Application of the tidally averaged equilibrium cohesive sediment concentration for determination of physical parameters in the erosion-deposition fluxes

A puzzling fact for the Partheniades-Krone formula is the adoption of very contrasting values for the empirical parameters (e.g., the erosion coefficient and the critical shear stresses) but satisfactory reproduction of the suspended sediment concentration (SSC). Here, a theoretical equation for the tidally-averaged equilibrium (TAE) condition is derived by setting the integrated erosion flux throughout a tidal period equivalent to the integrated deposition flux throughout the same tidal period, leading to a new constraint condition on these parameters if values of the TAE-SSC are available. A preliminary check using the measured data of the Yangtze Estuary shows that a larger critical shear stress for erosion would require a smaller critical shear stress for deposition, both of which must be enhanced if the erosion coefficient further increases. Contrasting sets of parameter values derived by this constraint are fed into a coupled hydro-sediment-morphodynamic model to simulate cohesive sediment transport in the Yangtze Estuary. The results confirm that very contrasting parameter values can indeed lead to satisfactory reproduction of the temporal variations of the SSC (e.g., those in July 2016, including both spring tide and neap tide). This is further demonstrated by the numerical modelling of cohesive sediment transport in an idealized symmetrical estuary. These results indicate that the TAE condition can be used as a constraint for determining the erosion coefficient and the critical shear stresses for erosion and deposition. In addition, two simplified equations of the bed sediment mass conservation (no erosion version and the no deposition version) are derived as complements for obtaining a unique set of the three parameter values, provided that the simultaneous measured time series of SSC, bed shear stress and bed level can be collected at the same gauging station.