Observations and measurements of geoscientific systems and their dynamical phenomena are genuinely obtained as time series or spatio-temporal data whose dynamics usually manifests a nonlinear multiscale (in terms of time and space) behavior. During the past decades, dynamical system, information theoretic, and stochastic approaches have rapidly developed and allow gaining novel insights on a great diversity of phenomena like weather and climate dynamics, turbulence in fluids and plasmas, or chaos in dynamical systems.

In this short course, we will provide an overview on a selection of contemporary topics related with complex systems based approaches and their utilization across the geosciences, exemplified by recent successful applications from various fields from paleoclimate over present-day atmospheric dynamics to Space Weather. The focus will be on tipping points and associated early warning indicators, the identification of causal relations among a multitude of observables, and how to combine both approaches in a multi-scale dynamical framework. The discussed data analysis tools are promising for investigating various aspects of both known and unknown physical processes.