Estimates of anthropogenic carbon in the Indian Oceanwith allowance for mixing and time-varyingair-sea CO2disequilibriumTimothy M. Hall,1Darryn W. Waugh,2Thomas W. N. Haine,2Paul E. Robbins,3and Samar Khatiwala4Received 8 July 2003; revised 12 December 2003; accepted 7 January 2004; published 25 February 2004.[1] We apply to the Indian Ocean a novel technique to estimate the distribution, totalmass, and net air-sea flux of anthropogenic carbon. Chlorofluorocarbon data are used toconstrain distributions of transit times from the surface to the interior that areconstructed to accommodate a range of mixing scenarios, from no mixing (pure bulkadvection) to strong mixing. The transit time distributions are then used to propagate tothe interior the surface water history of anthropogenic carbon estimated in a waythat includes temporal variation in CO2air-sea disequilibrium. By allowing for mixingin transport and for variable air-sea disequilibrium, we remove two sources of positivebias common in other studies. We estimate that the anthropogenic carbon mass inthe Indian Ocean was 14.3–20.5 Gt in 2000, and the net air-sea flux was 0.26–0.36 Gt/yr.The upper bound of this range, the no-mixing limit, generally coincides with previousstudies, while the lower bound, the strong-mixing limit, is significantly below previousstudies.INDEX TERMS: 1635 Global Change: Oceans (4203); 4568 Oceanography: Physical:Turbulence, diffusion, and mixing processes; 4806 Oceanography: Biological and Chemical: Carbon cycling;4808 Oceanography: Biological and Chemical: Chemical tracers; KEYWORDS: carbon, ocean, transport,mixing, age, Indian OceanCitation: Hall, T. M., D. W. Waugh, T. W. N. Haine, P. E. Robbins, and S. Khatiwala (2004), Estimates of anthropogenic carbon inthe Indian Ocean with allowance for mixing and time-varying air-sea CO2disequilibrium, Global Biogeochem. Cycles, 18,GB1031, doi:10.1029/2003GB002120.1. Introduction[2] The ocean sequesters a large fraction of the CO2arising from human activity. While great progress has beenmade in estimating the distribution and mass of anthropo-genic carbon in the ocean from observations, considerableuncertainty remains. The task is difficult because theanthropogenic signal of dissolved inorganic carbon (DDIC)DIC) is of the order of 100 times smaller than natural DIC,which has complex, poorly known biochemical sources andsinks. Various DDIC inference techniques have been devel-oped [Brewer, 1978; Chen and Millero, 1979; Gruber et al.,1996; Goyet et al., 1999; Thomas and Ittekkot , 2001;McNeil et al., 2003], and while comparison among themshows qualitative agreement, there are considerable quanti-tative differences [Wanninkhof et al., 1999; Sabine andFeely, 2001; Coatanoan et al., 2001].[3] Several assumptions are common t o most DDICinference techniques, raising the possibility of overall biasacross the range of estimates. Chief among these are (1) theassumption that mixing is a negligible component oftransport and (2) the assumption of ‘‘constant disequilib-rium’’ that DDIC in surface waters has kept pace withincreasing atmospheric CO2. Both of these assumptionshave been questioned, but the errors incurred by makingthem have remained unclear. A number of studies havedemonstrated that eddy mixing a long constant densi tysurfaces (isopycnals) plays a major role in propagatingtracers [e.g., Jenkins, 1988; Robbins et al., 2000] and mustbe taken into acc ount when interpreting trac er-derivedtimescales [e.g., Thiele and Sarmiento, 1990; Sonnerup,2001; Waugh et al., 2003]. Information on the mixing,however, has not generally been in corporate d in theobservation-based DDIC estimates. In addition to theweak-mixing and constant disequilibrium assumptions,techniques that derive DDIC from total DIC measurementsaccount for biochemical sources and sinks of DIC byusing stoichiometric (Redfield) ratios among carbon, oxy-gen, and alkalinity, whose uncertainty impacts the DDICestimates [Wanninkhof et al., 1999].GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 18, GB1031, doi:10.1029/2003GB002120, 20041NASA Goddard Institute for Space Studies at Columbia University,New York, New York, USA.2Department of Earth and Planetary Sciences, Johns HopkinsUniversity, Baltimore, Maryland, USA.3Scripps Institution of Oceanography, University of California, SanDiego, California, USA.4Lamont-Doherty Earth Observatory, Columbia University, Palisades,New York, USA.Copyright 2004 by the American Geophysical Union.0886-6236/04/2003GB002120$12.00GB1031 1of11[4] In this study we apply to the Indian Ocean a techniquethat avoids these assumptions. As in other studies weexploit the fact that DDIC is well approximated as a passive,inert tracer transported by a steady state circulati on onsurfaces of constant density (isopycnals) in response toanthropogenic forcing in surface waters. Unlike other stud-ies we relate interior DDIC to the DDIC history at thesurface in a way that explicitly allows for mixing. CFC-12data are used to constrain distributions of transit times fromthe surface to the interior that are designed to accommodateany proportion of diffusive mixing and bulk advection. Thetransit time distributions are then used to propagate to theinterior the surface history of DDIC estimated in a mannerthat allows for time-varying CO2disequilibrium. Theassumptions of no mixing and constant disequilibrium bothlead to positive bias. By removing them, we obtain a rangeof values for Indian Ocean mass and net air-sea flux ofanthropogenic carbon, all of which are consistent with theCFC data. The upper limit of the range approximatelycoincides with previous studies, while the lower limit isroughly one third lower.2. Methodology[5] We exploit the approximation, also made in otherstudies, that DDIC penetrates the ocean as a passive, inerttracer. This is reasonable because, while the distribution ofDIC itself is controlled by biology, upper ocean productivityis limited by nutrients, not carbon, and thus to first order theaddition of anthropogenic carbon does not alter the rate ofbiological uptake and downward transport of carbon. Fur-thermore, as in other studies we assume the ocean circulationto be in steady state. McNeil et al. [2003] estimated frommodel studies that present-day secular change in the oceancirculation due to global warming alters carbon uptake byonly 1%. Decadal and shorter time variability in the interiorocean does not affect our analysis significantly because manydecades of tracer signal