# Estimation of Changes in Sediment Transport along the Free-Flowing Middle Danube River Reach
## 4 Results  
### Results of the Homogeneity Tests for the Hydrological Data  
Homogeneity tests for water level yearly characteristics were performed by [PERSON] et al. in 2021 [5], and the results are presented in Figure 3a-c only for the Baja GS, as all gauging stations along the investigated reach showed very similar behavior. Both minimum and mean water stages and levels were highly inhomogeneous, with large \(D\)-statistic values (>0.3) and very low probabilities (\(p\)) (less than 0.01; at some GSs, these were not even traceable; see Table 1). For the sake of the completeness of the results and the explanation for why the evaluation of the sediment transport was limited to one part of the investigated reach, the \(D\)-statistics and \(p\)-values are taken from [5] and presented again in Table 1.  
The homogeneity test was also performed for discharges, and the results are presented in Table 2, as in [5], but only for the two gauging stations, as was explained in Section 3.1. They are graphically presented only for the Baja GS (Figure 3d-f), as they are very similar for all other GSs. Unlike the water level data, the yearly characteristic discharges at the investigated gauging stations are homogeneous for all three characteristics--minima, means, and maxima (all \(D\)-statistic values are less than 0.2, and values of probability  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Gauging Station**} & \multicolumn{3}{c}{**Minima**} & \multicolumn{3}{c}{**Means**} & \multicolumn{3}{c}{**Maxima**} \\ \cline{2-10}  & \(D\) & \(p\) & **Homog.** & \(D\) & \(p\) & **Homog.** & \(D\) & \(p\) & **Homog.** \\ \hline Dunaijyairos & 1.000 & \textless{}0.0001 & NO & 0.943 & \textless{}0.0001 & NO & 0.343 & 0.033 & NO \\ Dunafoldvar & 0.971 & \textless{}0.0001 & NO & 0.857 & \textless{}0.0001 & NO & 0.257 & 0.197 & YES \\ Paks & 0.714 & \textless{}0.0001 & NO & 0.543 & \textless{}0.0001 & NO & 0.159 & 0.837 & YES \\ Baja & 0.457 & 0.001 & NO & 0.400 & 0.007 & NO & 0.114 & 0.976 & YES \\ Mohács & 0.457 & 0.001 & NO & 0.429 & 0.003 & NO & 0.086 & 1.000 & YES \\ \cline{2-10} Bezdan & 0.371 & 0.016 & NO & 0.371 & 0.016 & NO & 0.114 & 0.976 & YES \\ Apatin & 0.429 & 0.003 & NO & 0.371 & 0.016 & NO & 0.114 & 0.976 & YES \\ Bogojevo & 0.429 & 0.003 & NO & 0.429 & 0.003 & NO & 0.171 & 0.683 & YES \\ Backa Palanka & 0.257 & 0.255 & YES & 0.357 & 0.038 & NO & 0.121 & 0.976 & YES \\ Novi Sad & 0.229 & 0.320 & YES & 0.171 & 0.683 & YES & 0.114 & 0.976 & YES \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of the homogeneity test of water level yearly characteristics [5].  
Figure 3: Results of the two-tailed (\(\alpha\) = 0.05), two-sample Kolmogorov–Smirnov test of the homogeneity of the time series of (**a–c**) water stages and (**d,e**) discharges at the Baja GS. The first row of panels (**a,d**) refers to the water stage and discharge minima, respectively; the second row (**b,e**) refers to the mean values, respectively; and the third row (**c,f**) refers to the water stage and discharge maxima, respectively. It is readily apparent that the time series of water stage minima and means are non-homogeneous (red frames), while all discharge data and water stage maxima are homogeneous (green frames). Blue lines—data for the first 35 years (1950–1984). Red lines—data for the second time interval of 35 years (1985–2019).  
(\(p\)) are much larger than 0.70). In the same study ([5]), it was shown that the annual discharge minima, means, and maxima showed no trend at the downstream end of the study reach over the last 70 years.  
The results of the discharge normality test are visualized in Figure 4. Although the frequency of the measured data (green columns) shows slight asymmetry, the test undoubtedly indicates that all three yearly discharge characteristics follow normal distributions at all four gauging stations.