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Seasonality of low flows and dominant processes in the Rhine River

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Abstract

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).

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Acknowledgements

We acknowledge the financial support of the Dr. Ir. Cornelis Lely Stichting (CLS), Project No. 20957310. Discharge data for the Rhine River were provided by the Global Runoff Data Centre (GRDC), Koblenz (Germany). The GIS base maps with delineated 134 catchments of the Rhine basin were provided by Eric Sprokkereef, the secretary general of the Rhine Commission (CHR).

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Authors and Affiliations

  1. Department of Civil Engineering, Engineering Faculty, Süleyman Demirel University, 32260, Isparta, Turkey

    Hakan Tongal

  2. Water Engineering and Management, Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Mehmet C. Demirel & Martijn J. Booij

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  1. Hakan Tongal
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  2. Mehmet C. Demirel
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  3. Martijn J. Booij
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Correspondence to Hakan Tongal.

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Tongal, H., Demirel, M.C. & Booij, M.J. Seasonality of low flows and dominant processes in the Rhine River. Stoch Environ Res Risk Assess 27, 489–503 (2013). https://doi.org/10.1007/s00477-012-0594-9

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