Relationship Between Ensemble Mean Square and Ensemble Mean Skill in Four Climate Models

In this study, we investigated the uncertainty of ensemble prediction of the ENSO (El Niño and Southern Oscillation) and the AO (Arctic Oscillation) variability, using four different climate models and various ensemble schemes. Several important issues related to climate predictability including uncertainty measures and dominant precursors that control the uncertainty were addressed. It was found that the ensemble mean (EM) square is a useful measure for the uncertainty of both the ENSO and the AO dynamical prediction. The relationship between EM2 and the prediction skill depends on the measure of skill. When correlation- based measures are used, the prediction skill is likely to be a linear function of EM2, i.e., the larger the EM2 the higher skill the prediction; whereas when RMSE-based (root mean square of error) metrics are used, a "triangular relationship" could be suggested between them, namely that when EM2 is large, the prediction is likely to be reliable whereas when EM2 is small, the prediction skill is much variable. In contrast to ensemble numerical weather predictions (NWP), the ensemble spread in the ensemble prediction of these climate models was found to have little connection with the prediction skill. This is probably due to a small variation of ensemble spread in the climate models, which may be associated with the intrinsic nature of ensemble climate predictions (ECP).