This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updati...

Ensemble Kalman Filtering is a sequential Monte Carlo method commonly used in meteorology to track atmospheric states and make numerical weather predictions (NWP). With the intent to introduce statisticians to this important area of application we address some of the practical aspects of the ensemble Kalman Filter in dynamic systems. We focus on three topics related to NWP: extending the ensemb...

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated c...

The ensemble Kalman filter provides an easy-to-use, flexible, and efficient option for data assimilation problems. One of its attractive features in land surface applications is its ability to provide distributional information about variables, such as soil moisture, that can be highly skewed or even bimodal. The ensemble Kalman filter relies on normality approximations that improve its efficie...

The present paper aims to provide a brief review on several deterministic ensemble Kalman filtering (EnKF) methods and the related practical techniques to prevent filter divergence. Since Evensen (1994), several formulations of EnKF have been proposed, and Whitaker and Hamill (2002) suggested that a deterministic method, a.k.a. an ensemble square root filter (EnSRF, Andrews 1968), is expected t...

The present paper aims to provide a brief review on several deterministic ensemble Kalman filtering (EnKF) methods and the related practical techniques to prevent filter divergence. Since Evensen (1994), several formulations of EnKF have been proposed, and Whitaker and Hamill (2002) suggested that a deterministic method, a.k.a. an ensemble square root filter (EnSRF, Andrews 1968), is expected t...

We present a method to control unbalanced fast dynamics in an ensemble Kalman filter by introducing a weak constraint on the imbalance in a spatially sparse observational network. We show that the balance constraint produces significantly more balanced analyses than ensemble Kalman filters without balance constraints and than filters implementing incremental analysis updates (IAU). Furthermore,...

We consider the problem of propagating an ensemble of solutions and its characterization in terms of its mean and covariance matrix. We propose differential equations that lead to a continuous matrix factorization of the ensemble into a generalized singular value decomposition (SVD). The continuous factorization is applied to ensemble propagation under periodic rescaling (ensemble breeding) and...

In this seminar we show clean comparisons between EnKF and 4D-Var made in Environment Canada, briefly describe the Local Ensemble Transform Kalman Filter (LETKF) as a representative prototype of Ensemble Kalman Filter, and give several examples of how advanced properties and applications that have been developed and explored for 4D-Var can be adapted to the LETKF without requiring an adjoint mo...