GLOBAL BIOGEOCHEMICAL CYCLES, DOI:10.1029/2008GB003349 AUXILIARY MATERIAL Oceanic sources, sinks, and transport of atmospheric CO 2 Nicolas Gruber 1 , M. Gloor 2 , S. E. Mikaloff Fletcher 3 , S. C. Doney 4 , S. Dutkiewicz 5 , M. Follows 5 , M. Gerber 6 , A. R. Jacobson 7 , F. Joos 6 , 8 , K. Lindsay 9 , D. Menemenlis 10 , A. Mouchet 11 , S. A. M ¨ uller 6 , J. L. Sarmiento 3 , and T. Takahashi 12 River fluxes In steady-state, that part of the input of inorganic and organic carbon into the ocean by rivers that escapes burial is released back into the atmosphere as a flux of CO2 across the air-sea interface [Sarmiento and Sundquist , 1992]. While the burial rate of carbon on the seafloor of the deeper ocean is reasonably well established (∼0.1 Pg C yr −1 as organic carbon and ∼0.1 Pg C yr −1 as CaCO3), the burial in shallow sediments as well as the net input of carbon by rivers beyond the river mouth is poorly established. One reason is that most transport estimates of riverine carbon pertain to a location far upstream of the river mouth, and therefore do not include the myriad of transformation processes that occur in the estuaries and in the very nearshore environments. The most commonly adopted estimate for the river input of carbon is 0.4 Pg C yr −1 in the form of organic carbon, and 0.4 Pg C yr −1 as inorganic carbon [Sarmiento and Sundquist , 1992]. Assuming a burial flux of 0.2 Pg C yr −1 , requires a CO2 outgassing of 0.6 Pg C yr −1 in steady-state. More recent analyses suggest a much larger input of organic carbon, per- haps as large as 1 Pg C yr −1 [Richey, 2004], although it is unclear how much of this flux makes it past the estuary. Nor is it known to which extent current river input estimates reflect anthropogenically perturbed systems or pre-industrial conditions. As the ultimate aim of the inversion is to estimate the contem- porary CO2 flux across the air-sea interface, we have to evaluate whether our inversely based estimates include this steady-state out- gassing of river-derived carbon, or whether we need to apply cor- rections. The answer to this question depends on two independent aspects: First, in what respect does the ΔCgas ex tracer reflect the gain of (inorganic) carbon from rivers and its subsequent loss by air-sea exchange? Second, what fraction of the global outgassing of 1 Environmental Physics, Institute of Biogeochemistry and Pollutant Dynamics, ETH Z ¨ urich, Z¨ urich, Switzerland. 2 Earth and Biosphere Institute & School of Geography, University of Leeds, UK. 3 Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ. 4 Marine Chemistry and Geochemistry, Woods Hole Oceanographic Institution, Woods Hole, MA. 5 Department of Earth, Atmosphere, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA. 6 Climate and Environmental Physics, Physics Institute, University of Bern, Bern, Switzerland. 7 NOAA Earth System Research Lab, Global Monitoring Division, Boulder, CO. 8 Oeschger Centre, University of Bern, Bern, Switzerland. 9 Climate and Global Dynamics, National Center for Atmospheric Research, Boulder, Colorado, USA. 10 Estimating the Circulation and Climate of the Ocean (ECCO), Jet Propulsion Laboratory, Pasadena, CA. 11 Astrophysics and Geophysics Institute, University of Liege, Liege, Belgium. 12 Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY. Copyright 2008 by the American Geophysical Union. 0886-6236/08/$12.00 river-derived carbon is actually reflected in the data set employed in our study, whose sampling locations are predominantly in the open ocean? The answer to the first question depends critically on the carbon- to-phosphorus ratio in both the inorganic and organic fractions of the river supply. For clarity, we discuss separately how the inver- sion attributes the organic and inorganic carbon that is added to the ocean by rivers. With regard to the input of dissolved inorganic matter, rivers tend to have a very low ratio of phosphate to DIC [Meybeck, 1993]. As a result, DIC added to the ocean via rivers is reflected on a nearly mol to mol basis as a gain in ΔCgas ex . When that river derived CO2 is eventually outgassed to the atmosphere, there is a corresponding decrease in ΔCgas ex. In a perfectly sampled ocean, a perfect inver- sion, i.e. an inversion free from systematic biases, will infer from this increase of ΔCgas ex in coastal regions an uptake of CO2 from the atmosphere, and will infer from the decrease in ΔCgas ex in the open ocean an outgassing of CO2, with the two fluxes balancing each other. With regard to organic carbon, there are similarities and dif- ferences. As is the case for the river input of dissolved inorganic matter, the phosphorus-to-carbon ratio in dissolved organic matter is much smaller than the canonical stoichiometric ratio of marine organic matter (Redfield ratio). Thus, the remineralization of this organic carbon leads to an increase in ΔCgas ex on a nearly mol to mol basis, which is then interpreted by the inversion as an uptake of CO2 from the atmosphere. This organic carbon derived CO2 will eventually outgas, which will be reflected in ΔCgas ex as a decrease, and hence correctly attributed in the inversion to a sea-to-air flux. Thus, analogous to inorganic carbon, the air-sea fluxes estimated by a perfect inversion of a perfectly sampled ocean will balance globally. There is an important difference to the river input of in- organic carbon, however, as organic carbon changes ΔCgas ex only at the location where it is remineralized. Thus, the riverine organic carbon signal is not attributed to an air-to-sea flux in the region where the rivers enter the oceans, but rather attributed to the ocean region where the organic carbon is remineralized. In summary, the oceanic inversion of ΔCgas ex tends to find a globally balanced flux even in the presence of a steady-state out- gassing of riverine carbon. This balance emerges because the in- version incorrectly interprets the addition of carbon by rivers as an air-to-sea flux, while it correctly determines the sea-to-air flux associated with the outgassing of the riverine carbon. Therefore, we need to subtract from the “raw” inversion estimates the riverine carbon signal that was incorrectly attributed by the ocean inversion to an air-to-sea flux. To achieve this we add to our “raw” inverse fluxes a regionally specific estimate of the net riverine carbon input (the total input of river carbon minus the carbon that gets buried on the seafloor [Jacobson et al., 2007]). Specifically , we adopt an estimate of 0.45 Pg C yr −1 for the global total outgassing of riverine carbon based on the analysis of Jacobson et al. [2007] and distribute this flux re- gionally on the basis of the spatially resolved GEM-CO2 product, which is based on the work of Ludwig et al. [1996] (see Jacobson et al. [2007] for further details). The magnitude of the global ad- justment as well as its regionalization is uncertain, so that we assign an uncertainty of ±50% to these riverine carbon fluxes (see Table S1). 1