Measurements of the δ13C of dissolved inorganic carbon primarily during World Ocean Circulation Experiment and the Ocean Atmosphere Carbon Exchange Study cruises in the 1990s are used to determine ocean-wide changes in the δ13C that have occurred due to uptake of anthropogenic CO2. This new ocean-wide δ13C data set (∼25,000 measurements) substantially improves the usefulness of δ13C as a tracer of the anthropogenic CO2 perturbation. The global mean δ13C change in the surface ocean is estimated at −0.16 ± 0.02‰ per decade between the 1970s and 1990s with the greatest changes observed in the subtropics and the smallest changes in the polar and southern oceans. The global mean air-sea δ13C disequilibrium in 1995 is estimated at 0.60 ± 0.10‰ with basin-wide disequilibrium values of 0.73, 0.63, and 0.23‰ for the Pacific, Atlantic, and Indian oceans, respectively. The global mean depth-integrated anthropogenic change in δ13C between the 1970s and 1990s was estimated at −65 ± 33‰ m per decade. These new estimates of air-sea δ13C disequilibrium and depth-integrated δ13C changes yield an oceanic CO2 uptake rate of 1.5 ± 0.6 Gt C yr−1 between 1970 and 1990 based on the atmospheric CO2 and 13CO2 budget approaches of Quay et al.  and Tans et al.  and the dynamic method of Heimann and Maier-Reimer . Box-diffusion model simulations of the oceanic uptake of anthropogenic CO2 and its δ13C perturbation indicate that a CO2 uptake rate of 1.9 ± 0.4 Gt C yr−1 (1970–1990) explains both the observed surface ocean and depth-integrated δ13C changes. Constraining a box diffusion ocean model to match both the observed δ13C and bomb 14C changes yields an oceanic CO2 uptake rate of 1.7 ± 0.2 Gt C yr−1 (1970–1990). The oceanic CO2 uptake rates derived from anthropogenic changes in ocean δ13C are similar to rates determined by atmospheric CO2 and O2 budgets [Battle et al., 2000], atmospheric δ13C and CO2 measurements [Ciais et al., 1995], and GCM simulations [Orr et al., 2001].
 Accurate model predictions of future levels of atmospheric CO2 are essential to predict future climate change. Ocean models of anthropogenic CO2 uptake are a major component of these predictions. Comparing the output of ocean models against independent determinations of ocean CO2 uptake is a key test of model accuracy. Several nonmodel methods have been used to determine the rate of oceanic uptake of CO2. Measured atmospheric O2 and CO2 rates of change yield oceanic uptake rates of 2.0 ± 0.6 Gt C yr−1 for the 1990s [Battle et al., 2000]. Measured differences between the pCO2 in the atmosphere and surface ocean, coupled with estimates of air-sea CO2 gas transfer rates, yield oceanic uptake rates of 2.8 Gt C yr−1 in 1995 [Takahashi et al., 2002] after including the 0.6 Gt C yr−1 input via rivers [Siegenthaler and Sarmiento, 1993]. Atmospheric CO2 and 13CO2 budgets yield oceanic CO2 uptake rates of ∼1.5 Gt C yr−1 in the 1990s [Ciais et al., 1995]. In comparison, ocean general circulation models (GCMs) predict CO2 uptake rates of 1.9 ± 0.4 Gt C yr−1 for the 1980s [Orr et al., 2001] and simpler one- or two-dimension ocean models, tuned to reproduce the ocean's bomb 14C distribution, predict rates of 1.7–2.2 Gt C yr−1 for the 1980s [e.g., Siegenthaler and Joos, 1992; Jain et al., 1995; Kheshgi et al., 1999].
 Measured changes in the 13C/12C of the dissolved inorganic carbon (DIC) in the ocean provide another means to estimate of the anthropogenic CO2 uptake rate in the ocean [Quay et al., 1992; Tans et al., 1993; Bacastow et al., 1996; Heimann and Maier-Reimer, 1996; Kheshgi et al., 1999]. However, for all these studies most of the uncertainty of the calculated oceanic CO2 uptake rate resulted from a lack of oceanic 13C/12C measurements. Thus, the full potential of 13C/12C as a tracer of anthropogenic CO2 uptake in the ocean has not been realized despite the advantage that 13C/12C has over the more commonly used bomb 14C tracer due to the similar atmospheric histories for the 13C/12C and CO2 perturbations. The present study substantially expands the oceanic δ13C observational database by including measurements made during the ocean-wide World Ocean Circulation Experiment (WOCE) and the Ocean Atmosphere Carbon Exchange Study (OACES) programs in the 1990s. This new δ13C data set (∼25,000 measurements) provides a much-improved estimate of the changes in the oceanic δ13C and, as a result, more accurate estimates of the oceanic uptake rate of anthropogenic CO2. In this presentation, unless specified otherwise, δ13C represents the 13C/12C of the DIC.
Quay et al.  used the observed change in depth-integrated δ13C inventory profiles between the 1970s and 1990s to determine an oceanic CO2 uptake rate of 2.1 ± 0.8 Gt C yr−1. This ocean “13C inventory” method utilized atmospheric and oceanic CO2 and 13CO2 budgets to solve for the net oceanic and biospheric uptake rate of CO2. Tans et al.  modified the Quay et al. budget approach by substituting the rate of air-sea CO2 and 13CO2 exchange for the rate of ocean δ13C inventory change. He determined a much slower oceanic CO2 uptake rate of 0.2 Gt C yr−1 using this air-sea “13C disequilibrium” method. Heimann and Maier-Reimer  introduced a “dynamic constraint” method, which utilized the strong correlation between the atmospheric time histories of anthropogenic δ13C and CO2 changes, to calculate an oceanic CO2 uptake rate of 3.1 ± 1.6 GtC yr−1. They calculated an oceanic CO2 uptake rate of 0.64±1.6 Gt C yr−1, using the air-sea 13C disequilibrium method of Tans et al. that included a riverine CO2 flux of 0.6 Gt C yr−1. Because each of the three 13C-based approaches had significant uncertainty, Heimann and Maier-Reimer used an optimization approach to determine a set of budget parameters, within their respective uncertainties, that yielded the same oceanic CO2 uptake rate from all three approaches. This parameter set yielded an oceanic CO2 uptake rate of 2.1 ± 0.9 Gt C yr−1. They estimated that the uncertainties in the observed oceanic 13C inventory change and air-sea 13C disequilibrium accounted for ∼75 and 50%, respectively, of the errors in the calculated CO2 uptake rates using the inventory approaches [Quay et al., 1992; Heimann and Maier-Reimer, 1996] and disequilibrium approach [Tans et al., 1993], respectively. Gruber and Keeling  used the global data set of surface δ13C measurements reported by Gruber et al.  to determine an air-sea δ13C disequilibrium of 0.62 ± 0.10‰. They determined an oceanic CO2 uptake rate of 1.5 ± 0.9 Gt C yr−1 between 1985 and 1995 using this disequilibrium value and the method of Tans et al. . These three 13C-based methods, described in more detail below, did not rely on models to estimate the oceanic uptake rate of anthropogenically produced CO2.
Bacastow et al.  used a box-diffusion ocean model and the measured δ13C decrease of −0.18 ± 0.05‰ per decade in surface waters at Station S in the subtropical North Atlantic between 1984 and 1993 to estimate an oceanic CO2 uptake rate between 1 and 3.2 Gt C yr−1. The large CO2 uptake range was due to the uncertain extrapolation from δ13C measurements at only one site to an ocean-wide surface δ13C change. Kheshgi et al.  utilized a global carbon cycle model (including atmospheric, biospheric, and oceanic reservoirs) and the observed changes in atmospheric and oceanic 14C and δ13C to calculate a mean oceanic CO2 uptake rate of 1.7 ± 0.7 Gt C yr−1 for 1970–1990.
 In this study, we present the results of δ13C measurements on samples collected from all three ocean basins in the 1990s primarily during WOCE and OACES cruises. Our data analysis focuses on the time rate of change of the ocean δ13C between the 1970s and 1990s, rather than the current δ13C distribution itself. We use these new data to determine more representative estimates of the global oceanic δ13C surface change (−0.16 ± 0.02‰ per decade), δ13C inventory change (−65 ± 33‰ m per decade), and the air-sea δ13C disequilibrium (0.60 ± 0.1‰). These revised estimates of δ13C inventory change and air-sea δ13C disequilibrium yield an oceanic CO2 uptake rate of 1.5 ± 0.6 Gt C yr−1 from 1970 to 1990 that is consistent with the 13C inventory, 13C disequilibrium, and dynamic constraint methods discussed above. In comparison, a box-diffusion ocean model that simulated the observed δ13C changes in surface ocean and depth-integrated inventory yielded an oceanic CO2 uptake rate of 1.9 ± 0.4 Gt C yr−1 (1970–1990). The same box-diffusion model (BDM) used to simulate both the observed δ13C changes and bomb 14C accumulation (in 1975) yielded a CO2 uptake rate of 1.7 ± 0.2 Gt C yr−1.
2.1. Methods Using δ13C to Determine an Oceanic CO2 Uptake Rate
 The 13C inventory approach [Quay et al., 1992] formulated the time rate of change of atmospheric CO2 concentration and δ13C in terms of the CO2 input from fossil-fuel combustion and net uptake of CO2 by the terrestrial biosphere and ocean. For each source and sink term the 13CO2 budget required a δ13C signature. The net oceanic uptake rate of CO2 (Soc) can be expressed in terms of the atmospheric 12CO2 and 13CO2 budgets as follows [Heimann and Maier-Reimer, 1996]:
where R is the 13C/12C, Qf is the CO2 loading rate from fossil-fuel combustion, Ca is the CO2 burden in the atmosphere, Aoc is the area of the ocean, Coc is the DIC concentration of the upper ocean, D is the depth-integrated change in the ocean δ13C, Fab is the gross atmosphere to biosphere CO2 flux, αab is the fractionation during photosynthesis, Rabeq represents the isotopic composition of the atmosphere in isotopic equilibrium with the current biosphere (i.e., Rabeq = Rb/αab), Fob is net marine productivity, αob is the fractionation during marine photosynthesis, Robeq represents the isotopic composition of surface water DIC in isotopic equilibrium with current marine organic carbon (Rob), i.e., Robeq = Rob/αob. The time rate of change is represented by the symbol ' (e.g., Ća) and the subscripts oc, b, f, and a represent ocean, biosphere, fossil fuel, and atmosphere, respectively. Since Soc is expressed in terms of the oceanic inventory changes in DIC and δ13C, Soc includes uptake of CO2 that occurs via riverine input of organic and inorganic carbon in excess of that buried in the deep sea, i.e., ∼0.6 Gt C yr−1 [Siegenthaler and Sarmiento, 1993]. That is, riverine-derived CO2 accumulates in the ocean as a result of a diminished efflux of CO2 gas to the atmosphere as the atmospheric CO2 concentration rises from its preindustrial level. The oceanic uptake rate of CO2 is determined from measurements of the time rate of change of concentration and δ13C of atmospheric CO2, ocean average depth-integrated change in the δ13C of the DIC, and the δ13C of CO2 released from fossil fuels and biospheric carbon reservoir. An estimate of the δ13C disequilibrium between the atmosphere and terrestrial biosphere; that is, Rabeq − Ra, is required. This term, multiplied by the gross atmosphere-biosphere CO2 flux, is referred to as the biospheric δ13C Suess effect. Heimann and Maier-Reimer  showed that changes in the δ13C of the marine organic carbon pool are small when compared with the δ13C changes in the marine DIC and terrestrial carbon pools.
Tans et al.  modified the above approach by substituting the air-sea 13CO2 flux for the depth-integrated inventory change in δ13C to calculate the net oceanic CO2 uptake rates. The oceanic uptake rate of CO2 was determined from Tans et al.'s δ13C disequilibrium approach using the relationship determined by Heimann and Maier-Reimer :
where αma is the isotopic fractionation effect during sea to air CO2 evasion, Fam is the gross air-sea CO2 influx rate, and Fr is the riverine organic and inorganic carbon input rate minus the deep-sea carbon burial rate. The difference between the δ13C of the atmosphere (Ra) and that expected in equilibrium with the surface ocean (Raeq) represents the air-sea δ13C disequilibrium (Raeq − Ra). Thus oceanic uptake of CO2 is determined from measurements of the time rate of change of concentration and δ13C of atmospheric CO2, δ13C of CO2 released from fossil-fuel combustion, 13C/12C disequilibrium between the surface ocean and atmospheric CO2, and gross air-sea CO2 exchange rate. An estimate of the biospheric δ13C Suess effect was needed in equation (2) as it was in equation (1). Since the δ13C inventory and disequilibrium methods share terms, the oceanic uptake rate of CO2 calculated using equation (2) is not entirely independent from the rate calculated using equation (1).
Heimann and Maier-Reimer  developed a third method to determine oceanic uptake rates of CO2 from ocean δ13C measurements. Their dynamic constraint approach essentially assumed that the penetration depth of the δ13C ocean inventory change is the same as the penetration depth of the ocean CO2 inventory change because of their similar atmospheric time histories. The expression relating the oceanic CO2 uptake rate to the ocean δ13C inventory change and air-sea CO2 gas exchange rate is as follows [Heimann and Maier-Reimer, 1996]:
where ξ is the buffer factor controlling the ratio of dissolved CO2 and DIC time rates of change, ΔRa is the historical (1800–1980) time rate of change of atmospheric δ13C, and ΔPa/Pao represents the relative historical (1800–1980) increase in the atmospheric CO2 concentration. Thus the oceanic CO2 uptake rate is determined from measurements of the change in ocean δ13C inventory (D), historic δ13C, concentration changes for atmospheric CO2, estimates of the gross air-sea CO2 exchange rate, and the ocean buffer factor. Heimann and Maier-Reimer used a comparison of their dynamic method to GCM simulations of the anthropogenic δ13C and CO2 perturbation to conclude that the key assumptions in the dynamic method resulted in <10% inaccuracy. The dynamic method, although not independent from the approaches used by Quay et al.  and Tans et al.  differs significantly from these approaches in that it does not require an estimate of the biospheric δ13C Suess effect.
 The final method we use to calculate oceanic CO2 uptake rates from ocean δ13C measurements utilized a one-dimensional box-diffusion ocean model [Oeschger et al., 1975]. Certainly BDMs oversimplify the ocean (e.g., mixing rates are parameterized, the ocean is homogenized horizontally, etc.) when compared to GC. However, BDMs predict anthropogenic CO2 uptake rates of ∼2 Gt C yr−1 (for the 1980s) that are similar to the rates predicted by GCMs when BDMs are calibrated to observed tracer distributions like bomb 14C [Caldeira et al., 2000]. The simplicity of BDMs is a significant advantage for testing the sensitivity of the predicted uptake rates to uncertainties in the tracer distributions. To date, bomb 14C has been the tracer of choice for calibrating BDMs and testing GCMs used for predicting CO2 uptake rates [e.g., Siegenthaler and Sarmiento, 1993; Jain et al., 1995; Caldeira et al., 2000; Orr et al., 2001]. Potentially, δ13C is a better tracer of anthropogenic CO2 uptake in the ocean because of the strongly correlated time histories of the concentration and δ13C of atmospheric CO2. Heimann and Maier-Reimer  used a GCM simulation of the anthropogenic CO2, δ13C and bomb 14C to show that the correlation of model predicted CO2 uptake rates with depth-integrated δ13C change was much stronger than the correlation with bomb 14C inventory. To date, however, the utilization of δ13C as a tracer has been limited by lack of ocean data.
 The BDM used in the present study had a 75 m deep surface layer, 37 layers each 25 m deep and 30 layers each 100 m deep. The buffer factor, calculated from an initial alkalinity of 2325 μeq kg−1 and DIC concentration of 2000 μmol kg−1, increased from about 9 to 10 during the period of the anthropogenic perturbation. The isotopic fractionation factors during air-sea CO2 exchange and for DIC speciation were taken from Zhang et al. . The BDM was forced with the atmospheric CO2 record between 1830 and 1998 based on measurements from Law Dome ice cores [Etheridge et al., 1998] and the South Pole [Thoning and Tans, 2000]. Since these observations represented southern hemisphere conditions, the atmospheric CO2 concentrations were increased by up to 1.6 ppm to represent a global mean values based on a comparison of the CO2 records collected by CMDL at South Pole and other sites since the late 1970s. The atmospheric δ13C was calculated from the CO2 concentration using a polynomial fit of the relationship between δ13C and CO2 measured in a Law Dome ice core (1830–1978) and at Cape Grim between 1978 and 1997 by Francey et al.  where the average error in the fit was 0.03‰. The mean atmospheric CO2 increased from 284 to 363 ppm and mean atmospheric δ13C decreased from −6.4 to −7.9‰ between 1830 and 1997. The ocean uptake of bomb 14C was simulated in the model using a compilation of atmospheric time histories of 14C measured at Wellington, New Zealand [Manning and Melhuish, 1994], Vermunt, Germany [Levin et al., 1994], and Schauinsland, Germany [Levin and Kromer, 1997].
 During each model run, the changes of surface layer and depth-integrated DIC, δ13C and Δ14C were determined as were the air-sea pCO2 and δ13C disequilibrium. Between 1970 and 1990 the changes in the mean penetration depths of the anthropogenic CO2 and δ13C were calculated, as was the mean penetration depth of bomb 14C in 1975. Because of the similarity of the anthropogenic CO2 and δ13C atmospheric time histories, the model predicted δ13C penetration depth between 1970 and 1990 was, on average, 94% of the CO2 penetration depth. In contrast, the bomb 14C penetration depth in 1975 was, on average, only 65% of the CO2 penetration depth between 1970 and 1990 because the peak in atmospheric bomb 14C occurred only ∼10 years earlier. The predicted bomb 14C burden was twice as sensitive as the δ13C inventory change to the air-sea CO2 exchange rate; that is, a 25% change in the gas transfer rate yielded a 23% change in the bomb 14C inventory, a 11% change in the δ13C inventory and a 3% change in the CO2 inventory.
2.2. Ocean δ13C data
 The δ13C depth profiles (n = 1265) were collected on 64 cruises during the 1990s primarily as part of the WOCE and the OACES programs (Table 1 and Figure 1). Additionally, about half of the ∼2500 surface δ13C samples were collected while underway between stations, on transit legs or via ships of opportunity (Figure 1). Because of the dominance of the WOCE cruises in the Pacific Ocean, this basin has the best sample coverage whereas the South Atlantic and South Indian Oceans are only sparsely covered by our data (Figure 1). To expand our coverage in the Atlantic and Indian Oceans, surface δ13C data were included from SAVE cruises in the Atlantic during 1988–1989 [Gruber et al., 1999], Polarstern cruises in the South Atlantic during 1989 [Mackensen et al., 1993], and French cruises in the South Indian during 1991–1993 [Francois et al., 1993; Bentaleb et al., 1998; Archambeau et al., 1998].
Table 1. Cruises During the 1990s on Which Samples Were Collected for δ13C Measurement (see Figure 1 for Locations)
 The δ13C measurements were made either at the Stable Isotope Laboratory at the University of Washington (UW) or at the National Ocean Sciences AMS facility (NOSAMS) at Woods Hole Oceanographic Institution (WHOI). Although different sample preparation procedures were followed at the UW [Quay et al., 1992] and WHOI [McNichol et al., 2000], the overall precision of the δ13C measurements in each laboratory was slightly better than ±0.03‰ based on replicate measurements of standards and sample pairs collected from the same Niskin. An interlaboratory offset of 0.01 ± 0.02‰ (n = 10) was determined by comparing δ13C measurements of seawater standards. A comparison of deep water samples (>1200 m) collected at the same station locations (n = 15) during repeat WOCE cruises in the Indian Ocean (Figure 1) and measured in each laboratory yielded a mean interlaboratory offset of 0.02‰ that was within the measurement uncertainty. The δ13C depth profiles measured during WOCE and OACES cruises in the 1990s provide the first ocean-wide high quality δ13C data set and are available at the WOCE data archive.
3. Results and Discussion
3.1. Surface Water δ13C Trends
 Consistent trends appear in the δ13C distribution of surface ocean water (Figure 2). The highest δ13C values in each basin are found at 35°–50°S and the lowest values are found in the Southern Ocean. In the tropical and subtropical ocean, higher δ13C values are found in the Atlantic as compared with Indian or Pacific oceans. Since the meridional δ13C variability generally is greater than zonal variability, a plot of the zonally averaged δ13C values versus latitude shows the major spatial trends in the surface ocean δ13C (Figure 3). The low δ13C values in the Southern Ocean and maximum values at 35°–50°S are consistent in all three basins as is a δ13C minimum in the subtropical gyres of each basin. Slight minima are seen in the equatorial Pacific and Atlantic oceans. Surface δ13C values north of 50°S are consistently lowest in the Indian Ocean and highest in the Atlantic Ocean. These main features agree well with the trends of surface δ13C data collected between 1978 and 1993 reported by Gruber et al. . The zonal-averaged and area-weighted mean δ13C values for the surface water of the Pacific, Atlantic, and Indian oceans are 1.55, 1.56, and 1.37‰, respectively, yielding a global ocean average of 1.51‰. For this calculation, the surface δ13C values (collected over a 10 year interval) were adjusted to a collection year of 1995, using estimates of the time rates of change for surface water δ13C for each basin discussed below.
 One way to estimate the temporal change in surface ocean δ13C is to compare the recent (1990s) data with the values measured in the 1970s and 1980s. In the Pacific Ocean, a comparison of δ13C measurements made during the RITS93 cruise in April 1993 and the HUDSON cruise in May 1970 [Kroopnick et al., 1977] demonstrates the overall decrease in the surface ocean that has occurred over the last two decades (Figure 4). The area-weighted average surface δ13C value, based on data from these two cruises only, decreased from 2.00‰ in 1970 to 1.61‰ in 1993. The largest δ13C decrease occurred in the subtropical gyres, whereas little or no δ13C decrease was observed the subpolar gyre and Southern Ocean. Similar latitudinal positions of the δ13C maxima and minima appeared in 1970 and 1993 indicating that the processes controlling the surface δ13C distribution are robust despite the overall temporal decrease in δ13C resulting from uptake of anthropogenic CO2. This particular snapshot comparison benefits from the two cruises being located along the same longitude (140°–150°W) and occurring at the same time of year (May and April) which should reduce the effect of seasonal and spatial biasing.
 A similar meridional trend in the δ13C time rate of change is seen in the Indian Ocean when δ13C data measured during WOCE in 1995 and GEOSECS in 1978 [Kroopnick, 1985] are compared (Figure 4). The largest δ13C decrease occurs in the subtropics and little change is observed south of 50°S. In the North Atlantic, δ13C values measured during the Transient Tracer in the Ocean (TTO) program in 1981 and 1983 [Gruber et al., 1999] were compared with values measured during four cruises between 1992 and 1995 (Figure 4). The meridional trend of δ13C change in the North Atlantic was consistent with that observed in the North Pacific. The greatest δ13C decrease occurred in the subtropical gyre and significantly smaller changes were observed in the subpolar and equatorial regions.
 We have compared these snapshots of δ13C decrease with other estimates of surface ocean δ13C change. In the subtropical North Pacific, we have measured a surface δ13C decrease rate of −0.24 ± 0.02‰ per decade at the time-series station ALOHA (23°N 158°W) since 1990 (Figure 5) that agrees well with the −0.25 ± 0.02‰ per decade rate independently measured at ALOHA by Gruber et al. . Sonnerup et al.  estimated the change in the δ13C of surface waters in the Pacific Ocean using reconstructions of the preformed δ13C values along isopycnals surfaces and CFC water mass ages. They found that the rate of surface δ13C decrease at the isopycnal outcrop locations ranged from −0.07 to −0.15‰ per decade between 60° and 45°S and from −0.18 to −0.21‰ per decade between 35° and 40°N (Figure 6). Gruber et al.  estimated a δ13C decrease rate of −0.15 ± 0.06‰ per decade in the tropical Pacific based on a comparison of δ13C measurements made on equatorial cruises during the 1980s and 1990s. All of these independent estimates of the surface δ13C decrease agree, both in magnitude and meridional trend, with the surface δ13C decrease derived from the snapshot comparison of the HUDSON and RITS93 cruises (Figure 6). We estimated a basin-wide δ13C decrease of −0.18‰ per decade for the Pacific (60°S–55°N) based on the estimates of δ13C decrease shown in Figure 6 and using the meridional trend of the δ13C change derived from the HUDSON versus RITS comparison to interpolate over latitudes. (Note: As discussed below, there is a mean 0.14‰ offset between δ13C values measured for deep waters (>2000 m) during the HUDSON and WOCE cruises. If we corrected the surface δ13C data from HUDSON for this offset, a 0.06‰ per decade correction, a larger δ13C change is calculated and the agreement with the other independent estimates degrades substantially (Figure 6). For the purpose of interpolation, therefore, we use the time rate of δ13C change calculated using uncorrected HUDSON surface data.)
 In the Indian Ocean, the surface water δ13C time rate of change over the last ∼20 years has been estimated based on a snapshot comparison of GEOSECS and WOCE δ13C measurements [Gruber et al., 1999], preformed δ13C calculations [Sonnerup et al., 1999], and a multiple regression method used to compare GEOSECS and WOCE δ13C data [Sonnerup et al., 2000]. Gruber et al.  estimated a surface δ13C decrease of −0.20 ± 0.04‰ per decade (area-weighted) between 35°S and 5°N based on the changes observed between GEOSECS (1978) and WOCE (1995). The small number of GEOSECS surface δ13C data (n = 46), especially south of 30°S where only six measurements were made (Figure 4), limits the certainty of this direct comparison. Sonnerup et al.  determined surface δ13C change rates of −0.12 to −0.18‰ per decade between 48°S and 35°S based on the calculated time rate of change of preformed δ13C along isopycnals (Figure 6). Sonnerup et al.  used a multiple linear regression approach to estimate the surface δ13C change between GEOSECS and WOCE that had two advantages: first, it used all the GEOSECS stations, not just the ones where δ13C was measured and, second, it was not sensitive to seasonal biasing. For example, the scatter of the snapshot-derived estimates of surface δ13C change is much greater than that of the regression-derived estimate (Figure 6) and likely resulted from seasonal biasing. The mean δ13C change in the Indian Ocean between 5°N and 60°S, based on the values presented in Figure 6, yielded a basin-wide change of −0.14‰ per decade between 1978 and 1995.
 In the North Atlantic, the surface δ13C change is determined by comparing measurements in 1981–1983 [Gruber et al., 1999] during Transient Tracers in the Ocean (TTO) and in 1992–1995 during RITS and other cruises (Figure 4). This snapshot comparison yielded a δ13C decrease of −0.22 ± 0.02‰ per decade for the subtropics (15°–45°N) that agreed well with the δ13C decrease rates of −0.25 ± 0.02‰ per decade measured at Station S (32°N 64°W) between 1984 and 1995 [Bacastow et al., 1996; Gruber et al., 1999] and −0.24 to −0.27‰ per decade determined by Körtzinger et al.  from the time rate of change of preformed δ13C along isopycnal surfaces that outcrop at subtropical latitudes in the North Atlantic. The northward decrease in the δ13C time rate of change derived from the snapshot comparison (Figure 6) agreed well with a similar trend determined by the time rate of change of preformed δ13C along isopycnals in the North Atlantic by Sonnerup et al.  and Körtzinger et al. . However, the δ13C time rates of change determined from preformed δ13C changes for subpolar latitudes (>50°N) were greater than the rates calculated from the snapshot comparison (Figure 6). This difference may result from the seasonal biasing of the snapshot method. The TTO cruises occurred between April and October whereas the RITS cruises were in July and August when a summertime increase of up to 1‰ in the surface δ13C can occur at these latitudes [Gruber et al., 1999]. For the North Atlantic, the area-weighted δ13C decrease rate between 10°S and 65°N, based on the values presented in Figure 6, was −0.19‰ per decade.
 The ocean-wide surface δ13C change between the 1970s and 1990s was −0.16‰ per decade based on the estimates of −0.18, −0.14, and −0.19‰ per decade for the Pacific, Indian and Atlantic oceans, respectively. It was assumed that there was no surface δ13C decrease south of 60°S, based on the insignificant δ13C decrease observed south of 60°S in the Pacific and Indian oceans (Figure 6), and that the surface δ13C decrease rate in the South Atlantic was equal to that calculated for the South Pacific and Indian oceans at −0.17‰ per decade. Although individual estimates of the δ13C change (e.g., measurements at Station S and ALOHA, estimates based on preformed δ13C calculations, snapshot comparisons at specific locations) have typical uncertainties of ±0.05‰ per decade [e.g., Bacastow et al., 1996; Gruber et al., 1999; Sonnerup et al., 1999], the uncertainties in the basin- and ocean-wide mean surface δ13C change are significantly lower. A Monte Carlo method was used to determine the uncertainty of the area-weighted mean δ13C change rate for the Pacific, Atlantic and Indian oceans (Figure 6). In this procedure, a mean δ13C time rate of change and its standard deviation (SD) was determined for every 5°-latitude band. Then randomly selected values for the δ13C time rate of change for each latitude band were chosen, with a probability based on an assumed normal distribution described by the mean and SD. A basin-wide mean δ13C change rate was determined by area-weighting the time rate of change of each latitude band. This procedure was repeated 1000 times and the mean basin-wide δ13C time rate of change and its SD was determined from these 1000 values. The analysis yielded an error of ±0.02‰ per decade for the basin-wide average δ13C change. This error does not include the uncertainty introduced by systematic errors (e.g., laboratory offsets, seasonal biases, interpolation biases, etc.). However, the 0.05‰ per decade range for the mean surface δ13C change determined among the three ocean basins, utilizing different historic δ13C data sets, suggests that a ±0.02‰ per decade error is reasonable and systematic errors do not dominate. The Monte Carlo approach yielded an uncertainty of ±0.01‰ per decade for the global ocean. Previously, Sonnerup et al.  estimated a global ocean δ13C change of −0.15 to −0.17‰ per decade using a GCM-based extrapolation of the δ13C change they had determined for the Indian Ocean. Gruber et al.  estimated a global surface ocean δ13C decrease of −0.18‰ per decade between 1980 and 1995 based on their measurements at ALOHA, Station S, tropical Pacific and Indian Ocean.
 How does this surface ocean δ13C change compare to the atmospheric δ13C change? Gruber et al.  calculated an atmospheric δ13C decrease rate of −0.18 ± 0.01‰ per decade based on a regression of seasonally adjusted measurements at Mauna Loa and South Pole between 1980 and 1995 by Keeling et al. . An atmospheric δ13C decrease rate of −0.22 ± 0.03‰ per decade is determined from a linear regression of the annual mean δ13C values calculated using the monthly mean δ13C measurements at Mauna Loa and South Pole between 1978 and 1988 reported in Keeling et al. . Francey et al.  reconstructed a time history of the δ13C of atmospheric CO2 using archived air samples collected at Cape Grim, Australia, and from air samples recovered from ice cores collected in Antarctica. The Cape Grim data collected between 1978 and 1997 yielded a δ13C time rate of change of −0.23 ± 0.01‰ per decade while adding ice core-derived δ13C measurements to extend the record back to 1970 yielded a δ13C change of −0.24 ± 0.01‰ per decade. Accepting the δ13C record from Cape Grim as representative of the atmospheric change, then the surface ocean δ13C decrease of −0.16‰ per decade between the 1970s and 1990s represents ∼70% of the atmospheric δ13C decrease.
 The δ13C decrease in the surface layer of the ocean depends primarily on three factors: the atmospheric time history of the δ13C change rate, the surface ocean δ13C air-sea equilibration time, and the renewal time of the surface layer. For an isolated 75 m deep surface layer and a CO2 gas transfer rate of ∼5 m d−1, the expected δ13C decrease rate would equal about the rate of atmospheric δ13C change between 1970 and 1990. This results from the trend in the time history of the rate of atmospheric δ13C decrease, which reached a maximum in the early 1980s and has decreased since [Körtzinger et al., 2002], and the 10 year air-sea equilibration time for δ13C. Notably, the expected δ13C decrease for an isolated surface layer between 1980 and 1990 would exceed the concurrent atmospheric δ13C decrease because of the lag in air-sea δ13C equilibration and the decreasing rate of atmospheric δ13C change observed since 1980.
 If surface waters are renewed slowly, like in the subtropical ocean, then the expected δ13C decrease approaches an air-sea equilibrium condition, as illustrated above. For example, the observed δ13C decrease rate of −0.024‰ per decade at the subtropical ALOHA and BATS time-series stations approximately equals the atmospheric δ13C change rate. In contrast, where surface waters are renewed rapidly, the δ13C decrease will be slower than the atmosphere because the surface waters will not have a chance to isotopically equilibrate with the atmosphere. For example, slow surface ocean δ13C change rates of approximately −0.05‰ per decade have been observed in the Southern Ocean [McNeil et al., 2001]. Similarly, the GCM simulation of the anthropogenic δ13C change in the ocean by Bacastow et al.  predicted maximum rates of δ13C change in the subtropics of approximately −0.26‰ per decade between 1983 and 1995, minimum rates at approximately −0.06‰ per decade in the Southern Ocean and a mean ocean rate of −0.17‰ per decade. The global surface ocean δ13C decrease between 1970 and 1990 predicted by the GCM simulations by Heimann and Maier-Reimer  and Murnane and Sarmiento  at −0.13 and −0.12‰ per decade, respectively, were significantly smaller than our estimate of −0.16‰ per decade.
3.2. Air-Sea δ13C Disequilibrium
 The δ13C of the surface ocean is not in isotopic equilibrium with atmospheric CO2. If it were, the δ13C of the surface ocean would everywhere equal the δ13C of the atmospheric CO2 multiplied by the equilibrium isotope fractionation factor between CO2 gas and oceanic DIC. In the Pacific Ocean, for example, the meridional trend of the zonally averaged surface δ13C values in the 1990s varies much less than expected if the ocean were in isotopic equilibrium with atmospheric CO2 (Figure 7). Surface ocean δ13C is higher than expected at atmospheric equilibrium in the subtropical and tropical oceans and lower than expected in the polar and southern oceans. The primary reason that the surface ocean δ13C departs from atmospheric equilibrium is the ∼10 year air-sea isotopic equilibration time for the DIC pool that allows mixing and biological productivity to keep the surface ocean δ13C out of atmospheric equilibrium. The air-sea δ13C disequilibrium is defined here as the δ13C of the atmospheric CO2 expected at equilibrium with the surface ocean minus the observed δ13C of the atmosphere.
 In preindustrial times, a meridional trend of air-sea δ13C disequilibrium similar to that measured today (Figure 7) likely existed. Globally averaged, however, the preindustrial surface ocean δ13C must have been close to, but not quite at, atmospheric equilibrium. The riverine flux of organic carbon to the ocean that was not balanced by organic matter burial (∼0.6 Gt C yr−1; Siegenthaler and Sarmiento, 1993] likely kept the surface ocean δ13C value slightly lower than expected at equilibrium with atmospheric CO2 by about 0.16‰. The magnitude of this preindustrial δ13C disequilibrium can be estimated by assuming the δ13C anomaly associated with the riverine carbon flux (0.6 GtC yr−1 at −20‰) was balanced by the isotopic anomaly associated with the air-sea CO2 gas exchange flux (74 Gt yr−1 at −0.16‰). Once the atmospheric δ13C of CO2 decreased due to fossil fuel burning, the δ13C of the surface ocean decreased as some of this δ13C depleted anthropogenic CO2 was taken up by the ocean. The δ13C decrease rate in the surface ocean generally lags the δ13C decrease of the atmospheric CO2 because of the decade long air-sea isotopic equilibration time for DIC. Thus the average δ13C of the surface ocean went from being slightly lower (in preindustrial times) to slightly higher (in the industrial era) than expected at atmospheric equilibration; that is, the mean air-sea δ13C disequilibrium went from slightly negative to slightly positive.
 The importance of the air-sea δ13C disequilibrium value was pointed out by Tans et al. , who used their estimate of 0.43‰ in the 1970s to determine an oceanic CO2 uptake rate of 0.2 Gt C yr−1. Their disequilibrium estimate for the 1970s, however, was significantly uncertain due to a lack of high quality oceanic δ13C measurements. (The GEOSECS δ13C data for the Atlantic and Pacific oceans are problematic [Kroopnick, 1985] whereas those for the Indian Ocean are high quality based on a mean ±0.03‰ agreement between deep water values measured during GEOSECS and WOCE.) Recently, Gruber and Keeling  used surface ocean δ13C measurements made between 1985 and 1995 to determine a global average δ13C disequilibrium of 0.62 ± 0.10‰ for 1990.
 We calculated the air-sea δ13C disequilibrium for each ocean basin and for the global ocean using the δ13C data (n = 2500) measured during the 1990s. We calculated the average disequilibrium over 5° latitude bands using zonally averaged surface ocean δ13C measurements, which were adjusted to 1995 using δ13C time rates of change discussed above (see Figure 6), atmospheric δ13C values in 1995 from the CMDL measurement network [Trolier et al., 1996], annual mean surface ocean temperatures [Levitus and Boyer, 1994], and equilibrium isotopic fractionation effects for CO2 gas and DIC determined by Zhang et al. . The meridional trend in the δ13C disequilibrium is consistent in each ocean basin with the most positive values found in the tropics and negative values found poleward of ∼50° (Figure 8). The area-weighted average air-sea δ13C disequilibrium for the Pacific, Atlantic, and Indian oceans in the 1995 was 0.98, 0.79, and 0.60‰, respectively. Including a weighting factor proportional to the CO2 gas exchange rate [Wanninkhof, 1992] calculated from NCEP wind speeds for 1995 [Kalnay et al., 1996], the average disequilibrium decreases significantly in the Pacific, Atlantic, and Indian oceans to 0.73, 0.63, and 0.23‰, respectively. The range in mean δ13C disequilibrium between basins is primarily the result of lower surface δ13C values for the Indian Ocean (Figure 3) and higher SSTs (area-weighted) for the Pacific Ocean, which in turn reduce the air-sea δ13C equilibrium fractionation. The basin-wide values yield a global mean disequilibrium of 0.88‰ (area-weighted) and 0.60‰ (area and gas exchange rate weighted). Although this latter value compares well with the 0.62‰ value for 1990 calculated by Gruber and Keeling , the agreement is misleading. They used a 1990 global mean atmospheric δ13C value of −7.65‰, derived from measurements reported by Keeling et al. , for the disequilibrium calculation. The atmospheric δ13C measurements made at NOAA's Climate Monitoring and Diagnostics Laboratory (CMDL) network [Trolier et al., 1996] yield a global mean δ13C value of −7.78‰ in 1990. If the atmospheric δ13C measurements from CMDL for 1990 were used with the surface ocean δ13C measurements of Gruber and Keeling  a global air-sea disequilibrium of 0.75‰ would result.
 The error in the air-sea δ13C disequilibrium value is important because the rates of biospheric and oceanic uptake of CO2 determined from model inversions of the atmospheric CO2 and δ13C meridional gradients [e.g., Ciais et al., 1995; Francey et al., 1995; Keeling et al., 1995] indicate that a 0.1‰ error in the air-sea δ13C disequilibrium used in the inversion method results in a 0.5 Gt C yr−1 uncertainty in the partitioning of CO2 uptake between the biosphere and ocean [Ciais et al., 1995]. A similar sensitivity exists for the oceanic CO2 uptake rates calculated using the disequilibrium method of Tans et al. . The uncertainty in the air-sea δ13C disequilibrium depends on the uncertainties in the mean δ13C values for the surface ocean and atmosphere and in the isotopic fractionation effects during CO2 equilibration with seawater, which in turn, primarily depends on the variability of the sea surface temperature. For each 5° latitude band, the uncertainty of the disequilibrium was calculated by propagating the ±1 SD uncertainties of the sea surface temperature, surface ocean δ13C value, atmospheric δ13C value, and fractionation effect. The ±1 SD for the individual terms were ±1.5°C for the sea surface temperature [Levitus and Boyer, 1994], ±0.15‰ for the mean surface ocean δ13C, ±0.06‰ for the atmospheric δ13C [Gruber and Keeling, 2001], and ±0.05‰ for the fractionation factors [Zhang et al., 1995] which yielded an average uncertainty of ∼0.30‰ for the air-sea disequilibrium over a 5° latitude band. Another estimate of the uncertainty in the disequilibrium was obtained by calculating the disequilibrium for each individual surface δ13C measurement and then calculating the error in the mean disequilibrium value (i.e., SD/) for a given 5° latitude band. The average error derived this way was ±0.10‰ for the Pacific Ocean.
 We calculated the uncertainty in the basin- and ocean-wide mean disequilibrium using a Monte Carlo approach, as discussed above, and the mean values and SDs for the disequilibrium values calculated for 5° latitude bands in each basin. The basin- and ocean-wide uncertainty (±1 SD) in the mean disequilibrium was ±0.05‰. This error does not account for systematic errors, e.g., measurements offsets between laboratories (like that discussed above for δ13C of atmospheric CO2), temporal and spatial biases in the data, etc. One estimate of a systematic error due to spatial and temporal biasing of the oceanic δ13C measurements was obtained by calculating a synthetic global mean surface ocean δ13C distribution. This synthetic δ13C distribution was calculated by determining the relationship between measured δ13C values and SST, salinity, nitrate, phosphate, and oxygen using a multiple linear regression approach. Then the climatological mean annual values for these parameters [e.g., Levitus and Boyer, 1994] were used to determine the global distribution of the mean annual surface δ13C. The global mean air-sea δ13C disequilibrium calculated using this regression-derived δ13C distribution was 0.57‰ (area and gas exchange rate weighted) that compares well with the 0.60‰ value calculated from the δ13C data. We estimated an overall error of ±0.1‰ for the mean global air-sea δ13C disequilibrium of 0.60‰ in 1995 based on the calculated uncertainty in our mean (±0.05‰) and possible systematic errors.
3.3. Ocean δ13C Inventory Changes
 Since the depth-integrated δ13C rate of change (i.e., δ13C inventory change) depends on the oceanic uptake rate of anthropogenic CO2, measurements of the δ13C inventory change yield estimates of anthropogenic CO2 uptake rate [Quay et al., 1992]. The δ13C depth distributions measured during WOCE and OACES cruises in the 1990s yield an improved estimate of the ocean-wide δ13C inventory change. The most direct estimate of the δ13C inventory change results from comparing recent δ13C depth profiles with those collected previously at a nearby location (Figure 9). The WOCE/OACES δ13C measurements yield 23 locations where recent δ13C depth profiles can be compared with earlier ones. In the Pacific Ocean, 10 WOCE δ13C depth profiles were compared with depth profiles measured during the HUDSON, ANTIPODES and GEOSECS Test cruises between 1969 and 1971 [Kroopnick et al., 1970, 1977]. In the Indian Ocean, 13 WOCE δ13C depth profiles were compared to GEOSECS measurements in 1978 [Kroopnick, 1985]. No δ13C depth profile comparisons were made in the Atlantic Ocean because of the problems with the GEOSECS data.
 Determining the depth-integrated δ13C change using station pair comparisons requires evaluating whether an offset exists between earlier and more recent δ13C measurements. We determined the magnitude of the offset for each station using a comparison of the deep water (>2000 m) δ13C values. The deep water offsets ranged from −0.14 to 0.17‰ (Table 2) with one consistent pattern. The seven HUDSON stations had δ13C values for deep water that were lower than the WOCE values by an average of 0.14 ± 0.05‰. A similar δ13C offset between HUDSON and WOCE deep water was determined by Lerperger et al. . The comparison between WOCE and GEOSECS δ13C measurements in the deep Indian Ocean indicated no significant offset (0.02 ± 0.05‰). For every station comparison where a deep water δ13C offset was determined the entire δ13C depth profile was corrected for the offset. The depth-integrated δ13C inventory change based on individual station comparisons ranged from 0 to −179‰ m per decade with the greatest changes occurring in the Indian Ocean (Table 2). The meridional trend in δ13C inventory change is clear in both the Pacific and Indian oceans with the largest changes occurring in the subtropical gyres, smaller changes near the equator, and little or no change in the subpolar gyre and Southern Ocean (Figure 10).
Table 2. The Changes in Depth-Integrated δ13C Based on Comparisons Between Stations Collected in the 1970s and 1990s
The HUDSON and ANTIPODES cruises were in 1970 and 1971, respectively. The GEOSECS test station was in 1969 and the Indian Ocean GEOSECS was in 1978. The cruise dates for the recent cruises are found in Table 1.
The deep water (>2000 m) offset was calculated as recent δ13C minus earlier δ13C.
Estimated from average HUDSON offset of −0.14‰ because there were no deep water δ13C measurements at HUDSON-Eqt station.
Sonnerup et al.  reconstructed the change in δ13C along isopycnals due to anthropogenic CO2 uptake using measurements of δ13C and oxygen in the 1990s and determined the along-isopycnal rate of δ13C change using CFC ages of the water. Their depth-integrated δ13C changes ranged from −100 to −260‰ m per decade for the subtropical regions in the Pacific, North Atlantic and Indian oceans, with the greatest changes occurring in the North Atlantic Ocean (Figure 10). Sonnerup et al.  calculated the δ13C inventory changes between GEOSECS (1978) and WOCE (1995) in the Indian Ocean using a multiple linear regression method that was independent of the preformed method. A significant advantage of this approach was that the δ13C change was calculated for all the WOCE stations where δ13C was measured (n = 35) rather than just for the WOCE stations where a GEOSECS station was located nearby for direct comparison (n = 13). Sonnerup et al. found a clear meridional trend in the δ13C inventory change in the Indian Ocean with the largest changes (approximately −120‰ m per decade) occurring in the subtropical gyre, smaller changes in the equatorial ocean (approximately −35‰ m per decade) and little change in the Southern Ocean (approximately −10‰ m per decade). This latitudinal trend agreed well with the results of the direct station comparisons (Figure 10).
 The similarity of the meridional trend in the δ13C inventory change with that for CFC-11 and bomb 14C was noted by Sonnerup et al.  and Quay et al. , respectively. Likewise, estimates of the accumulation of anthropogenic CO2, via reconstructions [e.g., Gruber, 1998] and GCM simulations [e.g., Orr et al., 2001], show a similar meridional trend with maxima in the subtropics and minima in the equatorial and polar oceans. In this sense, the observed meridional trend in the δ13C inventory change is not surprising. The greatest inventory change for these anthropogenic tracers occurs in regions of surface water convergence and the smallest change occurs in regions of divergence. The deeper isopycnal surfaces and longer residence times for surface waters due to convergent surface Ekman flow in the subtropics result in greater accumulation rates of anthropogenic tracers. In contrast, the shallower isopycnal surfaces and shorter surface water renewal times due to divergent surface Ekman flow in the subpolar gyres, equatorial ocean, and Southern Ocean result in reduced accumulation of anthropogenic tracers.
 To extrapolate the individual station estimates of δ13C inventory change to the global ocean, we relied on the correlation between the change in δ13C inventory and accumulation of bomb 14C inventory [Quay et al., 1992]. This correlation allowed us to take advantage of the near global coverage of bomb 14C data obtained during GEOSECS. There is a significant correlation (r2 = 0.69) between the δ13C inventory change and bomb 14C inventory in 1975 [Broecker et al., 1995] for the 23 station comparisons in the Pacific and Indian oceans (Figure 11). Adding the five estimates of δ13C inventory change derived from preformed δ13C time rates of change [Sonnerup et al., 1999] improved the correlation (r2 = 0.78) significantly (Figure 11). An ocean-wide δ13C inventory change of −65 ± 33‰ m per decade for 1970–1990 was determined using a linear regression approach that accounts for errors in both variables [Ricker, 1973] and an ocean-wide average 14C burden of 8.5 × 109 atoms cm−2 [Broecker et al., 1995]. This value is significantly lower than the −104 ± 23‰ m per decade estimated by Quay et al.  based on seven depth profile comparisons in the Pacific Ocean. Since the uncertainty in the global inventory change was not reduced with the additional station comparisons, it likely represents the limit of the correlation between the anthropogenic perturbations of δ13C and bomb 14C (in 1975). Potentially, the correlation between δ13C and 14C changes might be improved using the bomb 14C inventories measured during WOCE, since the 14C perturbation time scale during WOCE (1990s) is closer to that of the δ13C inventory changes.
 A mean ocean-wide penetration depth of the δ13C change between the 1970s and 1990s of 406 ± 213 m is calculated by dividing the mean δ13C inventory change (−65 ± 33‰ m per decade) by the surface ocean δ13C change (−0.16±0.02‰ per decade).
 An oceanic CO2 uptake rate of 1.2 ± 1.2 Gt C yr−1 between 1970 and 1990 was determined from an oceanic δ13C inventory change of −65 ± 33‰ m per decade using the inventory approach (equation (1)) of Quay et al. . This same δ13C inventory change yielded an oceanic uptake rate of 2.0 ± 1.5 Gt C yr−1 using the dynamic constraint approach (equation (3)) of Heimann and Maier-Reimer . To apply the δ13C disequilibrium approach of Tans et al. , the disequilibrium value of 0.60 ± 0.10‰ estimated for 1995 had to be adjusted to an average value between 1970 and 1990 since the disequilibrium has been increasing over time. We used the BDM results to determine the relationship between the disequilibrium in 1995 and the average value between 1970 and 1990 and estimated that a mean disequilibrium of 0.48‰ for 1970–1990 corresponded to a disequilibrium of 0.60‰ in 1995. An oceanic CO2 uptake rate of 1.2 ± 1.0 Gt C yr−1 was determined from an oceanic air-sea δ13C disequilibrium of 0.48 ±0.10‰ using the Tans et al.  approach (equation (2)). The errors in the CO2 uptake rates estimated by these three approaches were determined using a Monte Carlo method incorporating ±1 SD uncertainties for each of the terms in equations (1)–(3) (Table 3). For the inventory method [Quay et al., 1992] and dynamic method [Heimann and Maier-Reimer, 1996], the error resulted primarily (∼80%) from the ±33‰ m per decade uncertainty in the δ13C inventory change. For the disequilibrium method [Tans et al., 1993], the error resulted primarily (∼50%) from the ±0.1‰ uncertainty in the air-sea δ13C disequilibrium. Previously, Heimann and Maier-Reimer  determined CO2 uptake rates of 2.3 ± 1.2, 0.6 ± 1.6, and 3.1 ± 1.6 Gt C yr−1 using the inventory, disequilibrium, and dynamic methods, respectively, and the larger δ13C inventory change (−104 ± 30‰ m per decade) and slightly smaller air-sea disequilibrium (0.43 ± 0.2‰) estimates reported in Quay et al.  and Tans et al. , respectively.
 We determined the oceanic CO2 uptake rate that satisfied all three of the above methods using a Monte Carlo method. Values for the terms in equations (1)–(3) were randomly chosen, with a probability based on their mean and standard deviations (Table 3), and values for the oceanic uptake rates were calculated using each method (i.e., equations (1)–(3)). This procedure was repeated 200,000 times and the set of three uptake rates for each random scenario was stored. Of the 200,000 scenarios, only the ones that yielded the same CO2 uptake rate (to within ±0.05 Gt C yr−1) for all three methods were selected. The mean and standard deviation of oceanic CO2 uptake rates from these selected scenarios was 1.5 ± 0.6 Gt C yr−1. Previously, Heimann and Maier-Reimer  determined an oceanic CO2 uptake rate of 2.1 ± 0.9 Gt C yr−1 that satisfied all three δ13C methods using the δ13C inventory and disequilibrium estimates reported by Quay et al.  and Tans et al. , respectively.
 In addition, we determined oceanic CO2 uptake rates using BDM simulations of the anthropogenic CO2, δ13C, and bomb 14C perturbations. Using a Monte Carlo approach we randomly selected, over large ranges, the air-sea CO2 gas transfer rate (0.5–10 m d−1) and vertical mixing rate (200–50,000 m2 yr−1) that yielded a wide range of modeled CO2 uptake rates, i.e., 0.4–4 Gt C yr−1 (mean for 1970–1990). The Monte Carlo approach was used to randomly select values for the atmospheric δ13C and Δ14C, air-sea δ13C isotopic fractionation factors and buffer factor that accounted for their uncertainties of 0.06‰, 4‰, 0.1‰, and 0.5, respectively. The CO2, δ13C, and 14C changes in the surface layer and depth-integrated inventories were then calculated for ∼8500 model scenarios. Model scenarios that yielded the observed δ13C and 14C changes in the surface layer and depth-integrated inventories were selected and the mean and SD of the CO2 uptake rates for these selected model scenarios were determined.
 A CO2 uptake rate of 2.2 ± 0.6 Gt C yr−1 (1970–1990) was determined from the BDM scenarios that yielded a δ13C inventory change of −65 ± 33‰ per decade. In this case, only 61% (i.e., f = 0.61) of the total (8500) model scenarios predicted the observed δ13C inventory change of −65 ± 33‰ m per decade. A CO2 uptake rate of 1.9 ± 0.5 Gt C yr−1 (f = 0.14) was determined for the model scenarios that yielded the observed surface ocean δ13C change rate of −0.16 ± 0.02‰ per decade. A CO2 uptake rate of 2.2 ± 0.7 Gt C yr−1 (f = 0.42) was determined for the model scenarios that yielded the observed bomb 14C inventory of 8.5 ± 1.7 × 109 atoms cm−2 in 1975 [Broecker et al., 1995]. A CO2 uptake rate of 2.2 ± 0.5 Gt C yr−1 (f = 0.11) was determined for the model scenarios that yielded the observed surface ocean bomb 14C of 155 ± 15‰ in 1975.
 The depth-integrated δ13C and 14C changes imposed weaker constraints on the randomly chosen model scenarios than the surface δ13C and Δ14C changes (as indicated by the f values). Smaller uncertainties in CO2 uptake rates determined by the BDM resulted when both surface and inventory constraints were simultaneously used to select model scenarios. The reduced uncertainty occurred because the BDM predicted depth-inventory changes are inversely correlated with the surface changes for δ13C and 14C (Figure 12). A CO2 uptake rate of 1.9 ± 0.4 Gt C yr−1 (f = 0.14) was determined for model scenarios selected that met both the surface and depth-integrated δ13C changes. A similar CO2 uptake rate of 1.8 ± 0.2 Gt C yr−1 (f = 0.04) was determined for model scenarios selected that met both the surface and depth-integrated bomb 14C changes. When the four constraints imposed on the BDM results by surface and depth-integrated changes for both δ13C and bomb 14C were combined, the CO2 uptake rate was 1.7 ± 0.2 Gt C yr−1 (f = 0.02) for 1970–1990 (corresponding to 2.0 ± 0.2 Gt C yr−1 for 1980–1990).
 The CO2 uptake rate predicted by the BDM (1.9 ± 0.4 Gt C yr−1) constrained by the observed δ13C changes was significantly higher than the uptake rates determined by the δ13C inventory (1.2 ± 1.2 Gt C yr−1) and δ13C disequilibrium (1.2 ± 1.0 Gt C yr−1) approaches and similar to the uptake rate of 2.0 ± 1.5 Gt C yr−1 determined by the dynamic approach. There are significant uncertainties in the parameters values used to calculate the CO2 uptake rates using the inventory, disequilibrium, and dynamic approaches. We found that values for the δ13C inventory change, air-sea δ13C disequilibrium, and biospheric Suess effect of −76 ± 12‰ m per decade, 0.50 ± 0.09‰ and 23 ± 6 Gt C ‰ yr−1, respectively, yielded a mean CO2 uptake rate of 1.9 ± 0.4 Gt C yr−1 by all three δ13C approaches that agreed with the BDM results. These parameter values represent only slight adjustments from their a priori values (Table 3) and are well within their respective uncertainties. These results demonstrate that the nonmodel approaches using ocean δ13C inventory changes and air-sea δ13C disequilibrium are compatible with the results of the BDM simulations, within the uncertainties of the δ13C observations.
 Following the strategy proposed by Broecker and Peng , we determined the carbon turnover time for the terrestrial biota using the a posteriori value for the biospheric δ13C Suess effect needed to make the oceanic uptake rates determined from the δ13C inventory, disequilibrium, and dynamic approaches agree with the BDM results. A biospheric 13C Suess effect of 23 ± 6 Gt C ‰ yr−1 coupled with a net terrestrial production rate of 60 Gt C yr−1 [Saugier et al., 2000] yields a biospheric δ13C disequilibrium of 0.38 ± 0.10‰. This biospheric disequilibrium represents the δ13C offset between CO2 currently taken up and released by the biosphere. This value agrees, within its uncertainty, with the values of 0.33 and 0.41‰ estimated from terrestrial biospheric models applied by Fung et al.  and Wittenburg and Esser , respectively. A mean age of 17 ± 4 years for CO2 released from the terrestrial biota is calculated by dividing the biospheric δ13C disequilibrium by the atmospheric time rate of change of 0.23‰ per decade and assuming that the photosynthetic fractionation factor has remained constant over time.
 Ocean models constrained by the anthropogenic change in surface and depth integrated δ13C yield a smaller uncertainty (by >50%) in CO2 uptake rates than either of the nonmodeling methods that utilize atmosphere and ocean CO2 and 13CO2 budgets [Quay et al., 1992; Tans et al., 1993] or the similarity between ocean penetration depths of the δ13C and CO2 perturbations [Heimann and Maier-Reimer, 1996]. This occurs primarily for two reasons. First, the lower limit of the BDM is zero CO2 uptake, whereas the analytical solutions to equations (1)–(3) can yield negative CO2 uptake rates given the uncertainty in the individual terms. Second, the uncertainty in the CO2 uptake rate derived from the BDM primarily results from the uncertainties in the measured change in the ocean's δ13C inventory or surface water. In contrast, the errors in the analytical solutions to equations (1) and (2) are also significantly affected by the error in the biospheric δ13C Suess effect. If future measurements of the anthropogenic δ13C inventory change in the ocean reduce its uncertainty by 50%, then the error in the CO2 uptake rate would decrease from ±1.2 to ±0.7 Gt C yr−1 for the δ13C inventory approach and from ±1.5 to ±0.9 Gt C yr−1 for the dynamic constraint approach, assuming the uncertainties in the other terms in equations (1) and (3) remain unchanged. If future measurements reduce the error in the air-sea δ13C disequilibrium by 50%, then the error in the CO2 uptake rate calculated by the δ13C disequilibrium approach would decrease only slightly from ±1.1 to ±1.0 Gt C yr−1.
 Despite the apparent advantage of the BDM (or GCM) approach, this method assumes the model predicted relationship between the anthropogenic δ13C and CO2 ocean change equals the observed relationship in the ocean. (This same modeling assumption is made when bomb 14C is used to adjust model estimates of anthropogenic CO2 uptake.) Until this assumption is verified, the accuracy of the model predicted CO2 uptake rates is uncertain. Initial observations of the anthropogenic δ13C versus CO2 relationship in the ocean differ substantially (∼5X) for the Southern Ocean [McNeil et al., 2001] versus the North Atlantic Ocean [Körtzinger et al., 2002]. Thus additional measurements of the anthropogenic δ13C versus CO2 change in the ocean will be required to test the model predicted relationship.
 Measurements of the ocean-wide δ13C distribution during the 1990s significantly improved the determination of the ocean δ13C changes that have occurred due to the uptake of anthropogenically produced CO2. These new data indicate that the global mean rate of δ13C inventory change was −65 ± 33‰ m per decade between the 1970s and 1990s. Between 1970 and 1990, the ocean-wide surface δ13C decrease rate of −0.16 ± 0.02‰ per decade represents about 70% of the measured atmospheric δ13C decrease over the same period [Francey et al., 1999]. The largest surface and inventory δ13C changes occurred in the subtropical gyres with smaller changes in the equatorial and polar oceans and little or no change in the Southern Ocean. The air-sea δ13C disequilibrium was determined to be 0.60 ± 0.10‰ in 1995.
 These ocean-wide δ13C changes yield CO2 uptake rates of 1.2 ± 1.2, 1.2 ± 1.0, and 2.0 ± 1.5 Gt C yr−1 (1970–1990) using three budget approaches applied previously by Quay et al. , Tans et al. , and Heimann and Maier-Reimer , respectively. BDM simulations that predict the observed surface and inventory δ13C changes yield a CO2 uptake rate of 1.9 ± 0.4 Gt C yr−1. The same oceanic CO2 uptake rate of 1.9 Gt C yr−1 would be determined by the Quay et al., Tans et al., and Heimann and Maier-Reimer approaches if the δ13C inventory change and disequilibrium values are increased only slightly, and well within the uncertainties, from the mean observed values. BDM simulations of the observed surface and inventory change for both δ13C and bomb 14C yield a CO2 uptake rate of 1.7 ± 0.2 Gt C yr−1 (1970–1990) and 2.0 ± 0.2 Gt C yr−1 (1980–1990). With the data in hand, the surface ocean changes of δ13C and bomb 14C yield stronger constraints on the CO2 uptake rates determined by the BDM than the depth-integrated changes.
 The recent high quality ocean-wide δ13C data used in this study will yield better utilization of δ13C as a tracer of anthropogenic CO2 uptake in the ocean in the future because it serves as an excellent baseline to accurately determine future ocean δ13C changes. Thus, the advantage that δ13C has as a tracer of ocean CO2 uptake; that is, it will continue to track the future atmospheric CO2 increase, will be more fully utilized. Measured ocean δ13C changes offer the opportunity to use both budget and model approaches to determine oceanic (and terrestrial) CO2 uptake rates. More accurate budget estimates of ocean CO2 uptake rates will serve as important tests for model simulations. Ocean model simulations that can match anthropogenic changes in δ13C (and other tracers) increase our confidence in predictions of future oceanic CO2 uptake rates and, consequentially, atmospheric CO2 levels.
 We thank everyone who has helped to collect samples for us over the last 10 years. We especially appreciated the efforts of Brian Salem, Heather Aceves, Melinda Brockington, and several UW students who have helped with both sample collection and preparation in our lab. In particular, we want to acknowledge the financial support that NOAA's Office of Global Programs, most recently provided via the Joint Institute for the Study of Atmosphere and Oceans (JISAO) under NOAA Cooperative Agreement NA67RJ0155, since we started the ocean δ13C measurement program in 1991. This is JISAO contribution 885.