The Relationship between Ensemble Spread and Ensemble Mean Skill

Statistical considerations suggest that 1) even for a perfect ensemble (one in which all sources of forecast error are sampled correctly) there need not be a high correlation between spread and skill, 2) the correlation between spread and skill should be larger where the day-to-day variability of spread is large, and 3) the spread is likely to be most useful as a predictor of skill when it is ''extreme,'' that is, when it is either very large or very small compared to its climatological mean value. The authors investigate the relationship between spread and skill in an operational setting by analyzing ensemble predictions produced by the National Centers for Environmental Prediction. The geographical dependence of the spread-skill relationship is found to be related to the geographical dependence of day-to-day variability of spread. Dynamical mechanisms for spread variability are investigated using a linear quasigeostrophic model. Problems associated with the sample size needed to define what constitutes an extreme value of spread at a given location are discussed.