The Probability Anomaly Correlation and Calibration of Probabilistic Forecasts

The Probability Anomaly Correlation and Calibration of Probabilistic Forecasts

An ordinary regression of predicted versus observed probabilities is presented as a direct and simple procedure for minimizing the Brier Score (BS) and improving the attributes diagram. The main example chosen to show how this works applies to seasonal prediction of extratropical sea surface temperature by a global coupled numerical model. In connection with this calibration procedure, the probability anomaly correlation (PAC) is developed. This emphasizes the exact analogy of PAC and minimizing BS to the widely used anomaly correlation (AC) and minimizing mean squared error in physical units.