Global and multi-scale aspects of magnetospheric dynamics: From modeling to forecasting

The Earth's magnetosphere is a spatially extended nonlinear system driven far from equilibrium by the turbulent solar wind. On global scales the magnetospheric behavior is well organized and coherent while on small scales it exhibits dynamical features in a wide range of spatial and temporal scales. While the presence of both global and multi-scale features of the magnetosphere is well recognized, isolating them and understanding their relative roles have been long standing issues. The main goal of this thesis is the development of a comprehensive data-derived model of solar wind - magnetosphere coupling that accounts for both global and multi-scale dynamical features. A new method of embedding analysis based on the notion of mean-field dimension is introduced. It yields a probability density function in the reconstructed phase space which provides the basis for the probabilistic modeling of the multi-scale dynamical features and is also used to extract the global portion of the solar wind-magnetosphere coupling. The manifold of its input-output phase portrait reveals the existence of two energy levels in the system with non-equilibrium features typical of non-equilibrium phase transitions. The multi-scale features appear as fluctuations about this manifold. Their statistical properties depend on the state of the system and can be described in terms of a conditional probability. Its analysis shows that the observed complexity of the magnetospheric time series is mainly due to the scale-invariance of the solar wind driver rather than to the complexity of the magnetospheric dynamics itself. This provides the basis for a new approach to data-derived modeling. The global behavior can be described by a low-dimensional dynamical model based on the mean-field concept while the high-dimensional multi-scale features on the other hand are described in terms of conditional probabilities. In the case of the solar wind - magnetosphere coupling such a combined approach yields an improved and effective tool for forecasting space weather. Many complex systems exhibit large-scale organized behavior with scale-free properties over a wide range of spatial and temporal scales and this integrated approach that accounts for the dynamical and statistical properties together provides a new framework for modeling and prediction of such systems.