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Nordic seas transit time distributions and anthropogenic CO2

Are Olsen,1,2 Abdirahman M. Omar,1,3 Emil Jeansson,1 Leif G. Anderson,2

and Richard G. J. Bellerby1,3

Received 4 May 2009; revised 27 November 2009; accepted 15 December 2009; published 7 May 2010.

[1] The distribution and inventory of anthropogenic carbon (DICant) in the Nordic seasare determined using the transit time distribution (TTD) approach. To constrain the shapeof the TTDs in the Nordic seas, CO2 is introduced as an age tracer and used in combinationwith water age estimates determined from CFC‐12 data. CO2 and CFC‐12 tracer agesconstitute a very powerful pair for constraining the shape of TTDs. The highestconcentrations of DICant appear in the warm and well‐ventilated Atlantic water that flowsinto the region from the south, and concentrations are typically lower moving west intothe colder Arctic surface waters. The depth distribution of DICant reflects the extent ofventilation in the different areas. The Nordic seasDICant inventory for 2002 was constrainedto 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 usingfour other approaches, revealing significant differences with respect to the TTD‐derivedestimates, which can be related to issues with some of the underlying assumptions of theseother approaches. Specifically, the Tracer combining Oxygen, inorganic Carbon andtotal Alkalinity (TrOCA) method appears to underestimate DICant in the Nordic seas, theDC* shortcut and the approach of Jutterström et al. (2008) appear to overestimate DICant atmost depths in this area, and finally the approach of Tanhua et al. (2007) appears tounderestimate Nordic seas DICant below 3000 m and overestimate it above 1000 m.

Citation: Olsen, A., A. M. Omar, E. Jeansson, L. G. Anderson, and R. G. J. Bellerby (2010), Nordic seas transit timedistributions and anthropogenic CO2, J. Geophys. Res., 115, C05005, doi:10.1029/2009JC005488.

1. Introduction

[2] The rising concentration of carbon dioxide (CO2) inthe atmosphere is currently exercising a very significantinfluence on the evolution of the global climate system[Forster et al., 2007]. The increase in CO2 is caused byfossil 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 is2.2 ± 0.3 Gt C [Gruber et al., 2009], corresponding toabout 25% of the emissions. The current uptake by the landbiosphere is of approximately equal magnitude [Manningand Keeling, 2006]. On longer timescales the oceans appearto be the more important sink. For instance, Sabine et al.[2004] estimated the integrated ocean CO2 sink betweenthe industrial revolution and 1994 to be 118 Gt C, corre-sponding to 50% of the emitted CO2 and after consideringthe magnitude of the emissions in themselves and the atmo-spheric CO2 inventory, Sabine et al. [2004] deduced thatthe land biosphere must have been a net CO2 source over

that period. As regard the future, coupled climate‐carboncycle model simulations indicate a sustained or increasingocean sink, while the terrestrial sink may diminish[Friedlingstein et al., 2006].[3] A sustained ocean sink for anthropogenic carbon

(DICant) relies on vertical mixing since this transports waterthat has been exposed to the present atmosphere from theupper to the deeper ocean while it brings older unexposedwater to the surface. This results in a transfer of DICant

from the surface to the deep ocean, which has the largervolume thus, storage capacity. The Nordic seas (Figure 1)are potentially important in this respect, as they annuallygenerate 6 Sv of overflow water [Hansen and Østerhus,2000], which is a main source of North Atlantic deepwater [Dickson and Brown, 1994]. The overflow water isprimarily formed by modification of North Atlantic Water(NAW) that enters from further south as the northwardextension of the Gulf Stream, North Atlantic Current andNorth Atlantic Drift system [Eldevik et al., 2009] and whichhave high concentrations of DICant [Olsen et al., 2006].[4] However, despite their potential importance, there

have only been two dedicated basin‐scale studies to deter-mine the DICant content of waters in the Nordic seas: Chenet al. [1990] and Jutterström et al. [2008]. Chen et al.[1990] presented sections of DICant (actually DTCO2

0, thedifference of preformed normalized total carbon in old andnew waters), using the data from the Hudson 1982 cruise

1Bjerknes Centre for Climate Research, Uni Research, Bergen, Norway.2Department of Chemistry, Gothenburg University, Gothenburg,

Sweden.3Geophysical Institute, University of Bergen, Bergen, Norway.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2009JC005488

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, C05005, doi:10.1029/2009JC005488, 2010

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and the method of Chen and Millero [1979]. However,studies have revealed issues with the data [Olsen, 2009a,2009b] as well as the method [e.g., Shiller, 1981; Chen etal., 1982; Broecker et al., 1985; Chen and Drake, 1986].In particular, in the Nordic seas one cannot expect thedeep waters to be fully devoid of anthropogenic CO2. Theapproach of Jutterström et al. [2008] used observedrelationships between nitrate, phosphate, and DIC versusCFCs and assumptions on the DICant content of CFC freewaters to determine DICant concentrations in this area. Buttheir method was only applicable in waters colder than 1°Cand with salinity lower than 35, which leaves out the NAWin the Norwegian Atlantic Current (NAC), a key feature ofthe area and which carries DICant from further south intothe region [Olsen et al., 2006]. This omission implies that theirNordic seas DICant inventory estimate of 1.2 Gt C may bebiased low.[5] In this paper the transit time distribution (TTD)

approach of Hall et al. [2002] is used to determine DICant.The method has been employed in several regions, includingthe North Atlantic [Waugh et al., 2004; Steinfeldt et al.,2009], Arctic Ocean [Tanhua et al., 2009], Indian Ocean[Hall et al., 2004], and Labrador Sea [Terenzi et al., 2007]as well as on the Global Data Analysis Project (GLODAP)[Key et al., 2004] data set [Waugh et al., 2006]. The TTDapproach is in principle an extension of the DC* shortcutmethod of Gruber et al. [1996] which determines DICant

from water mass ages derived from observations of transienttracers and assuming a single ventilation time for each waterparcel. The TTD method takes mixing into account by usingthe spectrum of waters mass ages found in each water parcelto determine DICant.[6] In this contribution we derive the parameters charac-

terizing the TTD in the Nordic seas, determine the distri-bution and inventory of DICant in the area, compare the

results of this approach with those of four other widely usedapproaches, and rationalize the difference that we observe.

2. Data and Methods

2.1. Data

[7] The data used in this studywere collected at three cruisescarried out in the Nordic seas in 2002 and 2003. The 2002cruise of I/BOden, the 2002 cruise of R/VKnorr, and the 2003cruise of R/V G.O. Sars. The expocodes for the cruises are77DN20020420, 316N20020530, and 58GS20030922,respectively. A map of the Nordic seas with the stationsoccupied on these three cruises is provided in Figure 1. Thedata have been described by Olsen et al. [2006], Jeanssonet al. [2008], and Jutterström et al. [2008] and only a briefsummary of their stated precision and accuracy is providedhere. The precision of the DIC and alkalinity data (Alk) havebeen estimated to approximately ±1 mmol kg−1 and accuracywas ensured by analyses of certified reference material(CRM) supplied by A. Dickson, Scripps Institution ofOceanography, USA [Jutterström et al., 2008; Olsen et al.,2006]. Oxygen and CFC data were all obtained with a pre-cision of ∼1% [Jutterström et al., 2008]. The data from thethree cruises are included in the CARINA data synthesisproduct [Key et al., 2010] and they have been found to beinternally consistent [Falck and Olsen, 2010; Jeansson et al.,2010; Olsen et al., 2009; Olsen, 2009a, 2009b], except theCFC‐12 data obtained at the G.O. Sars cruise, which shouldbe adjusted by a factor of 0.95 [Jeansson et al., 2010]. Thisadjustment was applied to the data used in the work presentedhere. To avoid complications due to the seasonal cycle andthe recent decline in the atmospheric CFC concentrations,only data from deeper than 250 m are used for the calcula-tions presented here.

Figure 1. Map of the Nordic seas including the sampling positions of the data used in this analysis. TheNordic seas is the ocean area limited by the Greenland‐Scotland ridge to the south and the Fram Strait tothe north. Bathymetry drawn at 250, 1000, 2000, and 3000 m. The lines along 70°N and from Iceland tothe northern Greenland Sea indicate the location of the sections plotted in Figure 4.

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2.2. TTD Method

[8] The TTD framework applies to passive tracers with atime‐dependent surface history. For these, the interior oceanconcentrations at location r and time t can be expressed as(assuming steady transport and uniform c0 over the sourceregion)

cðr; tÞ ¼Z10

c0ðt � �ÞGðr; �Þd�; ð1Þ

where c0 is the time‐dependent surface history of the tracerin question and G(r, t) is the distribution of transit times (theTTD) at the location. Here we use three passive tracers,CFC‐11, CFC‐12, and anthropogenic CO2. For the twoformer, the surface history was determined using theatmospheric history compiled by Walker et al. [2000], andsolubility calculated from temperature and salinity accord-ing to Warner and Weiss [1985], assuming a surface satu-ration of 98% which is consistent with the observations ofJutterström et al. [2008]. The DICant history was deter-mined as the difference between the preindustrial equilibri-um DIC and that at time t, using updated Law Dome andMauna Loa atmospheric CO2 mole fraction records. Thisrequires estimates of preformed alkalinity, Alk0, and thesewere obtained from salinity using the relationships specifi-cally determined for the Nordic seas by Nondal et al.[2009]. Preformed silicate and phosphate was set to 8 and1 mmol kg−1, respectively, typical concentrations of Nordicseas surface water in winter as determined from theCARINA data set [Key et al., 2010; Olafsson and Olsen,2009]. The CO2 system calculations were carried outusing CO2sys [Lewis and Wallace, 1998] for Matlab [vanHeuven 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]

Gð�Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

�3

4��2�3

rexp

�� � � �ð Þ24�2�

!; ð2Þ

where G is the mean age of the water sample, D is the widthof the TTD, and t is the age of the water, the transit time.When the ratio between D and G is known the TTD can bedetermined by using a single transient tracer. For our DICant

calculation we use observations of CFC‐12, combined withan estimate of Nordic seas D/G, derived as described insection 2.3.

2.3. Determination of TTD Parameters

[10] The ratio between D and G describes the shape of theTTD. Large ratios imply broad TTDs indicating that prop-agation of surface signals occurs over a wide range of transittimes. The smaller the ratio the less mixing and, thus, thenarrower range of transit times. The special case D/G = 0indicates that tracer signals are propagated into the oceaninterior through pure bulk advection. The ratio, whichreflects the degree of ocean mixing, is expected to vary andmust be determined on regional scales.[11] To constrain D/G for the Nordic seas we follow the

approach of Waugh et al. [2004], i.e., by comparing the

relationship between tracer ages. Tracer concentrations inthemselves could have been compared in order to removethe effect of the nonlinear relationship between concentra-tion and age that is typical for many tracers. However, thisapproach did not provide any additional information, and wechose to compare the ages to enable direct comparison ofour 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 withthe atmospheric history of the tracer in question

cðtÞ ¼ c0 t � �ð Þ; ð3Þ

where c(t) is the interior concentration, c0 is the surfaceconcentration history, and t is the tracer age. This assumesthat tracer signals are propagated into the ocean interiorthrough pure bulk advection so that a single transit timerather than a distribution of transit times describes thetimescale of ocean transport from one location to another,i.e., D/G = 0. Any given D/G value will lead to a specificrelationship between tracer ages from tracers with differentsurface histories, and the true D/G value can be identified bycomparing observed tracer age relationships with theoreti-cal ones, i.e., those expected for given D/G values [Waughet al., 2004]. For the North Atlantic, for instance, Waugh etal. [2004] constrained D/G to 0.75 or larger using thisapproach. Assuming a D/G of unity has since then becomemore 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 D/G. Pairs with surfacehistories that differ in shape results in the strongest con-straint. For instance, the pair CFC‐11 and CFC‐12 does notimpose strong constraints on D/G. This is also the case forthe Nordic seas, as is illustrated in Figure 2 which comparesthe observed relationships between Nordic seas tCFC‐11 andtCFC‐12 values with the theoretical relationships betweenthese tracer ages estimated for different D/G values. Thepattern is more or less similar to that observed in NorthAtlantic data by Waugh et al. [2004, Figure 3a], and itimposes little, if any constraint on the D/G values. In fact,the observed relationships do not appear compatible withany of the theoretical ones for ages less than 25 years. Thesame was observed in the North Atlantic data presented byWaugh et al. [2004], and they proposed that it was causedby different surface saturations of these two tracers.However, assuming different surface saturation affects theobserved and theoretical CFC‐11‐CFC‐12 relationshipsequally. Therefore, invoking different surface saturations forthe two tracers did not make the observed relationships fallat the family of theoretical ones. We therefore believe thatthis feature may indicate that the data for at least one of thetwo CFC components are slightly biased (∼5%, section A1).This possibility does not have any large influence on ourresults, as is fully evaluated in Appendix A.[14] Waugh et al. [2003] evaluated the ability of several

tracer pairs to constrain D/G, illustrated in their Figure 8. Itis evident from their Figure 8 that CFC‐12 and a radioactivetracer with a decay rate similar to the atmospheric CO2

growth rate is one of the more suitable pairs. This impliesthat the pair tCFC‐12 − tCO2 would impose strong constraintson D/G. This strategy is followed in the present study.

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[15] To use CO2 as an age tracer, i.e., to find the carbondioxide tracer age, we employ the conceptual framework ofthe DC* approach of Gruber et al. [1996] for estimatinganthropogenic carbon concentrations. This frameworkassumes pure bulk advection which allows for the separationof observed inorganic carbon concentrations into (1) thewater sample’s equilibrium concentration when at the sur-face, (2) the degree of disequilibrium the water sample hadwhen at the surface, which is assumed to be constant overtime, and (3) the change of dissolved inorganic carbonconcentration that has taken place since the water parcel leftthe surface, associated with remineralization and calciumcarbonate dissolution

DICobs ¼ DICeq@pCO2ðt��Þ þ DICdiseq þ�DICbio: ð4Þ

The DICeq@pCO2(t−t) term holds a time stamp, and thisallows for the calculation of the CO2 tracer age. Theapproach requires an independent estimate of DICdiseq andhas not, as far as we are aware, been described in the lit-erature. The lack of this implementation is a result of the farfrom homogenous surface distribution of CO2 saturationdegree [e.g., Takahashi et al., 2009]. However, for theNordic seas this can be circumvented by using the rela-

tionship between surface pCO2 and SST identified by Olsenet al. [2003], as will be described in the following.[16] The determination of the carbon disequilibrium,

DICdiseq, takes advantage of a fundamental assumption ofthe TTD, as well as of the DC* approach for calculation ofDICant, namely that the disequilibrium has remained con-stant with time. Despite recent observations that indicateotherwise for parts of the Nordic seas over the last twodecades [Olsen et al., 2006], this appears to be a reasonableassumption for the region as a whole over the time since theindustrial revolution. The effect of assuming otherwise isevaluated in section A1. Now, given that the surface dis-equilibrium is assumed to be constant, there is no need topropagate it using TTDs, because this method must only beemployed for propagation of transients. Thus, if it can beparameterized in terms of conservative properties, thisparameterization can be applied to every water sample to getan estimate of the original DICdiseq when at the surface. Thisenables us to utilize the northern North Atlantic wintertimepCO2‐SST relationship [Olsen et al., 2003] to determineDICdiseq since

DICdiseq ¼ DICdiseq;95 ¼ DIC95 � DICeq;95; ð5Þ

where

DICeq;95 ¼ f pCOatm;952 ;Alk0; Si0;PO0

4; Sal; �� �

ð6Þ

and

DIC95 ¼ f pCO952 ;Alk0; Si0;PO0

4; Sal; �� �

; ð7Þ

where the function is the thermodynamic equations relatingthe inorganic carbon species. The pCO2

95 was found usingthe equation determined by Olsen et al. [2003]

pCO952 ¼ 391:13� 8:71�� 0:36�2 þ 0:11�3

� �e0:0423 ��5ð Þ ð8Þ

and pCO2atm,95 was determined from the 1995 atmospheric

mole fraction according to Dickson et al. [2007] using apressure of 1013.25 hPa, and in situ � and salinity.[17] The impact of remineralization and CaCO3 dissolu-

tion on DIC, DDICbio, was determined as

�DICbio ¼ rC:O2AOU � 1

2Alk � Alk0 þ rN :O2AOU� �

; ð9Þ

where rC:O2 and rN:O2 are the carbon to oxygen and nitrogento oxygen remineralization ratios, respectively, and AOU isthe apparent oxygen utilization. The remineralization ratiosderived by Körtzinger et al. [2001] were used, and the sen-sitivity of the calculations to the choice of rC:O2 and rN:O2is quantified in section A1. For AOU the following expres-sion was used

AOU ¼ Osat2 � Oobs

2 ��O2; ð10Þ

where O2sat is the oxygen saturation concentration and O2

obs

is the observed oxygen concentration. The term DO2 is thesurface disequilibrium at the time of subsurface water massformation, which is winter. As defined here, positive valuesmean undersaturation. Wintertime Nordic seas DO2 is sig-nificant and must be accounted for. For instance, the sim-

Figure 2. Relationship between Nordic seas tCFC‐12 andtCFC‐11 determined by comparing pCFC (from measuredCFC and the equation of Warner and Weiss [1985], assum-ing 98% saturation) with the atmospheric CFC history ofWalker et al. [2000] through equation (3). Solid lines showthe theoretical relationships determined for TTDs with D/Granging from 0.25 to 2 by steps of 0.25. The D/G = 0.25curve has been labeled. A D/G = 0 corresponds to tCFC‐11 −tCFC‐12 = 0 over the whole range of tCFC‐12. The breaks inthe relationships and negative tCFC‐11 − tCFC‐12 values attCFC‐12 of approximately 15 years or less are the result ofthe recent decline of atmospheric CFC‐11 and CFC‐12concentrations. This prohibits determination of a uniquetracer age for samples within the range of declining values,and tCFC‐11 and tCFC‐12 were set to zero in these periods.The period is longer for CFC‐11 than for CFC‐12.

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ulated disequilibrium [Ito et al., 2004] in the Nordic seas isbetween 0 and 20 mmol l−1 (from their Figure 1), and wasattributed to fast heat loss with oxygen uptake lagging.Observations confirm the simulation of Ito et al. [2004]. AtOWSM at 66°N and 2°E, Falck and Gade [1999] estimated amean disequilibrium ranging from approximately 10mmol l−1

in January to 5 mmol l−1 in March (from their Figure 3) and inthe Barents Sea, the study of Olsen et al. [2002] revealeddisequilibriums of typically between 10 and 20 mmol l−1

during winter. For a better constraint on Nordic seas DO2

during winter, the CARINA O2 values [Falck and Olsen,2010] were examined. Average DO2 in wintertime Nordicseas surface waters was determined to 15 ± 7 mmol kg−1. Anupper temperature cutoff of 1°C was used here in order toavoid unduly influence of Norwegian Atlantic Currentwaters. Given these observations aDO2 value of 15mmol kg−1

is used in equation (10). The sensitivity of our calculations tothe value of DO2 is evaluated in section A1.[18] With DDICbio and DICdiseq in place, DICeq@pCO2(t−t)

is derived using equation (4). The time stamp, t, is extractedby first finding

pCO t��ð Þ2 ¼ f DICeq@pCO2 t��ð Þ;Alk0; Si0;PO0

4; Sal; �� �

ð11Þ

then converting this to the corresponding xCO2(t−t) and

matching this to the atmospheric CO2 history throughequation (3).

3. Results

3.1. TTD Parameters Derived From CFC‐12 and CO2

Ages

[19] Figure 3 compares the CO2 and CFC‐12 tracer ages.For waters with tCFC‐12 less than 20 years, tCO2‐tCFC‐12does not provide enough resolution to determine D/G, nei-ther did tCFC‐11‐tCFC‐12. However, for waters with tCFC‐12greater than 20 years the theoretical relationships are far

better separated than those determined for tCFC‐11‐tCFC‐12(Figure 2), confirming that tCO2‐tCFC‐12 is a suitable pairfor constraining D/G. For instance, unlike tCFC‐11‐tCFC‐12,as well as several of the other tracer pairs considered byWaugh et al. [2004], the theoretical relationships betweentCO2 and tCFC‐12 clearly resolves differences of D/G valuesof 0.25. The observed relationships take on a range ofvalues. To a large extent we believe this is due touncertainties in the determination of tCO2, which areaddressed in section A1, but it may also reflect true varia-tions of the ratio. Important here is that essentially allobserved points fall above the theoretical relationship forD/Gof 0.5, and this should be considered the lower limit ofpossible Nordic seasD/G values. Most of the data fall withinthe space spanned by the theoretical lines for D/G 0.75 and1.5, and seem centered around unity. An absolute upperlimit cannot be determined with these data. Theoreticalrelationships up to 2.0 have been drawn in Figure 3, but itrequires unreasonably high D/G values, e.g., on the order of103–104, to explain some of the points, and their presenceare better explained as being the result of uncertainties in theparameters used for determination of tCO2. The Nordic seasTTD thus appear broad, and similar to those determined forthe surrounding ocean regions, i.e., North Atlantic [Waughet al., 2004] and Arctic Ocean [Tanhua et al., 2009],which is not unreasonable. Given these observations 0.5 isconsidered as the lower limit for probable Nordic seas D toG ratios, 1 the most probable, and 1.5 as the upper limit. Theupper limit of 1.5 was in part motivated by Figure 3, and inpart by the observations from further south [Waugh et al.,2004]. This range was robust even after consideration ofthe uncertainties of our approach (section A1).

3.2. Anthropogenic CO2 Distribution

[20] The distribution of anthropogenic CO2 in the year2002, determined from equation (1) and a D/G of unity isshown in Figure 4, along with the contours of potentialdensity (s�). Figure 4a shows a west‐east section along 70°Nand Figure 4b shows a section that goes approximatelysouth‐north, from the Iceland shelf edge into the GreenlandSea, both of these have been highlighted in Figure 1. Inparticular, in the section that goes across the Norwegian andIceland seas (Figure 4a), the distribution of DICant followsthe density surfaces. The largest concentrations, between40 and 45 mmol kg−1, are observed in the lightest waters, ofs� less than 27.98 which are found above 1000 m in theNorwegian Sea. This is the well‐ventilated and warmNorwegian Atlantic Current that transports DICant into andthrough the region. Immediately below this, the ArcticIntermediate Waters (AIW) are found, these have potentialdensities of up to 28.07 [Aagaard et al., 1985], and DICant

concentrations span the range of values from 15 to 35 mmolkg−1. The AIW is found at shallower depths in the IcelandSea, which is one of their formation areas [Blindheim,1990]. The isolines of DICant and s� slopes upward intothis area, which has lower DICant concentrations in theupper 1000 m than the Norwegian Sea. The DICant con-centration in the deep waters of the Norwegian Sea arebetween 5 and 15 mmol kg−1, this is lower than the con-centrations in the deep Greenland Sea, which are normallybetween 10 and 15 mmol kg−1 (Figure 4b). This is becausethe fraction of relatively old deep waters from the Arctic

Figure 3. Relationship between Nordic seas tCFC‐12 andtCO2, shown along with the theoretical relationships (solidlines) for TTDs with D/G ranging from 0.25 to 2 by stepsof 0.25. Every other curve has been labeled with its D/G.

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Ocean is higher in the Norwegian than in the Greenland Sea.The Greenland Sea is otherwise more vertically homoge-nous than both the Iceland and Norwegian Sea, reflectingthe more extensive convective activity in this area, and inthe central Greenland Sea the upper 1000 m have DICant

concentrations between 30 and 35 mmol kg−1.[21] The distribution of DICant in the upper 1000 m of the

Nordic seas is governed partly by ventilation time and partlyby temperature. The waters in the upper 1000 m in theGreenland Sea are around 5 years older than the NorthAtlantic Waters (NAW) of the Norwegian Atlantic Current.This age difference explains almost half of the difference inDICant concentrations of approximately 10 mmol kg−1. Therest of the difference is explained by the temperature dif-ference with the NAW being 5–10°C warmer than thewaters of the Greenland Sea. The Revelle factor is thuslower for the NAW, i.e., the capacity for DICant uptake islarger. In addition the alkalinity of NAW is greater, but thiseffect explains only about 1 mmol kg−1 of the difference inDICant.[22] 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 estimateof the surface to deep water export of DICant associated withthis process, we combine our DICant estimate with a volumeflux estimate from the literature. The total flux of coldoverflow water across the ridge has been estimated to almost6 Sv [Hansen and Østerhus, 2000]. The mean properties ofthe water were summarized by Eldevik et al. [2009]. TheDenmark Strait overflow water spans the theta and salinityranges of approximately 0–0.5°C and 34.85–34.9, respec-tively, while the respective ranges for Faeroe‐ShetlandChannel overflow water are approximately 0–0.5°C, and34.9–34.94. The waters with these properties were identifiedin our data, and although not marked in Figure 4, theycorrespond to waters found in the s� range of between 27.98and 28.02 and which have DICant of typically between 25and 30 mmol kg−1. Combining these concentrations with thevolume flux, gives us an annual mean export of DICant fromthe Nordic seas into the deep North Atlantic of between0.06 and 0.07 Gt C, which corresponds to 3% of the annualglobal ocean uptake of DICant of 2.2 Gt C [Gruber et al.,2009].

3.3. Anthropogenic CO2 Inventory

[23] The Nordic seas DICant inventory was determined byusing the approach described for the Arctic Ocean byTanhua et al. [2009] which interpolates each DICant profileonto 50 m depth intervals using a piecewise cubic Hermite,and then use the topography following mapping schemedescribed by Davis [1998] and Rhein et al. [2002] to mapthe interpolated data onto a regular grid. The upper 250 mwere not included in our calculations (section 2.1) so weassumed that these were saturated with DICant. The mappedcolumn inventories are shown in Figure 5. They range fromless than 10 to more than 70 mol m−2 and show a cleardependence on bottom depth (Figure 1). The largest columninventories are found over the deep Greenland, Lofoten andNorwegian Basins, while the smaller are found over theIceland Plateau, and the continental shelves. However, thedistribution over the three deep basins is also modulated bythe distribution of water masses and their DICant content.The depth of the layer of NAW is deeper in the LofotenBasin than in the Norwegian Basin [Orvik, 2004], and hencethe column inventory is greater over the Lofoten Basin thanover the Norwegian Basin. The column inventory is evengreater over the Greenland Basin, this is in part because theGreenland Basin is the deepest, but it is also because rela-tively recently ventilated water masses has penetrated dee-per here than in the other two deep basins, as can beappreciated from Figure 4.[24] The total inventory of the Nordic seas and its

subregions are provided in Table 1. The limits between thesubregions were set as by Jakobsson [2002] who followsInternational Hydrographic Organization [2001]. Theocean volumes estimated through our mapping routine(Table 1) do not match the volume estimates determinedfrom the International Bathymetric Chart of the ArcticOcean (IBCAO) exactly [Jakobsson, 2002]. This is causedby the lower resolution of the bathymetry (the 5 minTerrainBase of NOAA/National Geophysical Center) usedfor the mapping as well as the 50 m layer thickness.

Figure 4. Sections of Nordic seas DICant (mmol kg−1)along (a) the section at 70°N and (b) the section fromIceland (at approximately 67°N, 15°W) northeastward toGreenland Sea (to approximately 75°N, 0°E), where it turnsnorthward and ends at almost 79°N (as indicated by the linesin Figure 1). The dots show the sampling locations.

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Therefore all inventories have been scaled to the oceanvolumes published by Jakobsson [2002] using the simplenormalization equation

Invscaled ¼ InvorgV J

Vorg; ð12Þ

where Invorg and Vorg are the inventory and volume esti-mates determined through the mapping routine and VJ isthe volume estimates of Jakobsson [2002]. This scalingchanged the Greenland Sea inventory estimate by 2%, theNorwegian Sea estimate by 0.8%, and the estimates for theIceland Sea and Denmark Strait by 0.3% and 10%,respectively. The large relative change of the DenmarkStrait estimate is due to its small size and corresponds toonly 0.003 Gt C. These estimates indicate that the Nordicseas contain 1.24 Gt DICant. This is approximately 1% ofthe global ocean DICant inventory estimate of Sabine et al.[2004]. Given the estimates of the carbon transport of theoverflow waters of ∼3% of the annual global ocean DICant

uptake, determined above, the Nordic seas appear moreimportant for mediating surface to deep ocean DICant

transport than for storage. The small inventory of this areais a consequence of the small volume, corresponding to∼0.3% of the global ocean volume.[25] Our estimate of the Nordic seas DICant inventory can

be combined with the inventory estimate for the ArcticOcean of 3 Gt DICant, determined through a similarapproach by Tanhua et al. [2009]. This estimate was for theyear 2005, and assuming transient steady state our Nordicseas estimate scaled to 2005 is 1.3 Gt. Adding thesenumbers we get a year 2005 Arctic Ocean and Nordic seas

DICant inventory of 4.3 Gt C. This is 2.1 Gt C smaller thanthe estimate of Sabine et al. [2004] scaled to 2005, of 6.4 GtC [Tanhua et al., 2009] for these areas.[26] There are four significant sources of uncertainty that

affects our DICant estimates, as identified in section A2, andthus the Nordic seas inventory estimate: (1) lowering theD/Gratio increases the DICant estimates and vice versa, (2) theCFC‐12 data we have used are possibly biased high by 5%,which translates into a potentialDICant bias of between +0.25and +1.6 mmol kg−1, depending on depth, (3) a time variantCFC‐12 surface saturation will increase the DICant esti-mates, and (4) an increasing air‐sea CO2 disequilibrium willreduce the DICant estimates. These uncertainties will alsoaffect our Nordic seas anthropogenic carbon inventory esti-mate. An absolute upper limit of the Nordic seas DICant

inventory was determined by assuming a D/G of 0.5 and atime variant CFC‐12 surface saturation, this gave an inven-tory of 1.42 Gt C. An absolute lower limit was determinedby adjusting all the CFC‐12 data down by 5%, applying aD/G of 1.5, and assuming that the air‐sea CO2 disequilib-rium in the Nordic seas has increased over time. In additionwe assumed that the DICant concentration in the upper 250 mare the same as the concentrations in the 250–300 m depthlayer, rather than assuming that this layer is saturated withDICant as was originally done. This gave an inventory of0.86 Gt C. Thus our Nordic seas DICant inventory estimateof 1.24 Gt C may possibly deviate by −0.38 Gt C and+0.18 Gt C.

3.4. Comparison With Other Methods

[27] Figure 6 compares the TTD‐derived DICant estimateswith the estimates derived using the DC* shortcut approach

Figure 5. Nordic seas anthropogenic CO2 column inventory (mol m−2).

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[Gruber et al., 1996], the approach of Jutterström et al.[2008], the revised Tracer combining Oxygen, inorganicCarbon and total Alkalinity (TrOCA) approach [Touratier etal., 2007], and the approach of Tanhua et al. [2007] whichwe have labeled eMLRe (extended Multi Linear Regressionextension). This latter approach requires an estimate of theDICant increase over decadal timescales; these wereobtained from Olsen et al. [2006]. Unlike another compar-ison [Vázques‐Rodríguez et al., 2009], negative DICant

estimates have not been set to zero. The uncertainty of theTTD‐derived estimates is given by the gray area, with theupper and lower bounds determined in the same way as forthe inventory, i.e., by assuming D/G of 0.5 and time‐dependent CFC‐12 saturation for the upper bound, and byadjusting the CFC‐12 data down by 5%, and assuming D/Gof 1.5 and time‐dependent CO2 surface saturation for thelower.[28] The DICant estimates derived using the DC* shortcut

approach [Gruber et al., 1996] are larger than the upperbound of the TTD‐derived estimates, except in the upper1000 m. This is as expected since this approach is essen-tially an implementation of the TTD approach with D/G setto zero, i.e., one assumes that the tracer age represents thetrue and unique age of the water parcel, and the lower theD/G the higher the DICant.[29] The DICant estimates derived using the approach of

Jutterström et al. [2008] are also larger than the onesderived using the TTD approach, except for above 750 m,where the estimates derived with the approach ofJutterström et al. [2008] are lower than the estimate derivedusingD/G = 1. The lower values in the upper ∼750 m resultsfrom the fact that the method of Jutterström et al. [2008] isnot applicable in the Norwegian Atlantic Current, which haslarge concentrations of DICant. The larger values below this,is the result of assumptions employed when a key numberfor this approach was determined, the DICant at the time ofzero CFC‐11, which is used to determine the intercept of thetheoretical CFC‐11‐DIC regression line. This line is theexpected CFC‐11‐DIC relationship in the absence ofDICant, and DICant is estimated as the difference betweenobserved DIC and values estimated from this theoreticalline. The intercept was determined by Jutterström et al.[2008] through evaluating the relationship between cal-culated 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 mmol kg−1.

This estimate was subtracted from the observed intercept of2160.5 mmol kg−1, to give the intercept of the theoreticalrelationship of 2142.9 mmol kg−1. This approach assumesbulk advective transport, i.e., D/G = 0. Thus Jutterström etal. [2008] overestimates DICant at CFC = 0 which leads to atoo small intercept of the theoretical CFC‐11‐DIC rela-tionship. Using TTDs with D/G of 1.0 we get a DICant ofaround 5 mmol kg−1 at the time of zero CFC‐12, using thiswould lower the DICant estimates of Jutterström et al.[2008]. Despite of the differences in the DICant distribu-tion, the inventory determined by Jutterström et al. [2008] issimilar to our TTD‐derived inventory estimate of 1.24 Gt.This is partially because Jutterström’s method overestimatesDICant at depth while at the same time missing the highconcentrations in the NAW, and partly because theirinventory estimate does not include the upper 250 m, whichholds large amounts of DICant. For instance, of our TTD‐derived inventory estimate of 1.24 Gt DICant, ∼0.35 Gt isfound in the upper 250 m. Adding this to the estimate byJutterström et al. [2008] would increase their inventory to1.55 Gt DICant.[30] The DICant estimates derived through the revised

TrOCA approach [Touratier et al., 2007] are mainly nega-tive at depth, and this was also the case for estimates (notshown) derived using the original TrOCA approach[Touratier and Goyet, 2004a]. This is unrealistic, and inconflict with the use of anthropogenic CO2 as an explana-tion for the high TrOCA values in the Nordic seas observedby Touratier and Goyet [2004b]. The very low DICant

values derived through the TrOCA approach are in agreementwith the TrOCA based estimates of Vázques‐Rodríguez et al.[2009], which were derived using a subset of the data used inthis study. They are also in agreement with the 1990s (theirFigure 5), but not 1980s (their Figure 4) estimates ofTouratier and Goyet [2004a]. The difference between these

Table 1. Nordic Seas DICant Inventory Estimatesa

RegionVmapped

(103 km3)VJakobsson

(103 km3)DICant Inventory

(Gt C)

Greenland Sea 1395 1418 0.40Norwegian Sea 2360 2362 0.67Iceland Sea 415.8 417 0.14Denmark Strait 64.72 72 0.032Total 4197 4228 1.24

aDetermined using a D/G value of 1, a time‐invariant air‐sea CO2

disequilibrium, a surface CFC‐12 saturation of 98%, and assuming thatthe upper 250 m of the water column is saturated with anthropogenicCO2. See text for a discussion of the uncertainties. Vmapped is the volumemapped by our interpolation routines, and VJakobsson is the volumeestimates published by Jakobsson [2002].

Figure 6. Mean profiles of Nordic seas DICant determinedusing the TTD approach (solid lines) with upper and lowerbounds determined as described in the text, the eMLRe,the revised TrOCA, the DC* shortcut approach, and theapproach of Jutterström et al. [2008]. The mean profileswere determined by arithmetic bin averaging of theindividual profiles into 250 m intervals.

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two latter estimates may be due to lower accuracy of theolder data. Regardless, the TrOCA approach appears tounderestimate DICant in the Nordic seas. We believe thishappens because the empirical fit to determine TrOCA0 ofTouratier and Goyet [2004a], as well as that of Touratier etal. [2007], overestimates Nordic seas TrOCA0 values.TrOCA is essentially the carbon version of the tracer NOintroduced by Broecker [1974], and besides air‐sea gasexchange and nitrification/denitrification, their distributionsare governed by the same processes in the ocean. Hence,these are quite similar as can be appreciated from Figures 2cand 2f of Touratier and Goyet [2004b], and both tracers alsotend to decrease with increasing potential temperature[Touratier and Goyet, 2004a, Figure 2; Broecker, 1974,Figure 2]. This temperature dependency was utilized byTouratier and Goyet [2004a] and in large part by Touratieret al. [2007] for parameterizing the preindustrial distributionof TrOCA, TrOCA0. However, and analogously to NO,Nordic seas TrOCA0 are likely to fall below the valuesexpected from the TrOCA0‐� mixing line that applies else-where. For NO this is in large part due to the lower pre-formed nitrate concentrations in the Nordic seas [Broecker,1974, Figure 2] caused by the export production that occursas the waters travels northward as part of the thermohalinecirculation. Export production would also affect DIC, butwould be compensated by uptake of atmospheric CO2. Thedifference in preformed nitrate that explains the differencein NO between Weddell Sea water and Nordic seas wateris 11 mmol kg−1 (from Figure 2 of Broecker [1974]). Usingthe classical carbon‐to‐nitrogen remineralization ratio of106:16 [Redfield et al., 1963] this translates to a DICdifference of ∼72 mmol kg−1. Using the set of equations ofTouratier and Goyet [2004a] this would translate to a dif-ference in TrOCA0 values of 86 mmol kg−1 with the Nordicseas values being lower. The difference between our TTDand TrOCA based estimates of DICant implies that Nordicseas TrOCA0 is overestimated by between approximately 12and 18 mmol kg−1 (1.2*(DICant, TTD − DICant, TrOCA)), muchless than the 86 mmol kg−1 expected from export productionalone. We believe this reflects the compensating effect ofair‐sea CO2 exchange.[31] The final approach we have employed here is the

eMLRe [Tanhua et al., 2007]. The DICant estimates derivedthrough this approach are at the lower boundary of ourTTD‐derived estimates in deep waters and higher than theupper boundary in surface waters. The eMLRe method isessentially a scaling of recent changes in DICant with the fullgrowth history since preindustrial times. A fundamentalassumption here is that the relative DICant response to theatmospheric CO2 perturbation over the last few decades isthe same as the relative response to the full atmosphericperturbation. This assumption may be violated in the Nordicseas. At depth the fraction of deep waters from the ArcticOcean has increased over the last two decades [Blindheimand Rey, 2004; Skjelvan et al., 2008]. It is not unlikelythat these relatively older waters carry less DICant thanlocally formed relatively younger Greenland Sea DeepWater. Thus, the deep water DICant response to the atmo-spheric CO2 growth over the last two decades may beatypically low compared to the full increase. This wouldcause the eMLRe method to underestimate DICant at depth.As regard the surface waters, the response observed by

Olsen et al. [2006] in particular to the south, may be atyp-ically high and in part related to shifts in the ocean circu-lation associated with changes in the atmospheric circulationpattern [Thomas et al., 2008]. This would cause eMLRe tooverestimate DICant in surface waters.

4. Summary and Conclusions

[32] We have demonstrated that it is possible to calculate aCO2 age, which together with CFC‐12 ages does indeedconstitute a powerful pair for constraining the D/G of transittime distributions, as originally suggested by Waugh et al.[2003]. The number of uncertainties involved in the calcu-lation of the CO2 age, as treated in section A1, prohibits fullexploitation of the potential of this tracer pair, and calls forbetter parameterizations of wintertime sea surface DO2 andpCO2 using conservative parameters. Accurate determina-tion of the long‐term time variation of the air‐sea CO2

disequilibrium would also be worthwhile in this context. Wewere able to constrain Nordic seas D/G to between 0.5 and1.5, with 1 being the most probable value.[33] A very important, but hitherto not explicitly stated,

corollary of the calculations is that the assumptions that theair‐sea CO2 disequilibrium is time‐invariant and that tracerage represents the true water mass age, i.e., fundamentalassumptions of the DC* shortcut approach, are mutuallyexclusive in the Nordic seas. Had these assumptions beenconsistent with each other, then the tCO2‐tCFC‐12 estimatesof Figure 3 should all fall on the zero line. This is not thecase, and the observations can only be explained by in-voking transit time distributions, or an overall significantlydecreasing air‐sea CO2 disequilibrium in the subductingwaters of the Nordic seas, the latter is inconsistent withobservations over the last twenty years (section A1).[34] The calculations enabled us to determine a Nordic

seas anthropogenic CO2 inventory of 1.24 Gt C for the year2002, with 0.86 and 1.42 Gt C as the lower and upperbounds, corresponding to ∼1% of the global ocean inventory[Sabine et al., 2004]. While this number is not large inabsolute terms, it reflects the overall high DICant con-centrations of an area which comprises ∼0.3% of the globalocean volume. Combined with the estimate of Tanhua et al.[2009] we get a combined Nordic seas and Arctic Oceananthropogenic CO2 inventory for the year of 2005 of 4.3 Gt C,∼3–4% of the global ocean inventory.[35] The column inventory of the Nordic seas is basically

a function of water depth, modulated by the DICant con-centration and water mass distribution. The concentrationsare largest in the NAW in the Norwegian Atlantic Current,which has been exposed to the atmosphere on its waynorthward from the North Atlantic, and which is relativelywarm and thus has the greatest buffer capacity. The trans-port of DICant with this inflow is a key source of DICant tothe Nordic seas and the present results allows for a rudi-mentary assessment of the fate of this DICant. Olsen et al.[2006] estimated an annual influx of 0.12 Gt DICant bycombining a DICant estimate of 53 mmol kg−1 with a volumeflux estimate of 6 Sv of NAW flowing into the Nordic seas.Our DICant concentration estimates in the NAW are slightlysmaller (Figure 4); 45 mmol kg−1 does not appear unrea-sonable. This implies an inflow of ∼0.1 Gt DICant y−1, this is∼5% of the annual global ocean accumulation. The NAW

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circulates and overturn in the Nordic seas and Arctic Ocean,and constitutes the primary source of the overflow waterscrossing the Greenland‐Scotland ridge [Eldevik et al., 2009].As estimated in section 3.2, these waters transport ∼0.06 GtDICant y−1 (3% of annual global ocean accumulation) intothe deep North Atlantic. Thus, by difference and neglectingany surface outflows, ∼0.04 Gt (∼2% of the annual globalocean accumulation) of the DICant carried by the NAWaccumulates in the Nordic seas and Arctic Ocean each year.

Appendix A: Uncertainties

A1. Uncertainties of the TTD Parameters

[36] The calculation of tCO2 (section 2.3) involves anumber of assumptions and approximations that introduceuncertainties in the results, the most important are identifiedas (in random order) (1) the DO2 value, (2) the wintertimesea‐surface pCO2

95 estimates, (3) the equation for determi-nation of Alk0, (4) the carbon‐nitrogen and carbon‐oxygenremineralization ratios, and (5) the assumed CO2 surfacesaturations. The calculation of tCFC‐12 is sensitive to theaccuracy of the CFC‐12 data and the assumed CFC‐12surface saturation. The sensitivity of our results on probableNordic seas D/G values to each of these factors is evaluatedin the following.[37] The DO2 value directly influences the AOU esti-

mates, which are used for determination of DDICbio andthus tCO2. Changing the DO2 value changes the tCO2

estimates and thus the range of probable D/G values. Thestandard deviation of the Nordic seas winter time DO2

estimate was 7 mmol kg−1. The effect of this uncertainty onthe tCO2 − tCFC relationships is illustrated in Figure A1. Asthe value of DO2 is increased, the range of probable D/Gspans smaller values, and with a DO2 of 22 mmol kg−1, D/Gvalues of between 0.25 and 1 seems most probable. Basedon the available data, the DO2 value of 15 mmol kg−1 thathas been used throughout this work appears to be the bestestimate for typical Nordic seas surface winter water and wedo not expect that the range of D/G values that has beenassumed, i.e., 0.5 to 1.5, is biased. However, it is quite likelythat variability of the DO2 around its mean of 15 mmol kg−1

contributes to the spread of the observed tCO2‐tCFC‐12relationships. Ideally the distribution of Nordic seas DO2

should be better understood and preferably parameterizedin terms of conservative parameters.[38] The equation of Olsen et al. [2003] was used for

determining pCO295 that goes into the DICdiseq term of

equation (4). These estimates carry an uncertainty of ±10matm [Olsen et al., 2003]. The effect on the tCO2‐tCFC‐12relationships is illustrated in Figure A2. As the pCO2

95 islowered by 10 matm, the tCO2‐tCFC‐12 relationships spanlower values of probable D/G, and most values fall withinratios of between 0.25 and 1. The opposite effect is seenwhen 10 matm is added to the pCO2

95 values computed byequation (8). However, we do not believe that uncertaintiesof the pCO2

95 estimates has introduced biases in the range of

Figure A1. Relationship between Nordic seas tCFC‐12 andtCO2 for DO2 set to (a) 8, (b) 15, and (c) 22 mmol kg−1

shown along with the theoretical relationships for TTDswith D/G ranging from 0.25 to 2 by steps of 0.25. Thecurves for D/G of 0.5 and 1.0 have been labeled.

Figure A2. Relationship between Nordic seas tCFC‐12 andtCO2 when 10 matm is (a) subtracted or (c) added to thepCO2 estimates from equation (8). (b) The unperturbedvalues are shown. The lines show theoretical relationshipsfor TTDs with D/G ranging from 0.25 to 2 by steps of 0.25.The curves for D/G of 0.5 and 1.0 have been labeled.

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D/G values used for this work, as the ±10 matm reflects therandom error of the pCO2

95 estimates determined throughequation (8). But, it is quite likely that variability of the truepCO2

95 left unexplained by equation (8) is a significantcontributor to the spread of the observed tCO2‐tCFC‐12relationships.[39] The equations of Nondal et al. [2009], which were

employed here to determine Alk0, have a root mean squareerror of ±6 mmol kg−1. The effect of this uncertainty on thetCO2 is illustrated, through its effect on the tCO2‐tCFC‐12relationships, in Figure A3. Lowering Alk0 leads to a slightreduction of the probable D/G values and vice versa forincreasing Alk0. The effect is clearly smaller than the effectof the uncertainty in DO2 (Figure A1) as well as pCO2

95

(Figure A2) and not large enough to move the majority ofthe data out of the space spanned by the theoreticalrelationships for D/G of 0.5 and 1.5. Still, part of the vari-ation of the observed tCO2‐tCFC‐12 relationships is likelycaused by variations in Alk0 not explained by the equationsof Nondal et al. [2009].[40] The remineralization ratios are used for determination

of DDICbio and, hence, affect the tCO2 values. Severalestimates exits and the ones of Körtzinger et al. [2001] wereused in this study. In addition, the consequences of using theones of Redfield et al. [1963], Takahashi et al. [1985], andAnderson and Sarmiento [1994] were evaluated. The effecton the tCO2‐tCFC‐12 relationships was small (not shown)

and in general less than the effect caused by the uncertaintyof Alk0 depicted in Figure A3. However, using theremineralization ratios of Takahashi et al. [1985] had a cleareffect on the tCO2‐tCFC‐12, changing the range of probableD/G values to 0.25–1.0. This is because of the relatively lowrC:O2 of Takahashi et al. [1985], but this is an artifact astheir method did not account for the presence of anthropo-genic CO2 [Körtzinger et al., 2001]. Hence, the choice ofavailable unbiased remineralization ratios has in reality verylittle effect on the results presented here.[41] The accuracy of the CFC‐12 data will affect the

tCFC‐12 estimates. The information we have indicates thatthe CFC‐12 data we have used may possibly be biasedhigh, but not low, by up to 5%: (1) The CFC‐11‐CFC‐12relationships for the three cruises we have used all appearslightly low over the main range of values [Jeansson et al.,2010, Figure 6], and this indicates that the CFC‐11 data maybe biased low and/or the CFC‐12 data high. (2) The ob-served tCFC‐11‐tCFC‐12 relationships fell systematicallyabove the theoretical ones (Figure 2, section 2.3); this wasconsistent for the three cruises, and also indicates that theCFC‐11 data may be biased low and/or the CFC‐12 datahigh. Both of these features disappeared if the CFC‐11 datawere adjusted up by 5%, or the CFC‐12 data down by 5%(for the G.O. Sars cruise this adjustment comes on top of the5% reduction of CFC‐12 values already recommended byJeansson et al. [2010]). Hence a 5% bias in one of the CFCcomponents cannot be ruled out, but the effect of adjustingthe CFC‐12 data down by 5% was hardly discernible inFigure 3, however, and our assumed range of D/G values isrobust with respect to this potential source of error.[42] 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‐seaCO2 disequilibrium. The surface saturation of CFC‐12 willaffect the tCFC‐12 used for the determination of D/G,whereas temporal changes in the surface CO2 saturation, ordisequilibrium, will imply that equation (5) is incorrect andthus affect the determination of the CO2 tracer age. Theeffects of the CFC‐12 saturation are dealt with first.[43] In our calculations we have assumed a CFC‐12 sur-

face saturation of 98%. If the saturation is smaller than this,then our tCFC‐12 represents an overestimate, and a reductionwill shift the observed tCFC‐12 plotted in Figure 3 to the leftand the tCO2‐tCFC‐12 slightly up. The magnitude of thiseffect was determined by using the time‐variant surfacesaturation deduced by Tanhua et al. [2008] as a boundarycondition. This represents a reasonable degree of CFC‐12undersaturation: 86% until 1989, then increasing to 100% in1999 and remaining at that level thereafter. The effect on thetCFC‐12‐tCO2 relationships was very small and 0.5 remainedthe lower limit and 1.5 the reasonable upper limit.[44] As for the effect of the CO2 saturation degree, in our

calculations we have assumed that the CO2 disequilibriumhas remained constant with time. In the Nordic seas thedisequilibrium has changed over the past twenty years. Thework presented by Olsen et al. [2006] showed that in thenorthern regions it appears to have increased whiledecreasing in the south. As a first‐order approximation theyfound that the annual pCO2 changes in the upper 500 m ofthe Nordic seas between 1981 and 2002/2003 could beexpressed in terms of salinity: 2.074 × S −71.13, r2 = 0.6,

Figure A3. Relationship between Nordic seas tCFC‐12 andtCO2 when 6 mmol kg−1 is (a) subtracted or (c) added to theAlk0 estimates from the equations of Nondal et al. [2009].(b) The unperturbed values are shown. The lines showtheoretical relationships for TTDs with D/G ranging from0.25 to 2 by steps of 0.25. The curves for D/G of 0.5 and 1.0have been labeled.

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RMS = 0.2. The data we have used have a mean salinity of34.92, which gives a surface pCO2 change of 1.3 mtam y−1,which is approximately 80% of the atmospheric increase inthe same time interval. Thus the data indicates that overall,in the waters that subduct, the CO2 disequilibrium may beincreasing with time. For tCO2, this implies that the esti-mates we have presented in Figure 3 may be too small, i.e.,we have used DICeq,95 to estimate DICdiseq (equation (5)) andsince the majority of data are likely older than 1995 thisgives a too large disequilibrium, which translates into a toolarge DICeq@pCO2(t−t) and too small age. This would shiftthe observed tCO2‐tCFC‐12 relationships vertically upward.This would increase the lower limit of possible D/G values,but not affect the upper limit as the slopes of the theoreticallines are almost vertical in the range in question. Thus 0.5remains a lower limit of possible Nordic seas D/G values.

A2. Uncertainties of the DICant Estimates

[45] Several uncertain factors affect the DICant estimates,the most important are (in random order) (1) the D/G ratio,(2) the Alk0 estimate, (3) the accuracy of the CFC‐12 data,(4) the assumed CFC‐12 surface saturation, and (5) thepossibility of a changing CO2 disequilibrium.[46] A span of possible Nordic seas D/G values of

between 0.5 and 1.5 was determined. Lower D/G valuesgive higher DICant estimates, and the effect is larger forsmall D/G values than for higher. Reducing the D/G valuefrom 1 to 0.5 increases the DICant estimates by approxi-mately 4 mmol kg−1 at depth, and much less at the surface.Increasing the ratio to 1.5, lowers the DICant estimates byapproximately 1 mmol kg−1 at depth and much less at thesurface.[47] The preformed alkalinity estimates carries an uncer-

tainty of ±6 mmol kg−1 [Nondal et al., 2009]. Given a D/Gof 1, this translates into an uncertainty in DICant on the orderof ±0.1 mmol kg−1, which is insignificant.[48] The CFC‐12 data are possibly biased high by 5%

(section A1). This translates into a potential bias in ourTTD‐derived DICant estimates of +0.25 mmol kg−1 below1750 m, and then increasing almost linearly with depth to+1.6 mmol kg−1 at 250 m.[49] As for the effect of the surface CFC‐12 saturation on

the calculation of DICant for any given D/G; assuming alower CFC‐12 saturation will increase the DICant estimatesas the mean age will decrease, i.e., waters are younger andso they contain more anthropogenic CO2. The magnitude ofthis effect was evaluated by using the time variant surfacesaturation deduced by Tanhua et al. [2008], as a boundarycondition. This increased the estimates of DICant, byapproximately 0.5 mmol kg−1 for concentrations of 10 mmolkg−1, 1 mmol kg−1 for 20 mmol kg−1, up to 2.5 mmol kg−1 forconcentrations of 35 mmol kg−1, and then the impactbecame smaller and decreased to 0.5 mmol kg−1 for thelargest DICant at 45 mmol kg−1. The effect is thus quite smallin older waters since they contain little DICant and wereformed at a time when CO2 concentrations in the atmo-sphere rose slowly so a change of age distribution does nothave as large an impact on anthropogenic CO2 concentra-tions as it does in younger waters with higher concentrationsof DICant. For younger waters, with the highest concentra-tions of DICant, the effect is reduced since the assumed

CFC‐12 saturation approaches, and end up at approximatelythe saturation degree originally assumed, i.e., 98%.[50] Finally, as for the effect of changing CO2 disequi-

librium on the calculation of DICant for any given D/G,calculations showed that changes in disequilibrium trans-lates approximately linearly into DICant. Thus a surfaceocean pCO2 growth rate of 80% of that of the atmosphericpCO2, translates into a decrease of the DICant estimates of20%.

[51] Acknowledgments. Financial support for this work was sup-plied by the Research Council of Norway through A‐CARB (178167/S30), the EU IP CARBOOCEAN (5111176–2), and the Swedish NationalSpace Board through RESCUE‐II (62/07:2). The authors would like toexpress their gratitude to Denis Pierrot (NOAA/AOML) and Toste Tanhua(Leibniz Institute for Marine Sciences) for sharing their Matlab® codes andMartin Jakobsson (Stockholm University) for providing his area definingpolygons. Comments from two anonymous reviewers and editor FrankBryan were very helpful and highly appreciated. This is contributionA287 of the Bjerknes Centre for Climate Research.

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