#### 2.1. Data

[7] 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.* [2006], *Jeansson et al.* [2008], and *Jutterström et al.* [2008] 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 *μ*mol 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

[8] 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 c^{0} over the source region)

where *c*^{0} 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 CO_{2}. For the two former, the surface history was determined using the atmospheric history compiled by *Walker et al.* [2000], and solubility calculated from temperature and salinity according to *Warner and Weiss* [1985], assuming a surface saturation of 98% which is consistent with the observations of *Jutterström et al.* [2008]. The *DIC*^{ant} history was determined as the difference between the preindustrial equilibrium *DIC* and that at time *τ*, using updated Law Dome and Mauna Loa atmospheric CO_{2} mole fraction records. This requires estimates of preformed alkalinity, *Alk*^{0}, and these were obtained from salinity using the relationships specifically determined for the Nordic seas by *Nondal et al.* [2009]. Preformed silicate and phosphate was set to 8 and 1 *μ*mol 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 CO_{2} 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.* [1973] refit by *Dickson and Millero* [1987].

[9] 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 *DIC*^{ant} 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

[10] 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.

[11] To constrain Δ/Γ for the Nordic seas we follow the approach of *Waugh et al.* [2004], 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.* [2004].

[12] 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, *c*_{0} 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.* [2004] 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].

[13] As shown by *Waugh et al.* [2003] 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 *τ*_{CFC-11} and *τ*_{CFC-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.* [2004], 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.

[14] *Waugh et al.* [2003] 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 CO_{2} growth rate is one of the more suitable pairs. This implies that the pair *τ*_{CFC-12} − *τ*_{CO2} would impose strong constraints on Δ/Γ. This strategy is followed in the present study.

[15] To use CO_{2} 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.* [1996] 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 CO_{2} tracer age. The approach requires an independent estimate of *DIC*^{diseq} 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 CO_{2} saturation degree [e.g., *Takahashi et al.*, 2009]. However, for the Nordic seas this can be circumvented by using the relationship between surface *p*CO_{2} and SST identified by *Olsen et al.* [2003], as will be described in the following.

[16] The determination of the carbon disequilibrium, *DIC*^{diseq}, takes advantage of a fundamental assumption of the TTD, as well as of the ΔC* approach for calculation of *DIC*^{ant}, 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 *DIC*^{diseq} when at the surface. This enables us to utilize the northern North Atlantic wintertime *p*CO_{2}-SST relationship [*Olsen et al.*, 2003] to determine *DIC*^{diseq} since

where

and

where the function is the thermodynamic equations relating the inorganic carbon species. The *pCO*_{2}^{95} was found using the equation determined by *Olsen et al.* [2003]

and *pCO*_{2}^{atm,95} was determined from the 1995 atmospheric mole fraction according to *Dickson et al.* [2007] using a pressure of 1013.25 hPa, and in situ θ and salinity.

[17] The impact of remineralization and CaCO_{3} dissolution on *DIC*, Δ*DIC*^{bio}, was determined as

where *r*_{C:O2} and *r*_{N: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.* [2001] were used, and the sensitivity of the calculations to the choice of *r*_{C:O2} and *r*_{N:O2} is quantified in section A1. For AOU the following expression was used

where *O*_{2}^{sat} is the oxygen saturation concentration and *O*_{2}^{obs} is the observed oxygen concentration. The term Δ*O*_{2} 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 Δ*O*_{2} 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 *μ*mol 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.* [2004]. At OWS M at 66°N and 2°E, *Falck and Gade* [1999] estimated a mean disequilibrium ranging from approximately 10 *μ*mol l^{−1} in January to 5 *μ*mol l^{−1} in March (from their Figure 3) and in the Barents Sea, the study of *Olsen et al.* [2002] revealed disequilibriums of typically between 10 and 20 *μ*mol l^{−1} during winter. For a better constraint on Nordic seas Δ*O*_{2} during winter, the CARINA O_{2} values [*Falck and Olsen*, 2010] were examined. Average Δ*O*_{2} in wintertime Nordic seas surface waters was determined to 15 ± 7 *μ*mol 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 Δ*O*_{2} value of 15 *μ*mol kg^{−1} is used in equation (10). The sensitivity of our calculations to the value of Δ*O*_{2} is evaluated in section A1.

[18] With Δ*DIC*^{bio} and *DIC*^{diseq} in place, is derived using equation (4). The time stamp, *τ*, is extracted by first finding

then converting this to the corresponding *x*CO_{2}^{(t−τ)} and matching this to the atmospheric CO_{2} history through equation (3).