Multiscale measures of phase-space trajectories.

Characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series is one of the most intensively studied contemporary problems in nonlinear sciences. In this work, we address this problem by combining two established concepts-empirical mode decomposition (EMD) and generalized fractal dimensions-into a unified analysis framework. Specifically, we demonstrate that the intrinsic mode functions derived by EMD can be used as a source of local (in terms of scales) information about the properties of the phase-space trajectory of the system under study, allowing us to derive multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three well-known low-dimensional deterministic dynamical systems (the Hénon map, the Lorenz '63 system, and the standard map), three realizations of fractional Brownian motion with different Hurst exponents, and two somewhat higher-dimensional deterministic dynamical systems (the Lorenz '96 model and the on-off intermittency model). These examples allow us to assess the performance of our formalism with respect to practically relevant aspects like additive noise, different initial conditions, the length of the time series under study, low- vs high-dimensional dynamics, and bursting effects. Finally, by taking advantage of two real-world systems whose multiscale features have been widely investigated (a marine stack record providing a proxy of the global ice volume variability of the past 5×106 years and the SYM-H geomagnetic index), we also illustrate the applicability of this formalism to real-world time series.

Measuring Information Coupling between the Solar Wind and the Magnetosphere-Ionosphere System.

The interaction between the solar wind and the Earth's magnetosphere-ionosphere system is very complex, being essentially the result of the interplay between an external driver, the solar wind, and internal processes to the magnetosphere-ionosphere system. In this framework, modelling the Earth's magnetosphere-ionosphere response to the changes of the solar wind conditions requires a correct identification of the causality relations between the different parameters/quantities used to monitor this coupling. Nowadays, in the framework of complex dynamical systems, both linear statistical tools and Granger causality models drastically fail to detect causal relationships between time series. Conversely, information theory-based concepts can provide powerful model-free statistical quantities capable of disentangling the complex nature of the causal relationships. In this work, we discuss how to deal with the problem of measuring causal information in the solar wind-magnetosphere-ionosphere system. We show that a time delay of about 30-60 min is found between solar wind and magnetospheric and ionospheric overall dynamics as monitored by geomagnetic indices, with a great information transfer observed between the z component of the interplanetary magnetic field and geomagnetic indices, while a lower transfer is found when other solar wind parameters are considered. This suggests that the best candidate for modelling the geomagnetic response to solar wind changes is the interplanetary magnetic field component B z . A discussion of the relevance of our results in the framework of Space Weather is also provided.