Reply to "Which chaos in the rainfall-runoff process?"

The authors thank Schertzer et al. (2002) for their comment on their work (Sivakumar et al., 2001) on the investigation of the possible presence of low-dimensional chaotic behaviour (the term "chaos" was used therein to denote the low-dimensional chaos) in the rainfall-runoff process in the Gôta River basin in Sweden. The authors respond to this discussion with respect to: (a) the purpose of the study by Sivakumar et al. (2001), and the results achieved and conclusions drawn therein; and (b) the argument by Schertzer et al. (2002) regarding the possibility of finite correlation dimensions resulting from stochastic processes when the data size is small. The issue of minimum data size requirement for a reliable estimation of correlation dimension is discussed and the deficiencies in the existing guidelines that relate the data size to the embedding dimension are pointed out. While the authors agree with Schertzer et al. (2002) that low correlation dimensions might also result from stochastic processes, they opine that this is true only when the data size is extremely small. The authors argue that the low correlation dimension obtained by Schertzer et al. (2002) for the stochastic series is not due to the small data size.