On the concept of exposure time

The concept of exposure time offers an interesting alternative to the residence time for the quantitative assessment of the water renewal of estuaries and semi-enclosed basins. It can cope with the oscillations or meandering of the flow around the boundary of the control domain and is therefore particularly suited for tidal seas and sub-basins with strong mesoscale activity.

We show however that the exposure time in a control domain \omega cannot be properly defined if \omega is part of a larger bounded system unless some removal process is taken into account. It is therefore suggested to revise and extend the definition of the exposure time by including a first order decay : ``the exposure time for the rate constant \lambda is the total time spent in a control domain \omega by particles subject to a first order decay with a rate constant $\lambda$, irrespective of their possible excursions in and out the control domain''. The exposure time revised in this way is well-defined in all circumstances provided that the decay rate differs from zero but depends on the rate constant \lambda. Alternatively, in order to diagnose the movement of water masses, the first order decay can be considered only outside the control domain.