Joint frequency analysis of streamflow and sediment amount with copula functions in the Kızlırmak Basin, Turkey

The accurate determination of sediment amount is crucial for the design and operation of reservoirs. The sediment rating curve (SRC) is the most widely used method for determining sediment amount. The SRC was derived from streamflow and sediment amount measurements taken at hydrometric monitoring stations. However, when measurements cannot be made at these stations (such as flooding), sediment amount determination becomes difficult. Therefore, in recent years, researchers have used copula functions to determine the relationship between streamflow and sediment amount. In this study, the joint distribution functions of streamflow and sediment amount at five different stations (Avşar, Bulukabaşı, İnözü, Söğütlühan and Yamula) in the Kızılırmak Basin, one of the most important basins of Turkey, were determined. Initially, the relationship between streamflow and sediment amount was examined and a positive correlation was found between the parameters. Then, the marginal distributions of each dataset were determined and joint distributions were generated using the Burr, Roch-Alegre, BB1 and Tawn Copula functions. The root mean square error of the mean square error (RMSE) and Nash–Sutcliffe efficiency (NSE) were used to select the optimal joint function. According to the optimal joint function determined for each station, the common return periods for both the AND and OR scenarios were calculated. When joint return periods were analyzed, the amount of sediment exceeded the average amount of sediment at all stations.