Dynamic phenomena in geoscientific systems are often characterized by observational or modelled time series or spatio-temporal data, exhibiting nonlinear multiscale behavior in both time and space. Over the past decades, significant advancements have been made in dynamical system theory, information theory, and stochastic approaches. These developments have provided valuable insights into a wide range of phenomena, such as weather and climate dynamics, turbulence in fluids and plasmas, and chaos in dynamical systems.
In this short course, we will present an overview of contemporary topics that employ complex systems-based approaches in the geosciences. We will explore successful applications across the geosciences, including climate change. Our primary focus will be on understanding tipping points and early warning indicators associated with them, identifying causal relationships among sets of observables, and integrating these approaches within a multi-scale dynamical framework. By employing these data analysis tools, various aspects of both recurrent and emergent physical processes can be investigated.