Fundamental concepts of exchange and transport time scales in a coastal sea

Concepts of age, residence time, transit time, and turn-over time are summarized which are useful for describing the exchange and transport of water or materials in a coastal sea. The age of a particle is defined as a time which has elapsed since it entered the reservoir, and the residence time is defined as a time which will be taken for a particle to reach the outlet. Time scales based on the age are simply related with those based on the residence time. It is shown that a suitable time scale for representing the exchange characteristics is the average residence time and not the turnover time, which has often been used as the exchange time scale. Further, the ‘remnant function’ which describes the phenomena of exchange or transport is introduced, and is related to the residence time. Exchange and transport time scales in a coastal sea are discussed on the basis of the residence time which can be applied to not only steady-state cases, but also the cases where material is injected instantaneously. The average residence time in a one-dimensional channel and bay is obtained from the solutions of the advection-diffusion equation. If we know a flow speed and diffusion coefficient in a channel or bay regarded as one-dimensional, we can translate them into the average residence time. As an example, the average residence time of the Seto Inland Sea is discussed.