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Filtering the Stochastic Skeleton Model for the Madden–Julian Oscillation

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  • 1 Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, New York
  • | 2 Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, New York, and Center for Prototype Climate Modeling, NYU Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates
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Abstract

The filtering and prediction of the Madden–Julian oscillation (MJO) and relevant tropical waves is a contemporary issue with 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. A novel 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-oscillating modes and enhances the total computational efficiency. Both the full and the reduced filters succeed in filtering the MJO and other large-scale features with both homogeneous and warm pool 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.

Corresponding author address: Nan Chen, Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012. E-mail: chennan@cims.nyu.edu

Abstract

The filtering and prediction of the Madden–Julian oscillation (MJO) and relevant tropical waves is a contemporary issue with 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. A novel 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-oscillating modes and enhances the total computational efficiency. Both the full and the reduced filters succeed in filtering the MJO and other large-scale features with both homogeneous and warm pool 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.

Corresponding author address: Nan Chen, Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012. E-mail: chennan@cims.nyu.edu
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