Chaotic and fractal modeling of water-stage time series in a tidal river

In this paper, we examined the applicability of a state space predictor and a fractal dimension to the short-term prediction of water-stages in a tidal river. The previous researches showed that the state space predictor was an efficient tool, particularly in problems when the characteristics of process could hardly be described by only physical equations. The fractal dimension were also found an effective measure showing the possibility of predictions and to be calculated more precisely, using Higuchi's method, than those presented before. First, hourly water-stage time series was embedded into a state space using time delay coordinates. The induced mapping was then obtained from the embedded trajectory using a local approximation. This enabled us to make the short-term prediction of time series using the information based only on the past values. Second, the fractal dimension calculated by Higuchi's method was incorporated in the state space predictor to estimate the confidence limit of prediction. It was concluded that the state space predictor was a powerful tool in the short-term prediction of water-stages having a strong autocorrelation structure due to tidal motion. The maximum lead-time of prediction was efficiently determined using the fractal dimensions calculated by Higuchi's method.