## Appendix A Dependence of Hop Distances on Particle and Flow Features
### Appendix A.3 Dependence of Particle Velocity on Particle and Flow Features  
From Table 5 with fixed flow rates (Reynolds number), the probability of occurrence of high particle velocities increases with decrease in the particle density. For example, the probability of occurrence for high particle velocities (0.15-0.165 m/s) increased from 1.8% to 2.6% when the particle density decreased from 1224 to 1132 kg/m\({}^{3}\) with fixed Reynolds number of 50,789 for bed surface A. Meanwhile, the probability of occurrence for low particle velocities (0-0.015 m/s) increased from 17.3% to 25.1% when the particle density increased from 1085 to 1224 kg/m\({}^{3}\) for bed surface B with fixed Reynolds number of 51,499.  
From Table 6, the probability of occurrence for high particle velocities increases with increase in the flow Reynolds number while for low particle velocities it increases with decrease in flow Reynolds number for fixed particle density of 1132 kg/m\({}^{3}\). For example, the probability of occurrence for low particle velocities (0-0.015 m/s) decreased from 27.4% to 21.7% when the flow Reynolds number increased from 43,353 to 50,789 for bed surface A with fixed particle density of 1132 kg/m\({}^{3}\). While the probability of occurrence for high particle velocities (0.15-0.165 m/s) increased from 2.7% to 3.3% when the flow Reynolds number increased from 41,841 to 51,488 with fixed particle density of 1132 kg/m\({}^{3}\) for bed surface B.  
In Table 7, the flow conditions tested herein are also reported in terms of the particle Reynolds number for enabling further comparisons with the literature. This is important to assess, as sometimes a change in the near bed surface hydrodynamic forcing, may not be reflected in the change in flow Reynolds number (for example if the tailgate was raised while keeping the flow rate constant). In this case the Re number may be almost fixed while the particle Reynolds number may decrease, with a potential to also affect the transport rates.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Surface A**} & \multicolumn{4}{c}{**Surface B**} \\ \cline{2-7}  & \multicolumn{4}{c}{**Particle Density (kg/m\({}^{3}\))**} & \multicolumn{4}{c}{**Particle Density (kg/m\({}^{3}\))**} & \\ \cline{2-7}  & **1085** & **1132** & **1180** & **1224** & **1085** & **1132** & **1180** & **1224** \\ \hline \multicolumn{7}{c}{**Hop Velocity (m/s)**} & \multicolumn{4}{c}{**Probability of Occurrence (\%)**} \\ \hline
0–0.015 & 20.3 & 21.1 & 23.0 & 24.4 & 17.3 & 19.3 & 20.6 & 25.1 \\ \hline
0.015–0.03 & 16.7 & 17.1 & 18.1 & 18.8 & 15.5 & 16.1 & 16.8 & 19.1 \\ \hline
0.03–0.045 & 13.7 & 13.8 & 14.2 & 14.5 & 13.3 & 13.4 & 13.7 & 14.6 \\ \hline
0.045–0.06 & 11.2 & 11.2 & 11.2 & 11.1 & 11.4 & 11.1 & 11.2 & 11.1 \\ \hline
0.06–0.075 & 9.2 & 9.1 & 8.8 & 8.6 & 9.9 & 9.3 & 9.1 & 8.5 \\ \hline
0.075–0.09 & 7.5 & 7.3 & 6.9 & 6.6 & 8.3 & 7.7 & 7.5 & 6.4 \\ \hline
0.09–0.105 & 6.2 & 5.9 & 5.4 & 5.1 & 6.9 & 6.4 & 6.1 & 4.9 \\ \hline
0.105–0.12 & 5.0 & 4.8 & 4.3 & 3.9 & 5.7 & 5.3 & 5.0 & 3.7 \\ \hline
0.12–0.135 & 4.1 & 3.9 & 3.4 & 3.0 & 4.7 & 4.5 & 4.0 & 2.8 \\ \hline
0.135–0.15 & 3.4 & 3.2 & 2.7 & 2.3 & 3.8 & 3.7 & 3.3 & 2.2 \\ \hline
0.15–0.165 & 2.8 & 2.6 & 2.1 & 1.8 & 3.1 & 3.1 & 2.7 & 1.7 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The effect of different particle densities on the particle velocity exponential distribution model parameters, for bed surface A (and Reynolds number of 50,789), and bed surface B (and Reynolds number of 51,488). These tabulated data correspond to the results plotted in Figure 15b,d.