Low-Dimensional Chaos in River Flow Dynamics: Remarks on the Performance of Local Approximation Prediction and Inverse Chaos Identification Approaches

This study addresses the issue of whether or not river flow dynamics exhibit low-dimensional chaotic behavior, by investigating the ability of the inverse chaos identification approach (i.e. identification using prediction results) in river flow series. For this purpose, the study presents an extension of the application of a recently proposed "optimal inverse approach," which was previously demonstrated on artificial chaotic series and also tested on real river flow series. The present extension comes in the form of its application also to stochastic series. For purposes of consistency with flow series and assumption involved in chaos studies, the stochastic series is obtained by adding artificial noise to noise-free chaotic series instead of a complete random generation. However, to facilitate the interpretations, different levels of stochasticity are considered, by adding 5, 20, and 50 per cent noise levels. The artificial chaotic series studied is the Mackey-Glass series, and the daily flow series observed in Tryggevaelde catchment in Denmark and in Altamaha River in USA represent the real flow series. The results from the inverse approach indicate that the characteristics (i.e. absence of optimum combination of parameters) of the two river flow series are somewhat similar to those of the high-level noisy series, implying that these flow series may be on the stochastic domain rather than the chaotic domain. However, the predictions for these series are near-accurate, which indicates the appropriateness of the nonlinear local approximation prediction approach. Further, a comparison of the correlation dimensions of these flow series with those of the artificial series studied indicates that the flow series are more similar to the low-noisy chaotic series than to the high-noisy series, suggesting the presence of chaos. In view of these mixed results, utmost caution must be exercised in interpreting whether or not river flow dynamics exhibit chaotic behavior, but the usefulness of the local approximation prediction approach, developed within the context of chaos theory, cannot be dismissed.