Characterization and prediction of runoff dynamics: a nonlinear dynamical view

An attempt is made in this study to characterize and predict runoff dynamics, using ideas gained from nonlinear dynamical theory. Daily runoff data observed over a period of 19 years (January 1, 1975–December 31, 1993) at the Lindenborg catchment in Denmark is studied using a variety of techniques. First, the autocorrelation function and the Fourier power spectrum are used as indicators to obtain some preliminary information regarding the runoff behavior. A comprehensive characterization is done next through the correlation integral analysis, the false nearest neighbor algorithm, and the nonlinear prediction method, all of which use the concept of phase-space reconstruction, i.e., reconstruction of the single-dimensional (or variable) runoff series in a multi-dimensional phase-space to represent its dynamics. The average mutual information method is used to estimate the delay time for the phase-space reconstruction. The exponential decay in the autocorrelation function plot and the sharp spectral lines in the Fourier power spectrum seem to provide some preliminary indication regarding the possible presence of chaos in the runoff dynamics. The (low) correlation dimension (of about 3.76) obtained from the correlation integral analysis, the (low) global dimension (of 4 or 5) obtained from the false nearest neighbor algorithm, and the (low) optimal embedding dimension (of 3) from the nonlinear prediction method are in close agreement with each other, providing convincing evidence regarding the presence of low-dimensional chaotic behavior in the runoff dynamics. The near-accurate predictions achieved for the runoff series (correlation coefficient of about 0.99 and coefficient of efficiency of about 0.98) indicate the appropriateness of the chaotic dynamical approach for characterizing and predicting the runoff dynamics at the Lindenborg catchment.