Hey,

If you want your calculation of the residence time to be mathematically precise and also resolve its temporal and spatial variability, you should definitely look into the Constituent-oriented Age and Residence time Theory (CART;

http://www.elic.ucl.ac.be/repomodx/cart/ ). The forward model gives the first moment of the age distribution (i.e., mean age) and the corresponding adjoint gives the mean residence time. Both are 4 dimensional variables. The re-entry problem has also been addressed in the theory (a series of papers). The authors named the one neglecting re-entry "strict mean residence time" and other considering re-entry "exposure time". The commonly referred "flushing time" is just a spatial and temporal average of the 4 dimensional residence/exposure time. If you care only about the one-quantity flushing time, you could use tracer releases (Lagrangian or Eulerian) in a forward model to estimate, as the previous replies suggested. If you want to study the temporal and spatial variability of the residence time, tracer releases in a forward model become too expensive, and you should look into the CART theory. We have summarized the CART and applied it in the New York Bight area using the ROMS adjoint model in the following paper:

Zhang, W. G., J. L. Wilkin, and O. M. E. Schofield, 2010: Simulation of water age and residence time in New York Bight. J. Phys. Oceanogr., 40, 965-982.

Weifeng Zhang

WHOI