Measuring the potential predictability of ensemble climate predictions

In this study, ensemble predictions of the El Niño Southern Oscillation (ENSO) and the Arctic Oscillation (AO) were conducted using two coupled models and two atmospheric circulation models, respectively, as well as various ensemble schemes. Several measures of potential predictability including ensemble mean square (EM2), ensemble spread and the ratio of signal‐to‐noise were explored in terms of their ability of estimating a priori the predictive skill of the ENSO and AO ensemble predictions. The emphasis was put on examining the relationship between the measures of predictability that do not use observations and the model prediction skill of correlation and mean square error (MSE) that make use of observations. The relationship identified here offers a practical means of estimating the potential predictability and the confidence level of an individual prediction. It was found that the EM2 is a better indicator of the actual skill of ensemble ENSO and AO prediction than the ratio of signal‐to‐noise. When correlation‐based metrics 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 MSE‐based metrics are used, a “triangular relationship” is 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 highly variable. In contrast with ensemble weather prediction (NWP), the ensemble spread is not a good predictor in quantifying climate prediction skill in the models used in this study because the forced response may be much larger than the noise in the climate timescales compared to the NWP. A statistical framework was proposed to explain why EM2 is a good indicator of actual prediction skill in the ensemble climate predictions.