A note on the age of radioactive tracers

The age of a water mass is often estimated experimentally using the radio-age computed from the distribution of a radioactive tracer (radiocarbon, helium–tritium). Deleersnijder et al. J. Mar. Syst. 28 (2001) 229.] have shown that the radio-age underestimates the age of the water and is larger than the age of the radioactive tracer used for its evaluation. This result is generalized here to radio-ages computed from the ratio of two radioactive tracers. The differences between the different ages are also studied analytically and numerically as functions of the decay rate of the radioactive tracers.For small decay rates, the difference between the age of the water mass and the radio-age is shown to be proportional to the decay rate. It depends also on the level of mixing in the system; even radioactive tracers with small decay rates can provide poor estimates of the age of the water mass in a strongly diffusive flow. For small half lives, both the radio-age and the age of radioactive tracers decrease as the inverse of the square root of the decay rate.The same analysis applies to some extent to the estimates of the age of a water mass from stable tracers with known time dependent sources (e.g. chloroflurocarbons).