The ΔC* Technique

The ΔC* calculation used for this study is essentially the same as that originally described by Gruber et al. (1996) with two small differences: a modification of the preformed alkalinity term, TALK°, based on the new global survey data and the addition of a denitrification term in the biological correction:

ΔC* = C_m-C_eq280+117/170(O-O_sat)- 1/2(TALK-TALK°-16/170(O-O_sat))+106/104N*_anom  (2)

where C_m, TALK and O are the measured TCO₂, total alkalinity and dissolved oxygen concentrations for a given water sample in µmol/kg, O_sat is the calculated oxygen saturation value that the waters would have at their potential temperature and one atmosphere total pressure (i.e. if they were adiabatically raised to the surface), and N*_anom is the N* anomaly described later in this section. The stoichiometric ratios used here are from Anderson and Sarmiento (1994). C_eq280 is the TCO₂ the waters would have in equilibrium with a preindustrial atmosphere based on a linearized form of the Goyet and Poisson (1989) carbon equilibrium constants (Gruber et al. 1996):

 C_eq280 = 2072.0-8.982*(T-9.0)-4.931*(S-35.0)+0.842*(TALK°-2320.0)  (3)

The TALK° formulation of Gruber et al. (1996) was based on a multiple linear regression fit of surface TALK values from the GEOSECS, SAVE, and TTO cruises. Sabine et al. (1999) reevaluated this term with respect to the WOCE/JGOFS Indian Ocean data and found that the Gruber et al. values were biased low by about 7 µmol/kg. A revised equation was derived based on 2250 data points in the upper 60 m. The revised TALK° equation has an estimated standard error of ±8 µmol/kg: 

TALK° = 378.1(±9) + 55.22(±0.2)*S + 0.0716(±0.004)*PO 1.236(±0.07)* Θ (4)

where S is salinity, PO is a quasi-conservative tracer similar to that introduced by Broecker (1974) (PO = dissolved oxygen170*phosphate), and Θ is the potential temperature. A standard ANOVA analysis of the fit shows that all four terms were highly significant.

The TALK° term was re-examined again with respect to the Pacific data set. Neither the Sabine et al.(1999) nor the Gruber et al. (1996) equations were found to fit the shallow Pacific data perfectly. Both equations overestimated the alkalinity at low values and underestimated at higher values. A new equation was derived by Sabine et al. (2002) using all of the Pacific alkalinity data shallower than 60 m (~1900 data points). The standard error in the Pacific TALK° equation is ±9 µmol/kg.

TALK° = 148.7(±9) + 61.36(±0.3)*S + 0.0941(±0.005)*PO 0.582(±0.07)* Θ (5)

Sabine et al. (1999) also proposed a correction to the biological adjustment in (1) to account for denitrification in the water column. Denitrification remineralizes carbon with a very different stoichiometric ratio to nitrogen than standard aerobic respiration (Anderson 1995; Gruber and Sarmiento 1997):

C₁₀₆H₁₇₅O ₄₂N₁₆P + 150 O₂ = 106 CO₂ + 16 HNO₃ + H₃PO₄ + 78 H₂O,   (6)

C₁₀₆H₁₇₅O ₄₂N₁₆P  + 104 NO₃^- = 4 CO₂ + 102 HCO₃- + 60 N₂+ HPO₄^2- + 36 H₂O.  (7)

Sabine et al. estimated the denitrification signal using the N* tracer of Gruber and Sarmiento (1997). A slightly more generalized version of this equation has since been proposed by Deutsch et al. (2001):

N* = N 16*P +2.90.     (8)

The only change from the Gruber and Sarmiento (1997) equation was that the original equation was scaled by a factor of 0.87. The revised equation is simpler and is more general because it removes built in assumptions about the nitrogen loss from the organic reservoir (Deutsch et al. 2001). In practice, this modification actually has no impact on the final denitrification corrections since that signal is identified as an N* anomaly from the mean. The mean N* value for the Pacific data set was 1.5 µmol/kg, in agreement with the findings of Deutsch et al. (2001). The denitrification stoichiometric ratio of 106/104 from (7) (Gruber and Sarmiento, 1997) was used to correct the ΔC* values in (2) where N* showed a negative anomaly. The distribution of the anomalies (i.e. in the Arabian Sea, the eastern Tropical Pacific and to a lesser extent in the western subtropical North Pacific) also agrees with Deutsch and is discussed in detail in that work.

Determining ΔC_diseq

Rearrangement of (1) shows that ΔC* reflects both the anthropogenic signal and the preserved air-sea CO₂ difference expressed in terms of TCO₂ (i.e. ΔC* = C_anth + ΔC_diseq). For given isopycnal surfaces, the air-sea disequilibrium component can be discriminated from the anthropogenic signal using either information about the water age (e.g. from transient tracers such as CFCs or ³H-³He) or the distribution of ΔC* in regions not affected by the anthropogenic transient.  In the case where C_anth can be assumed to be zero over some portion of an isopycnal surface (i.e. ΔC* = 0 + ΔC_diseq), the disequilibrium term is set equal to the average of the ΔC* values for that portion of the surface. For shallow surfaces, that cannot be assumed to be free of anthropogenic CO₂, we use the ΔC*_t term of Gruber et al. (1996). ΔC*_t 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 are evaluated with respect to the CO₂ concentration the atmosphere had when the waters were last at the surface based, in this study, on the concentration ages determined from CFC-12 measurements (ΔC*_t12):

ΔC*_t12 = C_m-C_eqt+117/170(O-O_sat)-1/2(TALK-TALK°- 16/170(O-O_sat))+106/104N*_anom,  (9)

where C_eqt is TCO₂ calculated from TALK° and the atmospheric fCO₂ value at the time the waters were last at the surface (date of sample collection minus CFC age). The ΔC_diseq terms for these surfaces are then set equal to the mean of the ΔC*_t12 values on each surface.

The application of ΔC*_t12 is most easily explained with a figure (CLICK HERE). Panel (a) of the figure shows the measured TCO₂ concentration on an isopycnal surface in the Indian Ocean. The only outcrop of that surface is on the left hand side of the figure, at roughly 65°S. There is an increase of appoximately 140 µmol/kg on this surface from the remineralization of organic matter as the waters move into the ocean's interior. Correcting the waters for biology and the thermodynamic equilibrium concnetration gives a very different trend (see panel b). Note that the Y-scale is significantly smaller and the highest values are now closest to the outcrop in the south with a total range of about 30 µmol/kg. The third panel, (c), shows the ΔC*_t12 values plotted as a function of CFC-12 age. One can see that the mean disequilibrium value for this surface is about -20 µmol/kg. Subtracting 20 from the values in the middle panel, (b), then gives the anthropogenic CO₂ for that surface.

One must take great care in doing these calculations because the ΔC* and ΔC*_t12 approaches are only valid for limited portions of the water column and blindly applying these approches in regions that are not appropriate can result in inaccurate values that may appear to be valid. Please read the literature carefully before attempting these calculations.

References

• Anderson, L.A. 1995. On the hydrogen and oxygen content of marine phytoplankton, Deep-Sea Research I, 42:1675-1680.
• Anderson, L.A. and J.L. Sarmiento. 1994. Redfield ratios of remineralization determined by nutrient data analysis, Global Biogeochemical Cycles, 8:65-80.
• Broecker, W.S.1974. A conservative water-mass tracer, Earth Planet. Sci. Lett., 23, 100-107.
• Deutsch, C., N. Gruber, R.M. Key, J.L. Sarmiento, and A Ganachaud. 2001. Denitrification and N₂ fixation in the Pacific Ocean, Global Biogeochemical Cycles, 15:483-506.
• Goyet, C. and A. Poisson. 1989, New determination of carbonic acid dissociation constants in seawater as a function of temperature and salinity, Deep-Sea Research, 36:2635-1654.
• Gruber, N., J.L. Sarmiento and T.F. Stocker. 1996. An improved method for detecting anthropogenic CO₂ in the oceans, Global Biogeochemical Cycles, 10:809-837.
• Gruber, N. and J.L. Sarmiento. 1997. Global patterns of marine nitrogen fixation and denitrification, Global Biogeochemical Cycles 11:235-266.
• Sabine, C.L., R.M. Key, K.M. Johnson, F.J. Millero, A. Poisson, J.L. Sarmiento, D.W.R. Wallace and C.D. Winn. 1999. Anthropogenic CO₂ inventory of the Indian Ocean, Global Biogeochemical Cycles 13:179-198.
• Sabine, C.L., R.A. Feely, R.M. Key, J.L. Bullister, F.J. Millero, K. Lee, T.-H. Peng, B. Tilbrook, T. Ono, and C.S. Wong. 2002. Distribution of anthropogenic CO₂ in the Pacific Ocean, Global Biogeochemical Cycles, 16:4