Seasonality of Low Flows and Dominant Processes in the Rhine River

Published In

Stochastic Environmental Research and Risk Assessment

Document Type


Publication Date



Hydrologic models -- Evaluation, Rhine River -- Streamflow -- Forecasting, Water levels -- Rhine River -- Forecasting


Low flow forecasting is crucial for sustainable cooling water supply and planning of river navigation in the Rhine River. The first step in reliable low flow forecasting is to understand the characteristics of low flow. In this study, several methods are applied to understand the low flow characteristics of Rhine River basin. In 108 catchments of the Rhine River, winter and summer low flow regions are determined with the seasonality ratio (SR) index. To understand whether different numbers of processes are acting in generating different low flow regimes in seven major sub-basins (namely, East Alpine, West Alpine, Middle Rhine, Neckar, Main, Mosel and Lower Rhine) aggregated from the 108 catchments, the dominant variable concept is adopted from chaos theory. The number of dominant processes within the seven major sub-basins is determined with the correlation dimension analysis. Results of the correlation dimension analysis show that the minimum and maximum required number of variables to represent the low flow dynamics of the seven major sub-basins, except the Middle Rhine and Mosel, is 4 and 9, respectively. For the Mosel and Middle Rhine, the required minimum number of variables is 2 and 6, and the maximum number of variables is 5 and 13, respectively. These results show that the low flow processes of the major sub-basins of the Rhine could be considered as non-stochastic or chaotic processes. To confirm this conclusion, the rescaled range analysis is applied to verify persistency (i.e. non-randomness) in the processes. The estimated rescaled range statistics (i.e. Hurst exponents) are all above 0.5, indicating that persistent long-term memory characteristics exist in the runoff processes. Finally, the mean values of SR indices are compared with the nonlinear analyses results to find significant relationships. The results show that the minimum and maximum numbers of required variables (i.e. processes) to model the dynamic characteristics for five out of the seven major sub-basins are the same, but the observed low flow regimes are different (winter low flow regime and summer low flow regime). These results support the conclusion that a few interrelated nonlinear variables could yield completely different behaviour (i.e. dominant low flow regime).


Copyright Springer


*At the time of publication Mehmet C. Demirel was affiliated with the University of Twente



Persistent Identifier