Renewal time scales in tidal basins: Climbing the Tower of Babel

Transport time scales are key parameters to assess water renewal of estuaries and tidal basins and they have long been used to this purpose. In a modern-day Tower of Babel, an ever-increasing confusion has involved terminology, use and estimation of time scales, despite valuable efforts towards a sounder theoretical framework. Within the framework of tidally flushed, semi-enclosed basins with negligible freshwater inflow, water renewal is strongly controlled by diffusion. The inlet of a tidal basin acts alternatively as a source and as a sink. A significant fraction of effluent water can return to the basin each flood tide. Accordingly, to correctly assess water renewal of such basins, a region larger than the basin itself has to be considered. To account for the effects of return flow, the concept of exposure time was introduced as an alternative to the residence time. However, deep analysis of exposure time revealed unexpected complications that, in part, are still open questions. The present contribution extends the concepts of water age and local flushing time to account for the return flow, as for exposure time. These time scales are studied and compared to each other, aided by a modelling study focusing on the Venice lagoon. Also, approximate methods to estimate the real time scales are introduced and analysed. We show that the local flushing time well approximates, quantitatively, both water age and exposure time in steady periodic hydrodynamic condition. Conversely, wind-driven advection makes exposure time to be significantly different from water age and local flushing time.