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Ronny Berndtsson

Professor, Dep Director, MECW Dep Scientific Coordinator

Profile photo of Ronny Berndtsson

Dynamics of monthly rainfall-runoff process at the Göta basin : A search for chaos


  • B. Sivakumar
  • R. Berndtsson
  • J. Olsson
  • K. Jinno
  • A. Kawamura

Summary, in English

Sivakumar et al. (2000a), by employing the correlation dimension method, provided preliminary evidence of the existence of chaos in the monthly rainfall-runoff process at the Göta basin in Sweden. The present study verifies and supports the earlier results and strengthens such evidence. The study analyses the monthly rainfall, runoff and runoff coefficient series using the nonlinear prediction method, and the presence of chaos is investigated through an inverse approach, i.e. identifying chaos from the results of the prediction. The presence of an optimal embedding dimension (the embedding dimension with the best prediction accuracy) for each of the three series indicates the existence of chaos in the rainfall-runoff process, providing additional support to the results obtained using the correlation dimension method. The reasonably good predictions achieved, particularly for the runoff series, suggest that the dynamics of the rainfall-runoff process could be understood from a chaotic perspective. The predictions are also consistent with the correlation dimension results obtained in the earlier study, i.e. higher prediction accuracy for series with a lower dimension and vice-versa, so that the correlation dimension method can indeed be used as a preliminary indicator of chaos. However, the optimal embedding dimensions obtained from the prediction method are considerably less than the minimum dimensions essential to embed the attractor, as obtained by the correlation dimension method. A possible explanation for this could be the presence of noise in the series, since the effects of noise at higher embedding dimensions could be significantly greater than that at lower embedding dimensions.


  • Division of Water Resources Engineering

Publishing year







Hydrology and Earth System Sciences





Document type

Journal article


European Geophysical Society


  • Oceanography, Hydrology, Water Resources


  • Chaos
  • Correlation dimension
  • Noise
  • Nonlinear prediction
  • Phase-space
  • Rainfall-runoff
  • Runoff coefficient




  • ISSN: 1027-5606