The Continuous Ranked Probability Score for Circular Variables and its Application to Mesoscale Forecast Ensemble Verification

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An analogue of the linear continuous ranked probability score is introduced that applies to probabilistic forecasts of circular quantities. 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 continuous ranked probability score provides a direct way of comparing deterministic forecasts, discrete forecast ensembles, and post-processed forecast ensembles that can take the form of probability density functions. The circular continuous ranked probability score is used in this study to assess predictions of 10 m wind direction for 361 cases of mesoscale, short-range ensemble forecasts over the North American Pacific Northwest. Reference probability forecasts based on the ensemble mean and its forecast error history over the period outperform 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.1

Keywords: Proper scoring rule; von Mises distribution; Wind direction.


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