# Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data
## 2 Methodology
### Data Filtering  
After the expansion of the subset (containing 13 initial variables) with the additional computed 8 variables, data filtering was conducted to retain only data relevant for the aim of the paper, i.e., to study measurements referring to large sand-bed rivers. To obtain this \begin{table}
\begin{tabular}{c c c} \hline \hline
**Additional Variable** & **Equation** & \\ \hline Froude number & \(Fr=\frac{v}{\sqrt{S\cdot y}}\) & (1) \\ local shear stress & \(\tau=\gamma v\cdot y\cdot S\) & (2) \\ critical shear stress [34] & \(\tau_{c}=0.25\cdot\left(d_{50}\cdot\left[\frac{\left(\frac{y_{c}}{\tau_{c}} \right)-1\right)g}{\
u^{2}}\right]^{\frac{1}{3}}\right)^{-0.6}\cdot g\cdot( \rho_{s}-\rho_{w})\cdot d_{50}\cdot tan(\Phi^{*})\) & (3) \\ critical velocity [35] & \(v_{c}=\sqrt{\rho_{rd}\cdot g\cdot d_{50}}\cdot\left(0.0024\cdot\left(\frac{y}{d _{50}}\right)+2.34\right)\) & (4) \\ critical Froude number & \(Fr_{c}=\frac{v_{c}}{\sqrt{S\cdot y}}\) & (5) \\ densimetric Froude number & \(Fr_{d}=\frac{v}{\sqrt{(\rho_{rd}\cdot^{-1})\cdot g\cdot d_{50}}}\) & (6) \\ particle Reynolds number & \(\text{Re}_{p}=\frac{d_{50}\cdot\sqrt{\rho_{nd}\cdot^{-1}}\cdot g\cdot d_{50}}{ \
u^{2}}\) & (7) \\ \hline \hline \end{tabular}  
* \(\
u\) is kinematic viscosity of fluid. \(\Phi\) is the angle of repose of the particle [36]. \(\rho_{rd}\) is the submerged relative mass density of sediment particles.  
\end{table} 
Table 1: Additional variables included in the analysis. Figure 1: Flowchart of the proposed methodology to identify the most influential variables before developing a new model. data, several sets of filtering criteria were defined that correspond to the flow regime and riverbed morphology of the large rivers. The first set of filtering criteria is related to the flow regime. The flow of large rivers is subcritical due to the nature of the flow in lowland areas; hence, the Froude number can be used to distinguish subcritical and supercritical flow regimes. In open-channel flow, the critical flow regime is lower than its theoretical value (\(Fr=1\)) since the flow transition from wide channel to contraction is gradual. Different studies identified the transition between subcritical and supercritical flow regimes to be within the interval \(0.7<Fr<0.85\) for field conditions. For example, in the study by [PERSON] et al. [37], \(Fr\) values varied from 0.7 to 0.8, as in several other reports [18; 29; 38]. In this study, measurements with \(Fr>0.75\) were filtered out, i.e., applying [PERSON]'s approach [24]. Additionally, erroneous data related to Froude number were also filtered out--measurements of approach flow velocity (\(v\)) with missing or zero values were removed. The second set of filtering criteria was applied to preserve the data corresponding to large sand-bed rivers. To restrain the dataset to sand-bed rivers, the following criteria were used: sediment particle median size (\(d_{50}\)) ranging between 0.0625 mm and 2 mm. The geometrical standard deviation of the sediment (\(\sigma_{g}\)) presents a measure of the non-uniformity of the sediment [28]. Uniform sediment gradation associated with uniform sand is considered to be less than 1.3 [27] because larger \(\sigma_{g}\) values would indicate the presence of coarser gravel particles. After applied filtration, the average value of \(\sigma_{g}\) is 3.0, which shows slightly non-uniform sediments, which indicates potential bed armoring and consequently reduces scour depth [39]. To restrain the dataset to large rivers, measurements of flow depth (\(y\)) lower than 1.5 m were excluded from further analysis. The original PSDB-2014 database [26] contains no information regarding the river widths. [PERSON] and [PERSON] [40] have applied basin data to correlate known channel widths against drainage area, flow depth, and stream slopes.