Ensemble Kalman filter based data assimilation for tropical waves in the MJO skeleton model

The Madden–Julian oscillation (MJO) is the dominant component of tropical intraseasonal variability, with wide‐reaching impacts even on extratropical weather and climate patterns. However, predicting the MJO is challenging. One reason is the suboptimal state estimates obtained with standard data assimilation (DA) approaches. These are typically based on filtering methods with Gaussian approximations and do not take into account physical properties that are important specifically for the MJO. In this article, a constrained ensemble DA method is applied to study the impact of different physical constraints on the state estimation and prediction of the MJO. The quadratic programming ensemble (QPEns) algorithm utilized extends the standard stochastic ensemble Kalman filter (EnKF) with specifiable constraints on the updates of all ensemble members. This allows us to recover physically more consistent states and to respect possible associated non‐Gaussian statistics. The study is based on identical twin experiments with an adopted nonlinear model for tropical intraseasonal variability. This so‐called skeleton model succeeds in reproducing the main large‐scale features of the MJO and closely related tropical waves, while keeping adequate simplicity for fast experiments on intraseasonal time‐scales. Conservation laws and other crucial physical properties from the model are examined as constraints in the QPEns. Our results demonstrate an overall improvement in the filtering and forecast skill when the model's total energy is conserved in the initial conditions. The degree of benefit is found to be dependent on the observational setup and the strength of the model's nonlinear dynamics. It is also shown that, even in cases where the statistical error in some waves remains comparable with the stochastic EnKF during the DA stage, their prediction is improved remarkably when using the initial state resulting from the QPEns.

Unsatisfactory predictions of the MJO are partly due to DA methods that do not respect non‐Gaussian PDFs and the physical properties of the tropical atmosphere. Therefore the QPEns, an algorithm extending a stochastic EnKF with state constraints, is tested here on a simplified model for the MJO and associated tropical waves. Our series of identical twin experiments shows, in particular, that a constraint on the truth's nonlinear total energy improves forecasts statistically and can, in certain situations, even prevent filter divergence.

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