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

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.