A carbon cycle model is presented in which direct ventilation of intermediate and deep ocean waters in high latitudes is taken into account. The 1 1/2 -dimensional ocean model is an extension of a box-diffusion model including a deep-sea outcrop at the surface. If both are calibrated in a consistent way, the outcrop-diffusion ocean takes up more excess CO2 than the box-diffusion ocean because the outcropping deep water is essentially virgin as to fossil CO2. Two calibration methods are compared, using the distribution either of natural or of bomb-produced 14C. The latter leads to a higher oceanic uptake of excess CO2 than the former and to a better agreement with the observed atmospheric increase. Long-term model responses are also discussed.