Predictability and chaotic nature of daily streamflow

Abstract

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation dimension method (Grassberger-Procaccia algorithm) and false nearest neighbour method. Embedding dimensions of 6-7 obtained, indicate the possible presence of low-dimensional chaotic behaviour. The predictability of the system is estimated by calculating the system’s Lyapunov exponent. A positive maximum Lyapunov exponent of 0.167 indicates that the system is chaotic and unstable with a maximum predictability of only 6 days. These results give a positive indication towards considering streamflow as a low dimensional chaotic system than as a stochastic system. Prediction is done using local polynomial method for a range of embedding dimensions and delay times. The uncertainty in the chaotic streamflow series is reasonably captured through the ensemble approach using local polynomial method.