The Earth system is characterized by inherently nonlinear processes determining its structure and dynamics. Therefore, it is usually not possible to infer sufficiently holistic information from data when considering only classical linear concepts of statistics. As an alternative, a variety of complex systems based approaches have been developed, the foundations of which originate in the theory of nonlinear dynamical systems. In this short course, we will specifically introduce some prominent examples of contemporary analysis frameworks highlighting the methodological variety of complex systems based data analysis and modeling. We focus on applications of nonlinear time series analysis and complex network theory and combinations thereof to various geoscientific fields and problems.

The techniques discussed in this short course will be illustrated by applications to real-world geoscientific data. Course materials will be made available to the participants upon request after the course, including example codes for the platform-independent open-source software Python. Specifically, we will use and explain the Python package pyunicorn for geoscientific data analysis (https://github.com/pik-copan/pyunicorn) that is documented in Donges et al., Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos, 25, 113101 (2015).