C-age tracers in global ocean circulation models

The natural abundance of 14C in total CO2 dissolved in seawater is a property applied to evaluate the water age structure and circulation in the ocean and in ocean models. In this study we use three different representations of the global ocean circulation augmented with a suite of idealised tracers to study the potential and limitations of using natural 14C to determine water age, the time elapsed since a body of water had contact with the atmosphere. We find that, globally, bulk 14C-age is dominated by two equally important components, one associated with aging, i.e. the time component of circulation and one associated with a "preformed 14C-age". This latter quantity exists because of the slow and incomplete atmosphere/ocean equilibration of 14C in particular in high latitudes where many water masses form. The relative contribution of the preformed component to bulk 14C-age varies regionally within a given model, but also between models. Regional variability, e.g. in the Atlantic Ocean is associated with the mixing of waters with very different end members of preformed 14C-age. In the Atlantic, variations in the preformed component over space and time mask the circulation component to an extent that its patterns are not detectable from bulk 14C-age alone. Between models the variability of age can also be considerable (factor of 2), related to the combinations of physical model parameters, which influence circulation dynamics, and gas exchange in the models. The preformed component was found to be very sensitive to gas exchange and moderately sensitive to ice cover. In our model evaluation exercise, the choice of the gas exchange constant from within the current range of uncertainty had such a strong influence on preformed and bulk 14C-age that if model evaluation would be based on bulk 14C-age it could easily impair the evaluation and tuning of a models circulation on global and regional scales. Based on the results of this study, we propose that considering preformed 14C-age is critical for a correct assessment of circulation in ocean models.


Introduction
Coupled global ocean circulation models are often-used tools in studying the role of the oceans under a changing climate.They are, for example, used to predict future changes of ocean biogeochemistry.In this context, the time elapsed since the last contact of a water parcel with the atmosphere is of particular interest in order to understand the interaction of changes in climate, circulation and biogeochemical processes.A variety of tracers can be used to evaluate circulation and water age structure both in the real ocean and in biogeochemical ocean models (e.g.Lynch-Stieglitz, 2003).One tracer, 14 C-DIC, has become pivotal in such studies (Stuiver et al., 1983;Toggweiler et al., 1989;Jain et al., 1995;Caldeira et al., 2002;Matsumoto et al., 2004;Cao and Jain, 2005;Matsumoto, 2007). 14C is naturally produced in the upper atmosphere and enters the ocean via gas exchange.In the ocean's interior, there is no 14 C production, and radioactive decay with a half-life of 5730 yr reduces its concentration over time.This leads to a decrease of the 14 C / C ratio of dissolved inorganic carbon, which allows for the computation of 14 C-ages (yr) of the respective water.The natural distribution of 14 C in the ocean is often expressed in a delta notation relative to the 14 C / C ratio of the atmosphere ( 14 C = (R o / R a − 1) • 1000; R o and R a are the 14 C / C ratios of ocean and atmosphere (1890 AD; Stuiver and Polach, 1977), respectively).Surface water in equilibrium with the preindustrial atmosphere (1890 AD), ignoring isotope fractionation, would have a 14 C = 0 ‰ and a 14 C-age of 0 yr. 14C-DIC is widely used in model evaluation (Matsumoto et al., 2004) for two reasons.First, it can be directly mea-sured in the ocean.Second, it can be implemented at relatively low computational cost both into biogeochemical and ocean circulation models.
Several issues complicate the use of natural 14 C for databased evaluation of ocean-model circulation.First, there is the assumption of constant atmospheric 14 C boundary conditions often applied in ocean model 14 C experiments.On multi-millennial timescales, the atmospheric 14 C production and level is by no means constant (Bard, 1988;Adkins and Boyle, 1997;Franke et al., 2008a, b).Second, there are significant man-made changes to the 14 C / C distribution in the atmosphere and the ocean.The invasion of fossil fuel CO 2 , almost devoid of 14 C, into the ocean reduces the 14 C / C ratio (the Suess Effect; Suess, 1955).On the other hand, 14 C-CO 2 from atmospheric nuclear-bomb testing in the 1950s and 1960s has strongly increased it (Rafter and Fergusson, 1957).The combination of both effects masks the natural distribution of 14 C / C in the ocean considerably, in particular in the upper ocean (e.g.Stuiver, 1980;Fig. 1a).Third, it is usually assumed that the transport of 14 C / C from the surface to the deep sea via sinking organic particles can be neglected (Fiadeiro, 1982;Jahn et al., 2014).
Finally, the time to reach 14 C-CO 2 equilibration between atmosphere and surface ocean is of the order of a decade (Broecker and Peng, 1974), which is longer than water residence time at the surface.In particular, the entrainment of old, 14 C-depleted water does not allow surface 14 C / C ratios to reach equilibrium with the atmosphere.Thus, 14 C-ages in the surface ocean after correction for bomb 14 C are of the order of hundreds of years (Fig. 1b).Elevated surface ages have been confirmed by radiocarbon measurements in warm-water corals from periods before bomb testing or before the industrial era (e.g.Druffel, 1981) which shows that they are not an artefact of the corrections for bomb 14 C or the Suess effect.Surface water sinking into the interior of the ocean in high latitudes, however, is known to have an initial 14 C-age of up to 900 yr older than tropical and subtropical surface waters (Bard, 1988).Hence 14 C-ages in the interior ocean are not real circulation ages.They are not solely reflecting the passage time in the interior of the ocean, but are apparent ages only (e.g.Broecker, 1979).
In the context of ocean biogeochemistry the time elapsed since the last contact of a water parcel with the atmosphere, i.e. when it is assigned zero age, is of particular interest.For example, the estimation of rates of ocean respiration or CaCO 3 dissolution from cumulative tracer changes (Sarmiento et al., 1990;Broecker et al., 1991;Feely et al., 2002) requires reliable age determinations. 14C-ages of several hundred years for waters actually in contact with the atmosphere can thus pose a severe problem.Inferring true ages from 14 C-ages in the interior of the ocean obviously requires a correction for the "initial-age" effect before they can be used to derive the time component of circulation (Broecker, 1979;Bard, 1988;Campin et al., 1999).The term "bulk 14 Cage" ( 14 C-age bulk ) is used here to denote ages computed from the distribution of natural 14 C-DIC not corrected for the initial, preformed 14 C-DIC.We use the terms "preformed" 14 C-DIC and "preformed" 14 C-age (Emerson and Hedges, 2008) in analogy to preformed components of other ocean tracers such as nutrients, oxygen or alkalinity (Redfield et al., 1963, Najjar et al., 2007, Koeve et al., 2014).The common feature of bulk tracers is that their distribution within the ocean's interior is a combination of a preformed component entering the ocean interior via physical transport processes (subduction, downwelling), a component related to processes (sources or sinks) within the ocean (respiration, remineralisation, mineral dissolution, radioactive decay), and the mixing of both components as water masses mix (Duteil et al., 2012(Duteil et al., , 2013;;Koeve et al., 2014).Note that the term "reservoir age" is used in the radiocarbon and palaeo-climatological literature in a similar way in which "preformed age" is used in this paper.
It is standard procedure to use 14 C or bulk 14 C-ages uncorrected for preformed 14 C from models and observations to evaluate model circulation (e.g.Matsumoto et al., 2004).In this study we present model experiments using14 C-based tracers and a tracer of ideal age from three different ocean biogeochemical models.Our major objective is to gain insight into the magnitude and distribution of preformed 14 C-age both in models and in the real ocean.Further we will discuss how neglecting preformed 14 C-age and the use of bulk 14 C-ages may bias the assessment of ocean models and lead to a faulty tuning of the circulation in ocean models.A realistic model circulation, however, is not only a prerequisite to a reliable climate prediction but also a critical aspect in biogeochemical or carbon cycle model studies.Unrecognised issues in the model physics may give rise to a faulty tuning of biogeochemical processes, for example when bulk nutrient concentrations are used to evaluate a model's biogeochemistry (Duteil et al., 2012).

Models and modelling approach
We employ three different models, two of which use an offline approach and one is an online fully coupled earth system model.For the offline models we use the transport matrix method (TMM) described in detail by Khatiwala et al. (2005) and Khatiwala (2007).In this approach ocean-tracer transport is represented by a matrix operation involving the tracer field and a transport matrix extracted from a global circulation online model (Khatiwala, 2007).In particular, we use two matrices extracted from two versions of the MIT (Massachusetts Institute of Technology) generalcirculation model, a state-of-the-art primitive-equation model (Marshall et al., 1997).The coarse-resolution matrix (hereafter MIT2.8) was derived from a 2.8 • × 2.8 • global configuration of this model with 15 vertical layers, forced with monthly mean climatological fluxes of momentum, heat and freshwater, and subject to a weak restoring of surface temperature and salinity to observations.The higher resolution matrix (hereafter ECCO) is based on the data-assimilation model of the ECCO consortium (Estimating the Circulation and Climate of the Ocean; Stammer et al., 2004) and has a horizontal resolution of 1 • × 1 • and 23 vertical layers; for details see Khatiwala (2007) and Kriest et al. (2010Kriest et al. ( , 2012)).Wind-speed dependence of gas exchange applies winds from Trenberth et al. (1989) with a monthly resolution regridded to the respective model grid.Sea ice fields applied are the OCMIP-2 ice mask (Orr et al., 2000) for MIT2.8 and NASA ISLSCP (International Satellite Land Surface Climatology Project) climatology (http://iridl.ldeo.columbia.edu/SOURCES/.NASA/.ISLSCP/ .GDSLAM/.Snow-Ice-Oceans/.sea/.sea_ice/)for ECCO (S. Dutkiewics, MIT, personal communication, 2011).OCMIP is the Ocean Carbon cycle Model Intercomparison Project (http://ocmip5.ipsl.jussieu.fr/OCMIP/).
The third model used is the University of Victoria Earth System Climate Model (UVIC; Weaver et al., 2001), version 2.8 in the configuration used at the GEOMAR Helmholtz Centre for Ocean Research, Kiel, Germany (Oschlies et al., 2008) (Bitz et al., 2001).The biogeochemical ocean model of the UVIC is described in detail by Schmittner et al. (2008).
For the 14 C simulations with the TMM models, we largely follow the OCMIP-2 protocol (Orr et al., 2000;Jahn et al., 2014) and study the natural 14 C distribution in an abiotic setting and against an atmosphere of 14 C = 0 and a constant pCO atm 2 = 280 µatm.DIC and 14 C-DIC are prognostic model tracers of total dissolved inorganic carbon and its 14 C isotope, respectively.Alkalinity is prescribed from the model's salinity field assuming a fixed alkalinity / salinity ratio.OCMIP-2 14 C simulations are abiotic model runs; biotic fluxes of 14 C (as well as of DIC and alkalinity) are ignored following Fiadeiro (1982).Also the effect of isotope fractionation is not considered.Our notation of 14 C follows the OCMIP-2 protocol (Orr et al., 2000).
All model runs were integrated for several thousand years (for details see Sect. 3) and can be considered equilibrium runs.For UVIC the 14 C simulations can be made alongside a biotic model run (Schmittner et al., 2008).
Air-sea exchange of CO 2 and 14 CO 2 in all three models is treated according to Eqs. ( 1) and (2): where CO * 2(air) = CO 2 (sol) • pCO 2 (atm) • P (atm) .k w is the gas-transfer velocity, U is wind speed, n = 2, Sc is the Schmidt number, and η = 0.5.CO * 2(water) is the sum of CO 2 dissolved in seawater and H 2 CO 3 in surface water computed from the DIC concentration and an estimate of pH (e.g.Follows et al., 2006).CO * 2(air) is the equilibrium CO 2 concentration given atmospheric pCO 2 , CO 2 solubility and the local atmospheric pressure; CO 2 (sol) is the solubility of CO 2 , pCO 2 (atm) is CO 2 partial pressure in the atmosphere, P (atm) is the local atmospheric pressure, R (atm) is the 14 C / C ratio of the atmosphere and R (water) is the 14 C / C ratio of the surface water.In the standard configuration the gas-transfer velocity k w is computed using a value of a = 0.337, following the OCMIP-2 protocol.The term "ice" represents the fraction of water area covered by sea ice.
In the ocean, bulk 14 C-age (in units of years) can be computed (Stuiver and Polach, 1977)

Model tracers
In order to study the distribution of preformed 14 C in the interior of the ocean, we designed a suite of additional model tracers.
1. 14 C-DIC bulk : this is the tracer of natural 14 C-DIC implemented following the OCMIP-2 protocol.The age computed from this tracer via Eq.(3) has also been called "conventional 14 C-age" (Khatiwala et al., 2012) but is usually referred to as " 14 C-age" or "radiocarbon age".We will use the term 14 C-age bulk in order to highlight the fact that it consists of several components (see below).
2. age ideal : a tracer of the time elapsed since the last contact with the atmosphere.The "ideal age" model tracer (Thiele and Sarmiento, 1990;England, 1995;England and Maier-Reimer, 2001) works like a clock counting time after being restored to zero, which happens every time the water resides at the surface.Everywhere else it ages with a rate of 1 day day −1 and is subject to mixing and advection in the interior of the ocean.Synonyms of the age measured by this tracer used in the scientific literature include: "circulation age" (Matsumoto, 2007;Khatiwala et al., 2012), "ventilation age" (Adkins and Boyle, 1997;Campin et al., 1999), and "ideal age" (Thiele and Sarmiento, 1990).
3. 14 C-DIC pre : a preformed 14 C-DIC tracer is restored to the model's actual 14 C-DIC at the surface while in the interior of the ocean it is only mixed and advected but is not subject to radioactive decay.The respective preformed 14 C-age (yr) is computed from 14 C-age pre = −8267•log e ( 14 C-DIC pre / DIC pre ), where DIC pre is preformed total CO 2 .Note that in an abiotic run DIC pre is always equal to DIC.The term "reservoir age" has been used synonymously (Khatiwala et al., 2012, and references therein).
4. 14 C-DIC decay : a 14 C-DIC-decay tracer is set to zero in surface waters and numerically integrates 14 C decay of the 14 C-DIC tracer in the interior of the ocean.It is also advected and mixed in the interior of the ocean.Reference model runs (10 000 yr) are carried out with all three models.We apply a gas-transfer constant of a = 0.337, wind fields and ice cover as given in Sect.2.1 for these runs.Implemented tracers are DIC, 14 C-DIC bulk and age ideal .We use these tracers to approximate the preformed component of 14 C-age bulk in the different models by diagnosing it during post-processing from the difference of 14 C-age bulk and age ideal .Reference runs also serve as spin-up runs from which other model experiments are initialised.
To start with, we compare global mean profiles of 14 Cage bulk and age ideal (Fig. 2a).A number of features are evident.First, 14 C-age bulk is much larger than age ideal in any model.The global mean offset between the two age measures varies by up to a factor of 2 between models (Fig. 2b).In the deep ocean the offset is about 400 yr in MIT2.8 and 680 yr (800 yr) in ECCO (UVIC).The age offset may be either rather homogeneous vertically (MIT2.8)or have a marked vertical gradient of up to 400 yr difference between surface and deep water (ECCO and UVIC).Second, global mean surface 14 C-age bulk is smaller than the data-based estimate from the Global Ocean Data Analysis Project (GLODAP) in all three models (Fig. 2a).Third, a judgement based just on global mean profiles of 14 C-age bulk would indicate that over most of the ocean the UVIC model is the one in best agreement with observations.Furthermore, one might conclude that the MIT2.8 model appears to have too young waters and presumably too vigorous a circulation almost everywhere.
Interestingly, the age ideal tracer indicates just the opposite.Deep-ocean MIT2.8 waters have the highest ages pointing to a more sluggish circulation while in UVIC (and ECCO) deep-ocean waters are in fact younger, indicating a more vigorous circulation compared to the MIT2.8 model.Finally, in the upper 2000 m, the global mean profiles of the ideal age tracer suggest that the circulations are similar in all three models, at least much more similar than indicated by 14 Cage bulk .
In conjunction with the observations that oceanatmosphere 14 C equilibration is slow (Broecker and Peng, 1974) and surface-ocean 14 C-age bulk is well above zero (see Fig. 1b), we suspect that (most of) the difference between 14 C-age bulk and age ideal in the interior of the ocean is due to the 14 C-age bulk which a water mass had at the time when entering the ocean's interior, i.e. its preformed 14 C-age.
In Fig. 3, we present the large-scale distribution of 14 Cage bulk and age ideal from the ECCO model run along sections through the Atlantic Ocean (20 • W) and the Pacific Ocean (140 • W).Surface 14 C-age bulk is around 200 yr in the subtropical ocean basins, around 300 yr in the North Atlantic and around 1000 yr in the Southern Ocean.In the interior of the ocean, 14 C-age bulk increases from about 300 yr in the northern North Atlantic Ocean, almost continuously along the path of circulation originally proposed for the global conveyor belt by Broecker and Peng (1982), towards the deep northern North Pacific where 14 C-age bulk is about 2000 yr (Fig. 3a).In contrast, age ideal (Fig. 3b) is zero all over the surface ocean, and close to zero in the deep waters of the two major ocean ventilation regions, i.e. the northern North Atlantic and the Southern Ocean (Marshall and Speer, 2012).Elevated age ideal is found in the deepest waters of the Atlantic Ocean (700 yr) and in particular towards the northern North Pacific where maximum ages are around 1400 yr along the transect chosen.Basin-scale patterns of age ideal and 14 C-age bulk are similar in the Pacific mainly due to a very homogeneous N-S distribution of preformed age (Fig. 3c).In the Atlantic Ocean, however, the strong N-S gradient in preformed age masks important aspects of circulation in the 14 C-age bulk distribution.For example, the continuous northto-south increase in the 14 C-age bulk is not consistent with the strong ventilation in the Southern Ocean, but is mainly governed by waters of large preformed 14 C-age subducting in the Atlantic Sector of the Southern Ocean.
The preformed age shown in Fig. 3c is taken from the age pre tracer (Table 1).The sum of age ideal and this preformed age tracer agrees with the 14 C-age bulk within a few percent (see Fig. 3d for the residual).As we will explain and quantify in the following section, the residual derives from a non-linear effect of 14 C-DIC and DIC tracer mixing on computed age.To reflect this we write Eq. ( 4

Effects of tracer mixing on age estimates
In the following we will use dedicated model experiments carried out with the ECCO model, in order to quantify the relative importance of the three terms on the right-hand side of Eq. ( 4).We implement DIC and all six tracers described in Sect.2.2.We will use this combination of tracers to quantify the non-linearity arising from mixing of the 14 C-DIC and DIC tracers on computed 14 C-age components.To explore the effect of tracer mixing on 14 C-ages in more detail, we first apply the additional tracers 14 C-DIC pre and 14 C-DIC decay (Table 1).We initialise these tracers from the model output of the spin-up run (after 4000 yrs) with the DIC, 14 C-DIC and age ideal tracers assuming the "mixing residual" term of Eq. ( 4) to be zero everywhere.Running the model for another 6000 yr, we find the sum of the preformed and the decay tracers to match the 14 C-DIC tracer perfectly (Fig. 4a).The sum of ages ( 14 C-age pre + 14 C-age decay ), however, is smaller by 6 % on average than the age computed from the 14 C-DIC bulk tracer (Fig. 4b).
The difference between Fig. 4a and b, i.e. the low bias in ages computed from 14 C tracers relative to the tracer itself, is explained by the combination of the logarithmic transformation in the age computation (Eq. 3) and the effect of mixing of waters with different 14 C / C tracer ratios (Jenkins, 1987;Delhez et al., 2003;Khatiwala et al., 2001Khatiwala et al., , 2012)).
To make this effect visible and quantifiable in our model, we compare age estimates from two sets of tracers (Table 1) tracking (a) the circulation component of age, (b) preformed age, and (c) bulk age.One set of these tracers behaves ideally in the interior of the ocean, in the sense that where they are affected by mixing, the mixing products can be described by mixing along a linear mixing line.These tracers are the age ideal , age pre and age bulk tracers (Table 1).The latter two tracers inherit the age of 14 C-age bulk at the surface, while in the interior of the ocean they behave like ideal tracers, being either only transported (age pre tracer) or being both transported and ageing with a rate of 1 day day −1 (age bulk tracer).We compare ages derived from these ideally behaving tracers and the respective ages from the 14 C-based tracers, 14 C-age decay , 14 C-age pre and 14 C-age bulk .In all three cases (circulation component of age, preformed component of age and bulk age) we see that 14 C-based ages underestimate their ideally behaving counterparts.We present the results as anomalies (ideally behaving -14 C-based) of ages along the combined section through the Atlantic (30 • W), Southern (60 • S) and Pacific (140 • W) oceans (Fig. 5).The age anomaly age bulk − 14 C-age bulk (Fig. 5a) is close to zero in the surface ocean, in the northern North Atlantic, and in the Atlantic sector of the Southern Ocean.Away from these outcrop regions and largely following increasing ideal age (age ideal ), the anomaly increases to maximum values of about 50 yr in the (South) Atlantic Ocean and about 80 yr in the (North) Pacific Ocean.This difference is moderate and equivalent to a few percent of 14 C-age bulk .Preformed ages (Fig. 5b) show very small anomalies (age pre − 14 C-age pre ) of only a few years (and usually less than 1 % of age pre ), again with maxima in the South Atlantic Ocean and the North Pacific Ocean.The largest difference is found between age ideal and 14 C-age decay .In the deep northern North Pacific this difference is almost 200 yr (Fig. 5c).Over much of the Pacific Ocean it is equivalent to about 15 % of ideal age.
The effect of non-linear mixing on 14 C-ages has been studied previously (Deleersnijder et al., 2001;Holzer et al., 2010;Khatiwala et al., 2012).Applying a boundary propagator approach (Holzer et al., 2010), Khatiwala et al. (2012) found a difference between their mean age ( ) and their radiocarbon age ( C ) of usually less than 50 yr, which is comparable to the overall effect of non-linear mixing (age bulk − 14 Cage bulk ) (Fig. 6a) observed in our model, while the difference (age ideal − 14 C-age decay ) from our model (Fig. 6c) is considerably larger.This may be explained by methodological differences.While our 14 C-age decay is based on the numerical integration of 14 C decay, the definition of the radiocarbon age, 14 C(x) = 14 C 0 (x)e λ C (x) , of Khatiwala et al. (2012) uses 14 C 0 as the weighted average of the 14 C surface concentration.
The small difference age bulk − 14 C-age bulk (Fig. 5a) in combination with an almost perfect behaviour of the preformed-age tracers (Fig. 5b) suggests that our initial assumption (Sect.3.1; Fig. 2) that the preformed age can be well approximated by Eq. ( 5), i.e. the difference between the 14 C-age bulk and age ideal of a model, is justified.
14 C-age pre ≈ 14 C-age bulk − age ideal (5) In any case, preformed 14 C-ages estimated from this difference provide a conservative, lower-limit estimate of preformed age.In the ECCO model, this underestimate may be as large as 20 % in individual grid boxes (Fig. 4c).On average, however, it is about 7 % with higher values observed towards the North Pacific Ocean.This uncertainty is small given the order of 50 % contribution of the preformed age to bulk 14 C-ages presented in Sect.3.1.For the sake of saving computational time by having a reduced number of tracers, we hence ignore the mixing effect in the following section where we discuss a series of sensitivity runs.

Mechanisms controlling preformed 14 C-age
In this section we treat the major processes, which determine the magnitude of preformed 14 C-age, and how they influence model assessment if based on 14 C-age bulk .We perform several sensitivity experiments to study the sensitivity of preformed 14 C-age distribution to relevant model parameters.
All sensitivity experiments are carried out with the reduced set of model tracers (i.e. 14 C-DIC bulk and ideal age tracer, Table 1) and we diagnose the preformed 14 C-age offline during post-processing of model output using Eq. ( 5).This procedure is justified by the results presented in Sect.3.2. 14C-age bulk of several hundred years in the surface ocean (Fig. 1b) have been attributed to the long equilibration times of carbon isotopes (Broecker and Peng, 1974).While for CO 2 the equilibration time is governed by the product of the timescale of gas exchange (of the order of 1 month) and the ratio CO 2− 3 / CO aq 2 (10-15 in the surface ocean), the equilibration time of carbon isotopes scales with the ratio TCO 2 / CO aq 2 .Since there is about 10 times more total CO 2 than there are carbonate ions in seawater, the equilibration time of carbon isotopes is larger by about a factor of 10, i.e. of the order of a decade (Broecker and Peng, 1974).Elevated and variable 14 C-DIC bulk in the surface ocean suggests that the residence time of waters at the ocean surface is usually much shorter than this equilibration time and equilibrium with atmospheric 14 C is therefore not attained.The actual residence time (Bolin and Rohde, 1973;Takeoka, 1984) of waters in the surface ocean is not well known though.Diagnosing the residence time of surface waters, and particularly its regional variations with respect to the observed distribution of 14 C-DIC bulk at the surface, is not straightforward in our model.Instead, we take a first step into this direction and model the age of the surface water relative to its last stay below a given depth.For this purpose we modify the definition of our ideal age tracer such that it is set to zero everywhere below a model specific reference depth and allowed to age in layers higher up.The reference depths are 135 m in ECCO and 120 m in MIT2.8.The idea here is to have a reference depth larger than 100 m, a depth often used pragmatically to define the productive surface layer.Differences between the reference depths are simply due to the different vertical resolutions in the models.The time passed since the last residence below the surface is henceforth referred to as the "age relative to depth".In our MIT2.8model, for example, the age relative to depth ranges up to 2 years in subpolar and most Northern Hemisphere polar waters, up to 5 years in Southern Ocean polar waters and equatorial upwelling regions, and up to 7 years in the subtropical gyres (Fig. 6).In the ECCO model the age relative to depth in the Southern Ocean is lower.In general, in areas of deep convection or upwelling the age relative to depth is low while in areas characterized by horizontal advection and downwelling it is larger.Deep convection and upwelling are thus a continuous source of old waters low in 14 C to the surface ocean.Our estimates of the age relative to depth (Fig. 6) are qualitatively consistent with the observed distribution of 14 C-age bulk at the surface (Fig. 1b).Regions with low age relative to depth show high 14 C-age bulk , and vice versa.Still, our age relative to depth may be considered lower estimates of true residence or exposure time (Delhez et al., 2004) since the respective age tracer will be reset to zero each time a water parcel is below the reference depth, even if for a brief period only.
Most of the deep-ocean volume is ventilated from relatively small regions in the high latitudes.It is conditions in these regions that control the preformed 14 C-age distribution in the ocean's interior.One such region is the northern North Atlantic.Surface waters there, originating mainly from the low-latitude Atlantic Ocean, are to be converted into North Atlantic Deep Water (NADW).Source waters have been at or near the surface for several years allowing 14 C-DIC to approach equilibrium with the atmosphere.Furthermore, deep convection in the northern North Atlantic entrains relatively young waters into the surface each winter.Combined, both effects give rise to moderately negative surface 14 C and moderate 14 C-ages in the surface (Fig. 1b).
In the Southern Ocean the situation is different.Upwelling south of the Antarctic Polar Front brings very old waters to the surface.In fact, some of this water stems from the return flow of the global conveyor belt.Having left the ocean's sur-face in the northern North Atlantic it has travelled through the deep Atlantic Ocean, the Circumpolar Current system, further up to the North Pacific and back to the Southern Ocean isolated from the atmosphere all the time, which has been estimated to be of the order of 2700 yr (DeVries and Primeau, 2011).Other components of the water upwelling in the Southern Ocean have been ventilated relatively recently in the North Atlantic or have returned after a passage of about 2000 yr from the tropical Indian Ocean.Hence, waters upwelling in the Southern Ocean are in bulk much older and more depleted in 14 C-DIC, compared to those entering the deep-water formation regions at the surface of the North Atlantic.Combined with short surface residence times, this gives rise to much larger preformed 14 C-ages in the Southern Ocean deep-water formation regions, about 1000 yr in the real ocean (Bard, 1988;Fig. 1b).
Several factors could potentially influence the overall magnitude and distribution of preformed 14 C-age in models and the real ocean.These are (a) the intensity of upwelling in the Southern Ocean, (b) the rate of gas exchange, (c) ice coverage, (d) water residence time in the surface of the region of water mass formation and (e) the relative contribution of different source water regions (e.g.NADW and AABW, Antarctic Bottom Water) to the total deep-water formation rate.
The gas-exchange formulation (Eqs.1-3) is essentially identical in all three tested models.In particular the standard configurations of all models apply wind-speed squared and the OCMIP-2 gas-transfer constant of 0.337.This value is based on tuning one model of the OCMIP-2 family together with its given wind and sea ice fields against the bomb 14 C ocean inventory estimated from observations (Broecker et al., 1985) and considered correct at the time of the OCMIP-2 experiment.Evidence has since accumulated suggesting the bomb 14 C ocean inventory to be in fact smaller by up to 25 % (Sweeney et al., 2007).As a consequence, the gastransfer constant may need a corresponding reduction.Such a change in the gas-transfer constant has little effect on net oxygen or total-CO 2 fluxes between ocean and atmosphere.It has, however, a considerable effect on 14 C-age pre and hence also the 14 C-age bulk distribution in the ocean.Using all models, we repeat the standard experiment with a reduced gas-exchange rate.For this purpose we reduce the standard value of the gas-transfer constant from a = 0.337 to a value of a = 0.24 (see Eq. 2).This change causes the global mean profiles of preformed 14 C-ages (Fig. 7a) to increase by about 150 yr (ECCO, UVIC) to 200 yr (MIT2.8).
In the global mean profile this shift is almost uniform with depth.Concerning the global mean profiles of 14 C-age bulk , two features are evident (Fig. 7b).First, model surface values are now (a = 0.24) much closer to bulk ages derived from the "observed" natural 14 C as compared to our reference runs (a = 0.337; Fig. 2a).Reducing the gas-transfer constant hence solves one of the model-data comparison issues discussed in Sect.3.1 (Fig. 2a).At depth (ignoring the deepest layers below 4000 m) this increase shifts the global mean profile of the MIT2.8 much closer to observations.With the reduced gas-exchange constant 14 C-age bulk of the UVIC model appears to be too large compared to observations and the ECCO model appears to be the best-performing model in our model inter-comparison, except at the surface. 14C-based judgement of model circulation obviously is very sensitive to the air-sea exchange formulation, which, however, only affects preformed age, not age ideal .Using an improper gas-exchange formulation may hence adversely affect the interpretation of 14 C model experiments concerning a model's circulation dynamics.
One potential solution to this problem is to diagnose the most suitable gas-exchange constant for a given model and wind field by performing a bomb 14 C calibration experiment (Sweeney et al., 2007).The degree to which this is possible, however, is limited by several methodological problems.The number of 14 C ocean data available from early after the atomic bomb testing in the atmosphere, i.e. the 1970s (GEOSECS program, Broecker et al., 1985; see also Schlitzer, 2015) is small compared with the number of re- spective data from the 1990s, i.e. from the WOCE (World Ocean Circulation Experiment) and CLIVAR (Climate and Ocean: Variability, Predictability and Change) observational programs (Key et al., 2004).The bomb 14 C ocean inventory of the 1970s is hence less certain than that of the 1990s.This second time slice, however, may be too late to constrain the adequate gas-exchange coefficient of a model independent of the model's ocean circulation (e.g.Graven et al., 2012) as 14 C back fluxes from the ocean to the atmosphere (Naegler, 2009) become increasingly important.The separation of bomb 14 C and natural 14 C (Rubin and Key, 2002;Sweeney et al., 2007) as well as details of the model implementation of 14 C (Mouchet, 2013) add to inevitable uncertainties of a bomb 14 C calibration of the gas exchange in a given model.
Ice coverage is another factor potentially influencing the gas equilibration at deep-water formation sites (Ito et al., 2004;Duteil et al., 2013).Ito et al. (2004) reported ice cover to be responsible for about one-third of the oxygen disequilibrium observed in their model.In order to study the impact of ice cover on 14 C-gas exchange and hence preformed 14 C-age, we perform one model run with the ECCO model where ice cover was switched off for 6000 yr.Technically this run was initialised with data from year 4000 of the spinup and the value of "ice" in Eq. ( 1) was prescribed to zero.In this experiment preformed 14 C-age was reduced by up to 70 yr, or less than 10 % of its normal value (Fig. 8).Ice cover hence appears not to be of major importance in controlling preformed 14 C-ages.Campin et al. (1999) observed differences in the response of 14 C-age bulk and age ideal to atmospheric forcing representing the Last Glacial Maximum (LGM) and the present-day ocean, respectively.The associated difference of 14 C-age pre between LGM and today's ocean has been discussed to be re- lated to an intensified upwelling of 14 C-depleted Circumpolar Deep Water (Campin et al., 1999) or an ice-cover-induced reduction in 14 C-gas exchange during the LGM (Schmittner, 2003).Since in both studies, ice cover and circulation changed simultaneously, a direct comparison with our experiments is difficult.

Case studies
The overall importance, but also the inter-model variability, of the preformed 14 C-age is evident from Fig. 9.The preformed 14 C-age over much of the ocean contributes to bulk 14 C-age by about 50 % in UVIC and ECCO, with higher shares in young water in the upper ocean in all models.In MIT2.8 this fraction is smaller in the deep ocean (about 30 %) (Fig. 9a).In all models, the relative importance of the preformed age component decreases with distance from the deep-water formation regions (Fig. 9b).
Two cases are discussed in the following to demonstrate the adverse effects of neglecting the preformed component of 14 C-age.For both cases we make use of a series of model runs to study the sensitivity of 14 C-age bulk , age ideal and the diagnosed preformed 14 C-age to the choice of vertical background diffusivity in a model.The intensity of diapycnal mixing in the ocean is one of the key controls of ocean circulation and biogeochemical cycles (Bryan, 1987).For the experimental design we follow Duteil and Oschlies (2011), who used UVIC 2.8.Here, we apply the Kiel version of UVIC 2.9 (Keller et al., 2012) to which we added an age ideal tracer.We perform eight sensitivity runs assuming background mixing coefficients of K vbg = 0.01, 0.05, 0.1, 0.15, 0.2, 0.3, 0.4 and 0.5 cm 2 s −1 .Following Duteil and Oschlies (2011) a value of 1 cm 2 s −1 is added to the background diffusivity south of 40 • S to account for observed vigorous mixing in the Southern Ocean.Each of the model experiments has been integrated for 10 000 yr under preindustrial atmospheric and astronomical boundary conditions, i.e. all model runs assume constant atmospheric 14 C = 0 and pCO 2 of 280 µatm.
In the first example we consider the volume and the age of water in the oxygen minimum zone of the Pacific Ocean.Using UVIC 2.8, Duteil and Oschlies (2011) found domeshaped distributions for both volume and age with varying K vbg .Maximum suboxic volume and 14 C-age bulk were found at an intermediate K vbg of 0.2 cm 2 s −1 (Duteil and Oschlies, 2011, their Fig. 1b).Repeating these experiments with our version of UVIC 2.9, we find a very similar distribution with the 14 C-age bulk maximum also at K vbg = 0.2 cm 2 s −1 (Fig. 10a).At the highest (lowest) tested K vbg values of 0.5 (0.01) cm 2 s −1 the mean bulk 14 C-age is lower by 90 (70) yr.Separating bulk age into its circulation component (age ideal ) and its preformed component ( 14 C-age bulk − age ideal ), we find, however, very little sensitivity of age ideal to K vbg between 0.01 and 0.3.Only for high values of K vbg (0.3 to 0.5 cm 2 s −1 ), we find that the sensitivity of 14 C-age bulk is mainly due to changes in the circulation component of the age (Fig. 10b).For K vbg values below 0.2 cm 2 s −1 , more than 60 % of the gradient of 14 C-age bulk (against K vbg ) is from the preformed component (Fig. 10c).The similarity of patterns of suboxic volume and 14 C-age bulk led Duteil and Oschlies (2011) to conclude their model results to confirm the notion of a predominant control of suboxic water volume by physical ocean dynamics rather than by local export production and remineralisation.In quantitative terms, and for our model experiments, the suboxic volume appears to be linearly correlated with 14 C-age bulk (Fig. 10d).Variations of 14 C-age bulk explain 65 % (93 %) of the variation of the suboxic volume in the eastern tropical Pacific above 1000 m with n = 8 (n = 7, excluding the lowest value K vbg = 0.01), respectively.In fact, the relationship of suboxic volume and age ideal is not tight and does not confirm that circulation intensity exerts a simple physical control on the suboxic volume (Fig. 10e).A linear correlation explains about 18 % only of suboxic volume variation by the model's ideal age, i.e. the circulation component of 14 C-age.Interpreting 14 C- age bulk as a measure of circulation intensity, i.e. to neglect the preformed component, hence yields a faulty assessment of the physical drivers of oxygen minimum zone (OMZ) volume.Since a local preformed 14 C-age always represents the mixing of different surface water end members, the much larger predictive power of 14 C-age bulk (compared with that of age ideal ) may alternatively suggest that it is not predominantly circulation intensity (as measured by age ideal ) but the combination of different water supply paths (and their variability with K vbg ) which control OMZ volume.
In the second example, which is based on the same model runs, we explore N-S age gradients in the deep Atlantic Ocean.The mean 14 C-age bulk of waters below 1500 m in the Atlantic Ocean shows a marked N-S gradient, with higher values in the Southern Ocean.The slope of this gradient is highly sensitive to the choice of K vbg in the model (Fig. 11a; see also Fig. 3).Ideal age also shows sensitivity to K vgb , but the patterns are very different with the highest differences in the tropics and a low sensitivity to K vbg not only in the northern North Atlantic but also in the Southern Ocean (Fig. 11b).In fact, the observed patterns are largely due to the differences of the preformed component between model runs (Fig. 11c) with different K vbg .Similar to the OMZ example, patterns of 14 C-age bulk predominantly reflect the mixing of different surface water end members (here the North and South Atlantic end members) to the choice of K vbg and not its impact on circulation intensity (as measured by age ideal ).In particular the size of the southern end members of preformed 14 C-age vary with the choice of K vbg .In the run with the lowest K vbg , the southern end member of preformed 14 Cage (i.e.Southern Ocean surface 14 C-age bulk ; Fig. 12a-c) is almost twice as high, compared to that of the run with the highest K vbg .In turn, the differences seen in Southern Ocean preformed 14 C-age are related to the impact of the chosen value of K vbg on the circulation in the Pacific Ocean.With low K vbg , the deep North Pacific shows a 14 C-age bulk of up to 3000 yr while with high K vbg , this age is about 1500 yr only (Fig. 13).It is the upwelling of these 14 C-depleted waters in the Southern Ocean, which strongly impacts the southern end member of waters ventilating the South Atlantic.The northern end member contributes much less to the K vbg sensitivity of age gradients in the deep Atlantic (Fig. 11).Reading pat- terns of 14 C-age bulk in the South Atlantic in terms of circulation intensity, i.e. neglecting the differences of preformed 14 C-age between runs with different K vbg (which are due to differences in Pacific Ocean circulation in these model runs), would cause a faulty interpretation of the respective model circulation in the Atlantic Ocean.

Conclusion
Globally, 14 C-age bulk is dominated by two equally important components, one associated with the time elapsed since last contact with the atmosphere and one associated with a preformed age related to the slow and incomplete equilibration of 14 C with atmospheric 14 C in the surface ocean.While on average the preformed component accounts for about 50 % of the bulk 14 C-age, there is large variability.Regionally, and within a given model, the relative contribution of 14 C-age pre is up to 100 % near the ocean's surface, but is well below 50 % in the oldest deep waters typically observed in the deep North Pacific Ocean.Regional variability, e.g. in the deep Atlantic Ocean, where it is associated with mixing of end members with very different 14 C-age pre , may well mask the circulation component such that it is not visible from the distribution of 14 C-age bulk .Between models, the variability can also be considerable, likely due to an interplay of physical model parameters (e.g.diapycnal diffusivity, K vbg ) influencing the circulation dynamics within the ocean, and those which control gas exchange of 14 C with the atmosphere, like the gasexchange constant, ice coverage or the wind fields used.In our comparison of three different models, the choice of the gas-exchange constant (parameter a in Eq. 2) from a parameter range within current uncertainty may either make the UVIC model (Fig. 2a) or the ECCO model (Fig. 7b) compare most well with observed 14 C-age bulk .This is solely due to its impact on the preformed 14 C-age component and not related to the circulation of the model in question.A databased evaluation and tuning of a model's circulation which uses 14 C-age bulk without considering the variability of preformed 14 C-age is hence at risk of selecting the wrong circulation.
In the similar way, temporal changes (e.g. over glacialinterglacial cycles) of the deep-ocean 14 C-age distributions may be misunderstood if 14 C-age bulk is not corrected properly for the preformed component.For palaeoreconstructions the 14 C-age bulk of the deep ocean is preserved in the shells of benthic foraminifera and the surfaceocean 14 C distribution (i.e. the surface distribution of 14 Cage pre ) in their pelagic counterparts (Bard, 1988).However, the deep-ocean distribution of 14 C-age pre is very difficult to quantify since the actual mixing ratios of end members with different 14 C-age pre will also change along with a changing circulation (Campin et al., 1999), and it is not well known for time periods other than the present.Model experiments (Campin et al., 1999;Schmittner, 2003) showed that during the last glacial maximum waters in the deep Southern Ocean and South Atlantic appeared to be older (older 14 C-age bulk ) than in the late Holocene.An increase in Southern Ocean ice cover, which inhibited 14 C-gas exchange, was thought to explain much of the apparent age increase (Schmittner, 2003).The actual circulation age as measured by an age ideal tracer, however, was younger in the South Atlantic pointing to a more vigorous circulation (Campin et al., 1999).The shift to older 14 C-age bulk in that region was at least partly related to the increased invasion of Antarctic Bottom Water with a large 14 C-age pre compared to that of North Atlantic origin.The relative contribution to high 14 C-age pre from (a) the icecover-related inhibition of 14 C-gas exchange (Campin et al., 1999;Schmittner, 2003) and (b) intensified upwelling of old, 14 C depleted, water in the formation region of Antarctic Bottom Water has not yet been analysed for the last glacial maximum.In the simulations of present-day conditions in our study where the impact of ice cover on 14 C-gas exchange was switched off, leaving circulation unchanged, this impact was found to be relatively small (Fig. 9).During LGM, with a different circulation, the relative contribution from differences in ice cover compared to today may have been more important in defining the deep-ocean 14 C-age pre .
The third component of bulk 14 C-age, which is associated with the age computation being from a tracer ratio, has been quantified in detail in this study.It was found to be generally relatively small, in particular compared to the other two components, which is in agreement with other studies (Holzer et al., 2010;Khatiwala et al., 2012).We propose that in models the preformed component can be estimated from the difference of bulk 14 C-age and the model's ideal age (see Eq. 5).There is no straightforward age ideal in the real ocean though.Recent studies have tried to construct an equivalent from a multi-tracer analysis (e.g.Khatiwala et al., 2012).These data products will be very helpful together with the distribution of natural 14 C (GLODAP and GLODAP-2) to support data-based model evaluation.Model studies of ocean circulation and biogeochemical processes will benefit from this.
The general form of Eq. ( 5) is similar to equations describing the principal components of, e.g.phosphate and oxygen in the ocean.The observed phosphate concentration at any point in the ocean can be described as the sum of preformed phosphate and phosphate remineralised from decaying organic matter.Similarly, the observed oxygen concentration is the result of preformed oxygen reduced by oxygen consumption from the oxidation of organic matter.It is recognised that model evaluation and inter-comparison benefit from a separation of bulk ocean properties (phosphate, oxygen, alkalinity, etc.) into its preformed components, which return to the ocean's interior through physical transport processes, and the components which result from processing within the ocean (Najjar et al., 2007;Duteil et al., 2012Duteil et al., , 2013;;Koeve et al., 2014).Based on the results of this study, we propose that considering the preformed 14 C-age is equally critical for a meaningful assessment of the circulation of ocean models.
A realistic representation of ocean circulation is a critical aspect of any biogeochemical or carbon cycle model (Gnanadesikan et al., 2004;Doney et al., 2004) since timescales of circulation define how efficiently remineralised nutrients, oxygen deficits or respiratory carbon are stored in the interior ocean.It is only by means of age tracers such as those studied in this work, or CFCs if the upper ocean is concerned, that model circulations and the related timescales of storage can be evaluated against observations.In the case of the 14 C-age the interpretation of the observed age-tracer distribution requires an estimate of the 14 C-age pre .For the contemporary ocean this is achievable (Matsumoto, 2007;Holzer et al., 2010;Khatiwala et al., 2012).For studies of the palaeo-climate this is more difficult but obviously of similar importance (Campin et al., 1999).

Figure 1 .
Figure 1.(a) Global mean profiles (GLODAP) of bulk 14 C-age (red) and the pseudo age of 14 C-DIC not corrected for the effects of bomb and anthropogenic 14 C signatures.(b) Map of bulk 14 C-age at the surface of the ocean (GLODAP).

Figure 4 .
Figure 4. Scatter plots (a) of 14 C-DIC tracer concentrations vs. the sum of 14 C-DIC pre and 14 C-DIC decay tracer concentrations and (b) bulk 14 C-age vs. the sum of ages computed from 14 C-DIC preformed and decay tracers.Note that a few grid cells with 14 C-DIC concentrations below about 1300 mmol m −3 and bulk ages above about 2600 yr are not fully in steady state after the 2500 yr run time of this model experiment.We ignore these grid cells in the discussion.(c) Comparison of ages derived from the 14 C-DIC preformed tracer and by difference of the bulk 14 C-DIC tracer and the ideal age tracer.Red dashed line is the 1 : 1 line, dashed grey lines indicate −10 and −20 % isolines.

Figure 5 .
Figure 5. Anomalies (ideally behaving tracer − 14 C-based tracer) of bulk age (a), preformed component of age (b) and circulation component of age (c).

Figure 6 .
Figure 6.Age relative to depth (yr) computed for the MIT2.8(a) and ECCO (b) model (see text for details).

Figure 7 .
Figure7.Sensitivity of preformed and bulk 14 C-age to the choice of the gas-exchange parameter a of Eq. (1).Panel (a) preformed 14 C-age for a = 0.337 (solid lines) and a = 0.24 (dashed lines).Results from MIT2.8 (black), ECCO (red) and UVIC (blue) are shown.(b) Global mean profiles of 14 C-age bulk using a = 0.24.

Figure 8 .
Figure 8. Sensitivity of preformed 14 C-age to ice cover.Solid line: control with ice cover affecting CO 2 gas exchange; dashed: effect of ice cover on CO 2 gas exchange ignored.Results are from the ECCO model, both runs use identical circulation.

Figure 9 .
Figure 9. (a) Global mean profiles of the relative contribution (%) of preformed age (estimated as bulk 14 C-age − ideal age) to the bulk 14 C-age.(b) As Fig. 9a, but for the UVIC model in 2000 m depths, displaying that even in the oldest waters of the North Pacific the preformed age is a significant component of the bulk age.

Figure 10 .
Figure 10.Sensitivity of ages of suboxic waters to vertical diffusivity (K vbg ) in the UVIC model.(a) Bulk age, (b) ideal age and (c) preformed age.Scatter plots of bulk age (d) and ideal age (e) vs. volume of suboxic waters in the model runs.

3 Principal components of bulk 14 C-age 3.1 Ideal age and bulk 14 C-age distribution in three ocean models and the concept of preformed 14 C-age
The 14 C decay age (yr) is computed from 14 C-age decay = −8267 • log e [(DIC+ 14 C-DIC decay ) / DIC]. 5. age pre : in order to simplify the comparison between the ideal-age tracer and the age computed from the 14 C-DIC tracer, we designed another tracer of preformed 14 Cage.This tracer (age pre ) has units of time.At the surface it is assigned the bulk 14 C-age, which is computed at .age bulk : finally, we designed an explicit tracer which combines the behaviour of the age pre tracer at the surface and the ideal age tracer (age ideal ) in the interior of the ocean.At the surface age bulk is assigned the bulk 14 C-age, which is computed at any time step during model runtime from 14 C / C ratios.In the ocean interior it ages with a rate of 1 day day −1 and is subject to mixing and advection.This provides us with a duplicate set of tracers (Table 1) describing the preformed component, the circulation component and bulk.One set of the tracers is based on 14 C, the other on age.The complete set of tracers is presented and discussed for ECCO-model simulations.The tracers 14 C-DIC bulk and age ideal are implemented in all three models.The detailed experimental setups are presented together with the results in Sect.3.
any time step during model runtime from 14 C / C ratios.In the interior of the ocean this tracer is advected and mixed like all other tracers, but it does not age.While tracer 14 C-DIC pre (3) is one of concentration, age pre is one of time.6
(1) 14 C-ages: subject to non-linear mixing effect.(2) Ages: not subject to non-linear mixing effect.Figure 2. (a) Global mean profiles of bulk 14 C-age (solid lines) and ideal age (dashed lines) for three different global ocean circulation models (for colour code see figure insert) and the GLODAP database (solid magenta).(b) Global mean profiles of the difference between bulk 14 C-age and ideal age for three different global ocean circulation models (colour code as in a).
from the ECCO experiment along a combined section through the North Atlantic (30 • W), the Southern Ocean (60 • S), and the Pacific Ocean (140 • W).The preformed age is taken from the age pre tracer (see Sect. 2.2 for tracer definition).Panel (d) shows the residual ( 14 C-age bulk − age ideal − age pre ), i.e. the third term on the righthand side of Eq. (4).