Chaotic analysis of daily runoff time series using dynamic, metric, and topological approaches

The main goal of this work is summed up in a univariate chaotic analysis of the runoff series using a topological approach. As such, nineteen series of daily runoff from eight large watersheds in northern Algeria were analyzed. Firstly, preliminary analyses of two traditional dynamic and metric approaches have been tested. In the dynamic approach, three algorithms have shown that the largest Lyapunov exponent for the series is positive, which supports the hypothesis of the existence of chaos. In the metric approach, the Grassberger and Procaccia algorithm clearly shows the saturation of the correlation dimension, which indicates the existence of deterministic dynamics for all studied stations. Secondly, the application of the topological approach in this study constitutes in itself a new contribution to the demonstration of chaos in hydrology by using the recurrence plot (RP) and the recurrence quantification analysis (RQA). As such, the RP structures of the runoff series seem to be more comparable to chaotic systems. In addition, RQA parameters give high values of determinism and laminarity, which supports the hypothesis of the existence of deterministic chaos. The presence of chaos in the runoff series can be identified by the existence of a strong probability of recurrence, indicating a fairly low level of complexity and fairly high predictability. Ultimately, the comparison of these approaches together made it possible to confirm the hypothesis according to which the process generating the runoff series is deterministic and suggests low-dimensional chaotic dynamics.