Filtering the stochastic skeleton model for the Madden-Julian oscillation

The filtering and prediction of the Madden-Julian oscillation (MJO) and relevant tropical waves is a contemporary issuewith significant implications for extended range forecasting. This paper examines the process of filtering the stochastic skeleton model for the MJO with noisy partial observations. A nonlinear filter, which captures the inherent nonlinearity of the system, is developed and judicious model error is included. Despite its nonlinearity, the special structure of this filter allows closed analytical formulas for updating the posterior states and is thus computationally efficient. Anovel strategy for adding nonlinear observational noise to the envelope of convective activity is designed to guarantee its nonnegative property. Systematic calibration based on a cheap single-column version of the stochastic skeleton model provides a practical guideline for choosing the parameters in the full spatially extended system. With these column-tuned parameters, the full filter has a high overall filtering skill for Rossby waves but fails to recover the small-scale fast-oscillating Kelvin and moisture modes. An effectively balanced reduced filter involving a simple fast-wave averaging strategy is then developed, which greatly improves the skill of filtering the moisture modes and other fast-oscillatingmodes and enhances the total computational efficiency. Both the full and the reduced filters succeed in filtering theMJOand other large-scale features with both homogeneous and warmpool cooling/moistening backgrounds. The large bias in filtering the solutions by running the perfect model with noisy forcing is due to the noise accumulation, which indicates the importance of including judicious model error in designing filters.