Diagnosing the Flocculation–Transport Dynamics of Suspended Particulate Matter Using a Two-Class Population Balance Model and Bayesian Calibration

Abstract The dynamics of suspended particulate matter (SPM) plays a crucial role in determining water quality, sediment transport, and biogeochemical cycles in inland, estuarine, and coastal water resources. Flocculation processes strongly influence the SPM dynamics via aggregation and breakage under various hydrodynamic and biogeochemical conditions. This study introduces a mechanistic and diagnostic framework that combines a two-class population balance equation (TCPBE) model with Bayesian calibration to simulate flocculation?transport behavior in both laboratory- (time-dependent batch) and field-scale (one-dimensional vertical) systems. Laboratory experiments with biopolymer?clay and microalgae?clay mixtures and field observations from an estuarine turbidity maximum zone are used to derive a comprehensive data set for model validation. Bayesian inference enables the estimation of uncertain model parameters while characterizing their statistical properties, thus supporting the mechanistic interpretation of flocculation dynamics. By quantifying how ionic strength and microbial physiology regulate flocculation kinetics and elucidating the turbulence-driven coupling between flocculation kinetics and sediment transport over tidal cycles, the framework demonstrates its suitability as a process-based diagnostic tool capable of effectively capturing SPM dynamics under various conditions. This framework has strong potential to advance the understanding of flocculation dynamics and support a range of applications in inland and estuarine sediment-laden water systems, including river, reservoir, esturine and coastal waters.