Chaos theory in hydrology: important issues and interpretations

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 with which 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 problem of data size is not as severe as it was assumed to be, whereas the presence of noise seems to have much more influence on the nonlinear prediction method than the correlation dimension method. 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. (C) 2000 Elsevier Science B.V. All rights reserved.