Partial residence times: determining residence time composition in different subregions

Residence time (RT) is a diagnosis widely used to quantify the water exchange rate and mass transport timescale in semi-enclosed systems. The RT focuses on only the total time a water parcel spends in a system (i.e., control region). However, for a system that consists of several subregions (e.g., sub-bays or functional zones), the RT will not include information about the time spent in different subregions. To determine the RT compositions in different subregions, partial residence times (PRTs) are proposed and defined as the amount of time a water parcel spends in different subregions until leaving the control region. The equations for PRTs are derived using the adjoint method, which can quickly determine the variation of PRTs in time and space. To validate the PRT diagnostic equation and numerical model, a test is conducted in an idealized 1D channel with idealized tidal currents. The numerical results are in excellent agreement with the analytical solution. Finally, the PRT method is applied to tide-dominated Jiaozhou Bay. The PRTs in six functional subregions of Jiaozhou Bay are derived, and the detailed RT compositions of the different functional subregions are presented. The application indicates that PRTs could provide detailed information and new insights into the water exchange process.