Forecasting systems are indispensable for making informed decisions under uncertainty. Therefore, there is a need for an objective and well-understood framework for ``forecast verification'', i.e., qualitative and quantitative assessment of forecast performance.

Statistical methods compare historical forecasts with corresponding verifications, indicating whether the forecasting system behaved significantly differently (in a statistical sense) from what was expected. This requires that the forecasts have a well--defined statistical interpretation; whether a forecast represents a mean or a quantile makes a difference with regards to how we evaluate that forecast.

This short course will introduce the participants to the fundamentals of statistical forecast verification. Some necessary statistical theory will be presented, along with the concept of risk measures, which allows to provide forecasts with a precise statistical meaning. We furthermore illustrate the relation to scoring and identification functions, and discuss practical challenges with evaluating forecasts as spatial fields (as opposed to point by point). Specifically, the course will cover the following topics (more or less in that order)

(1) Forecast types, risk measures, scoring functions, and identification functions (20min)
(2) Tests and p-values (10min)
(3) How to evaluate forecasts for specific risk measures
(with hands-on part, 30min)
(3) How to evaluate forecasts of spatial fields
(with hands-on part, 30min)
(4) Open challenges (15min)

The target audience is researchers (from both academic institutions and operational centers) who are either new to forecast verification or have practical experience but want to learn more about the theory. The discussed methods are applicable not only in atmospheric forecasts but in many other fields such as parameter estimation, data assimilation, model evaluation, and machine learning.