Key uncertainties in the global carbon cycle are explored with a 2-D model for the oceanic carbon sink. This model has many enhancements over simple 1-D box-diffusion models, including mixed-layer inorganic carbon chemistry, climate-dependent air-sea exchange rates, and mixing of dissolved inorganic carbon into the deep ocean that is parameterized by 2-D eddy diffusion. At the same time it is much more computationally efficient than 3-D models which makes it applicable to a comprehensive parametric uncertainty analysis. By calibrating the key parameters of this ocean carbon sink model to widely referenced values, it produces an average oceanic carbon sink during the 1980s of 1.94 Pg/yr, consistent with the range estimated by the IPCC of 2.0 Pg/yr ± 0.8 Pg/yr (1994). The uncertainty range cited in the IPCC study and widely reported elsewhere is principally the product of the structural uncertainty derived from the results of several ocean carbon sink models of varying degrees of complexity. This range does not directly take into account the parametric uncertainty inherent in these models or how those uncertainties will impact on forecasts of future atmospheric CO2 concentrations.
      A sensitivity analysis of the parameter values used as inputs to the 2-D ocean carbon sink model developed for this study suggests that the IPCC's range for the oceanic carbon sink of 1.2 to 2.8 Pg/yr during the 1980s may be too conservative. By applying the Probabilistic Collocation Method to this simple ocean carbon sink model, the uncertainty in the size of the oceanic sink for carbon and hence future atmospheric CO2 concentrations is quantitatively examined. This uncertainty is found to be larger than that implied by the structural differences examined in the IPCC study alone. An average 1980s oceanic carbon sink of 2.06 ± 0.9 Pg/y (with 67% confidence) is estimated. This uncertainty is found to be dominated the uncertainty in by the rate of vertical mixing of dissolved carbon from the surface into the deep ocean which is parameterized in this study by vertical diffusion. A contribution of the uncertainty in vertical diffusion even increases with time from 83% in the 80s to about 97% in 2100. In contrast a contribution of an uncertainty in the rate of air-sea CO2 exchange decreases from 15% to less than 1% during the same period.
      It is observed that a wide range of parameter values can be used to balance the contemporary carbon cycle due to the large uncertainties in the total oceanic and terrestrial sinks. These parameter values yield correspondingly large differences in the range of future atmospheric CO2 concentrations when driven by forecasts of anthropogenic CO2 emissions scenarios over the next century. For a reference set of emissions similar to the IS92a scenario of the IPCC (1992), the uncertainty in the atmospheric CO2 concentration in 2100 is found to be 659 ppm ± 35 ppm (with 67% confidence). This uncertainty is solely due to uncertainties identified in the "solubility pump" mechanism of the oceanic sink, which is only one of the many large uncertainties lacking a quantitative examination in the global carbon cycle. Such uncertainties have implications for the predictability of atmospheric CO2 levels, a necessity for gauging the impact of different rates of anthropogenic CO2 emissions on climate and for policy-making purposes. Because of the negative feedback between the natural carbon uptake by the terrestrial ecosystem and atmospheric CO2 concentration, taking changes in the former into account leads to a smaller uncertainty in the latter compared to that in the case with the fixed terrestrial uptake.