Brewer (1978) and Chen and Millero (1979) made the first attempts to separate the relatively small anthropogenic TCO2 signal from measured TCO2 values nearly 25 years ago. They assumed that anthropogenic CO2 could be estimated by correcting measured sub-surface TCO2 concentrations for the contributions of organic matter decomposition and dissolution of carbonate minerals and taking into account the TCO2 concentration the water had in the preindustrial ocean when it was last in contact with the atmosphere, referred to as preformed TCO2 . Since the preindustrial ocean TCO2 concentrations were not measured, the large preformed TCO2 component was estimated from empirical relationships with nutrients and temperature and an assumption that the deep ocean contains no anthropogenic CO2. Gruber et al. (1996) improved the separation method by defining a quasi-conservative tracer, C*, that separates the preformed T2 into an equilibrium component that can be calculated from thermodynamics, and a substantially smaller disequilibrium component. Another strength of this approach is that it is not as strongly affected by mixing as the former methods. The separation can be summarized by:
TCO2(anth) (µmol/kg) = TCO2(meas) – ΔTCO2(bio) – TCO2(eq) – ΔTCO2(diseq) (1)
Where TCO2(anth) is the anthropogenic CO2 concentration of a sub-surface water sample; TCO2(meas) is the measured TCO2 concentration; ΔTCO2(bio) is the change in TCO2 as a result of biological activity (both organic carbon and CaCO3 cycling); TCO2(eq) is the TCO2 of seawater (at the temperature, salinity, and preformed alkalinity of the sample) in equilibrium with a pre-industrial CO2 partial pressure of 280 µatm; and ΔTCO2(diseq) is the air-sea CO2 disequilibrium a water parcel had when it was last in contact with the atmosphere, expressed in µmol/kg of TCO2
The first three terms on the right side of the equation can be calculated explicitly for each water sample and are called ΔC*:
ΔC* = TCO2(meas) - TCO2(eq) + 117/170(O2 - O2(sat)) - 1/2(TALK - Alk0 - 16/170(O2 - O2(sat))) + 106/104N*anom (2)
where TCO2(meas), TALK, and O2 are the measured concentrations for a given water sample in µmol/kg; Alk0 is the preformed alkalinity value; O2(sat) is the calculated oxygen saturation value that the waters would have if they were adiabatically raised to the surface; and N*anom is the net denitrification signal in the waters. Alk0 was estimated for each basin using a multiple linear regression of the surface alkalinity values to conservative tracers.
For any given water parcel in the interior of the ocean, the net air-sea disequilibrium value represents the weighted average of individual air-sea disequilibria from various source waters. We adopted an optimum multiparameter (OMP) analysis to evaluate the relative contributions of the different water sources on individual isopycnal surfaces. Two methods were then used to estimate the disequilibrium correction, ΔTCO2(diseq), for the different water sources (Eq. 1). For shallow or ventilated isopycnal surfaces that contain measurable levels of chlorofluorocarbons (CFC), the ΔTCO2(diseq) terms for the water sources were derived from the CFC-12 corrected ΔC* calculation, ΔC*t12. ΔC*t12 is derived in the same manner as ΔC*, but rather than evaluating the carbon concentration the waters would have in equilibrium with a preindustrial atmosphere, they were evaluated with respect to the CO2 concentration the atmosphere had when the waters were last at the surface based on the concentration ages determined from CFC-12 measurements. For isopycnal surfaces located in the interior of the ocean where CFC-12 is absent and where one can reasonably assume that there is no anthropogenic CO2, the ΔC* values in these waters are equal to ΔTCO2(diseq). To ensure that the ΔTCO2(diseq) values for deep density surfaces were not contaminated with anthropogenic CO2, we only used ΔC* values showing no obvious trend along the isopycnal surface.
Anthropogenic CO2 was estimated for the Indian (Sabine et al. 1999), Pacific (Sabine et al. 2002), and Atlantic (Lee et al. 2003) basins individually as the data were synthesized. A global anthropogenic CO2 inventory was determined by objectively gridding (Sarmiento et al. 1982) the individual basin estimates onto 33 depth surfaces with one degree resolution. These three sets of maps where merged with a fourth set of maps that was separately generated for the Southern Ocean. An error weighted mean was calculated for grid cells with more than one estimated value. Since the global survey had limited data coverage in the marginal basins (the South China Sea/Indonesian region, Yellow Sea, Japan/East Sea, Sea of Okhotsk, Gulf of Mexico, North Sea, Mediterranean Sea, and the Red Sea) and the Arctic Ocean (north of 65°N), these areas were excluded from the mapped regions.
The uncertainty in the total inventory is estimated to be approximately 16% based on uncertainties in the anthropogenic CO2 estimates and mapping errors. Uncertainties in the former arise from both random errors and potential biases. The random errors, including the precision of the original measurements, have been estimated to be about ±8 µmol/kg (Gruber et al. 1996; Sabine et al. 1999; Sabine et al. 2002; Lee et al. 2003; Gruber et al. 1998). This estimate is about twice as large as the standard deviation of the ΔC* values below the deepest anthropogenic CO2 penetration depth suggesting that the propagated errors may be a maximum estimate of the random variability. Based on these estimates, the limit of detection for this technique is assumed to be approximately 5 µmol/kg. The impact of these random errors on the uncertainty of the inventory is negligible, as a large number of samples were averaged to estimate the inventory.
The potential biases in the technique are much more difficult to evaluate and could include errors in the 1) biological correction resulting from the assumed stoichiometric relationships, 2) water mass age estimates based on CFCs, 3) assumption of minimal diapycnal mixing, 4) assumption that oxygen was in equilibrium in surface waters and 5) that the air-sea disequilibrium term is constant over time. Biases in the technique have been primarily evaluated with sensitivity studies and comparisons with other approaches (e.g. Gruber et al. 1996; Sabine et al. 1999; Sabine et al. 2002; Lee et al. 2003; Gruber et al. 1998; Wanninkhof et al. 1999; Coatanoan et al. 2001; Sabine and Feely 2001). These studies estimated the potential biases to be about 10-15%. The mapping errors can be estimated from the objective mapping calculations (Sarmiento et al. 1982), but are also difficult to assess quantitatively since the mapping errors are highly correlated both vertically and horizontally (Key et al. 2004). We assume that their contribution is smaller than 15%.
To arrive at a full global ocean inventory, Sabine et al. (2004) assume that the inventory in the unmapped regions south of 65oN (the marginal basins) scales with ocean surface area. This adds about 6 Pg C to the total. Including the Arctic Ocean (defined here as all ocean north of 65oN) using an area scaling approach would increase the total by about 3-4% to 116.5 Pg C. Willey et al. (2003) found that the Arctic Ocean accounted for approximately 5% of the global ocean CFC inventory in 1994. Given the correlation between CFC and anthropogenic CO2 inventories (McNeil et al. 2003), we adopt the scaling based on CFC inventories for the Arctic Ocean, and arrive at a final global anthropogenic CO2 inventory estimate of 118±19 Pg C. This inventory pertains to a nominal year of 1994, approximately the median year of our oceanographic measurements.
Fig. 1 shows representative sections of anthropogenic CO2 for each of the ocean basins. Surface values range from about 45 to 60 µmol/kg. The deepest penetrations are observed in areas of deep (e.g. North atlantic and intermediate (e.g. 40 - 50ºS) water formation. Integrated water column inventories of anthropogenic CO2 exceed 60 moles m-2 in the North Atlantic ( Fig. 2). Areas where older waters are upwelled, like the high latitude waters around Antartica and Equatorial Pacific waters, show relatively shallow penetration. Consequently, in these regions, anthropogenic CO2 inventories are all less than 40 moles m-2 (Fig. 2).
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