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Dynamics of monthly rainfall-runoff process at the Gota basin: A search for chaos
1Department of Land, Air & Water Resources, University of California, Davis, CA 95616, USA
2Department of Water Resources Engineering, Lund Institute of Technology, Lund University, P.O. Box 118, S-221 00 Lund, Sweden
3Institute of Environmental Systems, Faculty of Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 821-8581, Japan
e-mail for corresponding author: sbellie@ucdavis.edu
Abstract. 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 Gota 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.
Keywords: Rainfall-runoff; runoff coefficient; chaos; phase-space; correlation dimension; nonlinear prediction; noise
Final Revised Paper (PDF, 1699 KB)
Citation: Sivakumar, B., Berndtsson, R., Olsson, J., Jinno, K., and Kawamura, A.: Dynamics of monthly rainfall-runoff process at the Gota basin: A search for chaos, Hydrol. Earth Syst. Sci., 4, 407-417, 2000. Bibtex EndNote Reference Manager
