Time series analysis on marine wind-wave characteristics using chaos theory

• Investigating chaotic behavior of the wind-wave characteristics in three regions of the Caspian sea.
• Surrogate data method and spectral analysis are utilized to detect the nonlinearity and aperiodicity of the time series.
• Reconstruction of the phase space was based on the Takens׳ theorem.
• Results indicates the high-dimensional chaos of significant wave height and wave period parameters.
• Results indicates the low-dimensional chaos of wave direction parameter.

This paper discusses an attempt to identify the chaotic behavior of the dynamic system of wind-wave characteristics including significant wave height, wave period and wave direction in southern, central and northern regions of the Caspian Sea. Surrogate data method and spectral analysis are utilized to detect the nonlinearity and aperiodicity of the time series. The delay embedding theorem of reconstructing the phase space is applied to identify characteristics of the time series dynamic system. The false nearest neighbor analysis along with the correlation dimension estimation indicate the presence of high dimensional chaotic behavior with dimensions of the chaotic attractors at the range of 5.91, 6.30 and 7.55 for the significant wave height series and 6.59, 7.64 and 7.87 for the wave period for the southern, central and northern parts of the Sea. Higher correlation dimension of the northern station could be related to the physical characteristics of the sea bathymetry. However, the estimated correlation dimension indicates the low choaticity of the wave direction set (3.65, 3.70 and 3.77). Positive Lyapunov exponents obtained for all 9 data series prove the exponential divergence of the trajectories which support the presence of chaos in the wind-wave characteristics.