Mathematics plays a central role in the development of methods for the analysis and modelling of climate variability. Controlled physical experiments are out of question, and the only way we can study Earth’s climate system is through mathematical models, computational experiments, and data analysis.
Mathematical Models of the physical processes relevant for the climate system cannot (and should not) deliver a perfect one-to-one image of the underlying natural system. To nevertheless obtain a closed and consistent description of the system in terms of a hieracrchy of models with increasing complexity, great mathematical care is required when performing the necessary approximations and parametrizations, as well as when comparing model simulations to corresponding observational data.
This course focuses on techniques of mathematical modeling of different parts of the climate system that assist scientists in exploring the listed issues systematically. The course will cover a selection from the following topics
1. (Random) Dynamical Systems and Bifurcation Theory,
2. Introduction to the most relevant processes of climate dynamics
3. Conservation laws and simple climate models,
4. Mathematical models for the data-based characterization and modelling of the climate system
5. Mathematical description of critical transitions in the climate system