Flushing Time in Hydrodynamically Connected Estuaries: Source-Flux Consistency and Network-Dependent Renewal

Flushing time is widely used as a bulk metric to characterize hydrodynamic renewal in estuaries and coastal systems, most commonly estimated using salinity-based freshwater-fraction formulations. Although such bulk renewal times have been shown to diverge from tracer- or particle-based estimates under realistic forcing and geometric conditions, these discrepancies are typically attributed to hydrodynamic regime dependence or differences among transport timescale definitions. Here we show that, in hydrodynamically connected estuarine systems, an additional mechanism fundamentally affects the physical interpretation of flushing time. When freshwater connectivity is strong, the freshwater volume diagnosed from salinity may integrate contributions from multiple sources that follow distinct transport pathways, while the freshwater inflow flux represents only local discharge. This decoupling violates source–flux consistency and obscures the meaning of flushing time, even when salinity diagnostics and inflow estimates are individually well defined. Using a three-dimensional hydrodynamic model of Chesapeake Bay with source-resolving passive tracers, we distinguish between locally sourced and externally sourced freshwater and demonstrate that these components exhibit fundamentally different renewal behavior despite sharing the same freshwater identity. Enforcing source–flux consistency yields connectivity-adjusted flushing times that reconcile classical salinity-based estimates with independent tracer-derived renewal scales. Our results show that flushing time in large estuarine networks reflects both local renewal and cross-system freshwater redistribution, and is therefore more appropriately interpreted as a network-dependent transport metric rather than an intrinsic property of individual estuaries.