented by using the relationship between surface pCO2 and SST identified by Olsen et al. , as will be described in the following.
 The determination of the carbon disequilibrium, DICdiseq, takes advantage of a fundamental assumption of the TTD, as well as of the ΔC* approach for calculation of DICant, namely that the disequilibrium has remained constant with time. Despite recent observations that indicate otherwise for parts of the Nordic seas over the last two decades [Olsen et al., 2006], this appears to be a reasonable assumption for the region as a whole over the time since the industrial revolution. The effect of assuming otherwise is evaluated in section A1. Now, given that the surface disequilibrium is assumed to be constant, there is no need to propagate it using TTDs, because this method must only be employed for propagation of transients. Thus, if it can be parameterized in terms of conservative properties, this parameterization can be applied to every water sample to get an estimate of the original DICdiseq when at the surface. This enables us to utilize the northern North Atlantic wintertime pCO2-SST relationship [Olsen et al., 2003] to determine DICdiseq since
where the function is the thermodynamic equations relating the inorganic carbon species. The pCO295 was found using the equation determined by Olsen et al. 
and pCO2atm,95 was determined from the 1995 atmospheric mole fraction according to Dickson et al.  using a pressure of 1013.25 hPa, and in situ θ and salinity.
 The impact of remineralization and CaCO3 dissolution on DIC, ΔDICbio, was determined as
where rC:O2 and rN:O2 are the carbon to oxygen and nitrogen to oxygen remineralization ratios, respectively, and AOU is the apparent oxygen utilization. The remineralization ratios derived by Körtzinger et al.  were used, and the sensitivity of the calculations to the choice of rC:O2 and rN:O2 is quantified in section A1. For AOU the following expression was used
where O2sat is the oxygen saturation concentration and O2obs is the observed oxygen concentration. The term ΔO2 is the surface disequilibrium at the time of subsurface water mass formation, which is winter. As defined here, positive values mean undersaturation. Wintertime Nordic seas ΔO2 is significant and must be accounted for. For instance, the simulated disequilibrium [Ito et al., 2004] in the Nordic seas is between 0 and 20 μmol l−1 (from their Figure 1), and was attributed to fast heat loss with oxygen uptake lagging. Observations confirm the simulation of Ito et al. . At OWS M at 66°N and 2°E, Falck and Gade  estimated a mean disequilibrium ranging from approximately 10 μmol l−1 in January to 5 μmol l−1 in March (from their Figure 3) and in the Barents Sea, the study of Olsen et al.  revealed disequilibriums of typically between 10 and 20 μmol l−1 during winter. For a better constraint on Nordic seas ΔO2 during winter, the CARINA O2 values [Falck and Olsen, 2010] were examined. Average ΔO2 in wintertime Nordic seas surface waters was determined to 15 ± 7 μmol kg−1. An upper temperature cutoff of 1°C was used here in order to avoid unduly influence of Norwegian Atlantic Current waters. Given these observations a ΔO2 value of 15 μmol kg−1 is used in equation (10). The sensitivity of our calculations to the value of ΔO2 is evaluated in section A1.
Figure 3. Relationship between Nordic seas τCFC-12 and τCO2, shown along with the theoretical relationships (solid lines) for TTDs with Δ/Γ ranging from 0.25 to 2 by steps of 0.25. Every other curve has been labeled with its Δ/Γ.
Download figure to PowerPoint
 With ΔDICbio and DICdiseq in place, is derived using equation (4). The time stamp, τ, is extracted by first finding
then converting this to the corresponding xCO2(t−τ) and matching this to the atmospheric CO2 history through equation (3).