The leaky funnel model, a metaphor of the ventilation of the World Ocean as simulated in an OGCM



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    1. Université de Liège, Astrophysics, Geophysics and Oceanography Department, 17 Allée du Six-Août, 4000 Liège, Belgium
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    1. Université catholique de Louvain, Louvain School of Engineering, Centre for Systems Engineering and Applied Mechanics (CESAME), 4 Avenue Georges Lemaître, 1348 Louvain-la-Neuve, Belgium
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It is seen that an idealized model may suggest an appropriate scaling of the water age in the World Ocean, which is a measure of the ventilation rate. We use a 1-D advection–diffusion model in which the deep ocean is represented as a leaky funnel, allowing recirculation towards the surface. The analytical solutions to the steady-state problem are readily obtained. The three parameters of the leaky funnel model are estimated in such a way that the behaviour of the domain-averaged water age be as similar as possible to that derived from a 3-D model in a series of sensitivity runs. The agreement between both sets of mean ages is excellent, with a linear correlation coefficient very close to unity. A good agreement is also found for the age of radioactive tracers and the associated radioages. The parameters of the leaky funnel model have a clear physical meaning, that is, the order of magnitude of the horizontal velocity, the mean length of water parcel trajectories in the deep ocean, and a horizontal diffusivity scale. The values of all of them turn out to be consistent with our current knowledge of the World Ocean circulation.