Detection and predictive modeling of chaos in finite hydrological time series

Abstract

The ability to detect the chaotic signal from a finite time series observation of hydrologic systems is addressed in this paper. The presence of random and seasonal components in hydrological time series, like rainfall or runoff, makes the detection process challenging. Tests with simulated data demonstrate the presence of thresholds, in terms of noise to chaotic-signal and seasonality to chaotic-signal ratios, beyond which the set of currently available tools is not able to detect the chaotic component. The investigations also indicate that the decomposition of a simulated time series into the corresponding random, seasonal and chaotic components is possible from finite data. Real streamflow data from the Arkansas and Colorado rivers are used to validate these results. Neither of the raw time series exhibits chaos. While a chaotic component can be extracted from the Arkansas data, such a component is either not present or can not be extracted from the Colorado data. This indicates that real hydrologic data may or may not have a detectable chaotic component. The strengths and limitations of the existing set of tools for the detection and modeling of chaos are also studied.