EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Multiscale measures of phase-space trajectories

Tommaso Alberti1, Giuseppe Consolini1, Peter D. Ditlevsen2, Reik V. Donner3,4, and Virgilio Quattrociocchi1,5
Tommaso Alberti et al.
  • 1Istituto Nazionale di Astrofisica, Istituto di Astrofisica e Planetologia Spaziali, Roma, Italy (
  • 2University of Copenhagen, Niels Bohr Institute, Centre for Ice and Climate, Copenhagen, Denmark
  • 3Potsdam Institute for Climate Impact Research (PIK) - Member of the Leibniz Association, 14473 Potsdam, Germany
  • 4Department of Water, Environment, Construction and Safety, Magdeburg-Stendal University of Applied Sciences, 39114 Magdeburg, Germany
  • 5Dip. Scienze Fisiche e Chimiche, Universit\`a degli Studi dell'Aquila, Via Vetoio, L'Aquila, Italy

Several attempts have been made in characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series. Particularly, the study of their fractal structure has made use of different approaches like the structure function analysis, the evaluation of the generalized dimensions, and so on. Here we report on a different approach for characterizing phase-space trajectories by using the empirical modes derived via the Empirical Mode Decomposition (EMD) method. We show how the derived Intrinsic Mode Functions (IMFs) can be used as source of local (in terms of scales) information allowing us in deriving multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three pedagogical examples like the Lorenz system, the Henon map, and the standard map. We also show that this formalism is readily applicable to characterize both the behavior of the Earth’s climate during the past 5 Ma and the dynamical properties of the near-Earth electromagnetic environment as monitored by the SYM-H index.

How to cite: Alberti, T., Consolini, G., Ditlevsen, P. D., Donner, R. V., and Quattrociocchi, V.: Multiscale measures of phase-space trajectories, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-268,, 2019

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