Analysis and design of covariance inflation methods from functional viewpoint
This study shows that many unanswered problems in covariance inflation (CI) in the Ensemble Kalman Filter (EnKF) can be solved if we approach CI from functional viewpoint. Here each CI method is identified with an inflation function that alters the structure of analysis perturbations through their singular values. We tend to think inflation functions as functions that act on singular values of background or analysis perturbations. However, we have shown that the more fruitful outcome can be obtained if we consider inflation functions as functions of the singular values of ensemble transform matrices.
It turns out that the theory can cover all CI methods in practice including prior multiplicative inflation, RTPS, RTPP, the diagonal ETKF (DETKF), the Deterministic EnKF and suggest many new CI methods. RTPS, RTPP, and DETKF belong to the class of linear inflation functions. More surprisingly, the Deterministic EnKF is found to belong to the class of quadratic inflation functions with the linear terms omitted. Multiplicative inflation is an example of non-polynomial forms of inflation functions, which can be handled by certain EnKF methods. However, in this case, it is better to use adaptive non-parametric inflation functions estimated from the prior and posterior innovation statistics.
Dr. Le Duc Japan Agency for Marine-Earth Science and Technology