# Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data
## 3 Results
### Comparison with Different Scour Models  
To evaluate the relative performance of the dimensional model developed on specifically filtered data in the present study, a comparison with already developed empirical scour models was conducted (Figure 5). The link between selected models (Table 6) is their applicability for scour depth prediction in sand-bed rivers during the clear-water regime. However, there are some differences between them based on: variables used for scour prediction; source of large-scale data (field, combination of laboratory and field, and numerical data); and equation development technique (1 conventional MNLR equation, 2 recent MNLR equations, and 2 GEP methods). The conventional MNLR technique is an approach to developing functional dependencies using dimensional analysis and the Buckingham PI theorem to attain dimensional consistency. GEP is one of the evolutionary algorithms that can create simple and explicit equations and is therefore often used for developing scour depth expressions. Two governing variables that are included in all scour equations are water depth (\(\psi\)) and pier width (\(b\)), as presented in Table 6.  
The comparisons between previously developed empirical models (Table 6) and the dimensional model developed in this study, Equation (17), are presented in Figure 5, where the line of agreement indicates the perfect match between observed and predicted data, i.e., \(d_{s\_prnd}=d_{s}\). The circle points, obtained by using our dimensional model and the filtered dataset, are the same as in Figure 3. However, Figure 5 also displays the lines that were constructed by using predicted \(d_{s\_pred}\) data obtained by utilizing different models from Table 6. The following discussions will explain the performance of all models from Table 6. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**ID** & \(b_{\mathit{eff}}\) & \(y\) & \(v\) & \(v_{c}\) & \(\tau\) & \(\tau_{c}\) & \(Fr\) & \(Fr_{c}\) & \(Fr_{d}\) & \(Re_{p}\) & \(d_{s}\) & \(d_{s\_pred}\) & **Residuals** \\ \hline Obs96 & 4.88 & 9.81 & 2.13 & 5.11 & 38.51 & 0.27 & 0.22 & 0.52 & 27.57 & 17.90 & 0.67 & 3.50 & \(-\)2.83 \\ Obs293 & 11.58 & 4.85 & 2.68 & 2.30 & 95.08 & 0.31 & 0.39 & 0.33 & 29.82 & 28.11 & 2.50 & 5.15 & \(-\)2.65 \\ Obs252 & 5.54 & 13.47 & 2.35 & 7.44 & 72.45 & 0.26 & 0.20 & 0.65 & 32.61 & 14.39 & 1.80 & 4.08 & \(-\)2.28 \\ Obs52 & 9.63 & 3.60 & 0.79 & 1.30 & 7.76 & 0.49 & 0.13 & 0.22 & 5.46 & 117.86 & 0.43 & 2.36 & \(-\)1.93 \\ Obs57 & 2.50 & 9.33 & 1.55 & 4.09 & 17.38 & 0.33 & 0.16 & 0.43 & 16.63 & 31.55 & 0.43 & 2.22 & \(-\)1.79 \\ Obs340 & 5.97 & 8.35 & 1.22 & 3.28 & 11.47 & 0.37 & 0.13 & 0.36 & 11.37 & 47.57 & 5.15 & 2.95 & 2.20 \\ Obs307 & 0.61 & 2.77 & 1.13 & 1.14 & 5.17 & 0.42 & 0.22 & 0.22 & 8.86 & 79.52 & 2.87 & 0.65 & 2.22 \\ Obs346 & 6.10 & 22.52 & 2.43 & 9.11 & 66.29 & 0.34 & 0.16 & 0.61 & 24.65 & 36.96 & 7.10 & 4.73 & 2.37 \\ Obs324 & 1.07 & 4.54 & 1.77 & 2.17 & 53.46 & 0.31 & 0.26 & 0.33 & 19.65 & 28.11 & 3.66 & 1.27 & 2.38 \\ Obs343 & 4.33 & 5.67 & 2.93 & 3.32 & 32.81 & 0.25 & 0.39 & 0.45 & 41.99 & 13.07 & 6.22 & 3.57 & 2.65 \\ Obs329 & 1.07 & 4.15 & 1.71 & 2.00 & 48.80 & 0.31 & 0.27 & 0.31 & 18.97 & 28.11 & 4.05 & 1.23 & 2.82 \\ Obs316 & 0.61 & 2.19 & 0.67 & 0.97 & 4.52 & 0.42 & 0.14 & 0.21 & 5.27 & 79.52 & 3.29 & 0.47 & 2.82 \\ Obs344 & 4.37 & 5.21 & 2.44 & 2.98 & 16.62 & 0.26 & 0.34 & 0.42 & 33.88 & 14.39 & 6.43 & 3.26 & 3.17 \\ Obs347 & 4.27 & 9.78 & 2.90 & 5.62 & 9.60 & 0.25 & 0.30 & 0.57 & 41.55 & 13.07 & 7.65 & 3.86 & 3.79 \\ Obs348 & 10.09 & 9.00 & 0.65 & 3.60 & 48.40 & 0.36 & 0.07 & 0.38 & 6.24 & 43.61 & 7.80 & 2.90 & 4.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: List of potential outliers with corresponding measured and calculated influential variable values. [PERSON] and [PERSON] [19] (AL abbreviated) proposed a new scour equation obtained by the same dimensional MNLR technique and the identical PSDB-2014 database as used in this study.