On the concept of exposure time

We show however that the exposure time in a control domain ω cannot be properly defined if ω 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 λ is the total time spent in a control domain ω by particles subject to a first order decay with a rate constant λ, 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 λ. Alternatively, in order to diagnose the movement of water masses, the first order decay can be considered only outside the control domain.