Predicting the cloud patterns of the Madden-Julian Oscillation through a low-order nonlinear stochastic model

We assess the limits of predictability of the large-scale cloud patterns in the boreal winter Madden-Julian Oscillation (MJO) as measured through outgoing longwave radiation (OLR) alone, a proxy for convective activity. A recent advanced nonlinear time series technique, nonlinear Laplacian spectral analysis, is applied to the OLR data to define two spatial modes with high intermittency associated with the boreal winter MJO. A recent data-driven physics-constrained low-order stochastic modeling procedure is applied to these time series. The result is a four-dimensional nonlinear stochastic model for the two observed OLR variables and two hidden variables involving correlated multiplicative noise defined through energy-conserving nonlinear interaction. Systematic calibration and prediction experiments show the skillful prediction by these models for 40, 25, and 18 days in strong, moderate, and weak MJO winters, respectively. Furthermore, the ensemble spread is an accurate indicator of forecast uncertainty at long lead times.