Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems
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In this article, the continuous ranked probability score (CRPS) is decomposed into a reliability part and a resolution/uncertainty part, in a way similar to the decomposition of the Brier score.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 such a decomposition is illustrated for the ensemble prediction system running at the European Centre for Medium-Range Weather Forecasts. The evaluation of the CRPS and its decomposition proposed in this paper can be extended to systems issuing continuous probability forecasts, by realizing that these can be interpreted as the limit of ensemble forecasts with an infinite number of members.read more
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TL;DR: The second edition of "Statistical Methods in the Atmospheric Sciences, Second Edition" as mentioned in this paper presents and explains techniques used in atmospheric data summarization, analysis, testing, and forecasting.
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A New Vector Partition of the Probability Score
TL;DR: In this article, a new vector partition of the probability, or Brier, score (PS) is formulated and the nature and properties of this partition are described, as well as the relationships between the terms in this partition and terms in the original vector partition.