Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems

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Abstract
Some time ago, the continuous ranked probability score (CRPS) was proposed as a new verification tool for (probabilistic) forecast systems. Its focus is on the entire permissible range of a certain (weather) parameter. The CRPS can be seen as a ranked probability score with an infinite number of classes, each of zero width. Alternatively, it can be interpreted as the integral of the Brier score over all possible threshold values for the parameter under consideration. For a deterministic forecast system the CRPS reduces to the mean absolute error. In this paper it is shown that for an ensemble prediction system the CRPS can be decomposed into a reliability part and a resolution/uncertainty part, in a way that is similar to the decomposition of the Brier score. The reliability part of the CRPS is closely connected to the rank histogram of the ensemble, while the resolution/uncertainty part can be related to the average spread within the ensemble and the behavior of its outliers. The usefulness of s... Abstract Some time ago, the continuous ranked probability score (CRPS) was proposed as a new verification tool for (probabilistic) forecast systems. Its focus is on the entire permissible range of a certain (weather) parameter. The CRPS can be seen as a ranked probability score with an infinite number of classes, each of zero width. Alternatively, it can be interpreted as the integral of the Brier score over all possible threshold values for the parameter under consideration. For a deterministic forecast system the CRPS reduces to the mean absolute error. In this paper it is shown that for an ensemble prediction system the CRPS can be decomposed into a reliability part and a resolution/uncertainty part, in a way that is similar to the decomposition of the Brier score. The reliability part of the CRPS is closely connected to the rank histogram of the ensemble, while the resolution/uncertainty part can be related to the average spread within the ensemble and the behavior of its outliers. The usefulness of s...

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