The distribution and inventory of anthropogenic carbon (DICant) in the Nordic seas are determined using the transit time distribution (TTD) approach. To constrain the shape of the TTDs in the Nordic seas, CO2 is introduced as an age tracer and used in combination with water age estimates determined from CFC-12 data. CO2 and CFC-12 tracer ages constitute a very powerful pair for constraining the shape of TTDs. The highest concentrations of DICant appear in the warm and well-ventilated Atlantic water that flows into the region from the south, and concentrations are typically lower moving west into the colder Arctic surface waters. The depth distribution of DICant reflects the extent of ventilation in the different areas. The Nordic seas DICant inventory for 2002 was constrained to between 0.9 and 1.4 Gt DICant, corresponding to ∼1% of the global ocean DICant inventory. The TTD-derived DICant estimates were compared with estimates derived using four other approaches, revealing significant differences with respect to the TTD-derived estimates, which can be related to issues with some of the underlying assumptions of these other approaches. Specifically, the Tracer combining Oxygen, inorganic Carbon and total Alkalinity (TrOCA) method appears to underestimate DICant in the Nordic seas, the ΔC* shortcut and the approach of Jutterström et al. (2008) appear to overestimate DICant at most depths in this area, and finally the approach of Tanhua et al. (2007) appears to underestimate Nordic seas DICant below 3000 m and overestimate it above 1000 m.
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 The rising concentration of carbon dioxide (CO2) in the atmosphere is currently exercising a very significant influence on the evolution of the global climate system [Forster et al., 2007]. The increase in CO2 is caused by fossil fuel burning, cement production and land use change, while it is dampened by ocean and terrestrial CO2 uptake. The current annual ocean uptake of anthropogenic carbon is 2.2 ± 0.3 Gt C [Gruber et al., 2009], corresponding to about 25% of the emissions. The current uptake by the land biosphere is of approximately equal magnitude [Manning and Keeling, 2006]. On longer timescales the oceans appear to be the more important sink. For instance, Sabine et al.  estimated the integrated ocean CO2 sink between the industrial revolution and 1994 to be 118 Gt C, corresponding to 50% of the emitted CO2 and after considering the magnitude of the emissions in themselves and the atmospheric CO2 inventory, Sabine et al.  deduced that the land biosphere must have been a net CO2 source over that period. As regard the future, coupled climate-carbon cycle model simulations indicate a sustained or increasing ocean sink, while the terrestrial sink may diminish [Friedlingstein et al., 2006].
 A sustained ocean sink for anthropogenic carbon (DICant) relies on vertical mixing since this transports water that has been exposed to the present atmosphere from the upper to the deeper ocean while it brings older unexposed water to the surface. This results in a transfer of DICant from the surface to the deep ocean, which has the larger volume thus, storage capacity. The Nordic seas (Figure 1) are potentially important in this respect, as they annually generate 6 Sv of overflow water [Hansen and Østerhus, 2000], which is a main source of North Atlantic deep water [Dickson and Brown, 1994]. The overflow water is primarily formed by modification of North Atlantic Water (NAW) that enters from further south as the northward extension of the Gulf Stream, North Atlantic Current and North Atlantic Drift system [Eldevik et al., 2009] and which have high concentrations of DICant [Olsen et al., 2006].
 However, despite their potential importance, there have only been two dedicated basin-scale studies to determine the DICant content of waters in the Nordic seas: Chen et al.  and Jutterström et al. . Chen et al.  presented sections of DICant (actually ΔTCO20, the difference of preformed normalized total carbon in old and new waters), using the data from the Hudson 1982 cruise and the method of Chen and Millero . However, studies have revealed issues with the data [Olsen, 2009a, 2009b] as well as the method [e.g., Shiller, 1981; Chen et al., 1982; Broecker et al., 1985; Chen and Drake, 1986]. In particular, in the Nordic seas one cannot expect the deep waters to be fully devoid of anthropogenic CO2. The approach of Jutterström et al.  used observed relationships between nitrate, phosphate, and DIC versus CFCs and assumptions on the DICant content of CFC free waters to determine DICant concentrations in this area. But their method was only applicable in waters colder than 1°C and with salinity lower than 35, which leaves out the NAW in the Norwegian Atlantic Current (NAC), a key feature of the area and which carries DICant from further south into the region [Olsen et al., 2006]. This omission implies that their Nordic seas DICant inventory estimate of 1.2 Gt C may be biased low.
 In this contribution we derive the parameters characterizing the TTD in the Nordic seas, determine the distribution and inventory of DICant in the area, compare the results of this approach with those of four other widely used approaches, and rationalize the difference that we observe.
2. Data and Methods
 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 .
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.
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.
 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).
3.1. TTD Parameters Derived From CFC-12 and CO2 Ages
Figure 3 compares the CO2 and CFC-12 tracer ages. For waters with τCFC-12 less than 20 years, τCO2-τCFC-12 does not provide enough resolution to determine Δ/Γ, neither did τCFC-11-τCFC-12. However, for waters with τCFC-12 greater than 20 years the theoretical relationships are far better separated than those determined for τCFC-11-τCFC-12 (Figure 2), confirming that τCO2-τCFC-12 is a suitable pair for constraining Δ/Γ. For instance, unlike τCFC-11-τCFC-12, as well as several of the other tracer pairs considered by Waugh et al. , the theoretical relationships between τCO2 and τCFC-12 clearly resolves differences of Δ/Γ values of 0.25. The observed relationships take on a range of values. To a large extent we believe this is due to uncertainties in the determination of τCO2, which are addressed in section A1, but it may also reflect true variations of the ratio. Important here is that essentially all observed points fall above the theoretical relationship for Δ/Γ of 0.5, and this should be considered the lower limit of possible Nordic seas Δ/Γ values. Most of the data fall within the space spanned by the theoretical lines for Δ/Γ 0.75 and 1.5, and seem centered around unity. An absolute upper limit cannot be determined with these data. Theoretical relationships up to 2.0 have been drawn in Figure 3, but it requires unreasonably high Δ/Γ values, e.g., on the order of 103–104, to explain some of the points, and their presence are better explained as being the result of uncertainties in the parameters used for determination of τCO2. The Nordic seas TTD thus appear broad, and similar to those determined for the surrounding ocean regions, i.e., North Atlantic [Waugh et al., 2004] and Arctic Ocean [Tanhua et al., 2009], which is not unreasonable. Given these observations 0.5 is considered as the lower limit for probable Nordic seas Δ to Γ ratios, 1 the most probable, and 1.5 as the upper limit. The upper limit of 1.5 was in part motivated by Figure 3, and in part by the observations from further south [Waugh et al., 2004]. This range was robust even after consideration of the uncertainties of our approach (section A1).
3.2. Anthropogenic CO2 Distribution
 The distribution of anthropogenic CO2 in the year 2002, determined from equation (1) and a Δ/Γ of unity is shown in Figure 4, along with the contours of potential density (σθ). Figure 4a shows a west-east section along 70°N and Figure 4b shows a section that goes approximately south-north, from the Iceland shelf edge into the Greenland Sea, both of these have been highlighted in Figure 1. In particular, in the section that goes across the Norwegian and Iceland seas (Figure 4a), the distribution of DICant follows the density surfaces. The largest concentrations, between 40 and 45 μmol kg−1, are observed in the lightest waters, of σθ less than 27.98 which are found above 1000 m in the Norwegian Sea. This is the well-ventilated and warm Norwegian Atlantic Current that transports DICant into and through the region. Immediately below this, the Arctic Intermediate Waters (AIW) are found, these have potential densities of up to 28.07 [Aagaard et al., 1985], and DICant concentrations span the range of values from 15 to 35 μmol kg−1. The AIW is found at shallower depths in the Iceland Sea, which is one of their formation areas [Blindheim, 1990]. The isolines of DICant and σθ slopes upward into this area, which has lower DICant concentrations in the upper 1000 m than the Norwegian Sea. The DICant concentration in the deep waters of the Norwegian Sea are between 5 and 15 μmol kg−1, this is lower than the concentrations in the deep Greenland Sea, which are normally between 10 and 15 μmol kg−1 (Figure 4b). This is because the fraction of relatively old deep waters from the Arctic Ocean is higher in the Norwegian than in the Greenland Sea. The Greenland Sea is otherwise more vertically homogenous than both the Iceland and Norwegian Sea, reflecting the more extensive convective activity in this area, and in the central Greenland Sea the upper 1000 m have DICant concentrations between 30 and 35 μmol kg−1.
 The distribution of DICant in the upper 1000 m of the Nordic seas is governed partly by ventilation time and partly by temperature. The waters in the upper 1000 m in the Greenland Sea are around 5 years older than the North Atlantic Waters (NAW) of the Norwegian Atlantic Current. This age difference explains almost half of the difference in DICant concentrations of approximately 10 μmol kg−1. The rest of the difference is explained by the temperature difference with the NAW being 5–10°C warmer than the waters of the Greenland Sea. The Revelle factor is thus lower for the NAW, i.e., the capacity for DICant uptake is larger. In addition the alkalinity of NAW is greater, but this effect explains only about 1 μmol kg−1 of the difference in DICant.
 The AIW of the Nordic seas flows over the Greenland-Scotland ridge into the deep North Atlantic and is a main source of North Atlantic deep water [Swift et al., 1980; Dickson and Brown, 1994]. To obtain an estimate of the surface to deep water export of DICant associated with this process, we combine our DICant estimate with a volume flux estimate from the literature. The total flux of cold overflow water across the ridge has been estimated to almost 6 Sv [Hansen and Østerhus, 2000]. The mean properties of the water were summarized by Eldevik et al. . The Denmark Strait overflow water spans the theta and salinity ranges of approximately 0–0.5°C and 34.85–34.9, respectively, while the respective ranges for Faeroe-Shetland Channel overflow water are approximately 0–0.5°C, and 34.9–34.94. The waters with these properties were identified in our data, and although not marked in Figure 4, they correspond to waters found in the σθ range of between 27.98 and 28.02 and which have DICant of typically between 25 and 30 μmol kg−1. Combining these concentrations with the volume flux, gives us an annual mean export of DICant from the Nordic seas into the deep North Atlantic of between 0.06 and 0.07 Gt C, which corresponds to 3% of the annual global ocean uptake of DICant of 2.2 Gt C [Gruber et al., 2009].
3.3. Anthropogenic CO2 Inventory
 The Nordic seas DICant inventory was determined by using the approach described for the Arctic Ocean by Tanhua et al.  which interpolates each DICant profile onto 50 m depth intervals using a piecewise cubic Hermite, and then use the topography following mapping scheme described by Davis  and Rhein et al.  to map the interpolated data onto a regular grid. The upper 250 m were not included in our calculations (section 2.1) so we assumed that these were saturated with DICant. The mapped column inventories are shown in Figure 5. They range from less than 10 to more than 70 mol m−2 and show a clear dependence on bottom depth (Figure 1). The largest column inventories are found over the deep Greenland, Lofoten and Norwegian Basins, while the smaller are found over the Iceland Plateau, and the continental shelves. However, the distribution over the three deep basins is also modulated by the distribution of water masses and their DICant content. The depth of the layer of NAW is deeper in the Lofoten Basin than in the Norwegian Basin [Orvik, 2004], and hence the column inventory is greater over the Lofoten Basin than over the Norwegian Basin. The column inventory is even greater over the Greenland Basin, this is in part because the Greenland Basin is the deepest, but it is also because relatively recently ventilated water masses has penetrated deeper here than in the other two deep basins, as can be appreciated from Figure 4.
 The total inventory of the Nordic seas and its subregions are provided in Table 1. The limits between the subregions were set as by Jakobsson  who follows International Hydrographic Organization . The ocean volumes estimated through our mapping routine (Table 1) do not match the volume estimates determined from the International Bathymetric Chart of the Arctic Ocean (IBCAO) exactly [Jakobsson, 2002]. This is caused by the lower resolution of the bathymetry (the 5 min TerrainBase of NOAA/National Geophysical Center) used for the mapping as well as the 50 m layer thickness. Therefore all inventories have been scaled to the ocean volumes published by Jakobsson  using the simple normalization equation
where Invorg and Vorg are the inventory and volume estimates determined through the mapping routine and VJ is the volume estimates of Jakobsson . This scaling changed the Greenland Sea inventory estimate by 2%, the Norwegian Sea estimate by 0.8%, and the estimates for the Iceland Sea and Denmark Strait by 0.3% and 10%, respectively. The large relative change of the Denmark Strait estimate is due to its small size and corresponds to only 0.003 Gt C. These estimates indicate that the Nordic seas contain 1.24 Gt DICant. This is approximately 1% of the global ocean DICant inventory estimate of Sabine et al. . Given the estimates of the carbon transport of the overflow waters of ∼3% of the annual global ocean DICant uptake, determined above, the Nordic seas appear more important for mediating surface to deep ocean DICant transport than for storage. The small inventory of this area is a consequence of the small volume, corresponding to ∼0.3% of the global ocean volume.
Determined using a Δ/Γ value of 1, a time-invariant air-sea CO2 disequilibrium, a surface CFC-12 saturation of 98%, and assuming that the upper 250 m of the water column is saturated with anthropogenic CO2. See text for a discussion of the uncertainties. Vmapped is the volume mapped by our interpolation routines, and VJakobsson is the volume estimates published by Jakobsson .
 Our estimate of the Nordic seas DICant inventory can be combined with the inventory estimate for the Arctic Ocean of 3 Gt DICant, determined through a similar approach by Tanhua et al. . This estimate was for the year 2005, and assuming transient steady state our Nordic seas estimate scaled to 2005 is 1.3 Gt. Adding these numbers we get a year 2005 Arctic Ocean and Nordic seas DICant inventory of 4.3 Gt C. This is 2.1 Gt C smaller than the estimate of Sabine et al.  scaled to 2005, of 6.4 Gt C [Tanhua et al., 2009] for these areas.
 There are four significant sources of uncertainty that affects our DICant estimates, as identified in section A2, and thus the Nordic seas inventory estimate: (1) lowering the Δ/Γ ratio increases the DICant estimates and vice versa, (2) the CFC-12 data we have used are possibly biased high by 5%, which translates into a potential DICant bias of between +0.25 and +1.6 μmol kg−1, depending on depth, (3) a time variant CFC-12 surface saturation will increase the DICant estimates, and (4) an increasing air-sea CO2 disequilibrium will reduce the DICant estimates. These uncertainties will also affect our Nordic seas anthropogenic carbon inventory estimate. An absolute upper limit of the Nordic seas DICant inventory was determined by assuming a Δ/Γ of 0.5 and a time variant CFC-12 surface saturation, this gave an inventory of 1.42 Gt C. An absolute lower limit was determined by adjusting all the CFC-12 data down by 5%, applying a Δ/Γ of 1.5, and assuming that the air-sea CO2 disequilibrium in the Nordic seas has increased over time. In addition we assumed that the DICant concentration in the upper 250 m are the same as the concentrations in the 250–300 m depth layer, rather than assuming that this layer is saturated with DICant as was originally done. This gave an inventory of 0.86 Gt C. Thus our Nordic seas DICant inventory estimate of 1.24 Gt C may possibly deviate by −0.38 Gt C and +0.18 Gt C.
3.4. Comparison With Other Methods
Figure 6 compares the TTD-derived DICant estimates with the estimates derived using the ΔC* shortcut approach [Gruber et al., 1996], the approach of Jutterström et al. , the revised Tracer combining Oxygen, inorganic Carbon and total Alkalinity (TrOCA) approach [Touratier et al., 2007], and the approach of Tanhua et al.  which we have labeled eMLRe (extended Multi Linear Regression extension). This latter approach requires an estimate of the DICant increase over decadal timescales; these were obtained from Olsen et al. . Unlike another comparison [Vázques-Rodríguez et al., 2009], negative DICant estimates have not been set to zero. The uncertainty of the TTD-derived estimates is given by the gray area, with the upper and lower bounds determined in the same way as for the inventory, i.e., by assuming Δ/Γ of 0.5 and time-dependent CFC-12 saturation for the upper bound, and by adjusting the CFC-12 data down by 5%, and assuming Δ/Γ of 1.5 and time-dependent CO2 surface saturation for the lower.
 The DICant estimates derived using the ΔC* shortcut approach [Gruber et al., 1996] are larger than the upper bound of the TTD-derived estimates, except in the upper 1000 m. This is as expected since this approach is essentially an implementation of the TTD approach with Δ/Γ set to zero, i.e., one assumes that the tracer age represents the true and unique age of the water parcel, and the lower the Δ/Γ the higher the DICant.
 The DICant estimates derived using the approach of Jutterström et al.  are also larger than the ones derived using the TTD approach, except for above 750 m, where the estimates derived with the approach of Jutterström et al.  are lower than the estimate derived using Δ/Γ = 1. The lower values in the upper ∼750 m results from the fact that the method of Jutterström et al.  is not applicable in the Norwegian Atlantic Current, which has large concentrations of DICant. The larger values below this, is the result of assumptions employed when a key number for this approach was determined, the DICant at the time of zero CFC-11, which is used to determine the intercept of the theoretical CFC-11-DIC regression line. This line is the expected CFC-11-DIC relationship in the absence of DICant, and DICant is estimated as the difference between observed DIC and values estimated from this theoretical line. The intercept was determined by Jutterström et al.  through evaluating the relationship between calculated CFC-11 and DICant at a temperature, salinity, alkalinity, and saturation level typical for the Greenland Sea. For CFC-11 = 0 the DICant was found to be 17.6 μmol kg−1. This estimate was subtracted from the observed intercept of 2160.5 μmol kg−1, to give the intercept of the theoretical relationship of 2142.9 μmol kg−1. This approach assumes bulk advective transport, i.e., Δ/Γ = 0. Thus Jutterström et al.  overestimates DICant at CFC = 0 which leads to a too small intercept of the theoretical CFC-11-DIC relationship. Using TTDs with Δ/Γ of 1.0 we get a DICant of around 5 μmol kg−1 at the time of zero CFC-12, using this would lower the DICant estimates of Jutterström et al. . Despite of the differences in the DICant distribution, the inventory determined by Jutterström et al.  is similar to our TTD-derived inventory estimate of 1.24 Gt. This is partially because Jutterström's method overestimates DICant at depth while at the same time missing the high concentrations in the NAW, and partly because their inventory estimate does not include the upper 250 m, which holds large amounts of DICant. For instance, of our TTD-derived inventory estimate of 1.24 Gt DICant, ∼0.35 Gt is found in the upper 250 m. Adding this to the estimate by Jutterström et al.  would increase their inventory to 1.55 Gt DICant.
 The DICant estimates derived through the revised TrOCA approach [Touratier et al., 2007] are mainly negative at depth, and this was also the case for estimates (not shown) derived using the original TrOCA approach [Touratier and Goyet, 2004a]. This is unrealistic, and in conflict with the use of anthropogenic CO2 as an explanation for the high TrOCA values in the Nordic seas observed by Touratier and Goyet [2004b]. The very low DICant values derived through the TrOCA approach are in agreement with the TrOCA based estimates of Vázques-Rodríguez et al. , which were derived using a subset of the data used in this study. They are also in agreement with the 1990s (their Figure 5), but not 1980s (their Figure 4) estimates of Touratier and Goyet [2004a]. The difference between these two latter estimates may be due to lower accuracy of the older data. Regardless, the TrOCA approach appears to underestimate DICant in the Nordic seas. We believe this happens because the empirical fit to determine TrOCA0 of Touratier and Goyet [2004a], as well as that of Touratier et al. , overestimates Nordic seas TrOCA0 values. TrOCA is essentially the carbon version of the tracer NO introduced by Broecker , and besides air-sea gas exchange and nitrification/denitrification, their distributions are governed by the same processes in the ocean. Hence, these are quite similar as can be appreciated from Figures 2c and 2f of Touratier and Goyet [2004b], and both tracers also tend to decrease with increasing potential temperature [Touratier and Goyet, 2004a, Figure 2; Broecker, 1974, Figure 2]. This temperature dependency was utilized by Touratier and Goyet [2004a] and in large part by Touratier et al.  for parameterizing the preindustrial distribution of TrOCA, TrOCA0. However, and analogously to NO, Nordic seas TrOCA0 are likely to fall below the values expected from the TrOCA0-θ mixing line that applies elsewhere. For NO this is in large part due to the lower preformed nitrate concentrations in the Nordic seas [Broecker, 1974, Figure 2] caused by the export production that occurs as the waters travels northward as part of the thermohaline circulation. Export production would also affect DIC, but would be compensated by uptake of atmospheric CO2. The difference in preformed nitrate that explains the difference in NO between Weddell Sea water and Nordic seas water is 11 μmol kg−1 (from Figure 2 of Broecker ). Using the classical carbon-to-nitrogen remineralization ratio of 106:16 [Redfield et al., 1963] this translates to a DIC difference of ∼72 μmol kg−1. Using the set of equations of Touratier and Goyet [2004a] this would translate to a difference in TrOCA0 values of 86 μmol kg−1 with the Nordic seas values being lower. The difference between our TTD and TrOCA based estimates of DICant implies that Nordic seas TrOCA0 is overestimated by between approximately 12 and 18 μmol kg−1 (1.2*(DICant, TTD − DICant, TrOCA)), much less than the 86 μmol kg−1 expected from export production alone. We believe this reflects the compensating effect of air-sea CO2 exchange.
 The final approach we have employed here is the eMLRe [Tanhua et al., 2007]. The DICant estimates derived through this approach are at the lower boundary of our TTD-derived estimates in deep waters and higher than the upper boundary in surface waters. The eMLRe method is essentially a scaling of recent changes in DICant with the full growth history since preindustrial times. A fundamental assumption here is that the relative DICant response to the atmospheric CO2 perturbation over the last few decades is the same as the relative response to the full atmospheric perturbation. This assumption may be violated in the Nordic seas. At depth the fraction of deep waters from the Arctic Ocean has increased over the last two decades [Blindheim and Rey, 2004; Skjelvan et al., 2008]. It is not unlikely that these relatively older waters carry less DICant than locally formed relatively younger Greenland Sea Deep Water. Thus, the deep water DICant response to the atmospheric CO2 growth over the last two decades may be atypically low compared to the full increase. This would cause the eMLRe method to underestimate DICant at depth. As regard the surface waters, the response observed by Olsen et al.  in particular to the south, may be atypically high and in part related to shifts in the ocean circulation associated with changes in the atmospheric circulation pattern [Thomas et al., 2008]. This would cause eMLRe to overestimate DICant in surface waters.
4. Summary and Conclusions
 We have demonstrated that it is possible to calculate a CO2 age, which together with CFC-12 ages does indeed constitute a powerful pair for constraining the Δ/Γ of transit time distributions, as originally suggested by Waugh et al. . The number of uncertainties involved in the calculation of the CO2 age, as treated in section A1, prohibits full exploitation of the potential of this tracer pair, and calls for better parameterizations of wintertime sea surface ΔO2 and pCO2 using conservative parameters. Accurate determination of the long-term time variation of the air-sea CO2 disequilibrium would also be worthwhile in this context. We were able to constrain Nordic seas Δ/Γ to between 0.5 and 1.5, with 1 being the most probable value.
 A very important, but hitherto not explicitly stated, corollary of the calculations is that the assumptions that the air-sea CO2 disequilibrium is time-invariant and that tracer age represents the true water mass age, i.e., fundamental assumptions of the ΔC* shortcut approach, are mutually exclusive in the Nordic seas. Had these assumptions been consistent with each other, then the τCO2-τCFC-12 estimates of Figure 3 should all fall on the zero line. This is not the case, and the observations can only be explained by invoking transit time distributions, or an overall significantly decreasing air-sea CO2 disequilibrium in the subducting waters of the Nordic seas, the latter is inconsistent with observations over the last twenty years (section A1).
 The calculations enabled us to determine a Nordic seas anthropogenic CO2 inventory of 1.24 Gt C for the year 2002, with 0.86 and 1.42 Gt C as the lower and upper bounds, corresponding to ∼1% of the global ocean inventory [Sabine et al., 2004]. While this number is not large in absolute terms, it reflects the overall high DICant concentrations of an area which comprises ∼0.3% of the global ocean volume. Combined with the estimate of Tanhua et al.  we get a combined Nordic seas and Arctic Ocean anthropogenic CO2 inventory for the year of 2005 of 4.3 Gt C, ∼3–4% of the global ocean inventory.
 The column inventory of the Nordic seas is basically a function of water depth, modulated by the DICant concentration and water mass distribution. The concentrations are largest in the NAW in the Norwegian Atlantic Current, which has been exposed to the atmosphere on its way northward from the North Atlantic, and which is relatively warm and thus has the greatest buffer capacity. The transport of DICant with this inflow is a key source of DICant to the Nordic seas and the present results allows for a rudimentary assessment of the fate of this DICant. Olsen et al.  estimated an annual influx of 0.12 Gt DICant by combining a DICant estimate of 53 μmol kg−1 with a volume flux estimate of 6 Sv of NAW flowing into the Nordic seas. Our DICant concentration estimates in the NAW are slightly smaller (Figure 4); 45 μmol kg−1 does not appear unreasonable. This implies an inflow of ∼0.1 Gt DICant y−1, this is ∼5% of the annual global ocean accumulation. The NAW circulates and overturn in the Nordic seas and Arctic Ocean, and constitutes the primary source of the overflow waters crossing the Greenland-Scotland ridge [Eldevik et al., 2009]. As estimated in section 3.2, these waters transport ∼0.06 Gt DICant y−1 (3% of annual global ocean accumulation) into the deep North Atlantic. Thus, by difference and neglecting any surface outflows, ∼0.04 Gt (∼2% of the annual global ocean accumulation) of the DICant carried by the NAW accumulates in the Nordic seas and Arctic Ocean each year.
Appendix A:: Uncertainties
A1. Uncertainties of the TTD Parameters
 The calculation of τCO2 (section 2.3) involves a number of assumptions and approximations that introduce uncertainties in the results, the most important are identified as (in random order) (1) the ΔO2 value, (2) the wintertime sea-surface pCO295 estimates, (3) the equation for determination of Alk0, (4) the carbon-nitrogen and carbon-oxygen remineralization ratios, and (5) the assumed CO2 surface saturations. The calculation of τCFC-12 is sensitive to the accuracy of the CFC-12 data and the assumed CFC-12 surface saturation. The sensitivity of our results on probable Nordic seas Δ/Γ values to each of these factors is evaluated in the following.
 The ΔO2 value directly influences the AOU estimates, which are used for determination of ΔDICbio and thus τCO2. Changing the ΔO2 value changes the τCO2 estimates and thus the range of probable Δ/Γ values. The standard deviation of the Nordic seas winter time ΔO2 estimate was 7 μmol kg−1. The effect of this uncertainty on the τCO2 − τCFC relationships is illustrated in Figure A1. As the value of ΔO2 is increased, the range of probable Δ/Γ spans smaller values, and with a ΔO2 of 22 μmol kg−1, Δ/Γ values of between 0.25 and 1 seems most probable. Based on the available data, the ΔO2 value of 15 μmol kg−1 that has been used throughout this work appears to be the best estimate for typical Nordic seas surface winter water and we do not expect that the range of Δ/Γ values that has been assumed, i.e., 0.5 to 1.5, is biased. However, it is quite likely that variability of the ΔO2 around its mean of 15 μmol kg−1 contributes to the spread of the observed τCO2-τCFC-12 relationships. Ideally the distribution of Nordic seas ΔO2 should be better understood and preferably parameterized in terms of conservative parameters.
 The equation of Olsen et al.  was used for determining pCO295 that goes into the DICdiseq term of equation (4). These estimates carry an uncertainty of ±10 μatm [Olsen et al., 2003]. The effect on the τCO2-τCFC-12 relationships is illustrated in Figure A2. As the pCO295 is lowered by 10 μatm, the τCO2-τCFC-12 relationships span lower values of probable Δ/Γ, and most values fall within ratios of between 0.25 and 1. The opposite effect is seen when 10 μatm is added to the pCO295 values computed by equation (8). However, we do not believe that uncertainties of the pCO295 estimates has introduced biases in the range of Δ/Γ values used for this work, as the ±10 μatm reflects the random error of the pCO295 estimates determined through equation (8). But, it is quite likely that variability of the true pCO295 left unexplained by equation (8) is a significant contributor to the spread of the observed τCO2-τCFC-12 relationships.
 The equations of Nondal et al. , which were employed here to determine Alk0, have a root mean square error of ±6 μmol kg−1. The effect of this uncertainty on the τCO2 is illustrated, through its effect on the τCO2-τCFC-12 relationships, in Figure A3. Lowering Alk0 leads to a slight reduction of the probable Δ/Γ values and vice versa for increasing Alk0. The effect is clearly smaller than the effect of the uncertainty in ΔO2 (Figure A1) as well as pCO295 (Figure A2) and not large enough to move the majority of the data out of the space spanned by the theoretical relationships for Δ/Γ of 0.5 and 1.5. Still, part of the variation of the observed τCO2-τCFC-12 relationships is likely caused by variations in Alk0 not explained by the equations of Nondal et al. .
 The remineralization ratios are used for determination of ΔDICbio and, hence, affect the τCO2 values. Several estimates exits and the ones of Körtzinger et al.  were used in this study. In addition, the consequences of using the ones of Redfield et al. , Takahashi et al. , and Anderson and Sarmiento  were evaluated. The effect on the τCO2-τCFC-12 relationships was small (not shown) and in general less than the effect caused by the uncertainty of Alk0 depicted in Figure A3. However, using the remineralization ratios of Takahashi et al.  had a clear effect on the τCO2-τCFC-12, changing the range of probable Δ/Γ values to 0.25–1.0. This is because of the relatively low rC:O2 of Takahashi et al. , but this is an artifact as their method did not account for the presence of anthropogenic CO2 [Körtzinger et al., 2001]. Hence, the choice of available unbiased remineralization ratios has in reality very little effect on the results presented here.
 The accuracy of the CFC-12 data will affect the τCFC-12 estimates. The information we have indicates that the CFC-12 data we have used may possibly be biased high, but not low, by up to 5%: (1) The CFC-11-CFC-12 relationships for the three cruises we have used all appear slightly low over the main range of values [Jeansson et al., 2010, Figure 6], and this indicates that the CFC-11 data may be biased low and/or the CFC-12 data high. (2) The observed τCFC-11-τCFC-12 relationships fell systematically above the theoretical ones (Figure 2, section 2.3); this was consistent for the three cruises, and also indicates that the CFC-11 data may be biased low and/or the CFC-12 data high. Both of these features disappeared if the CFC-11 data were adjusted up by 5%, or the CFC-12 data down by 5% (for the G.O. Sars cruise this adjustment comes on top of the 5% reduction of CFC-12 values already recommended by Jeansson et al. ). Hence a 5% bias in one of the CFC components cannot be ruled out, but the effect of adjusting the CFC-12 data down by 5% was hardly discernible in Figure 3, however, and our assumed range of Δ/Γ values is robust with respect to this potential source of error.
 The final sources of uncertainty that will be discussed here are the effects of changes in surface saturation of CFC-12 and CO2, the latter is commonly referred to as the air-sea CO2 disequilibrium. The surface saturation of CFC-12 will affect the τCFC-12 used for the determination of Δ/Γ, whereas temporal changes in the surface CO2 saturation, or disequilibrium, will imply that equation (5) is incorrect and thus affect the determination of the CO2 tracer age. The effects of the CFC-12 saturation are dealt with first.
 In our calculations we have assumed a CFC-12 surface saturation of 98%. If the saturation is smaller than this, then our τCFC-12 represents an overestimate, and a reduction will shift the observed τCFC-12 plotted in Figure 3 to the left and the τCO2-τCFC-12 slightly up. The magnitude of this effect was determined by using the time-variant surface saturation deduced by Tanhua et al.  as a boundary condition. This represents a reasonable degree of CFC-12 undersaturation: 86% until 1989, then increasing to 100% in 1999 and remaining at that level thereafter. The effect on the τCFC-12-τCO2 relationships was very small and 0.5 remained the lower limit and 1.5 the reasonable upper limit.
 As for the effect of the CO2 saturation degree, in our calculations we have assumed that the CO2 disequilibrium has remained constant with time. In the Nordic seas the disequilibrium has changed over the past twenty years. The work presented by Olsen et al.  showed that in the northern regions it appears to have increased while decreasing in the south. As a first-order approximation they found that the annual pCO2 changes in the upper 500 m of the Nordic seas between 1981 and 2002/2003 could be expressed in terms of salinity: 2.074 × S −71.13, r2 = 0.6, RMS = 0.2. The data we have used have a mean salinity of 34.92, which gives a surface pCO2 change of 1.3 μtam y−1, which is approximately 80% of the atmospheric increase in the same time interval. Thus the data indicates that overall, in the waters that subduct, the CO2 disequilibrium may be increasing with time. For τCO2, this implies that the estimates we have presented in Figure 3 may be too small, i.e., we have used DICeq,95 to estimate DICdiseq (equation (5)) and since the majority of data are likely older than 1995 this gives a too large disequilibrium, which translates into a too large and too small age. This would shift the observed τCO2-τCFC-12 relationships vertically upward. This would increase the lower limit of possible Δ/Γ values, but not affect the upper limit as the slopes of the theoretical lines are almost vertical in the range in question. Thus 0.5 remains a lower limit of possible Nordic seas Δ/Γ values.
A2. Uncertainties of the DICant Estimates
 Several uncertain factors affect the DICant estimates, the most important are (in random order) (1) the Δ/Γ ratio, (2) the Alk0 estimate, (3) the accuracy of the CFC-12 data, (4) the assumed CFC-12 surface saturation, and (5) the possibility of a changing CO2 disequilibrium.
 A span of possible Nordic seas Δ/Γ values of between 0.5 and 1.5 was determined. Lower Δ/Γ values give higher DICant estimates, and the effect is larger for small Δ/Γ values than for higher. Reducing the Δ/Γ value from 1 to 0.5 increases the DICant estimates by approximately 4 μmol kg−1 at depth, and much less at the surface. Increasing the ratio to 1.5, lowers the DICant estimates by approximately 1 μmol kg−1 at depth and much less at the surface.
 The preformed alkalinity estimates carries an uncertainty of ±6 μmol kg−1 [Nondal et al., 2009]. Given a Δ/Γ of 1, this translates into an uncertainty in DICant on the order of ±0.1 μmol kg−1, which is insignificant.
 The CFC-12 data are possibly biased high by 5% (section A1). This translates into a potential bias in our TTD-derived DICant estimates of +0.25 μmol kg−1 below 1750 m, and then increasing almost linearly with depth to +1.6 μmol kg−1 at 250 m.
 As for the effect of the surface CFC-12 saturation on the calculation of DICant for any given Δ/Γ; assuming a lower CFC-12 saturation will increase the DICant estimates as the mean age will decrease, i.e., waters are younger and so they contain more anthropogenic CO2. The magnitude of this effect was evaluated by using the time variant surface saturation deduced by Tanhua et al. , as a boundary condition. This increased the estimates of DICant, by approximately 0.5 μmol kg−1 for concentrations of 10 μmol kg−1, 1 μmol kg−1 for 20 μmol kg−1, up to 2.5 μmol kg−1 for concentrations of 35 μmol kg−1, and then the impact became smaller and decreased to 0.5 μmol kg−1 for the largest DICant at 45 μmol kg−1. The effect is thus quite small in older waters since they contain little DICant and were formed at a time when CO2 concentrations in the atmosphere rose slowly so a change of age distribution does not have as large an impact on anthropogenic CO2 concentrations as it does in younger waters with higher concentrations of DICant. For younger waters, with the highest concentrations of DICant, the effect is reduced since the assumed CFC-12 saturation approaches, and end up at approximately the saturation degree originally assumed, i.e., 98%.
 Finally, as for the effect of changing CO2 disequilibrium on the calculation of DICant for any given Δ/Γ, calculations showed that changes in disequilibrium translates approximately linearly into DICant. Thus a surface ocean pCO2 growth rate of 80% of that of the atmospheric pCO2, translates into a decrease of the DICant estimates of 20%.
 Financial support for this work was supplied by the Research Council of Norway through A-CARB (178167/S30), the EU IP CARBOOCEAN (5111176–2), and the Swedish National Space Board through RESCUE-II (62/07:2). The authors would like to express their gratitude to Denis Pierrot (NOAA/AOML) and Toste Tanhua (Leibniz Institute for Marine Sciences) for sharing their Matlab® codes and Martin Jakobsson (Stockholm University) for providing his area defining polygons. Comments from two anonymous reviewers and editor Frank Bryan were very helpful and highly appreciated. This is contribution A287 of the Bjerknes Centre for Climate Research.