The leaky funnel model revisited

A former publication proposed an idealised view of the global ocean ventilation consisting in a flow through a porous pipe with decreasing section (a leaky funnel). The agreement between the domain-averaged ages as obtained with a coarse-grid 3-D ocean general circulation model (OGCM) and the leaky funnel is excellent. Further, the latter allows to infer characteristic scales, which are consistent with the current knowledge of the ocean ventilation. However, the method, based on numerical experiments in which the circulation fields of the OGCM were artificially modified, is questionable. Here, we revisit the leaky funnel and base our study on the global water age distribution φ(τ), where φ(τ)Δτ is the ocean volume fraction with age in the interval [τ, τ+Δτ]. The steady-state analytical solution for this distribution is shown to be in excellent agreement with numerical results from two coarse grid OGCMs: an outcome that helps strengthening the leaky funnel representation. The asymptotic analysis of φ(τ) suggests that, for large ages, water parcels have the same life expectancy, whatever their age. Further, the leaky funnel provides bulk characteristics of the circulation in OGCMs, which may serve as metrics in model intercomparison studies.