The concepts of age, residence time, exposure time and influence time provide space and time dependent quantitative measures of the rate at which water masses and pollutants enter and/or leave a control domain. To help avoid confusion between these concepts, this paper provides clear definitions of the residence time and the influence time. The similarities and differences between them are illustrated using both a simplified 1D advection-diffusion model and a realistic two-dimensional model of the Scheldt Estuary (Belgium and the Netherlands). The residence time of a water parcel in a control domain is the time taken by this parcel to leave the control domain for the first time. The influence time is the time required to replace the water in the domain of interest by renewing water. For steady flows, the influence time is numerically identical to the age of the renewing water, but the two timescales differ for unsteady flows. The residence time measures the influence of a hypothetical point discharge on a control domain. In environmental studies, it provides a measure of the effectiveness of hydrodynamic processes at helping a semi-enclosed basin to recover from a local pollution event. The influence time quantifies the local influence of a tracer that would be uniformly distributed in the control domain at the initial time. It is therefore a relevant diagnostic tool in impact studies focusing on the local persistence of a pollution problem initially affecting a large domain.
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