## 4 Hybrid Modeling
### Numerical Simulations  
In solutions of river flow and sedimentation issues, a variety of codes can be used, e.g., Delft3D [39], MIKE21 [40] and Telemac-Mascaret [41]. As reported in [42] and [43], some other recently developed models are also available for simulation of the hydro-sediment-morphodynamic processes. In the present study, Delft3D is adopted to simulate both the flow and morphological changes. Its governing equations include mass continuity, flow momentum, sediment transport, and bed deformation. Instead of the \(k\)-\(\varepsilon\) turbulence model, the \(k\)-\(\omega\) model is used to reasonably reproduce the reservoir flow with circulations. The suspended load transport is expressed by an advection-diffusion (mass balance) equation, and the bed-load transport is calculated with the van Rijn formula [44]. The bed-form changes are simulated with the specification of the bed-stability coefficient and the bed resistance. For a detailed description of the mathematical formulation, refer to the Delft3D website ([[https://oss.deltares.nl/web/delft3d](https://oss.deltares.nl/web/delft3d)]([https://oss.deltares.nl/web/delft3d](https://oss.deltares.nl/web/delft3d)), accessed on 1 January 2011) and some published results, such as [45; 46]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cross-Section** & **CS6** & **CS5** & **Y Axis** & **CS4** & **CS3** & **CS2** & **CS1** \\ \hline \(L_{0}\) **(m)** & 280 & 100 & 0 & 110 & 220 & 330 & 700 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Location of cross-sections CS1–CS6, measured along the river centerline. Figure 8: Experimental layout, with an inlet honeycomb to calm the inflow and an outlet flip gate to regulate the tailwater at a given flow rate. Near the left bank at each of CS1–CS6, a point gauge monitors the water level, a velocimeter records flow velocities, a 90\({}^{\circ}\) sharp-crested weir measures flow rates, and a PIV system, mounted under the roof, captures the surface flow velocity across the model. As known, sediment transport modeling suffers from uncertainty due to the complexity of the hydrodynamics and the variety of the governing factors. Most of the sediment transport formulae are a function of bed shear stress developed using specific data sets [47]. The van Rijn formula is calibrated based on both field measurements and flume studies. Previous studies show that it is suitable for situations where suspended load dominates [48]. For suspended load transport, the 3D equation reads  
\[\frac{\partial S}{\partial t}+\frac{\partial(uS)}{\partial x}+\frac{\partial(vS )}{\partial y}+\frac{\partial[(\omega-\omega_{\mathrm{s}})S]}{\partial x}= \frac{\partial}{\partial x}\bigg{(}\varepsilon_{\mathrm{s,x}}\frac{H \partial S}{\partial x}\bigg{)}+\frac{\partial}{\partial y}\bigg{(} \varepsilon_{\mathrm{s,y}}\frac{H\partial S}{\partial y}\bigg{)}+\frac{ \partial}{\partial z}\bigg{(}\varepsilon_{\mathrm{s,z}}\frac{H\partial S}{ \partial z}\bigg{)}-F_{\mathrm{S}} \tag{1}\]  
where \(x\), \(y\) and \(z\) = coordinates, \(u\), \(v\), \(\omega\) (m/s) = longitudinal, transversal and vertical velocity components, \(t\) (s) = time, \(\omega_{\mathrm{s}}\) (m/s) = sediment settling velocity, \(\varepsilon_{\mathrm{s,x}}\), \(\varepsilon_{\mathrm{s,y}}\) and \(\varepsilon_{\mathrm{s,z}}\) (m\({}^{2}\)/s) = eddy diffusivity of sediment fraction and \(F_{\mathrm{s}}\) = function of riverbed deformation. \(F_{\mathrm{s}}\) is dependent on sediment erosion and deposition, given by  
\[\gamma_{0}\frac{\partial Z_{\mathrm{b}}}{\partial t}=F_{\mathrm{s}} \tag{2}\]  
\[F_{\mathrm{s}}=D_{\mathrm{b}}-E_{\mathrm{b}} \tag{3}\]  
\[D_{\mathrm{b}}= \begin{cases}\omega_{\mathrm{s}}S_{\mathrm{b}}\Big{(}1-\frac{ \tau}{\tau_{\mathrm{d}}}\Big{)}&\tau\leq\tau_{\mathrm{d}}\\ 0&\tau_{\mathrm{d}}<\tau\end{cases}  \tag{4}\]  
\[E_{\mathrm{b}}= \begin{cases}M\Big{(}\frac{\tau}{\tau_{\mathrm{e}}}-1\Big{)}& \tau\geq\tau_{\mathrm{e}}\\ 0&\tau<\tau_{\mathrm{e}}\end{cases}