How accurate is the estimation of anthropogenic carbon in the ocean? An evaluation of the ΔC* method

The ΔC* method of Gruber et al. (1996) is widely used to estimate the distribution of anthropogenic carbon in the ocean; however, as yet, no thorough assessment of its accuracy has been made. Here we provide a critical re-assessment of the method and determine its accuracy by applying it to synthetic data from a global ocean biogeochemistry model, for which we know the "true" anthropogenic CO₂ distribution. Our results indicate that the ΔC* method tends to overestimate anthropogenic carbon in relatively young waters but underestimate it in older waters. Main sources of these biases are (1) the time evolution of the air-sea CO₂ disequilibrium, which is not properly accounted for in the ΔC* method, (2) a pCFC ventilation age bias that arises from mixing, and (3) errors in identifying the different end-member water types. We largely support the findings of Hall et al. (2004), who have also identified the first two bias sources. An extrapolation of the errors that we quantified on a number of representative isopycnals to the global ocean suggests a positive bias of about 7% in the ΔC*-derived global anthropogenic CO₂ inventory. The magnitude of this bias is within the previously estimated 20% uncertainty of the method, but regional biases can be larger. Finally, we propose two improvements to the ΔC* method in order to account for the evolution of air-sea CO₂ disequilibrium and the ventilation age mixing bias.