Ventilation rates estimated from tracers in the presence of mixing

The intimate relationship among ventilation, transit-time distributions, and transient tracer budgets is analyzed. To characterize the advective-diffusive transport from the mixed layer to the interior ocean in terms of flux we employ a cumulative ventilation-rate distribution, Phi(tau), defined as the one-way mass flux of water that resides at least time tau in the interior before returning. A one-way (or gross) flux contrasts with the net advective flux, often called the subduction rate, which does not accommodate the effects of mixing, and it contrasts with the formation rate, which depends only on the net effects of advection and diffusive mixing. As tau decreases Phi(tau) increases, encompassing progressively more one-way flux. In general, Phi is a rapidly varying function of tau( it diverges at small tau), and there is no single residence time at which Phi can be evaluated to fully summarize the advective-diffusive flux. To reconcile discrepancies between estimates of formation rates in a recent GCM study, Phi(tau) is used. Then chlorofluorocarbon data are used to bound Phi(tau) for Subtropical Mode Water and Labrador Sea Water in the North Atlantic Ocean. The authors show that the neglect of diffusive mixing leads to spurious behavior, such as apparent time dependence in the formation, even when transport is steady.