## 5 Analysis of Velocity Profile Distribution  
In order to analyze and verify the measurement results, we should compare the measured results by keeping the same condition at different times and using the statistical average to replace the water velocity in a certain short time, because it is impossible to reproduce an identical flow field in practice simultaneously. We used the iterative multigrid deformation technique to obtain the imaging particles' displacement or feature vector and translate the value to the measured flow velocity. The average velocity is statistically obtained by 50 sequential ultrasonic images, and the flow field is represented by the mean velocity in a certain area. Velocity profile distribution is obtained from the velocity flow field by averaging velocity value and depth direction for a certain range in each profile field. Lastly, we analyzed the whole line averages from the 50 flow fields. Additionally, the actual velocity profile distribution can be obtained using the ADCP method after a kind of experiment in the steady flow condition. The measured velocities \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Depth (cm)**} & \multicolumn{5}{c}{**Velocity (cm/s)**} \\ \cline{2-6}  & **ADCP** & **WDI64-32** & **WT64** & **WT32** & **WT16** \\ \hline
2.5 & 11.02 & 11.05 & 10.82 & 10.9 & 10.0 \\
5.0 & 10.99 & 10.95 & 10.69 & 11.1 & 11.51 \\
7.5 & 10.94 & 10.93 & 10.64 & 10.8 & 10.31 \\
10.0 & 10.93 & 10.88 & 10.72 & 10.85 & 10.89 \\
12.5 & 10.82 & 10.86 & 10.52 & 10.9 & 10.90 \\
15.0 & 10.77 & 10.77 & 10.47 & 10.7 & 10.31 \\
17.5 & 10.66 & 10.67 & 10.36 & 10.4 & 10.51 \\
20.0 & 10.49 & 10.58 & 10.35 & 10.54 & 10.59 \\
22.5 & 10.38 & 10.35 & 10.08 & 10.45 & 10.30 \\
25.0 & 10.17 & 10.22 & 9.87 & 10.35 & 10.10 \\
27.5 & 10.02 & 10.08 & 9.82 & 10.1 & 9.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The profile velocities data in silt carrying flow measured by using the ADCP, the WDI64-32, the WT64, the WT32, and the WT16, respectively. Figure 9: The raw vector maps obtained by different algorithms: (**a**) is the vector map obtained by the iterative multi-grid deformation technique with the size window interrogation from 64 \(\times\) 64 to 32 \(\times\) 32, referred to as WDI64-32; (**b**) is the vector map obtained by cross-correlation with the size of window templates 64 \(\times\) 64, referred to as WT64; (**c**) is the vector map obtained by cross-correlation with the size of window templates 32 \(\times\) 32, referred to as WT32; (**d**) is the vector map obtained by cross-correlation with the size of window templates 16 \(\times\) 16, referred to as WT16. of the ADCP method can be taken as the standard velocity and then compared with the results from our ultrasound PIV method. This is a suitable way to prove the velocity profile vectors obtained by our ultrasound PIV method. We had finished some comparisons at several locations. The profile velocities of the silt carrying flow field are measured and analyzed. A measured velocity profile distribution of silt carry flow is shown in Figure 9 and compared with several methods with different parameters, which are the measured results of velocity profile distribution for Figure 8. Related measured velocities data are compared in Table 2.  
We took the following measurements to calculate the flow field by using several methods compared with different parameters according to Section 3.3. The velocity profile measurement results of Figure 8 in silt carrying flow are shown in Figure 9. Figure 9a is the vector map obtained by iterative multi-grid deformation technique with the size window interrogation from 64 \(\times\) 64 to 32 \(\times\) 32, referred to as WDI64-32. Figure 9b is the vector map obtained by cross-correlation with the size of window templates 64 \(\times\) 64, referred to as WT64. Figure 9c is the vector map obtained by cross-correlation with the size of window templates 32 \(\times\) 32, referred to as WT32.