The Earth's magnetosphere is a spatially extended nonlinear system driven far from equilibrium by the turbulent solar wind. During substorms it exhibits both global and multi-scale features which reconciliation has been a long standing issue. This paper presents a data-derived model of the solar wind-magnetosphere coupling that combines a nonlinear dynamical description of the global features with a statistical description of the multi-scale aspects. This approach yields deterministic predictions of the global component of magnetospheric dynamics and probabilistic predictions of its multi-scale features.