(2) The Level-3 model

Notable evolutions of estuarine morphology generally take days, months, or even years, which is much slower than the variations of flow and sediment concentration fields. Impacts of short-term morphology evolutions of riverbeds on tidal currents and sediment transport are also minor. Using these facts, an accelerated calculation of bed deformations could be incorporated in sediment models through multiplying the flux of sediment exchange (between the flow and the riverbed) by a morphological scale factor [10,13,14]. This kind of model is called the Level-3 model.

For a Level-3 model, upstream boundary conditions (e.g., river discharges and sediment concentrations) of a given time interval are set with the average data in this time interval (often a month). Monthly averaged data is used to set the upstream boundary conditions, while water levels of two full-period neap-spring tides are imposed at seaward boundaries. As a result, for each month, only the process of two full neap-spring tides is simulated, and the bed deformation is scaled by a morphological scale factor. Obviously, a Level-3 model using a morphological scale factor does not simulate the real process of the flow, sediment transport, and bed evolution in the estuary.

(3) The Level-2 model

On the one hand, in an estuary, the rate of bed deformation is generally much slower than that of flow evolution, so a Level-1 model is not necessary. On the other hand, the Level-3 model does not simulate a real process of flow-sediment-riverbed evolution. In this study, the real hydrological and tidal processes are simulated. At each time step of a simulation, the calculation of hydrodynamics is done first, and the sediment transport is then solved, followed by a timely riverbed update. This kind of model is called the Level-2 model. Obviously, it is simpler than the Level-1 model and is expected to achieve higher accuracy than the widely used Level-3 model.

### *5.3. Di*ff*erences between the Spillover of Saltwater and Sediment*

A few quantitative studies on the spillover of saltwater from the North to the South Branches have been reported. Gu et al. [51] found that the spillover of saltwater might occur when the upstream runo ff was less than 30,000 m<sup>3</sup>/s and the tidal range at Station QLG was greater than 2 m, and became remarkable when the upstream runo ff was less than 20,000 m<sup>3</sup>/s and the tidal range at Station QLG was greater than 2.5 m. The mechanics and quantitative studies on the spillover of saltwater from the North to the South Branches can be found in [5]. These research results provide references for our study on the spillover of sediment-carrying flow.

It must be pointed that the spillover of sediment in the Yangtze Estuary is quite di fferent from that of saltwater. First, the source for the saltwater spillover is simply from seas, which is uniform at o ffshore boundaries. As stated in this study, the source for the sediment spillover is produced by the erosion of local riverbed mainly in the middle and upper reaches of the North Branch. Second, salinity can be regarded as a solute whose transport is assumed to fully follow the motion of flows. However, the transport of sediment is quite sensitive to flow intensities. Under weak flow intensity, the heavier particles of sediment will deposit on the riverbed. The flow intensity will determine if and when spillover occurs and its extent. Moreover, the intensity of the sediment spillover is also closely related to the constituents of bed materials. Studies on the sediment spillover are more challenging. This may be one reason that quantitative studies on the sediment spillover in the Yangtze Estuary have not been reported.

According to the aforementioned analysis, a qualified simulation of flow and sediment transport in the Yangtze Estuary (which can reproduce detailed fields of tidal flows and sediment concentration) generally requires a grid resolution higher than that used in the simulation of saltwater transport. High grid resolution is achieved with as few cells as possible by using a channel-refined unstructured grid in this study. Moreover, the semi-implicit method, the ELM, and the FVELM were combined to achieve solve the e fficiency problems of the model.
