The continuous ranked probability score for circular variables and its application to mesoscale forecast ensemble verification

摘要

An analogue of the linear continuous ranked probability score is introduced that applies to probabilistic forecasts of circular quantities, such as wind direction. This scoring rule is proper and thereby discourages hedging. The circular continuous ranked probability score reduces to angular distance when the forecast is deterministic, just as the linear continuous ranked probability score generalizes the absolute error. Furthermore, the circular continuous ranked probability score provides a directway of comparing deterministic forecasts, discrete forecast ensembles, and post-processed forecast ensembles that can take the form of circular probability density functions. The circular continuous ranked probability score is used in this study to compare predictions of 10 m wind direction for 361 cases of mesoscale, short-range ensemble forecasts over the North American Pacific Northwest. Simple, calibrated probability forecasts based on the ensemble mean and its forecast error history over the periodoutperform probability forecasts constructed directly from the ensemble sample statistics. These results suggest that short-term forecast uncertainty is not yet well predicted at mesoscale resolutions near the surface, despite the inclusion of multi-scheme physics diversity and surface boundary parameter perturbations in the mesoscale ensemble design.