Some theoretical and modelling aspects of the age as a tool for understanding marine flows

The age of a parcel of a constituent of seawater is defined to be the time elapsed since the parcel under consideration left the region where its age is prescribed to be zero. Estimating the age is thus an invaluable tool for understanding complex oceanic flows and the functioning of the numerical models used for representing them. In this paper, a general theory of the age is presented, in which advection, diffusion, production and destruction are properly accounted for. The partial differential equations used for the rigorous computation of the age as a function of space and time are established. This general theory is applied to the computation of the ventilation rates in the World Ocean. The results are compared with those of widely used carbon-14-like dating techniques. Using both numerical simulations and analytical developments, it is shown that the age of the radioactive tracer is smaller than the carbon-14-like age, which is larger than that of the passive tracer. The latter is equivalent to the ventilation or water age. The difference between the various ages, which is essentially due to the influence of mixing processes, increases as the timescale of decay of the radioactive tracer decreases