Simplifying and generalising Murphy's Brier score decomposition

Abstract

The decomposition of the Brier score into Reliability, Resolution and Uncertainty has become a standard method in forecast verification. In this note a very simple derivation of the familiar Brier score decomposition is presented. The Reliability and Resolution terms can be calculated as average Brier score differences between the issued forecast, the recalibrated forecast and the climatological reference forecast. The result suggests a simple way to calculate similar decompositions for arbitrary verification scores, and that recalibration methods and reference forecasts can be chosen more flexibly than is generally appreciated. A new decomposition of the continuous ranked probability score (CRPS) is proposed.