Abstract
Indices of prediction skill over the Madden-Julian oscillation (MJO) phase space are
examined with reanalysis and forecast data provided by the Japan Meteorological
Agency (JMA). In addition to the bivariate root-mean-square error (RMSE) and the
bivariate anomaly correlation coefficient (ACC), the mean-error vector is assessed.
Conventionally, the RMSE and ACC have been used, although this approach misses
information on the model bias for MJO events. Moreover, the ACC is not suitable for
models in which the MJO signal tends to damp in some phases, because the ACC
strongly depends on the MJO amplitude. The mean-error vector compensates for this
drawback by associating a model’s erroneous mean tendency with RMSE. For
example, the JMA forecast produces a leftward mean error vector field uniformly
distributed over the MJO phase space with its amplitude related to RMSE. RMSE
should be then used with the mean error vector for evaluating MJO prediction skill.