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

01/23/15 Mean D = 0.4‰ Compare 1970 with 1990

Change in profiles of d13C from 1970 to 1991 Need depth integrated change in global ocean d13C

Comparison of d13C and D14C in the Pacific. Similar distributions. Use ocean average bomb 14C of 8.9 x 109 atoms 14C/cm2 Calculate integrated d13C = 208 ‰m

12C Mass Balance The change of atmospheric CO2 concentrations between 1970 and 1990 depends on the time-integrated CO2 releases from fossil fuel combustion and cement production (Sff) and the terrestrial biosphere (Sbr), CO2 uptake by the terrestrial biosphere (Sbh), and net CO2 uptake by the ocean (Soc). This dependency is expressed as: V(Ct - Co) = (Sff + Sbr - Sbu – Soc)Dt (1) where V is the volume of the atmosphere (3.9 x 1018 M3), C is the atmospheric CO2 concentration (grams of carbon per cubic meter), t refers to 1990, o refers to 1970, S is a CO2 source or sink flux (grams of carbon per year), and Dt is 20 years. Because 99% of the carbon atoms exist as the 12C isotope, Eq. 1 represents essentially the time rate of change of the 12C02 species. The net biospheric CO2 flux is represented by Sbr - Sbu.

Because the net oceanic CO2 uptake between 1970 and 1990 equals the oceanwide increase in the depth-integrated concentration of DIC, Eq. 1 can be expressed as: V(Ct - C) = (Sff + Sbr – Sbu) Dt – Aoc ∫ (DICt - DICC) dz (2) where Aoc is the global ocean surface area (361 x 1012 m2), DIC is the DIC12 concentration (grams of carbon per cubic meter), and z is ocean depth. Soc Dt = Aoc ∫ (DICt - DICC) dz

13C mass balance The change of the concentration of atmospheric 13C02 between 1970 and 1990 can be expressed, with the use of a formulation similar to Eq. 2, as: V [Ct (13C/12C)at - Co (13C/12C)ao] = [Sff (13C/12C)ff + Sbr (13C/12C)br -Sbu(13C/12C)bu]Dt - A0C ∫ [DICt (13C/12C)st - (DICo (13C/12C)so] dz (3) where (13C/12C)at, (13C/12C)ff, (13C/12C)br and ( 13C/ 12C)bu, represent the isotopic compositions of CO2 in the atmosphere, CO2 released from fossil fuel combustion and cement production, and CO2 released from and taken up by the biosphere, respectively. (13C/12C)s represents the isotopic composition of oceanic DIC. Note: use 13C/12C ratio calculated from d13C = (13C/12Csample/13C/12Cstd - 1) x 1000

In order to describe the change in the atmospheric 13CO2 concentration in terms of the measured change in the depth integrated 13C/12C ratio of the DIC, the change in the oceanic DIC13 concentration is expressed as the sum of the changes in the oceanic DIC12 concentration and the (13C/12C) of the DIC, as follows: [DICt(13C/12C)st – DICo(13C/12C)so] = (13C/12C)st (DICt – DICo) + DICo[(13C/12C)st - (13C/12C)so] (4) The change in atmospheric 13CO2 concentration can be expressed as: V [Ct (13C/12C)at - Co (13C/12C)ao] = [Sff (13C/12C)ff + Sbr (13C/12C)br -Sbu (13C/12C)bu] Dt -{(13C/12C)st}Aoc ∫ [DICt - DICo] dz - {DICo} Aoc ∫ [(13C/12C)st - (13C/12C)so dz (5) where the {DICo} and {(13C/12C)st terms represent values averaged over the integration depth.

The net oceanic CO2 uptake rate (Soc) can be expressed in terms of the measured changes in the concentration and 13C/12C ratio of atmospheric CO2 and changes in the depth integrated 13C/12C ratio of the DIC by substituting for Sbr and Aoc ∫ [DICt – DICo] dz in Eq. 5 as follows: Soc [{(13C/12C)st} - (13C/12C)br] = Sff [(13C/12C)ff - (13C/12C)br] -Sbu[(13C/12C)bu- (13C/12C)br] + (V/Dt)(Ct-Co)(13C/12C)br -(V/Dt)[Ct(13C/12C)at - Co(13C/12C)ao] - {DICo}(Aoc)/Dt ∫ [(13C/l2C)st - (13C/12C)so] dz (6) d13Cff = -27.2‰ (for C3 plants) d13CB = -8‰ atmCO2: 324.0 to 351.0 ppmv d13Catm CO2 (1970 to 1990): -7.36 to -7.76 ∫13C/12C = -208‰ m from Fig 5 Soc = 2.1 Gt y-1 Sbr –Sbu = - 0.1 Gt y-1

Inverse estimates of anthropogenic CO2 uptake, transport, and storage by the ocean S. E. Mikaloff Fletcher, N. Gruber, A. R. Jacobson, S. C. Doney, S. Dutkiewicz, M. Gerber, M. Follows, F. Joos, K. Lindsay, D. Menemenlis, A. Mouchet, S. A. Müller, J. L. Sarmiento (2006) Global Biogeochemical Cycles GB2002 Regional air-sea fluxes of anthropogenic CO2 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 CO2 estimates. On the basis of the prescribed anthropogenic CO2 storage, we find a global uptake of 2.2 ± 0.25 Pg C yr−1, scaled to 1995.

Zonal average section used to constrain the model inversions Excess CO2 C* = Cmeas – C/O2 AOU Meridional section of global zonally averaged anthropogenic CO2 (μmol kg−1) used to constrain the inversion. Anthropogenic CO2 was estimated from dissolved inorganic carbon measurements using the ΔC* method of Gruber et al. [1996].

The 24 regions used for the ocean inversion.

Table 1. Evaluation of Model Skill Based on comparisons between CFC-11 model Simulations and the GLODAP Gridded CFC Data Set Inverse Anthropogenic CO2 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 KZ in the models

Inverse estimates of anthropogenic CO2 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)

Zonally and temporally integrated anthropogenic CO2 uptake by (top) the global ocean, (middle) the Atlantic Ocean, and (bottom) the Indo-Pacific Ocean from 1765–1995.

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 CO2 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 CO2 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 CO2 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 CO2, in particular the net uptake by the terrestrial biosphere.

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 1994 D nearly homogeneous Dt = 14 years 2008 Figure 1. The δ13C 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.

13C sections 1994 2008

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