## 2 Numerical Model
### Model Setup  
The spatial extent of the model ranges from 26.9\({}^{\circ}\) N to 34.4\({}^{\circ}\) N with a length of 810 km in the N-S direction and from 120.2\({}^{\circ}\) E to 125.6\({}^{\circ}\) E with a length of 500 km in the W-E direction. The model covers the entire YRE and Hangzhou Bay (HB) in order to present the complete typhoon track (shown in Figure 1) and to better express the hydrodynamics and saltwater exchange between the two estuaries. The horizontal computational domain is composed of an unstructured triangular mesh with 18,887 nodes and 33,656 elements, with the coarsest mesh at the east ocean boundary and the finest in the NB. The mesh size generally decreases from the sea toward the coast and estuary when considering both computational time and accuracy. A non-uniform 10-layer grid is adopted in the vertical direction, and the relative water depths are 0.05, 0.05, 0.1, 0.1, 0.2, 0.2, 0.1, 0.1, 0.05 and 0.05 from the surface to the bottom, which better reflect the impacts of wind, surface water level fluctuation and the bottom roughness (Figure 2). The real daily river discharges at Jiangyin and Cangqian at the upstream of the YRE and Hangzhou Bay were taken as river boundaries, respectively. The initial tidal level and velocity are set as 0. Because of the big computational domain and the open sea boundaries are very large, the open sea boundaries are specified as time-varying tidal levels derived from a harmonic model covering the entire China Sea and its adjacent seas, whose open boundary is driven by the Global Tidal Model [50], which accounts for 8 main astronomic  
Figure 2: The bottom roughness (\(k_{s}\)) of this model. components (_M2_, _K2_, _S2_, _N2_, _K1_, _P1_, _O1_, _Q1_). A non-slip condition is used on riverbanks and islands. To reproduce the intermittent appearance of the tidal flat, wet-dry moving boundaries were adopted. The depth thresholds in each element were used to classify each element as drying, flooding and wetting, with threshold depths of 0.005 m, 0.05 m and 0.1 m, respectively. The 6-hourly wind and air pressure (10 m above sea level) data in 2014, were downloaded from the ECMWF (European Centre for Medium-Range Weather Forecasts, [[http://apps.ecmwr.int/datasets/data/interim-full-daily](http://apps.ecmwr.int/datasets/data/interim-full-daily)]([http://apps.ecmwr.int/datasets/data/interim-full-daily](http://apps.ecmwr.int/datasets/data/interim-full-daily)), 1 September 2020) and were employed to determine the wind stress and atmospheric pressure. The bottom stress is determined by a quadratic friction law as follows:  
\[\overrightarrow{t_{b}}=\rho_{0}c_{f}\overrightarrow{u_{b}}|\overrightarrow{u _{b}}| \tag{1}\]  
where \(c_{f}\) is the drag coefficient defined as (2), \(\rho_{0}\) is the density of the water, \(\overrightarrow{u_{b}}\) is the flow velocity at a distance \(\Delta z_{b}\) above the seabed, and the drag coefficient is determined by assuming a logarithmic profile between the seabed and the point at the distance \(\Delta z_{b}\) above the seabed:  
\[c_{f}=\frac{1}{\left((\frac{1}{k})In(\frac{\Delta z_{b}}{m\overline{k_{s}}}) \right)^{2}} \tag{2}\]  
where \(k=0.4\) is the von Karman constant, and \(m\) is approximately \(1/30\), \(k_{s}\) is the roughness height varying in a range from 0.00027 to 0.0016 m [46]. The salinity at the upstream boundaries (Jiangyin and Cangqian) was set as zero. At the open sea boundary, the salinity is interpolated based on the measured data with a value of 32 psu in the whole vertical direction. The dispersion coefficient is one of the key calibration parameters for the Salinity Model. This model determines the dispersion coefficients as the horizonal and vertical eddy viscosity, used in the flow equations, multiplied by scaling factor. When the \(k\)-\(\epsilon\) turbulence model is used, the scaling factor is estimated by \(\frac{1}{\sigma_{T}}\), where \(\sigma_{T}\) is the Prandtl number. The turbulent viscosity was obtained from a standard \(k\)-\(\epsilon\) turbulence model [51].