Cycle Analysis Method of Tree Ring and Solar Activity Based on Variational Mode Decomposition and Hilbert Transform

Abstract

According to the correlation of tree ring and solar activity, the cycle analysis method based on variational mode decomposition (VMD) and Hilbert transform is proposed. Firstly, the tree ring width of cypress during 1700 to 1955 beside the Huangdi Tomb and the long-term sunspot number during 1700 to 1955, respectively, are decomposed by VMD into a series of intrinsic mode functions (IMFs). Secondly, Hilbert transformation on the decomposed IMF component is performed. Then, the marginal spectra are given and analyzed. Finally, their quasiperiodic properties are obtained as follows: the tree ring width has the quasiperiodicity of 2 to 7a, 10.8a, and 25a; the sunspot number has the quasiperiodicity of 8.3a, 9.9a, 11.1a, 52.2a, and 101.2a. The result obtained by analyzing that quasiperiodicity shows that the main periods of tree ring width and the sunspot number in the same period are basically consistent, and tree ring width has other cycles. This shows that sunspot activity is an important factor affecting tree ring growth, and tree ring width is influenced by other external environments.