Most often observations and measurements of geophysical systems and dynamical phenomena are obtained as time series. Dynamics of the system are inferred from characteristics of these time series which usually manifest a chaotic or stochastic behavior.
In this short course different approaches, based on dynamical systems theory, will be explained, including phase-space portraits, bifurcation theory, correlation dimension and entropic approaches, Langevin and Fokker-Planck equations, fractal analysis, and other concepts of nonlinear time series analysis, like recurrence quantification analysis. Methods will be illustrated in terms of recent successful applications from various fields of geosciences, ranging from climate to solar-terrestrial relations.
The focus will be on a comparison between different methods to investigate different aspects of both known and unknown physical processes.
Tommaso Alberti: "Chaotic approaches: fractals and their dimensions, self-organization, and turbulence"
Reik Donner: "Time series analysis: quantification of recurrence properties in geoscientific time series"