REVEALING THE CHAOTIC NATURE OF RIVER FLOW

Chaotic analysis has been performed on the river flow time series before and after
applying the wavelet based de-noising techniques in order to investigate the noise content effects
on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging
stations 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 was
found to be crucial in preventing removal of the vital data such as memory, correlation and trend
from the time series in addition to the noise during de-noising process. A comprehensive chaotic
assessment was conducted to study the relationship between the wavelet noise reduction processes
and the changes in the chaotic behavior of the river flow time series. To investigate the time series
chaotic behavior, some of the most common non-linear criteria are utilized which are distinguished
as the chaos indicators. The changes in the signal’s average power, the Lyapunov exponents, the
correlation dimension and the reconstructed phase space were estimated. Studying the average
signals power analysis’ results presents the evident impression of de-noising procedure on the river
flow time series. The variations of the Lyapunov exponents of time series as a consequence of
preprocessing indicated a significant influence of the wavelet based de-noising on revealing the
time series chaotic behavior. Results depicted that the lesser noise components result in lowering
the largest Lyapunov exponents. Besides, fractal dimension and correlation dimension of the denoised
series were almost the same while they were totally different before de-noising. This also
confirmed the commonly claimed sensitivity of correlation dimension to the existence of noise.
The correlation dimension results depicted an obvious difference between the signal’s chaotic
behavior before and after the do-noising procedure. Changes in the reconstructed phase spaces
were also noticeable after de-noising process by wavelet techniques. Results confirm the
importance of de-noising before any chaotic assessment. Also, results show that a chaotic
phenomenon such as river flow may depict completely random behavior due to the noise content
within it. Therefore, in order to better explore inherent chaotic behavior of natural time series, such
pre-processing can accompany common chaotic assessment procedures.