Wavelet-Induced Mode Extraction procedure: Application to climatic data

The Wavelet-Induced Mode Extraction procedure (WIME) [2] was developed drawing inspiration from Empirical Mode Decomposition. The concept involves decomposing the signal into modes, each presenting a characteristic frequency, using continuous wavelet transform. This method has yielded intriguing results in climatology [3,4]. However, the initial algorithm did not account for the potential existence of slight frequency fluctuations within a mode, which could impact the reconstruction of the original signal [4]. The new version (https://atoms.scilab.org/toolboxes/toolbox_WIME/0.1.0) now allows for the evolution of a mode in the space-frequency half-plane, thus considering the frequency evolution of a mode [2]. A natural application of this tool is in the analysis of Milankovitch cycles, where subtle changes have been observed throughout history. The method also refines the study of solar activity, highlighting the role of the "Solar Flip-Flop." Additionally, the examination of temperature time series confirms the existence of cycles around 2.5 years. It is now possible to attempt to correlate solar activity with this observed temperature cycle, as seen in speleothem records [1].[1] Allan, M., Deliège, A., Verheyden, S., Nicolay S. and Fagel, N. Evidence for solar influence in a Holocene speleothem record, Quaternary Science Reviews, 2018.[2] Deliège, A. and Nicolay, S., Extracting oscillating components from nonstationary time series: A wavelet-induced method, Physical Review. E, 2017.[3] Nicolay, S., Mabille, G., Fettweis, X. and Erpicum, M., A statistical validation for the cycles found in air temperature data using a Morlet wavelet-based method, Nonlinear Processes in Geophysics, 2010.[4] Nicolay, S., Mabille, G., Fettweis, X. and Erpicum, M., 30 and 43 months period cycles found in air temperature time series using the Morlet wavelet, Climate Dynamics, 2009.