Phase-space analysis of daily streamflow : characterization and prediction

Abstract This paper describes a methodology, based on dynamical systems theory, to model and predict streamflow at the daily scale. The model is constructed by developing a multidimensional phase-space map from observed streamflow signals. Predictions are made by examining trajectories on the reconstructed phase space. Prediction accuracy is used as a diagnostic tool to characterize the nature, which ranges from low-order deterministic to stochastic, of streamflow signals. To demonstrate the utility of this diagnostic tool, the proposed method is first applied to a time series with known characteristics. The paper shows that the proposed phase-space model can be used to make a tentative distinction between a noisy signal and a deterministic chaotic signal. The proposed phase-space model is then applied to daily streamflow records for 28 selected stations from the Continental United States covering basin areas between 31 and 35 079 km 2 . Based on the analyses of these 28 streamflow time series and 13 artificially generated signals with known characteristics, no direct relationship between the nature of underling stream flow characteristics and basin area has been found. In addition, there does not appear to be any physical threshold (in terms of basin area, average flow rate and yield) that controls the change in streamflow dynamics at the daily scale. These results suggest that the daily streamflow signals span a wide dynamical range between deterministic chaos and periodic signal contaminated with additive noise.