# Estimation of Changes in Sediment Transport along the Free-Flowing Middle Danube River Reach
## 4 Results
### Correlation between the Minimum Water Level and Cross-Sectional Area Changes at Gs  
The evolution of cross-sections at four GSs on the sand bed reach from Baja to Apatin is presented in Figure 7. Visual inspection of the cross-sections shows that they are more or less stable starting in 1985 (dark blue line). The most stable cross-section is in Baja (Figure 7a), where the amplitude of changes is the smallest. The cross-section in Apatin is the most unstable one, having the largest amplitudes in bed level changes (Figure 7d). The analysis of the cross-sectional area change compared with the first survey supports these visual observations (Table 3). This revealed that the Apatin cross-section became stable after 2004 upon additional river training work. Thus, 2004 was used as the reference \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Gauging**} & \multicolumn{3}{c}{**Minima**} & \multicolumn{3}{c}{**Means**} & \multicolumn{3}{c}{**Maxima**} \\ \cline{2-10}  & \(D\) & \(p\) & **Homogen** & \(D\) & \(p\) & **Homogen** & \(D\) & \(p\) & **Homogen** \\ \hline Baja & 0.139 & 0.896 & YES & 0.143 & 0.879 & YES & 0.190 & 0.569 & YES \\ Bezdan & 0.143 & 0.867 & YES & 0.171 & 0.683 & YES & 0.114 & 0.976 & YES \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the homogeneity test of yearly discharge characteristics (taken from [5]). The results of the analysis of rates of change in the cross-sectional area between the two successive surveys (\(\Delta A/\Delta t\)) at the four considered GSs are presented in Figure 8. They confirm the visual observations. The lowest rates are at Baja GS (Figure 8a). They are less than 20 m\({}^{2}\)/year or 0.75% of the cross-sectional area below EN + 2 m, except between 2004 and 2007 (23.5 m\({}^{2}\)/year) when there was a large flood wave in the spring of 2006 with very long overbank flow durations along the entire Danube River course. The most prominent morphological changes at the Mohacs GS happened between the first three surveys--an aggradation of approximately 50 m\({}^{2}\)/year (1975-1985) and a degradation of around 65 m\({}^{2}\)/year (1985-1988) (Figure 8b). These changes correspond to 2% and 2.6% of the cross-sectional area each. After that, \(\Delta A/\Delta t\) did not exceed 30 m\({}^{2}\)/year, except, again, between 2004 and 2007, when it was around 35 m\({}^{2}\)/year. Changes at Bezdan GS (Figure 8c) were less than 10 m\({}^{2}\)/year before 1997, i.e., less than 0.5% of the cross-sectional area. Between the following two surveys, the cross-section aggradated and degraded for equal amounts of approximately 45 m\({}^{2}\)/year or 2% of \(A\). After the large flood wave of 2006, the changes in the cross-sectional area increased, and between the last two surveys, they exceeded 20 m\({}^{2}\)/year, or 0.8% of \(A\). Finally, Figure 8d quantitatively confirms that the GS in Apatin is the most unstable in the reach. This section is one of 17 critical sectors for inland navigation in Serbia. The cross-sectional area aggradated at a rate of 137 m\({}^{2}\)/year between 1985 and 1988, which is 6.9% of \(A\). The aggradation/degradation between other surveys was always greater than 50 m\({}^{2}\)/year, or more than 3% of \(A\). Figure 5: Variations in the trends of changes in characteristic yearly water level values—minimum and mean along the free-flowing Middle Danube River reach. Figure 6: The total (\(\Delta Z\)) and yearly (\(\delta Z\)) change in water level minima based on the yearly time series trends based on rkm. Figure 8: Rate of change in the cross-sectional area in (**a**) Baja; (**b**) Mohács; (**c**) Bezdan; and (**d**) Apatina according to available bathymetric surveys. Red color is used for GSs on the Hungarian, and blue-color for GSs on the Serbian side. Figure 7: Evolution of cross-sections at GSs in (**a**) Baja, (**b**) Mohács, (**c**) Bezdan, and (**d**) Apatina.