Improving the CPC’s ENSO Forecasts using Bayesian model averaging

Statistical and dynamical model simulations have been commonly used separately in El Nino–Southern Oscillation (ENSO) prediction. Current models are imperfect representations of ENSO and each of them has strength and weakness for capturing different aspects in ENSO prediction. Thus, it is important to utilize the results from a variety of different models. The Bayesian model averaging (BMA) is an effective tool not only in describing uncertainties associated with each model simulation but also providing the forecast performance of different models. The BMA method was developed to combine the NCEP/CPC three statistical and one dynamical model forecasts of seasonal Ocean Nino Index (ONI) from 1982 to 2010. The BMA weights were derived directly from the predictive performance of the combined models. The highly efficient expectation–maximization (EM) algorithm was used to achieve numerical solutions. We show that the BMA method can be used to assess the performance of the individual models and assign greater weights to better performing models. The continuous ranked probability score is applied to evaluate the BMA probability forecasts. As an elaboration of the reliability diagram, the attributes diagram is used that includes the calibration function, refinement distribution, and reference lines. The combination of statistical and dynamical models is found to provide a more skillful prediction of ENSO than only using a suite of statistical models, a single bias-corrected dynamical model, or the equally weighted average forecasts from all four models. Probability forecasts of El Nino events based only on winter ONI values are reliable and exhibit sharpness. In contrast, an under-forecasting bias and less reliable forecasts are noted for La Nina.