Skill scores and correlation coefficients in model verification

Attributes of the anomaly correlation coefficient, as a model verification measure, are investigated by exploiting a recently developed method of decomposing skill scores into other measures of performance. 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 similar to 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), principally because of the appearance of substantial conditional biases in the forecasts. These biases, and the corresponding loss of skill, represent the penalty associated with retaining meteorological features in the geopotential height field when such features are not predictable. Some implications of these results for the practice of model verification are discussed.