It has long been recognised that forecasts for weather and climate (but also other complex dynamical phenomena) are more useful to essentially every user if, along with statements as to what is going to happen, they contain information as to how certain or uncertain these statements are. Popular ways to convey this information are forecast probabilities and ensemble forecasts (that is several scenarios of the future that are deemed equally likely).
In a general sense such forecasts make statements about the conditional probability of the verification given the information available at forecast time, and the statistical evaluation of forecasts aims to assess whether these statements are consistent with the data. A general problem with this are the intertemporal correlations between the verification-forecast pairs which cannot be ignored as can be demonstrated with simple toy examples. Standard goodness-of-fit tests though require verification-forecast pairs to be independent.
On the other hand, probabilistic forecast should, per definition, provide information about these intertemporal correlations. This presentation will demonstrate how this insight can be used to formulate tests that are valid with minimal extraneous assumptions. The well known rank histograms, which are used to ensemble forecasts, provide an example that will be analysed in detail.
Jochen Bröcker is an Associate Professor of Statistics and Meteorology, University of Reading. He obtained his PhD at the University of Goettingen in 2003 with the thesis “Approximations and Applications of Nonlinear Filters”. Before his position in Reading, he was held postdoc positions at the Technical University Krakow, London School of Economics, and Max Planck Institute for the Physics of Complex Systems Dresden.
His research interests in comprise Nonlinear Filtering and Data Assimilation, Random Dynamical Systems and Dissipative PDE’s, Probabilistic Forecasting, Calibration, Skill Scores, and Reliability, as well as Applications in Weather and Climate Predictions.