The sensitivity of oceanic δ13C fields to overturning and gas exchange is investigated in a suite of ocean general circulation models. The deep and oceanic mean δ13C in the models was sensitive to the balance between deep waters forming in the North Atlantic and the Southern Ocean. Increasing the Southern Ocean deep water formation rate to improve deep sea 14C and AOU fields was detrimental to model-data δ13C fidelity. A concurrent increase in North Atlantic Deep water would be needed to match the observed 14C and δ13C, constraining both the rate and schematics of model deep water formation, respectively, and improving sensitivity to future perturbations. Inter-basin trends in δ13C were sensitive to the rate of overturning in the models, with ‘high mixing’ model configurations matching the observations best. Models' anthropogenic δ13C changes, used as a diagnostic of model CO2 uptake, were in agreement with the observations, except at high southern latitudes (<50°S), where the model δ13C changes were greater than observed. There were predictive relationships among models' uptake of anthropogenic CO2 and depth-integrated δ13C changes. Model relationships between model anthropogenic CO2 uptake and the air-sea δ13C disequilibrium, and the sea surface δ13C, depend on preindustrial riverine fluxes of terrestrial organic carbon, and on the wind field used to drive the model circulation, respectively. Among the models tested, the relations among anthropogenic CO2 uptake and δ13C changes in the ocean are biased by the OCMIP practice of driving model momentum with one wind field, and gas exchange rates with another.
 One of the major goals of the Ocean Carbon Model Intercomparison Project (OCMIP) was development of tracer-based strategies for evaluating the accuracy of global ocean carbon cycle models [Najjar et al., 2007]. In particular, the sensitivity of oceanic nutrient, C, O2, and biological production fields to ocean model circulation has been highlighted [Najjar et al., 2007], which may provide valuable constraints on ocean models' physical parameterizations and forcing [Doney et al., 2004; Gnanadesikan et al., 2001, 2004]. Most of the OCMIP models were carbon cycling models embedded in ocean general circulation models (GCMs), whose implementation details differed widely. To facilitate model comparisons, all of the models had their gas exchange driven by a common wind field, wind speed dependence, and chemical parameterization. Also, the implementations of the biological cycling of ocean carbon were set to one consistent standard [Orr, 2002].
 Within OCMIP, model simulations of chlorofluorocarbon (CFC) uptake and 14C (natural and bomb produced), as compared with observations, were used as tools for assessing accuracy of model uptake of anthropogenic CO2 [Matsumoto et al., 2004]. Models that did a fairly good job of reproducing these tracer analogs to anthropogenic CO2 were reasoned to be the most likely to accurately represent anthropogenic CO2 inventories in the oceans. One reason these two tracers were applied is that the characteristic timescales of the two tracers (∼30 years for CFCs, a few thousand years for natural 14C) bracket that of anthropogenic CO2 (∼100 years). While the CFCs provide a key indicator of decadal time-scale, i.e., thermocline, ventilation, Matsumoto et al.  highlighted the importance of the Southern Ocean in controlling century-scale uptake of 14C, noting that this important region is critically sensitive to the models' applied surface forcing and physical (mixing) parameterizations. This is important because over longer timescales, anthropogenic CO2 uptake by the sea will be sensitive to the rate at which deep water formation occurs, and how effectively newly formed deep waters are equilibrated with respect to atmospheric CO2.
Gnanadesikan et al.  investigated the relationships among overturning and biological production in a family of GCMs, all built on a common architecture, but whose mixing rates were varied, globally and in the Southern Ocean only. In their experiments, nutrient cycling pathways and rates were highly sensitive to, in particular, the level of vertical mixing prescribed in the model. Gnanadesikan et al.  investigated the influence that the intensity of vertical and horizontal mixing assigned exerted on new production, deep ocean apparent oxygen utilization (AOU = O2 at atmospheric saturation − O2 measured) and 14C and implied circulation pathways and rates. Matsumoto et al.  also explored, within this same model geometry and physics, the effects that varying isopycnal and vertical mixing coefficients, and changes in the wind field would have on the model's CFC, natural 14C, and anthropogenic CO2 uptake.
 The models summarized in Gnanadesikan et al. [2001, 2004] were all built on the foundation of the Modular Ocean Model (MOM), on a ∼4° by 4° grid with 24 vertical levels. These models do not resolve effects of small scale shear dispersion and turbulent meso-scale eddies, but rely on a Gent-McWilliams (GM) scheme [Gent and McWilliams, 1990] to parameterize the along-isopycnal tracer transport resulting from non-resolved processes. While these coarse global ocean models have obvious limitations, some of the coarse grid model setups provide higher fidelity to observed oceanic tracer and anthropogenic CO2 burdens than do many higher resolution GCMs [Matsumoto et al., 2004]. Among the family of coarse models tested by Gnanadesikan et al. [2001, 2004], two provide fairly accurate simulations (hindcasts) of the ocean CFC, bomb 14C, and anthropogenic CO2 inventories [Matsumoto et al., 2004]. If the uptake of CFCs and bomb14C provide a meaningful test of models' CO2 uptake, then these models ought to be able to provide fairly accurate forecasts of the future of oceanic uptake of anthropogenic CO2, provided the large-scale circulation is largely steady over centennial timescales.
 Here we evaluate the δ13C of DIC (δ13C = ((13C/12C)sample/(13C/12C)std − 1) · 1000, where the standard is pee-dee belemnite) tracer as a constraint on air-sea exchange and deep and thermocline ventilation pathways in this same suite of models. The long air-sea equilibration time for sea surface δ13C provides an estimate of the balance of gas exchange and overturning, providing key tests of ocean models' longer (millennial) timescale equilibration to and uptake of the anthropogenic CO2 perturbation. Because of the temperature dependence of air-sea gas exchange fractionation for δ13C, the meridional gradient in the δ13C air-sea disequilibrium is substantial relative to the global mean δ13C disequilibrium, making δ13C a sensitive tracer to high latitude gas exchange and water mass formation rates. Also, anthropogenic changes of δ13C in the ocean provide a high signal-to-noise tracer of anthropogenic CO2, reflecting the entire anthropogenic CO2 timescale, providing a key test of model ventilation pathways over the ∼200 year course of the industrial revolution.
 Our first task is to evaluate the models' representations of the oceanic δ13C fields. In this, we find that the deep δ13C of the models (and the real ocean) are sensitive to the relative proportions of Northern- versus Southern- origin deep waters. Taking a closer look at the models' air-sea equilibration timescales, we evaluate their anthropogenic δ13C changes. The so-called “δ13C Suess Effect” has an advantage over CFCs and 14C in that the δ13C perturbation is caused by CO2 from fossil fuel and land use changes, so its evolution in the atmosphere and oceans tracks anthropogenic CO2's. Because the air-sea equilibration timescale for δ13C is 10 times longer than for CO2 [Broecker and Peng, 1974], it does not provide a perfect analogy to anthropogenic CO2, however. The longer equilibration time provides an opportunity to use the air-sea δ13C disequilibrium to evaluate the balance between overturning and gas exchange at high latitudes, potentially yielding improved constraints on models' century and longer timescale forecasts of oceanic anthropogenic CO2 uptake.
 We compare models using different wind fields, and evaluate the constraint that δ13C places on the wind speed dependence of air-sea gas exchange in the models. We evaluate the impacts of differing mixing rates in the ocean interior on the oceanic δ13C fields and anthropogenic δ13C changes, by considering anthropogenic δ13C responses in the full suite of coarse-resolution GCMs tested by Gnanadesikan et al. [2001, 2004]. Using these, we evaluate the global relations among δ13C perturbations and anthropogenic CO2 uptake in the MOM model suite to evaluate the models' relations among the depth-integrated δ13C change, sea surface δ13C change, air-sea disequilibrium, and the oceanic uptake of anthropogenic CO2. We use these global relations and δ13C observations to estimate oceanic uptake of anthropogenic CO2 to 1995, and to identify model configurations most likely to provide accurate CO2 uptake forecasts.
2. Model Descriptions and Experiments
 We used the Modular Ocean Model, Version 3 (“MOM-3”) [Pacanowski and Griffies, 1999] with zonal and meridional grid resolution of 4° and ∼4.5°, respectively, and 24 vertical levels. All versions included a Gent-McWilliams [Gent and McWilliams, 1990] mixing scheme, and were driven by steady climatological winds that varied seasonally. Vertical mixing in the upper ocean was prescribed as either 0.15, 0.3, or 0.6 cm2 s−1, with along-isopycnal mixing set at either 1000 or 2000 m2 s−1. The OCMIP-2 geochemical model that calculates organic matter production by restoring (τ = 30 days) sea-surface PO4 levels to seasonal climatological data was included. A more complete description of the model versions (LoLo, HiHi, LoHi, HiLo, P2, LoLoHS, and P2A) can be found in Gnanadesikan et al. . The LoLo, P2 and P2A models' response to anthropogenic CO2 were included in the Orr  and Matsumoto et al.  model intercomparison studies as part of OCMIP.
 The OCMIP carbon cycling scheme carries five biogeochemicals: phosphate, dissolved oxygen (O2), dissolved inorganic carbon (DIC), alkalinity (ALK), and dissolved organic phosphorous (DOP). At the sea surface dissolved CO2 was computed at each time step (from DIC and ALK) to determine air-sea CO2 exchange fluxes. Gas exchange piston velocities were computed using sea-ice cover, sea surface temperature (SST), and satellite (SSMI) winds using a quadratic dependence on wind speeds [Wanninkhof, 1992; Orr, 2002]. Organic matter is generated when model phosphate is restored to monthly mean climatological values [Louanchi and Najjar, 2000] on a 30-day e-folding timescale. of the surface phosphate removal is converted to DOP which follows the water, decaying on a 6 month timescale, while the remainder ( ) remineralizes directly below at depths >75 m following a canonical power law function mimicking the chemical effects of sinking organic particles [Martin et al., 1987]. DIC and O2 production and consumption, respectively, follow DOP and phosphate in the ratios C:P = 117:1 and O2:P = 170:0 [Anderson and Sarmiento, 1994].
 We added 13C to the OCMIP geochemical cycling scheme (see auxiliary material). The equilibrium fractionation between DIC and atmospheric CO2 (εDIC-g) was calculated from εDIC-g = 10.51 − 0.105*SST(°C) [Zhang et al., 1995]. The kinetic fractionation during CO2 gas invasion was a linear function of SST matching the −0.81‰ at 21°C and −0.95‰ at 5°C determined empirically by Zhang et al. . Fractionation during organic matter formation was calculated using the ∼22‰ difference observed between compilations of sea surface δ13C of DIC data [Quay et al., 2003] and particulate organic matter data [Goericke and Fry, 1994], while calcium carbonate formed was 1‰ enriched relative to DIC [Bonneau et al., 1980]. The model assumed that no 13C/12C fractionation occurred during remineralization of organic matter and dissolution of calcium carbonate.
 The general circulation model's 13CO2 and 12CO2 fields were equilibrated (∼15,000 model years) with the pre-industrial atmosphere, 278 ppm CO2 and δ13C = −6.28‰ for 1737 [Francey et al., 1999]. The model was then forced with the OCMIP atmospheric pCO2 history from a smoothing spline fit through the Siple ice core and Mauna-Loa CO2 records [Orr, 2002]. The temporal evolution of the δ13C of atmospheric CO2 (Figure 1) was taken from a spline fit through the Law Dome, Antarctica, ice core and firn record augmented by the Cape Grim air archive after 1978 [Francey et al., 1999]. The models neglect riverine transports of organic carbon, which are on the order of 0.6 Gt C yr−1 [Sarmiento and Sundquist, 1992; Siegenthaler and Sarmiento, 1993], and which would otherwise deplete the pre-industrial oceans' δ13C by on average 0.2‰ [Tans et al., 1993; Heimann and Maier-Reimer, 1996], so we subtract that offset from the model δ13C in the comparisons that follow.
 In the comparisons that follow we highlight results from three MOM configurations, “LoLo,” “HiHi,” and “P2A.” (The LoLo, HiHi and P2A model configurations were LL, HH and PRINCE2A in Gnanadesikan et al. , while LoLo and P2A appeared as “#11 - PRINCE,” and #19-SW, respectively in Matsumoto et al. .) The nomenclature “LoLo” indicates that low vertical (0.15 cm2 s−1) and low horizontal (1000 m2 s−1) mixing rates were used, respectively (see Gnanadesikan et al.  for details), while HiHi's corresponding mixing rates were 0.6 cm2 s−1 and 2000 m2 s−1. In P2A, LoLo was adjusted in the Southern Ocean to improve model-data fidelity in the deep sea AOU and Δ14C fields, primarily by enhancing Southern Ocean overturning and deep water production. This was done by increasing the vertical mixing rate to 1.0 cm2 s−1 south of 50°S, using ECMWF reanalysis winds, which are more intense than NCEP in the Southern Ocean, and using adjusted (larger) salt fluxes in the Southern Ocean [Gnanadesikan et al., 2004]. P2A's deep-sea Δ14C and AOU fields are, relative to LoLo, in much better agreement with the observations [Matsumoto et al., 2004; Gnanadesikan et al., 2004]. LoLo, HiHi, and P2A's δ13C and DIC fields spanned the range of MOM variants we tested, and were selected here because these model configurations and their AOU and Δ14C fields had already been documented, and they produced realistic pycnocline depths and CFC uptake [Gnanadesikan et al., 2004; Matsumoto et al., 2004].
4.1. The δ13C of the Deep Sea
 All of the models we tested overpredicted the deep sea, and oceanic mean, δ13C significantly (Table 1). The mean deep sea δ13C is controlled by a balance of remineralization of organic matter, which tends to decrease deep sea δ13C because δ13Corg ∼ −21‰, and input of sinking surface water, which in turn depends on air-sea exchange and organic carbon export. In the OCMIP carbon cycling scheme, δ13Corg is remineralized in ‘Redfield’ proportion (with δ13Corg ∼ −21‰) yielding a Δδ13C/ΔPO4 slope of 1:1.1 in the deep Pacific Ocean that is in agreement with the observations. The models' deep sea phosphate levels are in agreement (typically ± <0.1 μmol kg−1) with the observations. To investigate the cause of the models' δ13C overprediction, we compare the air-sea gas exchange influences on δ13C in the deep sea, in both data and model fields.
Table 1. Oceanic Mean δ13C and Surface δ13C in 1995 From the Suite of GCMs Testeda
Here, 1.1 represents “Redfield” remineralization of organic matter, δ13C is that measured, and 2.9 is a constant, in ‰, selected to yield a mean δ13Cas = 0‰ in the deep North Pacific Ocean, based on observations [Broecker and Maier-Reimer, 1992]. In the models LoLo and P2A, for δ13Cas to equal zero ‰ in the deep North Pacific, this constant would need to be higher, i.e., 3.52‰ and 3.75‰, respectively, because they overpredict the deep ocean δ13C. δ13Cas accounts, via phosphate, for the impacts of biological cycling on δ13C, and thus represents the cumulative contribution that air-sea exchange has made to the sample's δ13C [Broecker and Maier-Reimer, 1992].
 Meridional trends in the deep sea δ13Cas reveal some interesting features (Figure 2). In the Atlantic basin, deep δ13Cas is controlled by mixing between two contrasting end-members: North Atlantic Deep Water (NADW), whose δ13Cas is <−0.5‰, and Southern Ocean deep waters (SODW), whose δ13Cas is >0.2‰. These trends are reflected in the models as well. The meridional trends in deep-sea δ13Cas indicate that the δ13Cas in the deep Atlantic, and thus the mean δ13C, is controlled by a balance between NADW, whose δ13Cas < 0, and SODW, whose δ13Cas > 0. Thus gas exchange increases Southern Ocean deep waters' δ13C, and decreases NADW source waters' δ13C. The mean δ13C of the deep Pacific and Indian Oceans reflects the relative contributions of NADW and SODW and their air-sea exchange signatures.
 The reason that the North Atlantic and Southern Ocean end-member deep waters have distinctly different air-sea exchange signatures can be understood from the meridional trends in the air-sea disequilibrium of δ13C (Figure 3) in the surface ocean and from the formation histories of these deep waters. The observed δ13C in the surface ocean is relatively uniform compared to the range in δ13C in equilibrium with the atmosphere due to the slow air-sea equilibration time of the 13C/12C ratio of the entire DIC pool [Broecker and Peng, 1974]. The temperature dependence of air-sea δ13C fractionation means that air-sea exchange drives the sea surface δ13C higher in cold waters (∼2.7‰ at 0°C in 1995) at high latitudes, and lower in warm waters (∼0.4‰ at 20°C in 1995) at low latitudes [Zhang et al., 1995]. The deep δ13Cas trends (Figure 2) indicate that Southern Ocean deep waters have spent enough time at the sea surface in the Southern Ocean for air-sea gas exchange to enrich δ13Cas. This is also evident in the δ13C values, which achieve the highest values anywhere in the ocean at ∼45°S (Figures 4 and 5) due to the complementary enriching effects of gas exchange and biological carbon export there. In contrast, NADW exhibits the lowest δ13Cas of the deep sea (Figure 2). This is due to the overturning circulation structure of the North Atlantic Ocean where newly formed deep waters that are exported southwards are replaced, at the sea surface, by northward traveling subtropical waters. The Subpolar North Atlantic surface waters have, as noted before, been in contact with the atmosphere for long enough (>∼10 yrs) to have fully absorbed the anthropogenic δ13C perturbation [Körtzinger et al., 2003; Olsen et al., 2006; Quay et al., 2007] and, apparently, also the subtropical air-sea δ13C equilibration signal (toward lower δ13C values), before sinking as newly formed NADW (Figure 2). Thus the low δ13Cas of NADW reflects its preceding long surface residence history in the warmer subtropics, which is not reset to lower δ13Cas during those waters' shorter surface residence time in the colder subpolar North Atlantic. Because the δ13Cas of NADW is depleted relative to the mean δ13Cas, and relative to the δ13Cas of southern source deep waters, the δ13Cas of the deep sea is set by the relative proportions and air-sea equilibration extents of these two major sources of deep waters.
 To estimate the relative contributions of NADW and Southern source deep waters, we used the data and models' PO4 and salinity (S) signatures in the deep sea (Z > 2000 m). We computed preformed phosphate, or PO [Broecker, 1974], using AOU to correct for remineralization of organic matter:
Where P/O2 is the “Redfield” ratio in observations (1:175 [Anderson and Sarmiento, 1994]), or in the models (1:170). In the observations, the deep sea PO versus S plot indicates that Indo-Pacific deep waters are comprised of ∼40% NADW and ∼60% Weddell Sea Bottom Water (WSBW) [Broecker et al., 1998]. In LoLo these proportions are 33% NADW and 67% SODW. The weaker model contribution of NADW is reflected in the modeled mean ocean δ13C at 0.63‰ being ∼0.13‰ higher than observed (Table 1). In P2A, the deep water mass proportions are 18% NADW and 82% SODW, yielding an oceanic mean δ13C, 0.94‰, that is overestimated more significantly, by ∼0.4‰.
 We used a budget of deep sea 14C to estimate the deep water formation rates in the models. In P2A, the mean deep (>2000 m) Δ14C is −200‰, in reasonable agreement with the observations (−175‰) [Gnanadesikan et al., 2004; Matsumoto et al., 2004; Key et al., 2004], with NADW having Δ14C ∼ −50‰, and SODW's Δ14C is ∼ −160‰. Using the relative proportions estimated from PO and S, the weighted mean Δ14C of new deep waters is −140‰. A total of 40 Sv deep water formation is required to equal decay to P2A's mean deep sea Δ14C of −200‰. Of these 40 Sv, 7 Sv is NADW, which agrees with the 7.5 Sv of waters which flow Southward across 40°N deeper than 2000 m in the model Atlantic, and the remaining 33 Sv is SODW. In LoLo, the Δ14C derived deep water formation rate is only 20 Sv, with the same 7 Sv coming from NADW, and only 13 Sv from SODW, yielding a deep sea Δ14C that is underestimated significantly, −270‰.
 These calculations indicate that P2A's enhanced Southern Ocean overturning, while yielding more realistic deep sea Δ14C and AOU [Gnanadesikan et al., 2004], yielded a significant overestimate of the deep sea δ13C due to P2A's overweighting of SODW compared to the near-equal balance between northern and southern source deep waters in the real ocean (and in LoLo). Apparently, to simultaneously match the deep Δ14C and δ13C the model would require an enhancement of both deep water formation rates. Relatively smaller enhancements to LoLo's NADW formation rate would be required, relative to the significant changes in SODW implemented in P2A, to match the deep sea Δ14C because NADW's Δ14C (−50‰) is much higher than SODW's (−160‰).
Murnane and Sarmiento , using an earlier and coarser MOM setup with different biological and gas exchange parameterizations, estimated that in preindustrial times there was 120 Gt C ‰ yr−1 of carbon isotope anomaly transported in the ocean interior from the Southern to the Northern Hemisphere. This transport would have maintained a north to south gradient in the δ13C of atmospheric CO2 in preindustrial time, unless it was balanced by net northern hemisphere uptake of ∼5 Gt C yr−1 CO2 by the terrestrial biosphere. In all of our MOM variants, however, this transport is an order of magnitude smaller, ranging from 4 to 10 Gt C ‰ yr−1 in preindustrial times and 3 to 6 Gt C ‰ yr−1 during the 1990s. While our model runs do not support a significant preindustrial interhemispheric gradient in atmospheric δ13C, or alternatively a major terrestrial CO2 sink in the preindustrial northern hemisphere, this conclusion should be taken with caution as it apparently depends upon the ocean model used, and must depend on the relative production rates of northern- versus southern-hemisphere origin deep waters.
4.2. The δ13C of the Sea Surface
 The δ13C of the sea surface (Figure 4) reflects local balances of air-sea exchange, net biological production, and circulation, providing an integrated picture of all aspects of the model's C-cycling scheme. Here we compare the ocean models' sea surface δ13C values against the WOCE/OACES database collected during 1989 to 1999 and normalized, based on estimates of the anthropogenic δ13C change, to the year 1995 [Quay et al., 2003]. Due to ocean uptake of anthropogenic δ13C, the δ13C of the surface ocean and model surface DIC was decreasing on average by about −0.16 + −0.02‰ decade−1 during the 1990s [Quay et al., 2003]. As a result, a 1990s model-data comparison tests simultaneously the model's steady state δ13C fields, and simulation of the oceanic δ13C Suess effect. For example, a model overprediction of the 1990s δ13C in the upper ocean could be due to overestimation of the pre-industrial δ13C, and/or underestimation of the anthropogenic δ13C decrease.
 The models' meridional surface δ13C and δ13Cas trends, although exaggerated in amplitude, generally follow the trends observed in the Oceans, north of 50°S (Figure 5). In all of the MOM variants we tested, δ13C values of Southern Ocean surface waters were too high by on the order of 0.5‰, as discussed above. The magnitude of this southern ocean δ13C mismatch varied zonally, however. While the δ13C of surface waters at ∼66°S was around 1.8‰ in the models, the observed sea surface δ13C declines south of 60°S to values as low as 0.8‰ along some cruise sections (170°E and 90°E, for example), but to only ∼1.7‰ along others (105°W, for example). There is a possible seasonal bias in observed δ13C in the Southern Ocean because most cruises there occur in summer. In the models' Southern Ocean, δ13C values at the sea surface are highest in summertime, so seasonal aliasing of the observations would not explain the model data δ13C misfit. However, the PO4 climatology of the Southern Ocean also suffers from sparse wintertime coverage [MacCready and Quay, 2001], which would bias toward lower summertime PO4 values and higher sea surface δ13C in the models. It is also possible that model neglect of lower C:P ratios observed in Southern Ocean biological production [Arrigo et al., 2002] contributes to the models' δ13C overestimate. Alternatively, the models' δ13C overestimate could be due to excess air-sea equilibration of surface waters which would also yield an overestimate of the anthropogenic δ13C decrease in this century, as discussed below.
 Inter basin differences in the surface δ13C are prominent features in the data and models. The mean low latitude (40°S to 40°N) δ13C decreases from the Atlantic to the Pacific to the Indian Ocean (Figure 5). This inter basin trend could be due either to a trend in organic carbon export rates, or different residence times (and resulting air-sea δ13C equilibration) at the sea surface due to global-scale inter basin transports of surface waters. Although the model Indian Ocean's area averaged organic carbon export production was lower than in the Atlantic and Pacific basins north of 40°S, the low latitude Pacific's C export rates exceed the Atlantic's. The δ13C trends overall imply that Indian Ocean waters have resided at the sea surface the longest time, while Atlantic Ocean surface waters have, compared to the other basins, been more recently renewed. The models' tendency to overpredict the tropical Atlantic's surface δ13C could be due, in part, to local riverine input of terrestrial organic carbon. If the Amazon River's (20% of global riverine transport) DOC remineralizes on < decadal timescales, then the models' δ13C of sea surface DIC in the tropical Atlantic (30°S to 30°N, 10% of ocean area) would need to be adjusted downward by twice the 0.2‰ applied globally here. The inter basin differences were inversely proportional to the level of vertical mixing prescribed in the models. Models with more vigorous vertical mixing and resulting overturning, like HiHi, tended toward smaller inter basin δ13C differences that were more representative of those observed.
 The sea surface δ13Cas exhibits the same meridional structure and inter basin trends as observed (Figure 5). The low latitude surface δ13Cas is highest in the Atlantic Ocean, and decreases to the Pacific then Indian Oceans. The inter basin trends in δ13Cas imply that it is the inter basin differences in the δ13C equilibration with the atmosphere, reflecting seawater's residence times at the surface and the air-sea gas exchange rate, that drives the inter-basin differences in δ13C. Although the models' Southern Ocean (south of 60°S) δ13Cas were higher than observed, the overestimation in δ13Cas was much less (<1/2) than the overestimation of δ13C. This suggests that the δ13C overestimation is related, in part, to model overestimation of biological organic carbon production. It is unlikely that the models underestimate deep mixing, bringing up respiration-derived 13C depleted organic carbon, as their dominant ventilation pathway is deep convection in the Southern Ocean [Gnanadesikan et al., 2004].
4.3. The Anthropogenic δ13C Response
 The δ13C Suess effect provides a useful measure of how well the models' processes governing uptake of anthropogenic CO2 represent the real ocean's. The magnitude of the δ13C change at the sea surface reflects the local strength of overturning, which dilutes and therefore slows the response, and air-sea exchange, which enhances the response. In regions where upwelling replenishes surface water faster than air-sea exchange can equilibrate the water, like at the equator, the δ13C changes will be smaller than in regions with long surface water residence times, like the subtropics, where δ13C can fully equilibrate, and keep pace with, the atmospheric δ13C change (Figure 6). In the following comparisons we ignore the small additional decreases in ocean δ13C due to sea surface warming. A 0.2°C decade−1 increase in sea surface temperature would lead to δ13C decreases of up to 0.02‰ decade−1 in the real ocean but not in the models (A. Gnanadesikan, personal communication, 2011).
 Because the models yield fairly representative CFC fields [Matsumoto et al., 2004], the predicted 13C changes are expected to be fairly representative over most of the world ocean. Globally, the models' δ13C changes agreed well with the observations, indicating that in general they achieve an accurate balance of air-sea exchange and ventilation of underlying waters. The area-weighted observed mean sea surface δ13C change between the 1970s and 1990s was estimated at −0.16 + −0.02‰ decade−1 [Quay et al., 2003], compared with −0.14‰ decade−1 in P2A (Figure 6).
 Basinwide area-weighted mean δ13C changes in MOM agreed well with those available from compilations of data available over the past three decades. In the Indian Ocean, the mean 1978–1995 sea surface δ13C change from 55°S–0°N, 75°E–120°E was −0.16‰ decade−1 [Sonnerup et al., 2000], and from 60°S–5°N basinwide was −0.14‰ decade−1 [Quay et al., 2003]. Corresponding δ13C changes in P2A were slightly, but not significantly, greater at −0.18 and −0.16‰ decade−1, respectively. In the Pacific, the reverse was true. Basinwide δ13C changes from 1970 to 1993, 60°S–55°N were estimated at −0.18‰ decade−1 [Quay et al., 2003] and P2A's corresponding change was −0.16‰ decade−1. The Atlantic Ocean δ13C change for the time period 1981–2003, from 50°S to 65°N [Quay et al., 2007], on an areally weighted basis was −0.18 + −0.02‰ decade−1, slightly smaller than simulated by P2A, −0.20‰ decade−1.
 When considered over decades for which the data were available, the sea surface δ13C changes in the Atlantic (1980s and 1990s) and Pacific (1970s and 1980s) Oceans are comparable (−0.18‰ decade−1 [Quay et al., 2003]) and are significantly larger than in the Indian Ocean basin (−0.14‰ decade−1 during 1978–1995 [Quay et al., 2003]). This difference is smaller when the same time periods are compared, however. For example, using the time periods over which data were available (as above), in the model P2A the Atlantic, Pacific and Indian Ocean δ13C changes were −0.2, −0.16, and −0.16‰ decade−1, respectively. However, taken over 1970–1993, the Atlantic, Pacific, and Indian Ocean changes in P2A were comparable, −0.16, −0.16 and −0.15‰ decade−1, respectively.
 Despite some regional and specific differences in the modeled δ13C changes versus observations, the meridional trends and mean basin changes were fairly representative. For example, in the Indian Ocean, the overall meridional pattern and magnitude of the P2A δ13C change during 1978–1995 (88–115°E) agreed well with that observed between GEOSECS in 1978 and WOCE in 1995 (Figure 7). The models' meridional trend in and maximum depth penetration of the δ13C change were comparable to those observed (Figure 7). The data show the strongest gradient in surface changes at 50°–60°S, which were at a similar location in the models, but not as strong.
 P2A's δ13C changes, and meridional trends in δ13C changes, were in reasonably good agreement with the observations (Figure 8). P2A's root-mean square (RMS) agreement with available surface δ13C changes was ∼0.0135‰ decade−1, smaller than typical uncertainties in the sea surface δ13C change (±0.03‰ decade−1). In the Pacific basin, the model Southern Hemisphere δ13C changes were in excellent agreement with the δ13C changes we have available based on back-calculations using preformed δ13C and CFC ages [Sonnerup et al., 1999]. The North Pacific δ13C changes predicted by P2A for the 1970s and 1980s were at the low end of the range indicated by the Hawaii Time Series [Quay et al., 2003; Keeling et al., 2004] and by preformed δ13C [Sonnerup et al., 1999]. However, in the North Pacific, the P2A δ13C change agreed (RMS = 0.13‰, comparable to uncertainties in the reconstruction) with the total industrial-era anthropogenic δ13C change reconstructed along 165°E [Sonnerup et al., 2007]. In the Indian Ocean, P2A's 1978–1995 δ13C changes were in agreement with the observations south of 40°S, but were larger, by ∼0.05‰ decade−1, in the subtropical and equatorial Indian Ocean north of 40°S.
 The global ocean mean depth-integrated δ13C change between the 1970s and 1990s was estimated at −65 + −33‰ m decade−1 [Quay et al., 2003], with which the 1970–1990 average in P2A, −64‰ m decade−1 agreed well. The Indian Ocean average during 1978–1995, −69 + −5‰ m decade−1 [Sonnerup et al., 2000] was overestimated by P2A (−84‰ m decade−1). In the North Atlantic Ocean (0°–65°N), the 1981–2003 depth integrated change of −150 + −38‰ m decade−1 [Quay et al., 2007] was underestimated by P2A (−114‰ m decade−1). P2A's underestimate of the depth-integrated change is consistent with P2A's Atlantic overturning being slower than in the real ocean.
 In locations where we had both anthropogenic δ13C and DIC change estimates, we compared model with observed ratios of those changes defining
Because of the 10× longer air-sea equilibration time for δ13C compared with DIC, oceanic RC values are very sensitive to surface water renewal times [McNeil et al., 2001], and can provide valuable constraints in key water mass formation regions where uptake of anthropogenic CO2 is important and sensitive to change. Unfortunately, RC observations are limited to date to a pair of time series observations [Quay et al., 2003; Keeling et al., 2004], an evaluation of δ13C and DIC trends on isopycnals in the North Atlantic Ocean [Körtzinger et al., 2003], and to a pair of MLR-guided comparisons of historical with 1990s δ13C -DIC data sets in the Indian Ocean [Sonnerup et al., 2000; Sabine et al., 1999] and south of Australia [McNeil et al., 2001].
 In the North Atlantic, Körtzinger et al.  reconstructed RC in gas exchange equilibrium with the atmospheric changes during the 1970s–1990s, −0.024 ± 0.003‰ (μmol kg−1)−1. Our models yielded smaller RC on the order of −0.018‰ (μmol kg−1)−1, implying shorter surface water exposure times than observed. In the subtropical North Pacific Ocean, P2A and LOLO matched the time series RC estimate of −0.023‰ umol−1 kg based on δ13C and DIC measured at station ALOHA (22°45′N, 158°W) during 1988–2007 [Keeling et al., 2004].
 In the South Indian Ocean, where we have the most extensive coverage of RC, the base model, LoLo, overall overestimated RC, and failed to reproduce the meridional RC decrease South of 50°S (Figure 8). Because a few of our MOM variants were explicitly altered from the base LoLo version to enhance bottom water formation and overturning rates in the Southern Ocean only, it is worth exploring the model RC responses to these changes. Enhanced vertical mixing (to 1.0 cm2 s−1) in the Southern Ocean (LLHS), did not improve the meridional trend in Southern Ocean RC (Figure 8). The addition, to LLHS, of enhanced salt fluxes, use of ECMWF winds, and enhanced bottom water production (via restoring), did improve the meridional RC trend (P2A). However, the models' RC were still larger than observed, consistent with the sea surface δ13C overestimate and the sea surface δ13C change overestimate in this region (Figure 7). These all imply that either the models' surface water exposure times in the Southern Ocean are too long, or that the gas exchange rate is too high there, or both.
5. Global Model Relations Among the Anthropogenic CO2 Perturbations
 In this section we focus on the MOM models' global mean anthropogenic signals: we compare their surface and mean anthropogenic δ13C changes, air sea δ13C disequilibrium, and anthropogenic CO2 uptake across models and with available observations. Among the model variants examined here, the relationship between surface δ13C change and CO2 uptake rate during the 1970s and 1990s was linear (Figure 9). Models with relatively sluggish overturning, like LoHi, had relatively large surface δ13C decreases and low CO2 uptake rates, which means high model RC values. Rapidly overturning models (like HiLo) had small surface δ13C changes for their higher CO2 uptake rates (i.e., lower RC). Using NCEP winds [Kalnay et al., 1996] yielded a predictive relationship
 Where CO2uptake is the model CO2 uptake (Gt. C yr−1) and Δδ13Csfc is the global average sea-surface δ13C change rate (‰ decade−1) during 1970–1990. The standard error of the CO2 uptake estimate from a sea-surface δ13C change rate estimate is 1.4 Gt C yr−1. This relationship predicts a global ocean CO2 uptake of 1 Gt C yr−1 from the 1970s–1990s global mean sea surface δ13C change rate determined from observations, −0.16‰ decade−1 [Quay et al., 2003]. However, this result depends on the wind fields used to drive the model. Models driven by ECMWF winds yielded ∼0.2 Gt C per year higher CO2 uptake for a given sea surface δ13C change rate, and come closer to the 1970–1990 surface ocean δ13C change and integrated CO2 uptake of 1.7 Gt C yr−1 observed [Quay et al., 2003]. However, these models all follow the OCMIP standard wherein the sea surface gas exchange rate is driven by SSMI (satellite scatterometry) winds, regardless of the wind field used to drive the physical circulation. It is likely that the models' 13C–12C change relationship, which is sensitive to the balance between overturning and gas exchange, would agree better with the observations if the gas exchange and overturning were driven by the same wind field. That is to say, the shift in the surface δ13C versus CO2 uptake relationship that occurs when switching from NCEP to ECMWF winds (Figure 9) could be caused by the fact that the natural link between overturning and gas exchange is disrupted by the OCMIP practice of driving the model's momentum with one wind product, and gas exchange with another.
 The relationship between models' anthropogenic CO2 uptake and depth-integrated δ13C change (Figure 9) does not depend on the wind field used to drive model momentum. Anthropogenic CO2 uptake can be determined from observations of the depth integrated 13C change using:
 Where CO2uptake is the integrated CO2 uptake rate in the model (Gt. C yr-1) and ∫ Δδ13C(z)dz is the depth-integrated δ13C change (‰ m) during 1970–1990. The 1970–1990 ∫ Δδ13C(z)dz estimated by Quay et al.  was −130‰ m, which yields a CO2 uptake rate of 1.7 Gt C yr−1 using equation (5), as compared with the Quay et al.  estimate of 1.5 + −0.6 Gt C yr−1 based on the 1990s air-sea disequilibrium, and 1970–1990s integrated δ13C changes applied in the atmospheric CO2 and 13CO2 budget approaches of Quay et al. , Tans et al. , and Heimann and Maier Reimer . Quay et al.  constrained a 1-D box-diffusion model [Oeschger et al., 1975] to match both 1970–1990s δ13C and bomb 14C changes, yielding a global CO2 uptake rate of 1.7 ± 0.2 Gt C yr−1, which agrees with the result from equation (5).
 As established by Tans et al. , the air-sea δ13C disequilibrium (Δδ13Ca-s) at any time, coupled with an estimate of the ocean's global air-sea CO2 exchange rate, can be used to determine oceanic uptake of anthropogenic CO2. Among the models, the relationship between air-sea δ13C disequilibrium and CO2 uptake is:
 This approach depends on the preindustrial air-sea δ13C disequilibrium (Δδ13Ca-s preindustrial) which was driven by riverine fluxes of terrestrial organic carbon to the oceans and the observed ∼−21‰ depletion of that organic carbon relative to atmospheric δ13C. Sarmiento and Sundquist's  estimate of the riverine organic carbon flux, 0.6 Gt. C yr−1, yields a mean preindustrial air-sea disequilibrium of ∼0.2‰ [Tans et al., 1993]. A recent joint inversion of atmosphere and ocean CO2 fields [Jacobson et al., 2007] estimated the preindustrial riverine flux to be on the order of 0.4 Gt C yr−1, however, which implies a smaller preindustrial δ13C disequilibrium of ∼0.13‰. The Quay et al.  compilation of global δ13C data yielded an air-sea disequilibrium value of −0.6‰ in 1995, which yields (equation (6)) a global CO2 uptake rate of 1.7 Gt C yr−1 using the Sarmiento and Sundquist  riverine flux. This result agrees with that based on the depth-integrated δ13C change [Quay et al., 2003] and estimates of global ocean CO2 uptake [McNeil et al., 2003]. The preindustrial riverine flux of 0.4 Gt. C yr−1 [Jacobson et al., 2007] predicts a lower 1990s CO2 uptake rate of only 1.3 Gt C yr−1. However, the intercept in equation (6) depends on the gross air-sea CO2 exchange flux, which would need to be known with certainty before this approach could be used to distinguish the two preindustrial riverine flux scenarios.
 Models' limitations in simulating δ13C in the Southern Ocean were also evident in their 14C simulations. While P2A (and HiHi) predict realistic deep Pacific Δ14C [Gnanadesikan et al., 2004], the ventilation processes and pathways bringing 14C into the deep sea may not be representative of the real ocean's. In the ocean, deep sea Δ14C gradients from the deep Southern Ocean to the deep North Pacific are on the order of 75‰ (Table 3), with pre-bomb Southern Ocean surface Δ14C values on the order of −110‰. For P2A, HiHi, and LoLo the Southern Ocean to deep Pacific gradients were on the order of 120‰ and 152‰ and 220‰, with Southern Ocean surface Δ14C values of −95‰, −67‰, and −85‰, respectively (Table 2). From a 14C perspective, P2A performs best [Gnanadesikan et al., 2004]. However, δ13C observations add a significant constraint on deep ocean ventilation. Because of the contrasting air-sea exchange δ13C signatures (δ13Cas) of NADW and SODW, the deep ocean δ13C is sensitive to the balance between these two end-members. Our model δ13C simulations and comparisons, and comparisons to observations indicate that all of the MOM variants exhibit too strong SODW production, relative to NADW production, to ventilate the deep sea. A contributing factor to this problem is the fact that the Δ14C and δ13C of the Southern Ocean sea surface, and thus newly forming SODW, are too high compared to observations. An increase in NADW production would be more effective, relative to a comparable increase in SODW production, in bringing 14C into the deep ocean due to the higher Δ14C values of newly formed NADW (∼−50‰) relative to SODW (∼−110‰).
Table 2. Pre-bomb Volume-Weighted Mean Δ14C Values in the Model Year 1955, and Δ14C Observations, With the Bomb Component Removed, From the GLODAP Gridded Data Set [Key et al., 2004]a
Southern Ocean Deep Δ14C (‰)
Pacific Deep Δ14C (‰)
Southern Ocean Surface Δ14C (‰)
Ocean Surface (60°S–60°N) Δ14C (‰)
The Southern and Deep Oceans are defined as south of 53°S, and deeper than 2000 m, respectively. The deep Pacific was defined as north of 20°S in the Pacific Basin. The ocean surface mean Δ14C was restricted to the area 60°S to 60°N where the most quality observations are available.
Table 3. Global Mean Anthropogenic Perturbation Signals in the Models Tested
DIC Increase 1970–1990 (Gt. C Yr−1)
Depth-Integrated δ13C Change, 1970–1990 (‰ m)
Surface δ13C Change 1970–1990 (‰ decade−1)
Anthropogenic CO2 in 1990 (Gt. C)
Anthropogenic CO2 in 2100 Business as Usual IPCC (Gt. C)
1995 Air-Sea Disequilibrium, Area and Piston Velocity Weighted (‰)
Surface RC 1970–1990 (‰ (μmol kg−1)−1)
 Model-data fidelity in ventilating the deep-sea with respect to C isotopes is an important consideration in assessing the accuracy of model forecasts of ocean uptake of anthropogenic CO2 during the next century when more of the anthropogenic CO2 is taken up into the deep sea. Among the models tested, the highest/lowest uptake ratio was 1.5 in 1990 and >2.0 in 2100 (Table 3). Our model δ13C simulations indicate that unrealistic southern versus northern deep water production ratios imply inaccurate model CO2 uptake rates in response to future perturbations in the atmosphere, or in water mass production, i.e., of NADW, and circulation changes. The weaker NADW production rates in this suite of models could be due in part to their coarse spatial resolution (A. Gnanadesikan, personal communication, 2011).
 One simple explanation for the model-data mismatches in the sea surface meridional δ13C trends could be an exaggerated wind speed dependence of air-sea CO2 exchange rates in the models. In cold (high latitude) waters, air-sea exchange drives δ13C higher, while in warm (low latitude) waters, air-sea exchange drives δ13C lower (Figure 3). If the CO2 gas-exchange rates were overestimated at high latitudes under high wind speeds, and underestimated in the subtropics and tropics at low wind speeds, the model-data mismatches in δ13C and δ13Cas would result. This situation would also contribute to the model overprediction of the anthropogenic δ13C changes (and RC) in the Southern Ocean.
 When Krakauer et al.  inferred regional air-sea fluxes by ‘inverting’ ocean interior 14C data using an ocean model's interior transports, a much weaker dependence of gas exchange (κ) on wind speed (τ), was required, i.e., κ ∝ τ0.6, than the quadratic dependence (κ ∝ τ2) used here (and in OCMIP [Wanninkhof, 1992]). Since both gas-exchange parameterizations (tuned to 14C) yield the same global mean air-sea exchange, the Krakauer et al.  relationship indicates relatively larger (than Wanninkhof ) gas exchange rates at low wind speeds, and relatively smaller gas exchange rates at high wind speeds. When we instead used Krakauer et al.'s  wind speed dependence to equilibrate the δ13C in P2A it resulted in small changes in ocean model δ13C. At the surface, the δ13C (and δ13Cas) of the Southern Ocean and the tropics declined by ∼0.2‰, yielding improved RMS fits to the data in the Atlantic (improved from 0.43 to 0.33‰), Pacific (from 0.37 to 0.30‰), and global (from 0.37 to 0.32‰) oceans. However, the surface δ13C in the tropical Pacific and Atlantic, and Southern and deep Ocean δ13C were still too high. The smoother meridional sea surface δ13C trend resulting from use of Krakauer et al.'s  wind speed dependence was more representative of the observations, however. In another model experiment, we reduced P2A's southern ocean (south of 55°S) gas exchange rate by a factor of two, which was about the equivalent of using the Liss and Merlivat  wind speed dependence instead of Wanninkhof  in this region. The resulting surface δ13C was lower by 0.9‰ in the Southern Ocean and the deep waters of the Pacific and Atlantic Oceans' δ13C were lower by ∼0.4‰ and ∼0.2‰, respectively. Low latitude surface ocean δ13C declined by ∼0.3‰ in the tropical Pacific and Atlantic Oceans as well. These experiments demonstrate how the δ13C overestimation at the Southern Ocean sea surface contributes to the δ13C overestimate in the deep sea and at the low latitude surface, in these models and likely in others [Tagliabue and Bopp, 2008]. However, while a weaker wind speed dependence yielded more realistic δ13C, it did not yield significantly improved δ13C changes (nor RC) in the Southern Ocean.
 All of our experiments adopted the OCMIP standard gas exchange rates, based on satellite scatterometry (SSMI) winds, even though the model circulations were driven by climatological (NCEP or ECMWF) winds. An important next step in our modeling efforts will be to re-equilibrate our models using gas exchange rates computed from the actual wind fields used to drive the circulation. These efforts may significantly improve the MOM models' δ13C and anthropogenic δ13C response, as they may improve the connection between air-sea exchange and overturning that is reflected in ocean δ13C.
 The global MOM models overestimate the δ13C of the deep sea. Analysis of the deep sea δ13C and δ13Cas indicates that the magnitude of the overestimate depends on the relative production rates of North Atlantic (NADW) versus Southern Ocean (SODW) derived deep waters. The reason is that the air-sea exchange tendencies of these two deep waters have opposing influences on the deep sea δ13C. Thus the carbon isotopes can be used to calibrate models' deep water production rates overall (with Δ14C) and the relative weighting of that production from the North and South (with δ13C). Accurate deep water ventilation schematics would have important implications for century-scale forecasts of deep-sea CO2 uptake and its sensitivity to changing deep water formation rates.
 A contributing factor to the models' deep δ13C overestimates is their tendency to overestimate sea surface δ13C in the Southern Ocean. The fact that the model δ13C is overestimated more significantly than the δ13Cas indicates that the δ13C overestimates are in part due to Southern Ocean organic carbon production rates that are too high. This could be due to a seasonal bias in the climatological PO4 data set, most of which was collected in summertime when PO4 levels are lowest, or to regionally elevated C:P ratios in the OCMIP biological cycling scheme relative to reality [Arrigo et al., 2002]. The δ13C overestimation is likely also due, in part, to elevated gas exchange rates in the Southern Ocean. This interpretation is supported by the models' overestimation of the δ13C Suess effect in the Southern Ocean, which could be due to sea surface exposure times to the atmosphere that are too long, gas exchange rates that are too high, and/or mixing and overturning that is too shallow.
 In the low latitude oceans, the models' sea surface δ13C, and anthropogenic δ13C changes, were in reasonable agreement with the observations. In general, the models with relatively high mixing rates, and associated overturning, better represented the inter-basin trends in δ13C. The model δ13C changes indicate that the simulated upper ocean CO2 exchange rates with the atmosphere are reasonably accurate, as indicated also by their uptake of anthropogenic CO2 being in fair agreement with the anthropogenic CO2 accumulation reconstructed from observations [e.g., Sabine et al., 2004]. Within the range of model mixing (and overturning) scenarios we tested, there were linear relations among the oceanic δ13C changes and oceanic uptake of anthropogenic CO2 on decadal timescales. However, the model relations between sea surface δ13C changes and anthropogenic CO2 uptake depend critically on the wind field used to drive the circulation. In our model simulations, the sea surface balance between overturning and air-sea gas exchange is likely not accurate because the wind fields (from climatology) used to drive the circulation differ from the wind field (from satellites) used to drive model gas exchange rates. Inferences of long-term (century scale) CO2 uptake from changing δ13C would require that the models' deep-sea CO2 exchange rates and schematics be more accurate than in the suite of models tested here.
 This work would not have been possible without the generous help of Richard Slater and Jorge Sarmiento, and funding from the NOAA Global Carbon Cycle program. Anand Gnanadesikan provided a very constructive review. This is JISAO publication 1836 and PMEL publication 3634.