The course will discuss the following topics:

1. Mathematical Preliminaries
2. Predictability in Principle: Chaos and Ignorance, Uncertainty and Ambiguity
3. Predictability in Practice I: Weather-like Forecast Challenges
4. Predictability in Practice II: Climate-like Forecast Challenges

Focus is on the strengths and weaknesses of (probability) forecasts in weather and seasonal cases on their own. In particular issues of evaluation and the design of forecast systems (ensembles, multi-models, stochastic physics, ...) will be discussed. Different challenges arise in the climate context to form a rational framework for predictability when persuasive verification data is never going to be available.