Water age, exposure time, and local flushing time in semi-enclosed, tidal basins with negligible freshwater inflow

Within the framework of tidally flushed, semi-enclosed basins with negligible freshwater inflow, and under steady periodic flow conditions, three frequently used local transport time scales to quantify the efficiency of water renewal, namely water age, exposure time, and local flushing time are studied and compared to each other. In these environments, water renewal is strongly controlled by diffusion, and it is significantly affected by the return flow (i.e., the fraction of effluent water that returns into the basin on each flood tide). The definition of water age is here modified to account for the return flow, in analogy with exposure time and local flushing time. We consider approximate time scales, whose accuracy is analyzed, in order to overcome problems related to the size of the computational domain and to reduce the computational effort. A new approximate procedure is introduced to estimate water age, which is based on the water aging rate. Also, the concept of local flushing time as a relevant time scale is introduced. Under steady periodic conditions, we demonstrate that the local flushing time quantitatively corresponds to water age, and well approximates exposure time when the flow is dominated by diffusion. Since the effort required to compute water age and exposure time is greater than that required to compute the local flushing time, the present results can also have a practical interest in the assessment of water renewal efficiency of semi-enclosed water basins. The results of a modeling study, in which the lagoon of Venice is used as a benchmark, confirm the substantial quantitative equivalence between these three transport time scales in highly diffusive environments.