Earth’s climate is the paradigm of a dynamical system: multiscale, nonlinear, chaotic, stochastic, out of equilibrium and multistable. This makes dynamical systems theory a powerful tool for understanding the complex variability found in earth system models, paleo records and observations. However, there is often a barrier between the modern mathematical development of dynamical systems theory and the application of its concepts to real problems in climate science, especially concerning transient climate change.

Bridging between theory and application, this short course offers a modern dynamical systems 101 for climate scientists and modelers. We will particularly focus on the case of time-dependent (or non-autonomous) systems, which is crucial in the context of a changing climate. In an accessible and hands-on format, we will discuss key formal concepts behind tipping points, extremes, transient dynamics and climate predictability. Topics include metastability, tipping, extreme value theory, large deviation theory, chaos and predictability, response theory, ensemble design and interpretation as well as uncertainty quantification. The course will also showcase numerical analysis tools that can be used to apply dynamical systems ideas across the climate model hierarchy - from low-dimensional, conceptual models to earth system models.