We include a prognostic parameterization of carbon-13 into a global ocean-biogeochemistry model to investigate the spatiotemporal variability in ocean carbon-13 between 1860 and 2000. Carbon-13 was included in all 10 existing carbon pools, with dynamic fractionations occurring during photosynthesis, gas exchange and carbonate chemistry. We find that ocean distributions of δ13CDIC at any point in time are controlled by the interplay between biological fractionation, gas exchange, and ocean mixing. In particular, the deep ocean δ13CDIC is sensitive (by > 0.5‰) to the degree of ocean ventilation. On interannual timescales, although the variability in δ13CDIC is a first order function of the atmospheric δ13CO2 and overall carbon flux, the spatial distributions are controlled by the degree to which surface waters are exposed to the atmosphere. The δ13CPOC is highly sensitive to the species of inorganic carbon assimilated during photosynthesis (by 10 to 17‰), as well as the intrinsic growth rate and in situ [CO2(aq)], suggesting that phytoplankton utilize both HCO3− and CO2(aq). The relationship between Δδ13CDIC and anthropogenic carbon (Cant) varies by ±70% regionally and circulation and biotic effects can influence estimates of Cant that are based on Δδ13CDIC.
 The stable isotopes of carbon (12C and 13C) can be used as tracers of carbon cycle processes across multiple timescales. The 13C isotopic composition of ocean dissolved inorganic C (DIC) is evaluated relative to the PDB standard (δ13CDIC) and is typically between 0.5 and 2.5‰ in the modern surface ocean [e.g., Gruber et al., 1999]. Since the industrial revolution, the combustion of isotopically light organic C pools has markedly reduced atmospheric δ13CO2 and, as a consequence, the mean ocean δ13CDIC, allowing researchers to infer the oceanic uptake of anthropogenic CO2 to be between 1.9 and 2.1 Pg C a−1 between the 1970s and the 1990s [e.g., Quay et al., 1992, 2007; Tans et al., 1993; Ciais et al., 1995; Heimann and Maier-Reimer, 1996; Gruber et al., 1999; Sonnerup et al., 1999; Gruber and Keeling, 2001]. As the δ13CDIC signal is retained during the precipitation of calcite and aragonite by calcareous plankton and corals it can also provide information on carbon cycling and ocean circulation across paleo timescales [e.g., Lynch-Stieglitz et al., 2007]. Additionally, the isotopic composition of particulate organic C (POC, δ13CPOC) will reflect the conditions under which photosynthetic carbon fixation occurs [Farquhar et al., 1982] and might permit the reconstruction of past ocean CO2(aq) concentrations [Popp et al., 1997]. The relative contributions of 12C and 13C to a given ocean C pool (DIC or POC) are controlled by the external sources and sinks, as well as chemical and biological fractionation.
 Despite being quantitatively less important than biological cycling, fractionation during gas exchange and DIC chemistry is also an important control on δ13CDIC. The overall fractionation during gas exchange depends on the fractionation of 13C between the various C species that make up DIC, as well as that due to kinetic gas transfer and dissolution factors [Zhang et al., 1995]. The total fractionation during CO2 invasion is generally between 2.4 and 3‰ [Wanninkhof, 1985; Zhang et al., 1995], while that resulting from DIC chemistry is temperature dependant (increasing δ13CDIC in cold waters and vice versa) and between 8 and 10.5‰ [Zhang et al., 1995]. The impact of gas exchange on δ13CDIC depends on the residence time of ocean surface waters. Finally, ocean 13C distributions are also modified by ocean circulation and mixing.
 Understanding the factors that contribute to variability in ocean δ13C is important in evaluating modern spatiotemporal distributions of δ13C, as well as long term geologic records. In this study, we include a prognostic description of the cycle of 13C within the Pelagic Integration Scheme for Carbon and Ecosystem studies (PISCES) global ocean-biogeochemistry model [Aumont and Bopp, 2006] and conduct simulations under a constant ocean circulation from 1860 to 2000 that are forced by observed values of atmospheric CO2 and δ13CO2. Specifically, we appraise the role of physical and biological factors in controlling the surface and deep distributions of ocean δ13C, as well as the processes governing the temporal changes in ocean 13C pools over century timescales. We draw attention to the importance of deep ventilation near the Antarctic continental shelf in setting the deep ocean δ13CDIC. In addition, the degree of partitioning of 13C between dissolved and particulate pools is found to be dependant on the form of inorganic C used in photosynthesis. We also examine how the relationship between anthropogenic carbon (Cant) and changes in δ13CDIC compares to those derived from the earlier generation ocean-biogeochemistry model of Heimann and Maier-Reimer . While the overall historical trend in ocean δ13C is function of the net air-sea CO2 flux and the atmospheric δ13CO2, observed changes in δ13CDIC will reflect contributions from biotic and circulation effects, as well as Cant.
2.1. The PISCES Model
 The PISCES ocean-ecosystem model is extensively described by Aumont and Bopp . In brief, PISCES includes two phytoplankton functional groups (nanophytoplankton and diatoms), meso- and micro-zooplankton, 2 detrital size classes, calcium carbonate, DIC, CO32−, dissolved organic C, nitrate (NO3), phosphate (PO4), Silicic acid (Si(OH)4), and iron (Fe) [Aumont and Bopp, 2006]. Fixed ‘Redfield’ ratios are employed for NO3 and PO4, while the ratios of both Si, and Fe, to C vary dynamically as a function of the phytoplankton functional group and environmental variables. Air-sea gas exchange of CO2(aq) utilizes the quadratic parameterization of the wind speed dependence of the piston velocity [Wanninkhof, 1992]. PISCES has already been validated and employed for a wide range of studies [e.g., Bopp et al., 2005; Aumont and Bopp, 2006; Tagliabue et al., 2008] and is therefore an ideal platform for investigating the spatial and temporal variability in δ13C on decadal timescales [e.g., Rodgers et al., 2008].
 The physical model coupled to PISCES is based on the ORCA2 global ocean model configuration of OPA version 8.2 [Madec et al., 1998] and also includes a dynamic-thermodynamic sea ice model [Timmermann et al., 2003]. The mean horizontal resolution is approximately 2° by 2° cos latitude and the meridional resolution is enhanced to 0.5° at the equator. The model has 30 vertical levels, with an increment that increases from 10m at the surface to 500 m at depth (12 levels are located in the first 125 m).
 Our standard physical model employs climatological atmospheric forcing from various data sets. These include NCEP/NCAR 2m atmospheric temperature (averaged between 1948 and 2003) and relative humidity, ISCCP total cloudiness (averaged between 1983 and 2001), precipitation (averaged between 1979 and 2001), weekly wind stress based on ERS and TAO observations and creates a representation of ocean circulation/mixing that is forced by observational climatologies. Please see Aumont and Bopp  for more details and the associated references.
2.2. 13C Parameterization
 We explicitly resolve 13C in the existing 3 dissolved and 7 particulate C pools, with fractionation occurring during photosynthesis, precipitation of calcite, gas exchange and carbonate chemistry. We parameterize ɛp (‰), via the empirical relationship of Laws et al. , to be a function of the CO2(aq) concentration (μmol kg−1) and the specific growth rate (μi, d−1) of each phytoplankton group i.
 In an attempt to account for the influence of cell size on ɛp [Popp et al., 1998, 1999; Trull and Armand, 2001], as well as the observed minimum at high values of μ/CO2(aq) [Laws et al., 1997], we restrict the variation in ɛp to between 5 and 20, and 10 and 26‰ for diatoms and nanophytoplankton, respectively. Under our standard conditions we assume the rate of change in DIC13 into POC13 for phytoplankton group i(FPOC13i) is a function of net primary production (NPPi, mol C m−3 s−1), ɛpi, and the seawater ratio of DIC13 to DIC12 (RDIC).
 Calcite formation has a fixed fractionation of 1‰ and is related to RDIC. Fractionation during gas exchange, and the conversion of CO2(aq) to DIC, are represented using the equations of Zhang et al.  and are a function of temperature and the proportion of the DIC present as CO32−.
2.3. Model Experiments
 The physical circulation and climatological forcings (atmospheric temperature, relative humidity, cloudiness, precipitation, dust and wind stress) are unchanged for the duration of our study. Prior to the experimental runs, PISCES (including the new 13C parameterization) was spun up for 3000 years under preindustrial conditions. By this time, the average drift (i.e., during final 200 years of the model spin up) in the air-sea 12CO2 and 13CO2 fluxes were 0.07 Pg 12C a−1 century−1 and 0.09 Gg 13C a−1 century−1, respectively. Alternatively, the drift in the deep Pacific ocean δ13CDIC was 0.015 ‰ century−1, while in the North Atlantic it was 0.002 ‰ century−1. We then forced PISCES with yearly atmospheric pCO2 (μatm) [Keeling et al., 2001] and δ13CO2 (‰) data [Francey et al., 1999; Keeling et al., 2001] from 1860 to 2000 (see Figure 1, denoted PISCES-A). To appraise the relative contributions of atmospheric pCO2 and δ13CO2 to variability in δ13CDIC we also performed an experiment where only atmospheric pCO2 varied (δ13CO2 was fixed to the 1860 value, denoted PISCES-B). Additionally, a control simulation was conducted over the same time period, with atmospheric pCO2 and δ13CO2 fixed at 1860 levels (denoted PISCES-E).
 In order to asses the impact of assuming that phytoplankton only transport CO2(aq), we assumed that the cellular transport of 13DIC (equation (2)) is related to the seawater ratio of 13CO2(aq) to 12CO2(aq) (RCO2(aq), denoted PISCES-C). This was achieved by calculating 13CO2(aq) concentration from temperature and δ13CDIC following Rau et al.  alongside the 12CO2(aq) concentration already calculated in PISCES. In all other cases, we assume that phytoplankton transport DIC, which is akin to assuming virtually 100% of uptake from the bicarbonate pool. We also ran simulations that utilized an alternative representation of ocean physics, thereby allowing us to appraise the role of ocean circulation in controlling δ13CDIC (PISCES-D). In this simulation, the IPSL-CM4 coupled ocean-atmosphere model [Marti et al., 2005] was integrated for 300 years under pre industrial conditions and produced monthly climatologies that were used to drive PISCES offline [Bopp et al., 2005]. Both PISCES-C and PISCES-D were spun up for 3000 years under preindustrial conditions and then integrated from 1860 to 2000 forced by historical atmospheric pCO2 and δ13CO2 (Figure 1). For completeness, all model experiments are summarized in Table 1.
Table 1. A Summary of the Experiments Conducted in This Study
Change With Time?
less southern ocean ventilation
3. Results and Discussion
3.1. Surface Water Distributions of δ13CDIC and δ13CPOC
 Annually averaged surface water distributions of δ13CDIC from 1990 (Figure 2a) compare well with the compendium of observations (between 1978 and 1997) reported by Gruber et al. . Although PISCES does a good job of representing the inter-basin trends in δ13CDIC, the absolute values are generally approximately 0.2‰ too low, especially in North Pacific gyre (Figures 3, 4a and 4b and Table 2). At high latitudes, the differences between PISCES and observations is likely due to the seasonality in primary production, which results in δ13CDIC varying by as much as 0.5 and 1‰ in the Atlantic and Pacific Ocean, respectively (Figures 4a and 4b). The greatest seasonal variability in δ13CDIC is at Southerly high latitudes (Figures 4a and 4b) and is due to the elevated biological productivity that occurs on the Antarctic continental shelf during the austral spring and summer. The large negative excursion around 0° in Figure 4a is due to the Amazon outflow, which has very low δ13CDIC values, but only occupies a small geographic area (see Figure 2a), whereas in Figure 4b the low δ13CDIC values in the east equatorial Pacific are represented by the data (Figures 4b and 2a). At low latitudes, especially in sub tropical gyres, the model underestimates surface δ13CDIC (Figures 4a and 4b and Table 2), which is most likely a result of observations being collected between 1978 and 1997, a period over which the mean ocean δ13CDIC has declined by approximately 0.3‰ [Gruber et al., 1999]. In the Indian Ocean basin, PISCES does an excellent job of reproducing δ13CDIC observations (Figure 2a). Overall, while PISCES-A accounts for around 60% of the observed δ13CDIC standard deviation (for the year 1990, Figure 3, Table 2), it should be noted that the standard deviation of the data also includes the contribution of interannual variability between 1978 and 1997.
Table 2. A Summary of the Observational and Model δ13CDIC Statistics Over a Variety of Depth Ranges (Illustrated in Figure 3)a
 Surface distributions of δ13CDIC reflect the contributions of biological fractionation, gas exchange and ocean circulation. For example, seasonally high values of δ13CDIC at the highest latitudes, especially at the Polar Front and near the Antarctic shelf (Figures 4a and 4b) reflect fractionation during primary production. While one would expect upwelling zones to reflect the introduction of “light” DIC (from remineralization of POC13), it is also important to consider that deep water also contains an older (i.e., heavier) δ13CDIC signal from the atmosphere. Therefore fractionation during primary productivity [Gruber et al., 1999] and the upwelling of older water, as well as the influx of atmospheric 13CO2 will contribute to the δ13CDIC gradient downstream of upwelling zones (e.g., the Peru and Benguela upwelling zones, Figure 2a). On the other hand, low δ13CDIC values in subtropical gyres reflect both temperature dependent fractionation during gas exchange [Gruber et al., 1999], as well as the increased overall invasion of isotopically light atmospheric CO2.
 Predictions of δ13CPOC from PISCES-A (Figure 2b) reflect the major trends in measured δ13CPOC well. Overall, the majority of the global ocean displays a δ13CPOC of around −21 to −22‰ and declines in regions typified by substantial phytoplankton growth (e.g., the North Atlantic, Figures 2b, 4c and 4d). Between the sub-Antarctic and Antarctic regions of the Southern Ocean we predict a decline in δ13CPOC from −21 to −30‰ (Figure 2b), which corresponds well with measured changes of −20 to −30‰ [Dehairs et al., 1997; Popp et al., 1999; O'Leary et al., 2001]. This is related to both an increase in CO2(aq) concentrations in colder waters, which elevates ɛp, as well as greater total primary production near the Antarctic shelf. In the North Pacific, our predictions of between −24 and −28‰ (Figure 2b) compare well with observations of −23.5 to −26.6‰ [Guo et al., 2004; Chen et al., 2006]. The "heaviest' POC is predicted to be found at low latitudes (especially in the western subtropical Pacific, Figures 2b, 4b and 4c) and is due to the decline in ɛp that results from the lower CO2(aq) concentrations and high phytoplankton growth rates that prevail in warm surface waters. Overall, we find that δ13CPOC shows a high degree of absolute variability within both the Atlantic and Pacific Ocean basins (Figures 4c and 4d represent the total model variability in space and time), which is related to spatiotemporal heterogeneity in CO2(aq), phytoplankton growth rates and biological production that is induced by ocean mixing.
3.2. Controls on the Deep Ocean δ13CDIC
 While we accurately represent the decline in deep δ13CDIC from the Atlantic to Pacific deep ocean basins, values are consistently ∼0.4 ‰ too high during PISCES-A (Figure 3, Figure 5a, and Table 2). Although the deep ocean δ13CDIC is driven to low values by the remineralization of isotopically light POC that sinks from surface waters, mixing with the high δ13CDIC of ocean surface waters subsequently increases the deep δ13CDIC. The fact that the degree of mismatch between PISCES-A and observations is greatest in the Southern and Pacific Oceans (Figure 5a) suggests that deep water production near Antarctica might be important. This can be illustrated by examining the column inventory of CFC-11, which accumulates from the atmosphere and reflects the degree of ocean ventilation [e.g., Dutay et al., 2002]. PISCES-A uses an ocean circulation that has a high degree of deep water ventilation near the Antarctic continental shelf (Figures 6a and 6b), an important region of deep water formation for the deep Southern and Pacific Ocean basins. Increased mixing with high δ13CDIC surface waters therefore results in elevated δ13CDIC values throughout the deep Southern and Pacific Oceans, relative to observations (Figure 5a).
 By using an alternative representation of oceanic circulation that exhibits less Antarctic continental shelf ventilation (PISCES-D, Figure 6c), we find that the deep ocean δ13CDIC declines by 0.4 to 0.7‰ and by 0.3 to 0.4‰ throughout the Southern and Pacific Ocean basins, respectively, in an altogether better agreement with observations (Figures 3, 5b, and Table 2). In contrast, values of δ13CDIC in the deep Atlantic Ocean change little (Figure 5b). Additionally, PISCES-D also manages to better represent the observed variability in deep δ13CDIC, as illustrated by the increased normalized standard deviation (relative to PISCES-A, Figure 3, Table 2). Therefore the degree of deep water ventilation that occurs near the Antarctic continental shelf is critical in modifying the deep ocean δ13CDIC distribution that initially arises from the sinking and remineralization of POC. In addition, biological processes (such as fractionation during photosynthesis and respiration of organic matter) are of importance in setting the surface and deep end-member δ13CDIC. Finally, the timescales of atmospheric isotopic equilibration, fractionation during photosynthesis, and downwelling will constrain the relative influence of atmospheric δ13CO2 on the deep ocean δ13CDIC.
 Overall, it is clear that a multitude of processes, both physical (ocean ventilation and surface δ13CDIC near the Antarctic continental shelf, atmospheric equilibration) and biological (variability in ɛp that is a function of CO2(aq), μ and species composition), ultimately control the deep ocean δ13CDIC. Of these, changes in ocean ventilation herald the largest variation in δ13CDIC, highlighting the potential for physical processes to control the reduction in deep ocean δ13CDIC that occurred at the Last Glacial Maximum (LGM) [sensu Toggweiler, 1999]. In this sense, reduced ocean ventilation at the LGM [e.g., Lynch-Stieglitz et al., 2007] might amplify the response of deep ocean δ13CDIC to any decline that might have arisen from an increase in surface primary production.
3.3. Mode of Inorganic C Access
 Although surface δ13CDIC increases if we assume that phytoplankton only transport CO2(aq) during photosynthesis, deep values are relatively unmodified. The δ13CDIC of surface waters increases by around 0.4 to 0.5‰ at low latitudes and by as much as 1‰ in productive high latitude regions during PISCES-C (Figure 7a). Nevertheless, at depth, δ13CDIC changes little (±0.2‰, Figure 3, Figure 7b, and Table 2), suggesting that deep distributions of δ13CDIC might be relatively insensitive to changes surface fractionation. As outlined above, although the remineralization of light POC will reduce deep ocean δ13CDIC, mixing with the (now higher) δ13CDIC of surface waters dilutes much of the change at depth. Relative to observations, we end up overestimating surface δ13CDIC by around 0.6‰ during PISCES-C, but the representation of the observed seasonal variability improves (Figure 3 and Table 2). The better representation of surface δ13CDIC during PISCES-A may also be due to the overestimation of deep δ13CDIC during these simulations (Figure 5a and Table 2), which can mix into surface waters.
 Despite a potentially better fit to the δ13CDIC data, δ13CPOC declines dramatically if phytoplankton are assumed to only transport CO2(aq) during photosynthesis. In surface waters, δ13CPOC is reduced by 17 and 12‰ between high and low latitudes, respectively (Figure 7c). For reference, this would reduce Southern Ocean and Equatorial Atlantic δ13CPOC to <−45 and −30 ‰, respectively, well beyond observations of between −16 and −36 ‰ [e.g., Goericke and Fry, 1994]. This is because RCO2(aq) is always less than RDIC during PISCES-C and phytoplankton therefore accumulate less 13C (for a given rate of C fixation). However, this sensitivity will be related to the parameterization of ɛp (equation (1)), which was determined in equatorial Pacific [Laws et al., 1995]. Nevertheless, ɛp is around 20–22‰ and 18‰ in the Southern Ocean and equatorial Pacific, respectively (during PISCES-A) and compares well to observations of >20‰ in the Southern Ocean [Popp et al., 1999] and 16‰ in the equatorial Pacific [Bidigare et al., 1999]. Indeed, recent field observations in both the Southern Ocean and sub Arctic Pacific have found that between 50 and 90% of total phytoplankton DIC uptake was associated with direct HCO3− uptake, rather than CO2(aq) [Cassar et al., 2004; Tortell et al., 2006]. Accordingly, for our predictions of δ13CPOC to remain within the observational range we must assume that phytoplankton are not solely reliant on CO2(aq) for photosynthesis. In reality, it is likely that a range of strategies exist, that are driven by local conditions or perhaps species specific inorganic C transport mechanisms [e.g., Raven and Johnston, 1991].
3.4. Overall Response to Changes in Atmospheric pCO2 Between 1860 and 2000
 Globally, our results compare well to a recent data-based calculation of the oceanic sink for atmospheric CO2 over the past 194 years. Sabine et al.  used inorganic C measurements, alongside a tracer separation technique, to estimate the global ocean CO2 sink to be 118 ± 19 Pg C (between 1800 and 1994) and we find the ocean sink to be 93.65 Pg C over our shorter study period (between 1860 and 1994). Spatially, our results exhibit maximal Cant column inventories in regions typified by deep ventilation (Figure 6b and Figure 8b), primarily the north Atlantic, but also the Southern Ocean (e.g., around 40°S), in agreement with the estimates of Sabine et al.  (Figure 8a). The mean ocean sink for CO2 in the 1990s is 1.86 Pg C a−1 and increases by 0.31 Pg C a−1 between the 1980s and the 1990s. This agrees well with the recent Intergovernmental Panel on Climate Change (IPCC) report, which estimates (using a variety of techniques) a mean ocean sink of 1.8 ± 0.8 and 2.2 ± 0.4 Pg C a−1 during the 1980s and 1990s, respectively [IPCC, 2007].
3.5. The Ocean 13C Suess Effect
 Both the increased total flux of CO2 from the atmosphere to the ocean, as well as the reduction in δ13CO2, and gas exchange fractionation contributes to the rate of change in δ13CDIC (defined hereafter as the ocean 13C Suess effect) since 1860. We find the 13C Suess effect between 1860 and 2000 to be −0.07‰ decade−1 and increases to −0.18‰ decade−1 between 1970 and 2000 (a 2.6 fold increase). Observed changes in ocean δ13CDIC of −0.15 and −0.171 ‰ decade−1 between 1970 and 1990 [Bacastow et al., 1996 and Sonnerup et al., 1999, respectively] are in good agreement with our global estimate of −0.174‰ decade−1 for the same time period. We find that the ocean 13C Suess effect is always approximately 65% of the change in atmospheric δ13CO2 (0.11 and 0.27 ‰ decade−1 for 1860–2000 and 1970–2000, respectively), regardless of the time increment over which it is evaluated. This compares well with previous estimates of between 60 and 70% [Keeling, 1979; Broecker and Peng, 1993] and reflects longer equilibration time for 13C in the ocean, relative to the atmosphere. The change in atmospheric pCO2 alone (PISCES-B) contributes as little as 15% (−0.011‰ decade−1) to the overall 13C Suess effect between 1860 and 2000. Consequently, despite the importance of the total flux of CO2 and, to a lesser degree, temperature-dependent fractionation, the vast majority of the documented reduction in ocean δ13CDIC results from the dramatic decline in atmospheric δ13CO2 (Figure 1).
 The ocean 13C Suess effect displays a wide degree of spatial variability in surface waters, varying from almost 0 to < −0.24‰ decade−1 between 1970 and 2000 (Figure 9). This corresponds well with basin estimates of −0.18, −0.18, and −0.14 ‰ decade−1 in the Atlantic [Quay et al., 2007], Pacific [Quay et al., 2003], and Indian [Sonnerup et al., 2000] Oceans, respectively, as well as the poleward decline along 140°E in the Southern Ocean (from −0.16 to 0.06 ‰ decade−1) noted by McNeil et al.  (Figure 9). Overall, the largest reductions in δ13CDIC occur in the sub tropical gyres, with a marked decline in the 13C Suess effect at high latitudes and near tropical upwellings (especially in the Pacific, Figure 9).
 Understanding the spatial distribution of the 13C Suess effect necessitates a consideration of ocean mixing and circulation. In particular, upwelling of higher δ13CDIC (i.e., older) deep waters dilutes the surface 13C Suess effect (in the Eastern Pacific, for example, Figure 9), as well as minimizing the exposure of surface waters for the uptake of atmospheric CO2 and isotopic equilibration. Alternatively, in regions typified by little deep water ventilation (such as sub-tropical gyres) surface waters have a longer residence time and thus exhibit the greatest reductions in δ13CDIC (Figure 9). In the Southern Ocean, both the temperature dependent fractionation between CO2(aq) and DIC that follows gas exchange and surface water subduction prior to isotopic equilibrium reduces the 13C Suess effect (Figure 9) [McNeil et al., 2001]. At the Bermuda Atlantic Time Series (BATS, ∼30°N in Figure 4) and Hawaii Ocean Time Series (HOT, around 25°N in Figure 4) we only account for around half of the observed Δδ13CDIC of −0.025 ‰ a−1 [Gruber et al., 1999]. This is most likely due to the low resolution of our global model, relative to the individual ocean stations concerned, the absence of any interannual changes in circulation and, for BATS in particular, an under estimate of Cant in the western subtropical Atlantic (Figure 8).
3.6. Relating the Ocean Suess Effect to the Accumulation of Anthropogenic Carbon
 As Δδ13CDIC is often used to derive ocean uptake of Cant, it is of interest to examine the simulated relationship between the accumulation of Cant and the Δδ13CDIC. The Suess effect can be related to Cant via the parameter ‘RC’ (defined as: Δδ13CDIC/ΔDIC, McNeil et al. ). Between 1970 and 2000, we find a good relationship between depth integrated Δδ13CDIC (‰ m yr−1) and Cant (mole m−2) (Figure 10a) and derive a global average RC (RCglob) of −0.0164 ‰ (μmol kg−1)−1. While RCglob is similar to the global "dynamic constraint' of between −0.016 and −0.019‰ (μmol kg−1)−1 proposed by Heimann and Maier-Reimer , we caution against applying RCglob to sparse regional Δδ13CDIC observations, as RC varies by as much as ±70% locally (relative to RCglob, Figure 10b, as well as Heimann and Maier-Reimer ). Accordingly, RC has been observed to decline poleward from −0.015 to −0.007‰ (μmol kg−1)−1 in the Southern Ocean [McNeil et al., 2001] and we confirm that applying RCglob would underestimate Cant by 10 to 30% (Figure 10b). As the subduction of cold surface waters decouples Δδ13CDIC from ΔDIC, only a small change in δ13CDIC accompanies the accumulation of Cant (i.e., a low RC). In fact, the shallower penetration of Δδ13CDIC, relative to Cant, that was observed by McNeil et al.  along 140°E appears to be a consistent feature of the Antarctic region of the Southern Ocean (Figure 10b), suggesting RCglob cannot derive Cant in this important ocean region. While RC is almost equal to RCglob in the high North Atlantic, it increases sharply south of ∼40°N (to up to 0.028 ‰ (μmol kg−1)−1, Figure 10b), which is in accord with observations of −0.024‰ (μmol kg−1)−1 (or 50% greater than our RCglob) by Kortzinger et al. . In the central Pacific, RC remains within ±10% of RCglob, although we note higher values near HOT and the equatorial upwelling (Figure 10b).
 While quantitatively less important than the invasion of isotopically light Cant, increased biotic fractionation can also play a role in controlling the measured Suess effect. As the ocean DIC inventory increases, the greater concentration of CO2(aq) permits greater biotic fractionation against 13DIC [e.g., Laws et al., 1995, 1997]. Accordingly, ɛp increased by an average of 0.25 ‰, or 0.018‰ decade−1, relative to the overall Suess effect of −0.07‰ decade−1 (between 1860 and 2000, during PISCES-A) in surface waters. We suggest that the observed Suess effect (Δδ13CDICobs) will reflect contributions from the invasion of Cant (Δδ13CDICatm), as well as changes in biotic fractionation (Δδ13CDICbio) and ocean circulation (Δδ13CDICcirc). As there was no change in ocean circulation during our simulations (i.e., Δδ13CDICcirc = 0), the Suess effect associated with the uptake of Cant (Δδ13CDICatm) can be approximated to be −0.088 ‰ decade−1 (26% greater than Δδ13CDICobs). This would suggest that unless Δδ13CDICcirc and Δδ13CDICbio can be accounted for, any estimate of Cant that is based on Δδ13CDICobs will be conservative.
 In terms of understanding the ocean Δδ13CDIC and the uptake of Cant, our prognostic 13C parameterization results in a similar RCglob to previous models [e.g., Heimann and Maier-Reimer, 1996], but also permits us to better represent the observed regional heterogeneity in RC, especially in the Southern Ocean (Figure 10b). This is because earlier generation ocean models [e.g., Heimann and Maier-Reimer, 1996] utilized much longer timesteps (one month versus a few hours) and coarser vertical and horizontal resolution. Moreover, in the future this model configuration will be used to investigate changes in ocean δ13C that result from future or past changes in climate, as well as atmospheric pCO2 and δ13CO2. In doing so, it will be possible to address the impact on ocean δ13C of the variability in phytoplankton fractionation that results from changes in growth rate, and species composition (as estimated for [CO2(aq)] here) that are mediated by ocean circulation and/or exogenous nutrient delivery. For example, since dust deposition of iron is postulated to have been greater at the LGM, we would anticipate a concomitant decline in phytoplankton fractionation as growth rates increase and large diatoms replace smaller nanophytoplankton would reduce surface δ13CDIC. It is currently unclear how such processes will interact with the physically driven changes in the ocean δ13C at the LGM [e.g., Lynch-Stieglitz et al., 2007]. On the other hand, the future ocean will be warmer (ostensibly reducing δ13C via gas exchange fractionation) and will also display greater surface stratification [e.g., Sarmiento et al., 2004]. Reduced vertical mixing should elevate δ13C (via reduced mixing with light deeper waters), but will also increase phytoplankton fractionation due to the change in growth rate and species composition that results from lesser vertical nutrient supply [e.g., Bopp et al., 2005]. Our model can therefore be used to better constrain the relative contributions of changes in ocean circulation (Δδ13CDICcirc) and biological productivity (Δδ13CDICbio), as well as uptake of anthropogenic carbon (Δδ13CDICatm), to the measured ocean 13C Suess effect (Δδ13CDICobs).
 In general, biological and chemical fractionation processes will dictate the initial surface and deep patterns in δ13CDIC that are modified by ocean mixing. Elevated surface δ13CDIC values will be found in regions of high primary production or cold temperatures, while deep δ13CDIC will be reduced underneath zones of significant export flux, as well as along the deep ocean conveyor belt (via the remineralization of isotopically light POC). However, the ocean system is dynamic and the value of δ13CDIC in a given space and time is also controlled by physical mixing. High rates of ventilation will reduce and increase the surface and deep δ13CDIC, respectively (by as much as 0.7‰), as a function of the surface and deep end-members. While the 13C Suess effect is a first order function of the atmospheric δ13CO2 and overall C flux, the spatial distributions are also controlled by ocean ventilation and the degree isotopic equilibrium with the atmosphere. Accordingly, while we confirm a tight relationship between the depth-integrated Suess effect and anthropogenic carbon globally, there is a large degree of regional heterogeneity in RC (±60%) that should be considered when deriving the accumulation of Cant from local observations. In addition, the overall Suess effect reflects contributions from anthropogenic carbon, biotic processes (such as changes in fractionation) and ocean circulation. Including 13C in a state of the art ocean-biogeochemical model will permit the future appraisal as to the impact of biological variability in fractionation on ocean δ13C that is driven by future or past variability in circulation and/or exogenous nutrient inputs.
 We thank Nicolas Cassar, Niki Gruber, and two anonymous reviewers for their insightful comments on our manuscript. Funding was provided by the project ANR-GOBAC and all simulations were performed at the French National computing center IDRIS. This is LSCE contribution number 2907.