Skill scores and correlation coefficients in model verification

Abstract

A mean square error skill score based on historical climatology is decomposed into terms involving the anomaly correlation coefficient, the conditional bias in the forecast, the unconditional bias in the forecast, and the difference between the mean historical and sample climatologies. This decomposition reveals that the square of the anomaly correlation coefficient should be interpreted as a measure of potential rather than actual skill. The decomposition is applied to a small sample of geopotential height field forecasts, for lead times from 1 to 10 days, produced by the medium range forecast (MRF) model. After about 4 days, the actual skill of the MRF forecasts (as measured by the "climatological skill score') is considerably less than their potential skill (as measured by the anomaly correlation coefficient), due principally to the appearance of substantial conditional biases in the forecasts. -from Authors