Probabilistic predictions: interpretation, consistency check, and skill scores

Inherent uncertainties in models and initial conditions of complex systems render deterministic predictions useless - they are most certainly wrong. A fair assessment of the uncertainty of the future given the (lack of) knowledge of a complex system and its current state is possible by probabilistic predictions. The forecast product is a probability distribution which is supposed to characterize our knowledge about the future. Evidently, in practice also such predicted probabilities suffer from inaccuracies, i.e., they have to be validated by forecast/observation pairs. In this talk, I will use the example of temperature forecasts to illustrate the concept, methods for verification, and difficulties of this approach.