Predicting the Real-Time Multivariate Madden-Julian Oscillation Index through a Low-Order Nonlinear Stochastic Model

A new low-order nonlinear stochastic model is developed to improve the predictability of the Real-time Multivariate Madden-Julian oscillation (MJO) index (RMM index), which is a combined measure of convection and circulation. A recent data-driven, physics-constrained, low-order stochastic modeling procedure is applied to the RMM index. The result is a four-dimensional nonlinear stochastic model for the two observed RMM variables and two hidden variables involving correlated multiplicative noise defined through energy-conserving nonlinear interaction. The special structure of the low-order model allows efficient data assimilation for the initialization of the hidden variables that facilitates the ensemble prediction algorithm. An information-theoretic framework is applied to the calibration of model parameters over a short training phase of 3 yr. This framework involves generalizations of the anomaly pattern correlation, the RMS error, and the information deficiency in the model forecast. The nonlinear stochastic models show skillful prediction for 30 days on average in these metrics. More importantly, the predictions succeed in capturing the amplitudes of the RMM index and the useful skill of forecasting strong MJO events is around 40 days. Furthermore, information barriers to prediction for linear models imply the necessity of the nonlinear interactions between the observed and hidden variables as well as the multiplicative noise in these low-order stochastic models.