1. Sarmiento and Gruber (2002) Sinks for Anthropogenic Carbon Physics Today August 2002 30-36

2. 01/23/15 Mean  = 0.4‰

3. Change in profiles of  13C from 1970 to 1991

4. Comparison of  13 C and  14 C in the Pacific

5. 12 C Mass Balance The change of atmospheric CO 2 concentrations between 1970 and 1990 depends on the time-integrated CO 2 releases from fossil fuel combustion and cement production (S ff ) and the terrestrial biosphere (S br ), CO 2 uptake by the terrestrial biosphere (S bh ), and net CO 2 uptake by the ocean (S oc ). This dependency is expressed as: V(C t - C o ) = (S ff + S br - S bu – S oc )  t (1) where V is the volume of the atmosphere (3.9 x 10 18 M 3 ), C is the atmospheric CO 2 concentration (grams of carbon per cubic meter), t refers to 1990, o refers to 1970, S is a CO 2 source or sink flux (grams of carbon per year), and  t is 20 years. Because 99% of the carbon atoms exist as the 12 C isotope, Eq. 1 represents essentially the time rate of change of the 12 C0 2 species. The net biospheric CO 2 flux is represented by S br - S bu.

6. Because the net oceanic CO 2 uptake between 1970 and 1990 equals the oceanwide increase in the depth-integrated concentration of DIC, Eq. 1 can be expressed as: V(C t - C) = (S ff + S br – S bu )  t – A oc ∫ (DIC t - DIC C ) dz (2) where A oc is the global ocean surface area (361 x 10 12 m 2 ), DIC is the DIC 12 concentration (grams of carbon per cubic meter), and z is ocean depth. S oc  t = A oc ∫ (DIC t - DIC C ) dz

7. The change of the concentration of atmospheric 13 C0 2 between 1970 and 1990 can be expressed, with the use of a formulation similar to Eq. 2, as: V [C t ( 13 C/ 12 C) at - C o ( 13 C/ 12 C) ao ] = [S ff ( 13 C/ 12 C) ff + S br ( 13 C/ 12 C) br -S bu ( 13 C/ 12 C) bu ]  t - A 0C ∫ [DIC t ( 13 C/ 12 C) st - (DIC o ( 13 C/ 12 C) so ] dz (3) where ( 13 C/ 12 C) at, ( 13 C/ 12 C) ff, ( 13 C/ 12 C) br and ( 13 C/ 12 C) bu, represent the isotopic compositions of CO 2 in the atmosphere, CO 2 released from fossil fuel combustion and cement production, and CO 2 released from and taken up by the biosphere, respectively. ( 13 C/ 12 C) s represents the isotopic composition of oceanic DIC. Note: use 13 C/ 12 C ratio calculated from  13 C = ( 13 C/ 12 C sample / 13 C/ 12 C std - 1) x 1000 13 C mass balance

8. In order to describe the change in the atmospheric 13 CO 2 concentration in terms of the measured change in the depth integrated 13 C/ 12 C ratio of the DIC, the change in the oceanic DIC 13 concentration is expressed as the sum of the changes in the oceanic DIC 12 concentration and the ( 13 C/ 12 C) of the DIC, as follows: [DIC t ( 13 C/ 12 C) st – DIC o ( 13 C/ 12 C) so ] = ( 13 C/ 12 C) st (DIC t – DIC o ) + DIC o [( 13 C/ 12 C) st - ( 13 C/ 12 C) so ] (4) The change in atmospheric 13 CO 2 concentration can be expressed as: V [C t ( 13 C/ 12 C) at - C o ( 13 C/ 12 C) ao ] = [S ff ( 13 C/ 12 C) ff + S br ( 13 C/ 12 C) br -S bu ( 13 C/ 12 C) bu ]  t -{( 13 C/ 12 C) st }A oc ∫ [DIC t - DIC o ] dz - {DIC o } A oc ∫ [( 13 C/ 12 C) st - ( 13 C/ 12 C) so dz (5) where the {DIC o } and {( 13 C/ 12 C) st terms represent values averaged over the integration depth.

9. The net oceanic CO 2 uptake rate (S oc ) can be expressed in terms of the measured changes in the concentration and 13 C/ 12 C ratio of atmospheric CO 2 and changes in the depth integrated 13 C/ 12 C ratio of the DIC by substituting for S br and A oc ∫ [DIC t – DIC o ] dz in Eq. 5 as follows: S oc [{( 13 C/ 12 C) st } - ( 13 C/ 12 C) br ] = S ff [( 13 C/ 12 C) ff - ( 13 C/ 12 C) br ] -S bu [( 13 C/ 12 C) bu - ( 13 C/ 12 C) br ] + (V/  t )(C t -C o )( 13 C/ 12 C) br -(V/  t)[C t ( 13 C/ 12 C) at - C o ( 13 C/ 12 C) ao ] - {DIC o }(A oc )/  t ∫ [( 13 C/ l2 C) st - ( 13 C/ 12 C) so ] dz (6)  13 C ff = -27.2‰ (for C3 plants)  13 C B = -8‰ atmCO 2 : 324.0 to 351.0 ppmv   3 Catm CO 2 (1970 to 1990): -7.36 to -7.76 ∫ 13 C/ 12 C = -208‰ m from Fig 5

10. Inverse estimates of anthropogenic CO 2 uptake, transport, and storage by the ocean S. E. Mikaloff Fletcher,S. E. Mikaloff Fletcher, N. Gruber, A. R. Jacobson, S. C. Doney, S. Dutkiewicz,N. Gruber,A. R. Jacobson,S. C. Doney,S. Dutkiewicz, M. Gerber,M. Gerber, M. Follows, F. Joos, K. Lindsay, D. Menemenlis, A. Mouchet,M. Follows,F. Joos,K. Lindsay,D. Menemenlis,A. Mouchet, S. A. Müller,S. A. Müller, J. L. SarmientoJ. L. Sarmiento (2006) Global Biogeochemical Cycles GB2002 Regional air-sea fluxes of anthropogenic CO 2 are estimated using a Green's function inversion method that combines data-based estimates of anthropogenic CO2 in the ocean with information about ocean transport and mixing from a suite of Ocean General Circulation Models (OGCMs). We employ 10 OGCMs (3-D Models)and three scenarios representing biases in the data-based anthropogenic CO 2 estimates. On the basis of the prescribed anthropogenic CO 2 storage, we find a global uptake of 2.2 ± 0.25 Pg C yr −1, scaled to 1995.

11. Meridional section of global zonally averaged anthropogenic CO 2 (μmol kg −1 ) used to constrain the inversion. Anthropogenic CO 2 was estimated from dissolved inorganic carbon measurements using the ΔC* method of Gruber et al. [1996]. Excess CO 2 C* = C meas – C/O 2 AOU Zonal average section used to constrain the model inversions

12. The 24 regions used for the ocean inversion.

13. Table 1. Evaluation of Model Skill Based on comparisons between CFC-11 model Simulations and the GLODAP Gridded CFC Data Set Inverse Anthropogenic CO 2 Uptake, Pg C yr -1 scaled to 1995 (uptake required to recreate the C* distribution) BERN 2.05 ECCO 2.01 MIT 2.22 NCAR 2.18 PRINCE-LL 1.85 PRINCE-HH 2.33 PRINCE-LHS 1.99 PRINCE-2 2.17 PRINCE-2ª 2.25 UL 2.81 Mean 2.18 ± 0.25 Variability due to different K Z in the models

14. Inverse estimates of anthropogenic CO 2 uptake by the ocean (Pg C yr −1 ) for a nominal year of 1995 (positive values indicate flux into the ocean). Greatest uptake in the Southern Ocean (especially subpolar) (0.51 GtC y -1 )

15. Zonally and temporally integrated anthropogenic CO 2 uptake by (top) the global ocean, (middle) the Atlantic Ocean, and (bottom) the Indo-Pacific Ocean from 1765–1995.

16. Conclusions: The Green's function inverse approach presented here is currently the only method that has been applied globally to estimate the air-sea flux of anthropogenic CO 2 from data- based estimates of its ocean interior distribution. Our investigation using a suite of ten OGCMs suggests that the inversely estimated fluxes of anthropogenic CO 2 are generally insensitive to potential biases introduced by OGCM transport and mixing. This is not the case for all regions, though, as substantial uncertainties persist in a few of them, particularly in the Southern Ocean. We conclude that our best estimate for the oceanic uptake rate of anthropogenic CO 2 for a nominal year of 1995 is 2.2 Pg C yr −1, with an uncertainty due to errors in OGCM transport of ±0.25 Pg C yr −1. The ocean inversion provides strong constraints for the global budget of anthropogenic CO 2, in particular the net uptake by the terrestrial biosphere.

17. Figure 1. The δ 13 C values for surface water dissolved inorganic carbon (DIC) along 110°W (P18) in the eastern South Pacific Ocean are shown for 1994 (open circles, World Ocean Circulation Experiment (WOCE)) and 2008 (filled squares, Climate Variability (CLIVAR)). Inset shows sampling locations along 110°W. Young Ho Ko, Kitack Lee, Paul D. Quay and Richard A. Feely (2014) Decadal (1994–2008) change in the carbon isotope ratio in the eastern South Pacific Ocean. Global Biogeochemical Cycles  nearly homogeneous 1994 2008  t = 14 years

18. 1994 2008 13 C sections

19. The change in 13 C between 1994 and 2008 due to uptake of anthropogenic carbon. White line are CFC concentrations. Change in 13 C from 1994 to 2008