On the timescales relevant to a linear transport-decay reservoir model

Deleersnijder, Eric [UCL]

Timescales relevant to the dynamics of a tracer in a well-mixed domain (i.e. a reservoir) are studied. The exposure time is defined as the time that will be spent in the reservoir, taking into account a first-order decay process, transport toward the environment and the return flux — as appropriate. It is seen that the residence time is a particular case of the exposure time, which is believed to be the most general timescale looking into the future. In the linear model under consideration the exposure time is equal to the ratio of the mass of the tracer present in the reservoir to the rate of decrease of the tracer mass. If there is an incoming tracer flux, the age, a measure of the elapsed time, is an appropriate diagnosis. At a steady state, the exposure time and the age are equal. All of the aforementioned results may be used to assess the rate of water renewal, for the water may be regarded as a passive tracer.