# Estimation of Changes in Sediment Transport along the Free-Flowing Middle Danube River Reach
## 3 Materials and Methods  
### Methods of Statistical Analysis of Hydrological Data  
In the first phase of the hydrological study, analyses were performed using time series of water levels and discharges for the 70-year-long period between 1950 and 2019 for the entire free-flowing alluvial reach of the River Danube downstream of Budapest, Hungary, and upstream of Slankamen, Serbia (\(\sim\)300 km). This was considered necessary, as the older studies published on this topic used different periods, older datasets, and different/shorter river reaches, e.g., in [17]. The analysis included the official water level and discharge data of the Hungarian Hydrological Forecasting Service and the Hydrometeorological Service of the Republic of Serbia for a total of ten gauging stations (Figure 1b): Dunaujivaros (rkm 1581), Dunaujivaros (rkm 1560), Paks (rkm 1531), Baja (rkm 1479) and Mohacs (rkm 1447) in Hungary, and Bezdan (rkm 1425), Apatin (rkm 1402), Bogojevo (rkm 1367), Backa Palanka (rkm 1299), and Novi Sad (rkm 1255) in Serbia, similar to [PERSON] et al. [5].  
The first step in this analysis was a test of the homogeneity of the time series. Computations were made in XLStat (Addinsoft, 2023) [18]. A two-tailed, two-sample Kolmogorov-Smirnov test at a confidence level of \(\alpha=0.05\) was used. The homogeneity test was first performed for values of the yearly characteristics of water levels and discharges for all stations. Consequently, the trend analysis was performed for the annual characteristic values to find trend parameters. Given the fact that there are no large tributaries between  
Figure 1: (**a**) Map of Central Europe with the Danube River Basin and the Danube River (the investigated section is highlighted in red). (**b**) Detailed map of the investigated reach; the gauging stations used in the detailed analysis in the present study are marked with red dots.  
the upstream end of the reach and Apatin, it is presumed that discharges upstream of the Drava River confluence, which is downstream of Apatin, do not change significantly. That is why annual discharge data were analyzed only at two gauging stations, Baja and Bezdan, which are located upstream of the confluence of the Drava River. The discharges for the two stations were also tested for normality using XLSStat [19].  
For further analyses, as the intention was to connect water level changes with morphology, the two stations at the upstream end of the reach (Dunaiyyaros and Dunafoldvar) were excluded, as the bed material of the river there contains a relatively large portion of gravel, and according to previous studies [20] dredging played a role in the lowering of the water levels on this part of the reach. The two stations at the downstream end of the reach (Backa Palanka and Novi Sad) were also excluded as the backwater effect and sediment deposition upstream of the Iron Gate I Dam (~rkm 1000) can influence water levels there [14]. The trend of the yearly characteristic values of water level data at the six remaining stations (Paks, Baja, Mohacs, Bezdan, Apatin, and Bogojevo) was examined. All trend analyses were performed using linear regression with the least squares (LSQ) method in MS Excel.