Chaos theory in hydrology: important issues and interpretations

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Abstract
The application of the concept of chaos theory in hydrology has been gaining considerable interest in recent times. However,
studies reporting the existence of chaos in hydrological processes are often criticized due to the fundamental assumptions withwhich
the chaos identification methods have been developed, i.e. infinite and noise-free time series, and the inherent limitations of the
hydrological time series, i.e. finite and noisy. This paper is designed: (1) to address some of the important issues in the application of
chaos theory in hydrology; and (2) to provide possible interpretations to the results reported by past studies reporting chaos in
hydrological processes. A brief review of some of the past studies investigating chaos in hydrological processes is presented. An
insight into the studies reveals that most of the problems, such as data size, noise, delay time, in the application of chaos theory have
been addressed by past studies, and caution taken in the application of the methods and interpretation of the results. The study also
reveals that the problemof data size is not as severe as it was assumed to be,whereas the presence of noise seems to havemuchmore
influence on the nonlinear predictionmethod than the correlation dimensionmethod.The study indicates that the presence of noise in
the data could be an important reason for the low-prediction accuracy estimates achieved in some of the past studies. These
observations,with the fact that most of the past studies used the correlation dimension either as a proof or as a preliminary evidence
of chaos, suggest that the hypothesis of deterministic chaos, as the basis in those studies, for hydrological processes is valid and has
great practical potential. q2000 Elsevier Science B.V. All rights reserved.
Keywords: Chaos theory; Hydrological data; Identification methods; Correlation dimension; Nonlinear prediction; Data size; Noise

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