The global ocean has taken up a large fraction of the CO2 released by human activities since the industrial revolution. Quantifying the oceanic anthropogenic carbon (Cant) inventory and its variability is important for predicting the future global carbon cycle. The detailed comparison of data-based and model-based estimates is essential for the validation and continued improvement of our prediction capabilities. So far, three global estimates of oceanic Cant inventory that are "data-based" and independent of global ocean circulation models have been produced: one based on the Δ C* method, and two that are based on constraining surface-to-interior transport of tracers, the TTD method and a maximum entropy inversion method (GF). The GF method, in particular, is capable of reconstructing the history of Cant inventory through the industrial era. In the present study we use forward model simulations of the Community Climate System Model (CCSM3.1) to estimate the Cant inventory and compare the results with the data-based estimates. We also use the simulations to test several assumptions of the GF method, including the assumption of constant climate and circulation, which is common to all the data-based estimates. Though the integrated estimates of global Cant inventories are consistent with each other, the regional estimates show discrepancies up to 50 %. The CCSM3 model underestimates the total Cant inventory, in part due to weak mixing and ventilation in the North Atlantic and Southern Ocean. Analyses of different simulation results suggest that key assumptions about ocean circulation and air-sea disequilibrium in the GF method are generally valid on the global scale, but may introduce errors in Cant estimates on regional scales. The GF method should also be used with caution when predicting future oceanic anthropogenic carbon uptake.