REVEALING THE CHAOTIC NATURE OF RIVER FLOW

Abstract

Chaotic analysis has been performed on the river flow time series before and afterapplying the wavelet based de-noising techniques in order to investigate the noise content effectson chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gaugingstations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran.Noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step wasfound to be crucial in preventing removal of the vital data such as memory, correlation and trendfrom the time series in addition to the noise during de-noising process. A comprehensive chaoticassessment was conducted to study the relationship between the wavelet noise reduction processesand the changes in the chaotic behavior of the river flow time series. To investigate the time serieschaotic behavior, some of the most common non-linear criteria are utilized which are distinguishedas the chaos indicators. The changes in the signal's average power, the Lyapunov exponents, thecorrelation dimension and the reconstructed phase space were estimated. Studying the averagesignals power analysis' results presents the evident impression of de-noising procedure on the riverflow time series. The variations of the Lyapunov exponents of time series as a consequence ofpreprocessing indicated a significant influence of the wavelet based de-noising on revealing thetime series chaotic behavior. Results depicted that the lesser noise components result in loweringthe largest Lyapunov exponents. Besides, fractal dimension and correlation dimension of the denoisedseries were almost the same while they were totally different before de-noising. This alsoconfirmed the commonly claimed sensitivity of correlation dimension to the existence of noise.The correlation dimension results depicted an obvious difference between the signal's chaoticbehavior before and after the do-noising procedure. Changes in the reconstructed phase spaceswere also noticeable after de-noising process by wavelet techniques. Results confirm theimportance of de-noising before any chaotic assessment. Also, results show that a chaoticphenomenon such as river flow may depict completely random behavior due to the noise contentwithin it. Therefore, in order to better explore inherent chaotic behavior of natural time series, suchpre-processing can accompany common chaotic assessment procedures.