#### 2.2. Tracer Data

[11] For analytical precision and accuracies of the individual data sets we refer to the references in Table 1. The stated precisions are generally within WOCE standards. For this study, we used CFC-12 for most mean age and *C*_{ant} calculations since there is a positive atmospheric growth of CFC-12 through most of the sampling period, whereas CFC-11 concentration began to reverse in the early 1990s. For recently ventilated samples (i.e., pCFC-12 > 450ppt) we used measurements of SF_{6, }if available (i.e., part of the Beringia 2005 data), since SF_{6} based *C*_{ant} (and mean age) estimates are less sensitive to errors in assumed saturation and measurements [*Tanhua et al.*, 2008]. For SCICEX96 we used CFC-11 data, since no CFC-12 data are available [*Smethie et al.*, 2000]. A critical property of the transient tracers is the saturation at the time of formation. Even though the Arctic Ocean is covered with sea ice during most of the year, the available CFC measurements show saturation levels that are comparable to open ocean values. For this analysis we have therefore adopted the time-dependent saturation of CFCs demonstrated by *Tanhua et al.* [2008], i.e., it is assumed that the saturation was 86% up to 1989 after which it increased linearly to 100% by year 1999, whereas the saturation of SF_{6} is set at 85%.

#### 2.3. TTD Method to Estimate *C*_{ant} Concentrations and Mean Ages

[12] The *C*_{ant} concentration has been calculated using the transit time distribution (TTD) method [*Hall et al.*, 2002; *Waugh et al.*, 2004, 2006]. The TTD method is based on measurements of transient tracers and a transfer function to scale the tracer concentrations to *C*_{ant}. With the TTD method, the *C*_{ant} concentration is a function of tracer content as well as carbonate chemistry, as we will show below.

[13] The concentration, *c*, of a passive tracer can be determined at any point, *r*, at any time, *t*, with knowledge of the TTD and the input function of the tracer at the sea surface, *c*_{0} (*t*), according to;

where G(r,t) is the TTD. The input function, *c*_{0} (*t*), of the tracers at the sea surface is a function of the atmospheric history of the tracers and their solubilities. Here we have used the updated atmospheric history compilation by J. Bullister (available at http://cdiac.ornl.gov/oceans/new_atmCFC.html) for the CFCs and SF_{6}; for atmospheric CO_{2} we have used updated records from Mauna Loa and Law Dome. The solubilities of the CFCs and SF_{6} were calculated with the salinity and temperature relations provided by *Warner and Weiss* [1985] and *Bullister et al.* [2002], respectively. The transfer of inorganic carbon from the atmosphere to the ocean is further dependent on the buffer capacity (mainly a function of temperature and alkalinity) of seawater at the time when the water was last in contact with the atmosphere. It has been shown [*Jutterström and Anderson*, 2005] that the dissociation constants for the carbonate system from *Roy et al.* [1993] exhibit the best internal consistency for the Arctic Ocean. We therefore use those constants for the buffer capacity calculations together with the dissociation constants for boric acid from *Dickson* [1990]. We further use the surface salinity to alkalinity relation by *Brewer et al.* [1986] to determine the alkalinity of the water at the time of formation at the surface. Thus, with the knowledge of the atmospheric CO_{2} concentration together with the temperature and salinity of the water, the equilibrium concentration of dissolved inorganic carbon (DIC) can be determined for each sample for any time, t, assuming that the salinity/alkalinity relation is valid also for the Arctic Ocean. The *C*_{ant} concentration for the surface water is then calculated as the difference between the DIC concentration at time t and the preindustrial concentration.

[14] The TTD of each interior location is assumed to be best represented by inverse Gaussian functions [*Waugh et al.*, 2003] in which the mixing is represented by two parameters; Γ, the mean age; and Δ, the width of the TTD. It should be pointed out that the mean age in the TTD calculation is different from the “tracer age” that is obtained by comparing the CFC concentration in seawater directly with the atmospheric history of CFCs. The TTD method implicitly includes mixing in the age calculations. Typically, the mean age is significantly higher than the “tracer age”, and explains why there is such a large discrepancy between CFC ages and ages calculated with radioactive isotopes (i.e., ^{14}C).

[15] *Waugh et al.* [2004] demonstrated that the TTD of the ocean can be well approximated with ^{Δ}/_{Γ} = 1 using a combination of different tracers. With the assumption of a fixed relation between Γ and Δ, the TTD can be defined for each water sample by observation of a single transient tracer, such as CFC-12, CFC-11 or SF_{6}. Once the TTD is known, the concentration of any other tracer with a known input function, such as *C*_{ant}, can be determined. One way of testing the assumption of a fixed relation between Γ and Δ in the Arctic Ocean is to compare the mean ages at a station that has been repeated several times. Transient tracers will experience different input histories at different times, i.e., the seawater will have seen different parts of the atmospheric history. This is analogous to comparison of different tracers at the same point in time [e.g., *Waugh et al.*, 2003, 2004], with the difference that also changes in circulation/ventilation will influence the analysis. For this analysis we choose the North Pole, which has been sampled 3 times for CFCs in our data set, in 1991, 1994 and 2005. We calculated the mean age from these 3 repeats and compared the profiles (Figure 2). The upper water column (Figure 2, top) is fairly well ventilated, with mean ages less than 20 years. The exception is the data from1994, where significantly older water is present. This is a large change that can be explained neither by analytical/calibration errors nor by assuming any other ^{Δ}/_{Γ} ratio, but is representing circulation changes, i.e., older water is dominating the halocline and Atlantic Water layers at the North Pole in 1994 compared to 1991 and 2005. This is confirmed by the very similar silicate concentrations at 400-m depth in 1991 and 2005 (∼5 *μ*mol kg^{−1}), compared to the higher values in 1994 (∼6.6 *μ*mol kg^{−1}), indicating a shift of the front over the Lomonosov Ridge for the 1994 data, (Canada Basin Water is high in silicate at this depth [*Anderson et al.*, 1994; *Swift et al.*, 1997]). On the other hand, the 1991 and 2005 profiles are very similar to each other despite the two repeats being separated by 14 years, i.e., the two points in time will have experienced very different parts of the atmospheric history for CFC-12. If the ^{Δ}/_{Γ} ratio was assumed to be different from one and if the circulation was constant, then the calculated mean ages would be different for the two repeats. Since we have seen that the assumption of steady state circulation at the North Pole does not seem to hold true, it could be a coincidence if the two profiles match each other, i.e., errors in the ^{Δ}/_{Γ} ratio/analytical errors could cancel the effect of circulation changes. Another way of determining the ^{Δ}/_{Γ} ratio is to compare two tracers with sufficiently different input functions, sampled at the same occasion (i.e., no interference from circulation changes). We used SF_{6} and CFC-12 data from the Canada Basin for this comparison (similarly to the study by *Waugh et al.* [2004] and *Tanhua et al.* [2008], not shown), and the tracer distribution support the assumption of a ^{Δ}/_{Γ} ratio equal to unity.

[16] In order to estimate *C*_{ant} concentrations based on tracer data from over two decades, and assuming the concept of transient steady state, we scale the *C*_{ant} concentrations to year 2005, the date of the most recent data set in our analysis. This concept states that for tracers with exponentially changing surface water concentrations, the vertical tracer profiles will reach “transient steady state” after a time period several times longer than the exponential growth timescale of the tracer. Once transient steady state is reached, the tracer depth profile will have a constant “shape”, so that the tracer concentration at all depths changes proportionally to the surface concentration, i.e., if the change at the surface is known then the change at depth can be calculated [*Gammon et al.*, 1982; *Tanhua et al.*, 2007]. Since the atmospheric CO_{2} concentrations in excess of 280 ppm can be regarded as the anthropogenic part, *C*_{ant} can be treated as a transient tracer with an exponentially increasing atmospheric history with an e-folding time of ∼70 years, i.e., the transient steady state concept is valid for *C*_{ant}. In practice, this means that, for instance, the *C*_{ant} concentrations calculated for the 1994 cruise with the TTD method has been multiplied with 1.20 to be comparable to the 2005 values. In a similar manner, it is possible to scale the *C*_{ant} inventories from previous studies to year 2005 in order to compare the results.