## 2 Materials and Methods
### Hydrodynamic Model  
This research utilizdes the MIKE 21/3 coupled FM model, which includes the MIKE 21 Hydrodynamic Model (HD) and Spectral Wave (SW) and Sediment Transport (ST) modules to simulate hydrodynamics, wave characteristics, and sediment transport [24; 37]. The MIKE 21 module simulates variations in water elevation and discharge to consider the response functions of forces in rivers, lakes, estuaries, and coastal areas. It employs a numerical solution to the full, time-dependent, and nonlinear depth-averaged Navier-Stokes equations, based on the conservation of mass and momentum [25; 37]. Depth and water velocity were computed in a 2-dimensional grid using simplified equations, as outlined in Equations (2)-(4) below. \[\frac{\partial\zeta}{\partial t}+\frac{\partial p}{\partial x}+\frac{\partial q }{\partial y}=\frac{\partial d}{\partial t} \tag{2}\]  
\[\frac{\partial p}{\partial t}+\frac{\partial}{\partial x}\left(\frac{p^{2}}{h} \right)+\frac{\partial}{\partial y}\left(\frac{pq}{h}\right)+gh\frac{\partial \zeta}{\partial x}+\frac{gp\sqrt{p^{2}+q^{2}}}{C^{2}h^{2}}-\frac{1}{\rho_{w}} \left[\frac{\partial}{\partial x}(h\tau_{xx})+\frac{\partial}{\partial y} \big{(}h\tau_{xy}\big{)}\right]-\Omega q-fVV_{x}+\frac{h}{\rho_{w}}\frac{ \partial}{\partial x}(P_{a})=0 \tag{3}\]  
\[\frac{\partial q}{\partial t}+\frac{\partial}{\partial y}\left(\frac{q^{2}}{h} \right)+\frac{\partial}{\partial x}\left(\frac{pq}{h}\right)+gh\frac{\partial \zeta}{\partial y}+\frac{gq\sqrt{p^{2}+q^{2}}}{C^{2}h^{2}}-\frac{1}{\rho_{w}} \left[\frac{\partial}{\partial y}\big{(}h\tau_{yy}\big{)}+\frac{\partial}{ \partial x}\big{(}h\tau_{xy}\big{)}\right]+\Omega p-fVV_{y}+\frac{h}{\rho_{w}} \frac{\partial}{\partial y}(p_{a})=0 \tag{4}\]  
where \(h(x,y,t)\) represents the water depth (m); \(\zeta(x,y,t)\) signifies the time-varying water depth (m); \((x,y,t)\) denotes the surface elevation (m); \(p\),\(q(x,y,t)\) stand for flux density in the x, y directions (m\({}^{3}\)/s/m); \(C(x,y)\) is [PERSON]'s resistance (m\({}^{1}/^{2}/^{2}\)/s); \(g\) is the acceleration due to gravity (m/s\({}^{2}\));\(f(V)\) represents the wind friction factor; \(V,Vx,Vy(x,y,t)\) are wind velocity and components in the x, y directions (m/s); \(\Omega(x,y,t)\) denotes the Coriolis parameter, latitude-dependent (s\({}^{-1}\)); \(pa(x,y,t)\) indicates atmospheric pressure (kg/m/s\({}^{2}\)); \(\rho w\) is the density of water (kg/m\({}^{3}\)); \(x,y\) are spatial coordinates in meters; \(t\) signifies time (s); and  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Point Name**} & \multicolumn{2}{c}{**Coordinates**} \\ \cline{2-3}  & **Latitude** & **Longitude** \\ \hline ADCP & \(3^{\circ}53^{\prime}41.90^{\prime\prime}\) S & \(102^{\circ}16^{\prime}52.20^{\prime\prime}\) E \\ Tide & \(3^{\circ}54^{\prime}8.14^{\prime\prime}\) S & \(102^{\circ}17^{\prime\prime}28.65^{\prime\prime}\) E \\ Wind & \(3^{\circ}53^{\prime}30.50^{\prime\prime}\) S & \(102^{\circ}18^{\prime}0.39^{\_xx,xy,yy_ represent the effective shear stress components [38]. The stability in the MIKE model developed by DHI is controlled by the Courant Number or CFL Number, where the formula used is as follows [39]:  
\[C_{R}=C_{x}\frac{\Delta t}{\Delta x}+C_{y}\frac{\Delta t}{\Delta y} \tag{5}\]  
where \(C_{x}\) and \(C_{y}\) represent velocities; \(\Delta t\) denotes the time interval; and \(\Delta_{x}\) and \(\Delta_{y}\) are spatial increments, and the tidal wave velocity is derived from the following equation:  
\[C=\sqrt{gh} \tag{6}\]  
where \(g\) represents gravity, and \(h\) denotes water depth. The model can be considered stable when the CFL Number value is \(<\)1. For the MIKE 21 SW module, a spectral wave model is employed to simulate wave transformations [40]. The MIKE 21 SW encompasses directional decoupling and full spectral formulations where parameterization is performed within the frequency range by incorporating the zeroth and first-moment wave-action spectrum as parameters [41].