Is correlation dimension a reliable indicator of low‐dimensional chaos in short hydrological time series?

Abstract

The reliability of the correlation dimension estimation in short hydrological time series is investigated using an inverse approach. According to this approach, first predictions are made using the phase‐space reconstruction technique and the artificial neural networks. The correlation dimension is estimated next independently and is compared with the prediction results. A short hydrological series, monthly runoff series of 48 years (with a total of only 576 values) observed at the Coaracy Nunes/Araguari River watershed in northern Brazil, is studied. The correlation dimension results are in reasonably good agreement with the optimal embedding dimension obtained from the phase‐space method and the optimal number of inputs from the neural networks. No underestimation of the correlation dimension is observed due to the small data size, rather there seems to be a slight overestimation due to the presence of noise in the data. The results indicate that the accuracy of the correlation dimension may not be judged on the basis of the length of the time series but on whether the time series is long enough to reasonably represent the dynamical changes in the system. Such an observation suggests that the correlation dimension could indeed be a reliable indicator of low‐dimensional chaos even in short hydrological time series, which is certainly encouraging news for hydrologists who often have to deal with short time series.