Wavelet decomposition for detection of chaotic characteristics of monthly precipitation at Mokpo, Korea

In the present study, we apply deterministic chaos theory to investigate nonlinear dynamics in monthly precipitation at Mokpo, Korea, after wavelet decomposition. The wavelet transform is used not only for removal of noise but also for extraction of low and high frequency components in the data, representing low-dimensional dynamics. In order to determine an appropriate decomposition level for the wavelet transform, a correlation dimension analysis is applied for the respective low and high frequency signals after successive decomposition. The wavelet decomposition is performed up to 5th-level with orthogonal and compactly supported wavelets. Consequently, a long-term approximation (low frequency) and a short-term detail (high frequency) time series for the monthly precipitation obtained after 5th-level decomposition are investigated in terms of deterministic chaos theory. The data sets with low/high frequency components filtered by the wavelet transform are used for three-dimensional phase space analysis, respectively. Results show that both low and high frequency signals include clear chaotic signals and, therefore, might be governed by underlying dynamics based on different frequencies, respectively