Chaos analysis of groundwater depth time series using surrogate data method

Abstract

The investigation of chaos in time series is the basis of prediction with chaos theory. Though the science of chaos is a burgeoning field and the available methods to investigate the existence of chaos in a time series are in the state of infancy, a wide variety of methods are available. Among these methods, the correlation dimension method is the most popular one. According to this method, a finite correlation dimension is a sign of deterministic chaos, which is understood as the principal. However, a finite correlation dimension may also be observed from a linear stochastic process. Therefore, it is necessary to confirm the absence of linearity in the data to verify the results with application of the correlation dimension method. In this paper, after the reconstruction of phase space, the correlation dimension method was employed to analyze the chaotic characteristics for groundwater depth time series in Hetao Irrigation District of Yellow River in China. Considering that a finite correlation dimension is only the necessary condition of chaotic behavior, the surrogate data method which can distinguish nonlinear characteristics of time series was employed to analyze the chaotic characteristics for the groundwater depth series. As a comparison, classic Lorenz chaos time series and stochastic white noises were analyzed using the surrogate data method at the same time. The results show that there is somewhat chaos in the groundwater depth time series in Hetao District in Yellow River Basin. Meanwhile, the surrogate data method is the necessary complementarity of the correlation method to investigate the chaotic behavior for time series.